essays on wage determination -...

Essays on Wage Determination

2013-1

Kenneth Lykke Sørensen

PhD Thesis

DEPARTMENT OF ECONOMICS AND BUSINESS

AARHUS UNIVERSITY � DENMARK

Essays on Wage Determination


A PhD thesis submitted to

Business and Social Sciences, Aarhus University,

in partial fulfilment of the requirements of the PhD degree

in Economics and Business

Contents

Preface v

Summary vii

Summary in Danish (dansk resume) xi

1 Worker and Firm Heterogeneity in Wage Growth: An AKM Approach 1

2 Wage Sorting Trends 33

3 Return To Experience and Initial Wages: Do Low Wage Workers Catch Up? 51

4 Effects of Intensifying Labor Market Programs on Post-Unemployment Wages:

Evidence From a Controlled Experiment 85

iii

Preface

This thesis was written in the period from September 2009 to August 2012 while I was enrolled

as a PhD student at the Department of Economics and Business, Aarhus University. I would

like to thank the Department for giving me the opportunity to write this dissertation and for

providing an excellent research environment. In addition, I thank the Department for letting me

attend numerous courses and conferences, both abroad and in Denmark.

I would like to thank my main advisor, Michael Svarer, for being available and giving com-

ments whenever necessary and for understanding I was not a PhD student in need of weekly

meetings. The always relaxed tone has suited me very well. I would also like to thank my

secondary supervisor and co-author on chapters one, two and three in this dissertation (plus

yet another paper describing wage applications on Danish data, forthcoming in book on Danish

data, edited by Dale T. Mortensen) Rune Vejlin for all his efforts on these chapters. I have

learned a lot by working so closely alongside Rune and am grateful for all those many hours

both of us have put into the chapters. Also my other co-author on chapter two, Jesper Bagger,

deserves thanks. Especially for showing me the value of always pursuing an even better paper.

Thanks to Kirsten Stentoft for very competently proofreading my manuscripts. Furthermore,

I am, as almost all researchers (staff and visitors) at the Department working on Danish data,

indebted to my other secondary supervisor, Henning Bunzel. Thanks for always being willing

to put in uncountable hours in helping prepare data, communicating with Statistics Denmark,

debugging fortran code and for the always exiting talks about Linux servers, Fortran code, nu-

merical optimization, etc.

From January - June 2011 I visited the Department of Economics at the University of

Wisconsin-Madison. I would like to thank the Department for its hospitality. Especially, I

thank Rasmus Lentz for arranging and sponsoring my stay at the Department and Chris Taber

for being willing to discuss my papers. It was definitely an experience for life staying those six

months in Madison.

Of course, thanks also have to go to all my fellow PhD students at the Department. All of

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you guys have made some very long days behind the yellow walls much more interesting. I

have enjoyed sharing an office with Tine and Ritwik and special thanks go to Mark and Mikkel

for all those fantastic coffee breaks and great discussions, both the intellectual and the not-so-

intellectual ones.

Finally, thanks to Ellen and my family for coping with lots of talks about data problems,

annoying server conditions, labor economics, worker effects, etc., etc.


Aarhus, August 2012

Updated Preface

I would like to thank the members of the assessment committee, Lars Skipper (chair, Aarhus

University), Jakob Roland Munch (University of Copenhagen) and Francis Kramarz (CREST-

ENSAE, Paris) for carefully reading my thesis and for all their comments and suggestions for

improvements. I appreciate the time and effort the committee has put into delivering thoughtful

and usable comments, and firmly believe they have added value to the revised version of this

thesis.


Odense, January 2013

Summary

This thesis consists of four independent chapters insofar that all four chapters empirically es-

timate determination of wages using Danish data. However, the chapters do so in three very

different ways. Chapter one specifies a linear wage growth equation including unobserved

worker and firm heterogeneity. Chapter two is a note dealing with an indirect outcome of linear

wage equations with worker and firm fixed effects (like in chapter one). In chapter three we

use nonparametric methods to estimate the relationship between the wage in the first job and

the individual expected return to experience profile six to ten years after labor market entry.

Finally, chapter four uses duration analysis to estimate a post-unemployment wage hazard for

newly unemployed workers who participated in a field experiment where roughly half of them

was put into an intensified active labor market policy program.

In the first chapter, Worker and Firm Heterogeneity in Wage Growth: An AKM Approach

(published in LABOUR, 2011, vol. 25, 4, pp. 485-507, co-authored by Rune Vejlin), we

exploit the statistical methods developed by Abowd, Kramarz and Margolis (1999) (the so-

called AKM approach), later refined and extended by Abowd, Creecy and Kramarz (2002), to

estimate worker fixed effects and firm fixed effects in a linear wage growth specification. A

specific outcome of this method is the decomposition of the variance of wage growth. The

AKM decomposition has been used for analysis on a number of different datasets, but almost

all are estimating worker and firm effects on wages in levels. We contribute to the literature by

focusing on wage growth (although, in the chapter, we also estimate the traditional wage level

equation). From a policy perspective, it is important to know how the variance of wage growth

is distributed across firms. Imagine there is no variance in wage growth across firms. Then,

placing a worker in any firm will lead to higher wages independent of the worker-firm match.

If the variation in wage growth on the other hand primarily is caused by firm effects, it becomes

important for the worker to be placed in the best firms in order to receive higher wages. We

find that unobserved worker effects are more important for the variance in wage growth than

observables and unobserved firm effects. However, there is still a considerable amount of the

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variance of wage growth left unexplained.

Chapter two, Wage Sorting Trends (co-authored by Jesper Bagger and Rune Vejlin) is a note

that documents a trend in the correlation between worker fixed effects and firm fixed effects

estimated from an AKM wage equation. Studies using the AKM specification often report the

correlation between worker and firm effects as one number (Abowd et al. (2002), correlation

-0.28, France and -0.03, the US. Gruetter and Lalive (2004), correlation -0.22, Austria. An-

drews, Gill, Schank and Upward (2008), correlation -0.21 to -0.15, Germany and Sørensen and

Vejlin (2012), correlation -0.06 to 0.11, Denmark). We find a correlation of 0.05 and show

that it masks a systematic non-stationarity and the cross-section specific correlations show an

increasing trend over time. In the chapter, we decompose correlations and show that most of

this trend can be attributed to workers in the top quartile of worker effects. The increasing

wage sorting trend in the top quartile of worker effects could be related to high wage workers

employed in high wage firms being increasingly likely to transit to another high wage firm, or

to high wage workers employed in low wage firms being increasingly likely to transit to a high

wage firm. Our analysis supports the former relation.

In Chapter three, Return to Experience and Initial Wages: Do Low Wage Workers Catch

Up? (under Revision for Resubmision to the Journal of Applied Econometrics, co-authored by

Rune Vejlin) we use nonparametric methods to estimate the relationship between an individual

permanent component of wages and an individual return to experience in the early stages of a

worker’s labor market career. From chapter one and two we see that individual permanent com-

ponents matter for the explanation of wages. Another literature going all the way back to Mincer

(1958) has shown human capital (such as experience and education) to be important for wage

determination. Putting this together, we thus suspect that return to experience could change

with unobservable skills. We use and extend the identification of this relationship by Gladden

and Taber (2009) and estimate the expected return to experience for an individual worker given

his initial wages. We find an overall negative relationship between initial wages and return to

experience, but a positive relationship between return to experience and educational level (an

observable individual characteristic). Especially for vocational educated workers, the catching

up effect for low initial wage workers is relatively large. We relate these findings to three theo-

retical models: search theory, unobserved productivity and learning, and human capital theory.

Finally, chapter four, Effects of Intensifying Labor Market Programs on Post-Unemployment

Wages: Evidence From a Controlled Experiment analyzes how treatment of intensified active

ix

labor market policies (ALMP) (in this case frequent meetings with a case worker and early

entry into activation) affected average wages in jobs after leaving unemployment. An exten-

sive literature on ALMP (both experimental and non-experimental) has shown that intensifying

ALMP generally increases the exit rate out of unemployment and to some extend decreases the

re-entering rate into unemployment (see Card, Kluve and Weber (2010) for a meta analysis of

97 different studies on ALMP). However, Card et al. (2010) show that analyses with insignif-

icant or negative short term effects have positive medium or long term effects and vice versa.

In this chapter, I use an ALMP experiment conducted in two Danish counties, Storstroem (St.)

and Southern Jutland (S.J.) during the winter of 2005-2006 and estimate short, medium and

long term effects of treatment on wages. I find that men in St. experience a significant increase

in the wage hazard in the short term but no significant effects in the medium term and negative

effects in the long term (These are effects on the wage hazard, i.e. a positive estimate means

you become more likely to “exit” earlier out of the wage distribution. In other words, you are

more likely to receive a lower wage). Men in S.J. have significant negative average treatment

effects on the wage hazard both in the medium and long term. Women in S.J. have a signifi-

cant negative effect of treatment on the wage hazard in the short term and positive otherwise,

while the wage hazard of women in St. is affected negatively in the medium term and positive

otherwise.

ReferencesAbowd, J. M., R. H. Creecy and F. Kramarz (2002), Computing Person and Firm Effects Us-

ing Linked Longitudinal Employer-Employee Data, Technical Paper 2002-06, U.S. CensusBureau.

Abowd, J. M., F. Kramarz and D. N. Margolis (1999), High Wage Workers and High WageFirms, Econometrica, 67(2): 251–333.

Andrews, M. J., L. Gill, T. Schank and R. Upward (2008), High wage workers and low wagefirms: negative assortative matching or limited mobility bias?, Journal of the Royal StatisticalSociety, A(2008) 171(Part 3): 673–697.

Card, D., J. Kluve and A. Weber (2010), Active Labour Market Policy Evaluations: A Meta-Analysis, The Economic Journal, 120(November): F452–F477.

Gladden, T. and C. Taber (2009), The Relationship Between Wage Growth and Wage Levels,Journal of Applied Econometrics, 24: 914–932.

x

Gruetter, M. and R. Lalive (2004), The Importance of Firms in Wage Determination, IEW -Working Papers 207, Institute for Empirical Research in Economics - IEW.

Mincer, J. (1958), Investment in Human Capital and Personal Income Distribution, The Journalof Political Economy, 66(4): 281–302.

Sørensen, T. and R. Vejlin (2012), The importance of worker, firm and match fixed effects inwage regressions, Forthcoming in Empirical Economics.

Summary in Danish (dansk resume)

Denne ph.d.-afhandling bestar af fire uafhængige kapitler med løndannelsen som fælles tema.

Alle fire kapitler estimerer individuelle lønninger pa danske data, men med tre vidt forskellige

metoder. Første kapitel estimerer individuel lønvækst som en lineær funktion af individuelle

observerbare karakteristika og uobserverbare arbejder- og virksomhedsspecifik heterogenitet.

Kapitel to er en note, der ser pa et indirekte resultat fra AKM specifikationer (den type ligning

der bruges i første kapitel). Tredje kapitel benytter sig af ikke-parametriske metoder til at es-

timere en sammenhæng mellem den løn, en arbejder tjener i sit første job, og det afkast han/hun

kan forvente seks til ti ar frem, betinget pa den løn han/hun startede ud med. Til sidst estimerer

kapitel fire ved brug af forløbsstatistike metoder, hvordan lønhazarden pavirkes for arbejdere,

der har været igennem et intensivt arbejdsmarkedspolitisk tiltag.

Første kapitel, Worker and Firm Heterogeneity in Wage Growth: An AKM Approach (ud-

givet i LABOUR, 2011, vol. 25, 4, pp. 485-507, skrevet med Rune Vejlin), benytter statistiske

metoder udviklet af Abowd et al. (1999) (den sakaldte AKM metode), siden rettet og udvidet

af Abowd et al. (2002), til at estimere individuelle arbejder- og virksomhedsspecifikke effekter

i en lineær lønvækstspecification. Et specifikt udfald af AKM modellen er en dekomponering

af variansen pa venstresidevariablen. Derved findes et estimat pa forklaringsgraden af arbejder-

og virksomhedsspecifikke effekter af variansen pa lønninger. Denne metode har i litteraturen

været brugt pa adskillige datasæt, hvoraf hovedparten estimeres pa basis af lønninger i niveau.

I stedet fokuserer vi pa lønvæksten (for at kunne sammenligne med litteraturen estimerer vi

ogsa pa lønninger i niveau). Ud fra et politisk synspunkt er det vigtigt at vide, om der er var-

ians af lønvæksten pa tværs af virksomheder. Hvis ikke der er betydelig varians pa tværs af

virksomheder, vil en tilfældig placering af arbejdere betyde, at de kan forvente den samme

virksomhedsspecifikke lønvækst. Hvis der derimod er betydelig varians af lønvæksten mellem

virksomheder, vil det for arbejdere være essentielt at komme ind i den rigtige virksomhed for

at kunne forvente en større lønvækst. Vi finder i kapitlet, at uobserverbare arbejdereffekter er

vigtigere for at beskrive variansen af lønvæksten end uobserverbare virksomhedseffekter og ob-

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serverbare arbejderkarakteristika. Der er dog stadig en stor del af variansen af lønvæksten, som

ikke kan forklares ved denne dekomponering.

Kapitel to, Wage Sorting Trends (skrevet med Jesper Bagger og Rune Vejlin) er en note, der

dokumenterer og specificerer en tendens i korrelationen med uobserverbare arbejder- og virk-

somhedseffekter estimeret ud fra en AKM model som i første kapitel. Studier pa AKM dekom-

poneringen rapporterer som oftest korrelationen ved et enkelt punkt, Abowd et al. (2002) (-0,28

for Frankrig og -0,03 for USA), Gruetter and Lalive (2004) (-0,22 for Østrig), Andrews et al.

(2008) (-0,21 til -0,15 for Tyskland) og Sørensen and Vejlin (2012) (-0,06 til 0,11 for Danmark).

Vi finder en korrelation pa 0,05 og viser, at den dækker over en systematisk ikke-stationaritet.

Pa tværs af arene 1980-2006 viser korrelationen en stigende tendens. Vi dekomponerer kor-

relationen og viser, at hovedparten af denne ikke-stationaritet kan forklares af arbejdere i den

øverste kvartil blandt individuelle arbejderspecifikke effekter. Den stigende tendens for denne

gruppe af arbejdere kan relateres til flere arsager. Tendensen kan f.eks. skyldes, at high wage

arbejdere ansat i high wage virksomheder er mere tilbøjelige til at flytte til andre high wage virk-

somheder, eller at high wage arbejdere ansat i low wage virksomheder bliver mere tilbøjelige

over tid til at skifte til high wage virksomheder. Vores resultater peger i retning af det første.

I kapitel tre, Return to Experience and Initial Wages: Do Low Wage Workers Catch Up?

(under revision for resubmision til Journal of Applied Econometrics, skrevet med Rune Vejlin)

benytter vi ikke-parametriske metoder til at estimere en sammenhæng mellem en individuel

permanent komponent af lønninger og et individuelt afkast af erfaring i de tidlige ar af en arbe-

jders karriere. Kapitel et og to viste, at individuelle permanente komponenter er vigtige for at

beskrive en arbejders løn. En anden del af litteraturen helt tilbage til Mincer (1958) har vist, at

human kapital (som erfaring og uddannelse) er vigtige elementer i lønforklaringen. Sættes dette

sammen kunne vi derfor forvente at afkastet af human kapital (her erfaring) kan være forskel-

lig betinget af uobserverbare individuelle evner. Vi bruger og udvider identifikationsstrategien

fra Gladden and Taber (2009) til at estimere det forventede afkast til erfaring for en individuel

arbejder betinget af hans/hendes første løn. Resultaterne peger pa et negativt forhold mellem

initial løn og afkast af erfaring, men samtidigt et positivt forhold mellem afkast af erfaring og

uddannelsesniveau (en observerbar individuel karakteristik). Især for erhvervsuddannede arbe-

jdere finder vi en relativt stor catching-up effekt. Vi relaterer vores resultater til tre teoretiske

modeller: search theory, unobserved productivity and learning, og human capital theory.

xiii

Det fjerde og sidste kapitel, Effects of Intensifying Labor Market Programs on Post-Un-

employment Wages: Evidence From a Controlled Experiment analyserer, hvordan et intensivt

arbejdsmarkedspolitisk forløb under arbejdsløshed har pavirket lønninger op til tre ar efter arbe-

jdsløsheden. Der findes allerede en mængde litteratur pa omradet omkring arbejdsmarkedspoli-

tikker, der har vist, at en intensivering af forløbet giver en hurtigere afgang fra arbejdsløshed,

og for visse grupper nedsætter det raten tilbage i arbejdsløshed (Card et al. (2010) har en stor

metaanalyse af 97 forskellige studier omkring arbejdsmarkedspolitikker). Card et al. (2010)

viser, at analyser med insignifikante eller negative effekter pa kort sigt kan have positive effek-

ter pa mellem og langt sigt og omvendt. I dette kapitel benytter jeg et arbejdsmarkedpolitisk

eksperiment udført i Storstrøm (St.) og Sønderjyllands (S.J.) amter over vinteren 2005/2006 til

at estimere kort-, mellem- og langsigtseffekter af intensiveringen pa lønninger. Jeg finder, at

mænd i St. rammes af en signifikant stigning i lønhazarden pa kort sigt, men ingen signifikante

effekter pa mellemlangt sigt og negative effekter pa langt sigt (dette er effekter pa en lønhazard,

og en positiv effekt pa lønhazarden betyder, at sandsynligheden for at, en arbejder tjener en

lavere løn, stiger). Mænd i S.J., har derimod en signifikant negativ effekt pa lønhazarden pa

bade mellemlangt og langt sigt. For kvinder i S.J. har eksperimentet ligeledes haft en negativ

effekt pa lønhazarden pa kort sigt men positiv pa langt sigt, mens lønhazarden for kvinder i St.

er pavirket positivt af eksperimentet pa kort og langt sigt.

Referencer

Se referencer sidst i Summary sektionen (det engelske resume).

Chapter 1

Worker and Firm Heterogeneity in WageGrowth: An AKM Approach

Worker and Firm Heterogeneity in Wage Growth:

An AKM Approach∗

Kenneth Lykke Sørensen†

Aarhus University and LMDG

Rune Vejlin‡

Aarhus University and LMDG

Abstract

This paper estimates a wage growth equation containing human capital variables known from the

traditional Mincerian wage equation with year, worker and firm fixed effects included as well. The

paper thus contributes further to the large empirical literature on unobserved heterogeneity following the

work of Abowd, Kramarz and Margolis (1999). Our main contribution is to extend the analysis from

wage levels to wage growth. The specification enables us to estimate the individual specific and firm

specific fixed effects and their degree of explanation on wage growth. The analysis is conducted using

Danish longitudinal matched employer-employee data from 1980 to 2006. We find that the worker fixed

effects dominate both the firm fixed effects and the effect of the observed covariates. Worker effects

are estimated to explain seven to twelve percent of the variance in wage growth while firm effects are

estimated to explain four to ten percent. We furthermore find a negative correlation between the worker

and firm effects, as do nearly all authors examining wage level equations.

Keywords: MEE data, fixed effects, wage growth.

JEL codes: J21, J31

∗This paper has been published as: Worker and Firm Heterogeneity in Wage Growth: An AKM Approach,LABOUR, 2011, vol. 25, 4, pp. 485-507. We thank Michael Svarer, Henning Bunzel, one anonymous referee andparticipants at the European Society for Population Economics Conference in Essen, Germany (June 2010) andDGPE, Denmark (November 2009) for comments and the Labour Market Dynamics and Growth research unit,LMDG, Department of Economics and Business, Aarhus University for providing the data. Any remaining errorsare our. Vejlin greatly acknowledge financial support from the Danish Social Sciences Research Council (grant no.FSE 09-066745).

†Department of Economics and Business, Aarhus University, Fuglesangs Alle 4, DK-8210 Aarhus V, Den-mark. Correspondence to; Kenneth Lykke Sørensen, email: [email protected].

‡Department of Economics and Business, Aarhus University, Fuglesangs Alle 4, DK-8210 Aarhus V, Den-mark.

3

4 Chapter 1

1 Introduction

A well known fact about the labor market is that there exists a large degree of wage dispersion

in the levels of wages. The same fact can be said about wage growth, but this has not yet been

exploited to its full extent. Wage growth and wage levels are, of course, closely connected

as wage growth is the first difference of wage levels, but the explanation of wage growth is

different from the explanation of wage levels. Typically, observable characteristics are estimated

to explain around 30 percent of the variation in wage levels while they are able to explain

much less of the variation in wage growth.1 This leads to other differences in the explanation

given by the unobserved effects as well, and it is especially interesting that Abowd, Kramarz

and Margolis (1999) (henceforth denoted AKM), who introduced how to statistically analyze

simultaneous observed and unobserved individual- and firm-level heterogeneity, show that when

controlling for unobserved heterogeneity they can explain nearly all of the variation of wages.

The methods have ever since been broadly explored by authors like Abowd and Kramarz

(1999), Abowd, Finer and Kramarz (1999) (American data), Abowd, Creecy and Kramarz

(2002) (American and French data), Barth and Dale-Olsen (2003) (Norwegian data), Gruetter

and Lalive (2004) (Austrian data), Andrews, Gill, Schank and Upward (2008) (German data),

and Sørensen and Vejlin (2009) (Danish data). Often, the main focus has been on the question

of whether high wage workers are sorting into high wage firms.2 Almost all studies done to

date find small negative or zero sorting in wages. AKM show that the worker effects strongly

dominate the firm effects in explaining the wage determination. The worker effect together with

the correlation between the worker and the firm effects have been given most attention in the

literature. In the literature following AKM the common approach so far has been to focus on

the wage level, while very little effort has been spent on explaining the wage growth distribution

using these methods. The levels of wages have been the natural starting point of research for

several reasons. Firstly, wage levels have been the natural dependent variable in any human cap-

ital wage equation ever since Mincer (1958) developed the so-called Mincerian wage equation.

Secondly, much earlier research has been forced to use annual wage income making a credible

wage growth practically difficult to calculate as the direct wages will be troublesome to extract

1See e.g. Abowd, Kramarz and Margolis (1999, Table II), Barth and Dale-Olsen (2003, Table 2) and Mortensen(2005) for analysis of wage level equations. In section 5 Robustness we find a degree of explanation of 2.24 percentin an OLS regression on wage growth.

2A high wage worker is in the terminology by AKM a worker receiving above what he is expected to, givenhis level of observable characteristics. A high wage firm is a firm paying wages higher than expected given thesesame characteristics.

Worker and Firm Heterogeneity in Wage Growth 5

and compare with the corresponding wage one year before, since it might be contaminated by

different hours worked and changing bonus schemes, thus containing lots of measurement error.

The goal of this paper is to estimate an empirical model of wage growth allowing for both

worker and firm fixed effects. We argue that this is interesting from a policy perspective, since

if there is no variation in wage growth across firms then all workers need to do, is to find a job

in order to get higher wages. However, if most of the variation in wage growth comes from

firm effects then it will matter a lot for the worker which job he takes. Baker (1997), Gladden

and Taber (2009) and Sørensen and Vejlin (2011) show differences in wage growth given initial

wages. They particularly show that it matters for the worker which job he enters into as the

wage structure is different for different initial jobs. In other words, should labor market policy

be directed at simply allocating workers into any job or should it more try to find the “correct”

job for the specific worker. The more important firm specific effects are for variance in wage

growth, the more important for the worker it is to find the “correct” job. In much the same

way, were all workers born identically (i.e. zero worker specific effects) then guiding workers

into any job increasing overall physical experience the most would be optimal. With worker

specific effects (Sørensen and Vejlin (2011) refer to worker effects as worker specific return to

experience) the wage profile will be different for different jobs.

We show that much less of the variation of wage growth can be explained by observables,

worker and firm effects compared to the degree of explanation in the levels of wages. The

common result that unobserved worker heterogeneity is more important than unobserved firm

heterogeneity and observable covariates is found to be the case for the variance in wage growth

as well. Furthermore, we find a negative correlation between the estimated worker specific

effects and the estimated firm specific effects of a much stronger magnitude than typically found

in wage level analysis.

A more theoretical literature inspired by the empirical findings of AKM argues that the

fixed effects in the wage equation do not necessarily correlate very well with the underlying

productivity of the firm and worker, respectively. When motivating the AKM specification

as a structural representation of the wage equation, it is generally assumed that the outside

options of workers and firms are independent of the prevailing match. Recently, several studies

have illustrated the implications of relaxing this assumption. Eeckhout and Kircher (2009)

and Lopes de Melo (2008) both generate a non-monotonicity in the wage equation due to high

productivity firms facing better outside options than their counterparts when they match with a

6 Chapter 1

low productivity worker. A low productivity worker has to compensate a high productivity firm

for giving up the opportunity to match with a more productive worker. Eeckhout and Kircher

(2009) illustrate the insufficiency of wage data alone to identify sorting in the labor market:

for every production function that induces positive sorting they can find a production function

inducing negative sorting whilst generating identical wages. In Postel-Vinay and Robin (2002)

the dynamic nature of the wage bargaining process implies that although workers always move

up in the productivity distribution upon a job-to-job transition, a move may be associated with a

drop in wages. Bagger and Lentz (2008) adopt this wage setting in an on-the-job search model

with endogenous search effort and show that positive sorting can be consistent with a negative

correlation between the fixed effects in the wage equation. Shimer (2005) makes the same point

within an assignment model. This recent strand of the literature shows that one should be very

careful when interpreting AKM type wage decompositions and, hence, we do not push our

results in the direction of revealing the underlying productivity structure of the labor market.

Given the theoretical interest alluded to above, one of the contributions of this paper is also

to investigate whether or not the structural models need to take into account that the growth

rate of wages can be different for different workers. An implication of the human capital model

by Mincer (1974) is parallel log earnings profiles across schooling levels. Heckman, Lochner

and Todd (2003) test whether data support this parallel implication and find that only 1940s

and 1950s US Census data support parallel log earnings profiles across schooling levels, while

formal econometric tests reject any support for such parallelism for newer data (1960 to 1990).

Connolly and Gottschalk (2006) show that log earnings profiles are not even parallel when con-

trolling for workers making job-to-job transitions and workers experiencing a non-employment

spell between jobs with high educated workers experiencing higher wage growth than lower

educated workers.

Postel-Vinay and Robin (2002) and Bagger, Fontaine, Postel-Vinay and Robin (2007) pro-

duce wage equations in which the wage change does not depend on the worker, but only on the

current and the last firm that the worker was in. E.g., if it is a high productivity firm then wage

changes are large, since the initial wage is low, because the worker is willing to accept an initial

low wage at a high productivity firm in order to get higher wage raises in the future, and then

high wage firm matches all wage offers.

The paper is organized as follows: Section 2 presents our empirical model, discusses iden-

tification and summarizes the implementation procedure. We describe the Danish IDA data


in Section 3 and, in particular, the realized mobility patterns that are of high importance for

both identification and precision of the parameters. In Section 4 we present the results of the

wage decomposition and the analysis taking the estimated parameters as input. In section 5 we

analyze the robustness of our model. Section 6 concludes.

2 The Two-Way Fixed Effects Model

We will be using a wage specification inspired by Abowd et al. (1999) and Abowd et al. (2002)

with wage growth decomposed into a linear relationship between observed covariates, an unob-

served worker fixed effect, an unobserved firm fixed effect and an error term.

Let i ∈ I = {1, . . . , I} index workers and let worker i be represented by Ni observations

indexed by n ∈ Ni = {1, . . . , Ni} totaling N∗ =∑

i∈I Ni observations in the data. The set of

firms is J = {1, . . . , J}. We assume that worker i’s log wage growth from time t− 1 to time t

when employed at firm J(i, t) arises from the linear model given by3

∆wit = x′itβ + θi + ψJ(i,t) + εit, (1)

where ∆wit = wit − wit−1, xit is a 1 × K vector of observed time-varying covariates, β is

a conformable vector of slope parameters, θi and ψJ(i,t) are worker specific and firm specific

components of the variation of log wage growth, respectively. εit is the residual wage growth.

Our specification is different from the original AKM specification as the error structure allows

for time varying unobservables to have long term consequences on wage growth. Kramarz,

Machin and Ouazad (2009) have a specification much like ours. They analyze a value added

model in which they decompose the progress of children in the English primary education

system into a child fixed effect (corresponding to our worker effect), a school-grade-year effect

(corresponding to our firm effect) and an error term. A crucial difference between our analysis

and the one by Kramarz, Machin and Oazad is that we have up to 26 time periods per person

while they analyze the change in test scores for English primary school pupils over two periods;

period one at age 6/7 and period two at age 10/11.

We shall treat the residual εit in (1) as a genuine statistical residual. We thus impose the

3Note that for the comparison regressions of wages in levels, we use the same specification, but with wagelevels as left hand side variables instead of wage growth.

8 Chapter 1

identifying assumptions

E[εit|xit, i, t, J(i, t)] = 0, ∀ n ∈ Ni and ∀ i ∈ I (2)

Cov[εit, εhs|xit, xhs, i, h, t, s, J(i, t), J(h, s)] =

σ2 <∞ ∀ i = h, t = s

0 otherwise.(3)

Equation (2) ensures strict exogeneity, i.e. it rules out endogenous mobility.

2.1 Identification of the Person and Firm Fixed Effects

We need to make sure that both person and firm effects are identified. This is no trivial problem

though, since the usual techniques by sweeping out the singular row and column combinations

from the normal equations of the system cannot be done as the normal equations are solved

without actually computing the generalized inverse. Instead, person and firm effects can be

identified by forming groups of connected workers and firms using the grouping algorithm

developed by Abowd et al. (2002). To do this, one must use the movers to tie workers and firms

together such that each group consists of all the workers who have ever worked for any of the

firms within the group and all the firms at which any of the workers has ever been employed

at.4 This implies that a group is a connection of workers and firms in a graph theoretical sense.

The algorithm results are displayed in Table 1.

As none of the firms in group k is connected to any of the firms in group h for all k 6= h

we cannot compare firm and worker effects between groups. This leaves us with the option of

performing the analysis on each group separately or focusing on one group only within which

worker and firm specific effects can be identified using conventional methods from analysis of

covariance. Table 1 shows that after doing the graph theoretical grouping algorithm by Abowd

et al. (2002) the largest group contains almost all observations (99 percent), workers (98 percent)

and firms (91 percent) so we will focus on the largest group only and discard all observations

belonging to any other group than the largest. This is also the normal procedure in the literature.

It is useful to write equation (1) in matrix notation

w = Zβ + Dθ + Fψ + ε, (4)

4See ACK for a more detailed description of the grouping algorithm.


Table 1: Descriptive statistics merging from the grouping algorithm.

Number of Number of Number of Number of Number ofobservations workers firms groups estimable effects

Full sample 20,881,823 2,116,094 322,802 24,793 2,414,103(20,703,609) (2,083,391) (295,034) (1) (2,378,424)

MenHigh educ. 1,750,247 179,108 59,733 9,270 229,571

(1,682,834) (166,827) (47,019) (1) (213,845)Medium educ. 8,912,263 798,308 217,298 15,671 999,935

(8,823,828) (780,009) (198,844) (1) (978,852)Low educ. 4,074,495 401,943 147,853 14,171 535,625

(3,996,477) (385,574) (129,944) (1) (515,517)Total 14,737,005 1,379,359 268,088 20,578 1,626,869

(14,619,789) (1,354,251) (244,242) (1) (1,298,492)

WomenHigh educ. 515,512 87,387 33,262 9,715 110,934

(450,948) (71,760) (20,277) (1) (92,036)Medium educ. 3,555,893 404,602 139,539 18,360 525,781

(3,443,791) (382,385) (116,365) (1) (498,749)Low educ. 2,028,413 244,746 95,732 18,693 321,785

(1,914,928) (222,350) (71,028) (1) (293,377)Total 6,099,818 736,735 179,832 25,569 890,998

(5,949,155) (704,109) (149,086) (1) (853,194)

Note: The figures from the largest group of each sample are in parenthesis.

where w and ε are N∗× 1 vectors, D is an N∗×N matrix of worker dummy variables, F is an

N∗ × J matrix of firm dummy variables and Z is N∗ ×K matrix of covariates. θ is an N × 1

parameter vector, ψ is a J × 1 parameter vector and β is a K × 1 parameter vector.5

Equation (4) is known as the Least Squares Dummy Variable method (LSDV), which is a

two-way high dimensional fixed effects model. There are several ways to estimate such a model.

AKM note that the LSDV estimation of (4) requires the estimation of N worker effects and J

firm effects. Since N is often in millions and J is often in thousands, such an estimation is

unfeasible with standard approaches. We use the conjugate gradient (CG) algorithm also used

by Abowd et al. (2002) and Kramarz et al. (2009) to solve the problem. The CG algorithm

deals with the high dimensionality of the data by using sparse matrices and iterates the solution

according to a convergence criteria which we have set to 10−14.

3 Data

The data source used in this paper is the Integrated Database for Labor Market Research (IDA)

kept by Statistics Denmark (SD). The data are confidential but our access is not exclusive. IDA

5Note that (4) is actually a generalization of the model used by Abowd et al. (1999). Instead of using wagesin level we use wage growth and have furthermore assumed that the firm effects are all constant over time, hencem = 1 in AKM’s model.

10 Chapter 1

Table 2: Costs in terms of observations when narrowing down the sample.

Observation SampleCorrection cost size

Population 60,847,593Missing education information 1,256,538 59,591,055Labor market entry 11,064,910 48,526,145Private sector 18,207,737 30,318,408Students 938,862 29,379,546Experience outliers 15,168 29,364,378Full-time employment 2,402,026 26,962,352Non-positive hourly wages 65,571 26,896,781Non-credible hours 1,115,560 25,781,221Wages below P1 248,899 25,532,322Wages above P99 254,555 25,277,767Final corrections 4,395,944 20,881,823

is a matched employer-employee longitudinal database containing socio-economic information

on the entire Danish population, the population’s attachment to the labor market, and at which

firms the worker is employed. Both persons and firms can be monitored from 1980 onwards.

The reference period in IDA is given as follows; The linkage of persons and firms refers to

the end of November, ensuring that seasonal changes (such as e.g. shutdown of establishments

around Christmas) do not affect the registration, meaning that the creation of jobs in the indi-

vidual firms refers to the end of November. On the other hand, the background information on

individuals mainly refers to the end of the year.6 Our gross sample contains all workers having

their main employment at a private firm in the period of 1980− 2006.7

3.1 The Sample

The raw data consists of 60,847,593 yearly wage observations. We have detrended wages ac-

cording to the Danish 2006 consumer price index. The data is then narrowed down to the sample

of estimation by the following corrections according to Table 2.

First, since we divide the sample into educational groups, the observations with missing

educational information are deleted (1,256,538 observations deleted). Second, we only include

observations after the completion of the highest education (11,064,910 observations deleted).

I.e. if a worker has a job with some lower education and then achieves a new (mainly higher)

education, we only include the observations belonging to his last education and are thus delet-

ing all observations prior to the completion of his highest education. This is done such that

we are ensured not to compare e.g. an economist when working as an economist with when

6See a more detailed documentation on IDA constructed by SD:http://www.dst.dk/HomeUK/Guide/documentation/Varedeklarationer/emnegruppe/emne.aspx?sysrid=1013

7Since we will be using the first difference of wages the estimation period will be 1981− 2006.


he was working as a clerk in a department store before finishing his studies. The private and

public sector labor markets are very different, and we will only be looking at the private sector,

thus deleting all public sector observations (18,207,737 observations deleted). Furthermore, if a

worker is currently undertaking education he is deleted as well (938,862 observations deleted).

If the experience measure of a worker is negative or above his age less his years of educa-

tion the observation is deleted (15,168 observations deleted). All non-full-time employment

observations are deleted (2,402,026 observations) and so are observations with negative or non-

credible hourly wages (65,571 + 1,115,560 observations deleted).8 To deal with outliers, we

delete all observations with wages in the top and bottom percentile of the wage distribution

(248,899 + 254,555 observations), and finally, as we use yearly wage growth, we have deleted

all the observations in which we observe a worker for the first time. If, for some reason, we

miss any intervening observations for a worker we also delete the first subsequent observation

we have on him such that all wage growth observations are yearly (4,395,944 observations). I.e.

when analyzing wage growth the growth is always between consecutive years. The final sample

consists of 20,836,823 observations which then is divided into three educational groups, which

are low, medium and high for both men and women. These groups are thoroughly described in

the next section.

3.2 Observable Characteristics

The IDA data contains actual labor market experience but only measured from 1964 and on-

wards. Hence, for workers entering the labor market prior to 1964 this experience measure is

left-censored. Therefore, we construct our own measure of experience as potential experience

(age less the total length of education less schooling starting age) at the first observation for a

given worker and then add actual increments in experience. Woodcock (2008) uses a similar

measure except that he only knows whether or not a worker was employed sometime during

a quarter, whereas we have more precise information on actual experience accumulated dur-

ing each year. Sørensen and Vejlin (2009) also use this measure. Table 3 presents summary

statistics of our measure of experience. In our sample men are relatively more experienced than

women and low educated are more experienced than high educated. The latter partly reflects

that high educated enter the labor market later.

8The hourly wage measure is calculated on the basis of payments to the Danish mandatory pension scheme,ATP which is a step-function of hours worked. If Statistics Denmark report this hourly measure as non-credible,we delete the associated observation.

12 Chapter 1

Table 3: Descriptive Statistics of Labor Market Experience

Mean Median Std. dev. P10 P90 Total observations

Full sample 16.65 16.00 8.54 5.87 28.56 20,836,823

MenHigh edu. 16.21 15.50 8.68 5.24 28.33 1,750,247Medium edu. 17.52 17.00 8.48 6.75 29.20 8,912,263Low edu. 17.74 17.89 8.84 5.81 29.80 4,074,495Total 17.43 17.00 8.61 6.32 29.23 14,737,005

WomenHigh edu. 12.8 11.00 7.96 3.88 24.55 515,512Medium edu. 15.01 13.89 8.14 5.25 26.67 3,555,893Low edu. 14.91 14.18 7.85 4.97 25.85 2,028,413Total 14.79 13.77 8.05 5.00 26.07 6,099,818

The time varying observables, x′it, consist of calendar time and labor market experience.9

In the implementation we include a full set of year dummies and parameterize the experience

profile by including experience and experience squared. Time-invariant characteristics are gen-

der and length of education. We construct an education measure which divides the sample

into three mutually exclusive groups: less than 12 years of education, 12-14 years and more

than 14 years. The first group contains high-school drop-outs, the second contains high-school

graduates, individuals with a vocational education, and individuals with a short cycle tertiary

education, and the third contains those with medium and long cycle tertiary educations. We

will denote these educational groups as low, medium and high educated workers, respectively.

The IDA data does contain considerable further information on workers. However, this paper

focuses on disentangling worker and firm effects and not on which particular characteristics on

either the worker or firm side that drive wage growth differentials. Hence, the time-invariant

worker characteristics included in the analysis are chosen such that well-defined subsamples

can be formed on which separate analysis can be performed.

Since the firm effect in the AKM model is identified from workers moving between different

firms it is important to have long panels and a lot of job changes per worker. Table 4 shows the

distribution of number of observations for each worker. Each worker appears in the sample on

average 9.85 times with men being on average more frequently than women. We have more

than ten observations for almost 40 percent of the entire sample divided on 44 percent of the

male sample and 31 percent of the female sample. It is only 18 percent of the total number of

workers that appears less than three times in our total sample.

Table 5 reports the distribution of number of employers per worker. Approximately two

9In the robustness section we include dummies for marital status, parenthood and size of the firm current andone period before to check whether year dummies and experience profiles fully capture observable heterogeneity.


Table 4: Number of Observations per Worker

Average 1 2 3 - 5 6 - 10 11 - 20 21+ Total workers

Full sample 9.85 221,977 167,198 386,807 499,124 584,950 256,038 2,116,094(0.1049) (0.0790) (0.1828) (0.2359) (0.2764) (0.1210)

MenHigh edu. 9.77 17,585 13,741 32,480 44,762 50,926 19,614 179,108

(0.0982) (0.0767) (0.1813) (0.2499) (0.2843) (0.1095)Medium edu. 11.16 61,566 50,807 126,284 183,109 248,180 128,362 798,308

(0.0771) (0.0636) (0.1582) (0.2294) (0.3109) (0.1608)Low edu. 10.14 41,977 31,275 70,589 93,081 109,897 55,124 401,943

(0.1044) (0.0778) (0.1756) (0.2316) (0.2734) (0.1371)Total 121,128 95,823 229,353 320,952 409,003 203,100 1,379,359

(0.0878) (0.0695) (0.1663) (0.2327) (0.2965) (0.1472)

WomenHigh edu. 5.90 16,977 11,562 22,557 22,204 12,345 1,742 87,387

(0.1943) (0.1323) (0.2581) (0.2541) (0.1413) (0.0199)Medium edu. 8.79 48,775 35,616 83,420 98,159 106,227 32,405 404,602

(0.1206) (0.0880) (0.2062) (0.2426) (0.2625) (0.0801)Low edu. 8.29 35,097 24,197 51,477 57,809 57,375 18,791 244,746

(0.1434) (0.0989) (0.2103) (0.2362) (0.2344) (0.0768)Total 100,849 71,375 157,454 178,172 175,947 52,938 736,735

(0.1369) (0.0969) (0.2137) (0.2418) (0.2388) (0.0719)

Note: Numbers in parenthesizes denote percentages of subsamples.

thirds of all workers are in multiple firms and 40 percent of the workers in the entire sample

have three or more different employers. On average, each worker has 2.52 different employers.

45 percent of all men and 32 percent of all women have three or more employers. To compare

these figures, Abowd et al. (1999) have a maximum of ten years of observations, but only 10

percent of their workers are observed ten times and only one half of the workers in their sample

changes employers, i.e. we have more observations per worker and more frequent job changes

in our sample compared to the original sample used to estimate the AKM model.

The main interest in this paper is to estimate the effect of firm and worker heterogeneity on

wage growth. Figure 1 shows the cross-section distribution of wage growth over all years. The

wage growth distribution is almost symmetrical around a mean value of three percent and there

are considerable variations.

14 Chapter 1

Table 5: Number of Employers per Worker

Average 1 2 3 4 5 - 10 11+ Total workers

Full sample 2.52 772,003 501,601 345,654 231,683 262,153 3,000 2,116,094(0.3648) (0.2370) (0.1634) (0.1095) (0.1239) (0.0014)

MenHigh edu. 2.44 67,199 43,441 29,463 18,573 20,313 119 179,108

(0.3752) (0.2425) (0.1645) (0.1037) (0.1134) (0.0007)Medium edu. 2.80 238,394 186,110 142,408 101,481 128,142 1,773 798,308

(0.2986) (0.2332) (0.1784) (0.1271) (0.1605) (0.0022)Low edu. 2.63 144,643 89,662 63,678 45,311 57,739 910 401,943

(0.3599) (0.2230) (0.1584) (0.1127) (0.1437) (0.0023)Total 450,236 319,213 235,549 165,365 206,194 2,802 1,379,359

(0.3264) (0.2314) (0.1708) (0.1199) (0.1495) (0.0020)

WomenHigh edu. 1.77 50,603 19,494 9,459 4,491 3,336 4 87,387

(0.5790) (0.2231) (0.1082) (0.0514) (0.0382) (0.0001)Medium edu. 2.31 157,558 103,714 66,414 40,898 35,889 129 404,602

(0.3894) (0.2563) (0.1642) (0.1011) (0.0887) (0.0003)Low edu. 2.10 113,606 59,180 34,232 20,929 16,734 65 244,746

(0.4642) (0.2418) (0.1399) (0.0854) (0.0684) (0.0003)Total 321,767 182,388 110,105 66,318 55,959 198 736,735

(0.4367) (0.2475) (0.1495) (0.0900) (0.0760) (0.0003)

Note: Numbers in parenthesizes denote percentages of subsamples.

Figure 1: The distribution of wage growth for the entire sample 1980-2006.

02

46

Perc

ent

−1 −.9 −.8 −.7 −.6 −.5 −.4 −.3 −.2 −.1 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1Wage growth, percent

4 Results

In this section we present results for model (4). The model is estimated both in terms of wage

growth and wage levels, i.e. the original AKM model. This is done in order to compare the

two models. Model (4) is also estimated on subgroups, which allow for the firm effect, the

year effect and the experience profile to differ between subgroups, although the structure of the

identification process prevents us from comparing subgroups directly.


4.1 Contributions of Fixed Effects to the Variance of Wage Growth

Notice that the variance of either wage growth or levels can be decomposed into pairwise co-

variances between the dependent variable and independent variables. This is shown in equation

(5) by inserting for the wage growth equation

V ar(∆wit) = Cov(∆wit,∆wit) = Cov(∆wit, x′itβ + θi + ψJ(i,t) + εit)

= Cov(∆wit, x′itβ) + Cov(∆wit, θi) + Cov(∆wit, ψJ(i,t)) + Cov(∆wit, εit).

(5)

Dividing through by the variance of the dependent variable lets us interpret each component as

the relative contribution to the explanation of the variance of the dependent variable. I.e. the

degree of explanation by each component arising from the decomposition is given by10

Cov(∆wit, x′itβ)

V ar(∆wit)+Cov(∆wit, θi)

V ar(∆wit)+Cov(∆wit, ψJ(i,t))

V ar(∆wit)+Cov(∆wit, εit)

V ar(∆wit)= 1. (6)

This decomposition constitutes a nice measure of how ’important’ each component can be

said to be for the description of the variance of wage growth. Abowd et al. (1999) (and sub-

sequently Abowd et al. (2002)) make a decomposition much like this and find that the worker

effect is by far the most important component in determining the variance in wage levels leav-

ing only very little explanation to firm effects. Sørensen and Vejlin (2009) also decompose the

variance of wage levels following the method of Woodcock (2008) who shows how to decom-

pose the variance of wages when including worker fixed effects, firm fixed effects and a match

specific effect. Sørensen and Vejlin use the same raw data as us but with a slightly different

subgroup selection, and they include a match fixed effect besides worker and firm fixed effects.

Their paper also only uses the years from 1980 to 2003. They find that depending on skill

levels, the firm effect can be said to explain from 10 to 25 percent of the variation in wages.

Furthermore, they find that the degree of explanation given by firm effects is declining when

the skill level increases. Sørensen and Vejlin find the contributions to the explanation of the

variance in wages given by worker effects to range from 35 percent for low skilled workers to

45 percent for high skilled workers.

10Note that for a normal OLS regression with regular covariates included only, ∆wit = x′itβ+ εit the followingholds

Cov(∆wit,x′itβ)

V ar(∆wit)= 1− Cov(∆wit,ε)

V ar(∆wit)= R2.

16 Chapter 1

Table 6 shows summary statistics from the AKM model estimated on wage growth and

wage levels and the variance decomposition as shown above. First, turning to the model for

wage levels, i.e. the standard AKM model, we find that the worker fixed effects dominate the

explanation of the variance of wages explaining around 58 percent of wage variation in the es-

timation on the full sample. The firm fixed effects contribute with 14 percent, while experience

and year fixed effects (put together into Xβ) contribute with 9 percent. However, turning to

the subgroup analysis we find that the worker fixed effects mostly dominate for high educated,

while for low educated the worker and firm fixed effects are almost equally important. It seems

that the heterogeneity in the explanatory power of each is completely based on education and

not on gender, even though, of course, there are small differences between men and women.

Sørensen and Vejlin (2009) also find nearly the same contributions from firm fixed effects while

our worker effects contribute with more to the explanation of the variance in wages. Our co-

variates (experience and year effects) contribute with much less than what Sørensen and Vejlin

find. This difference can be explained by their inclusion of a match effect and a slightly dif-

ferent sample selection. Sørensen and Vejlin (2009) also find the same pattern in the subgroup

analysis. Thus, our sample seems to be able to produce results in the same range as known in

the literature.


Table 6: Regression results.

Wage growth Wage levels

Cov(w,Z) Cov(w,Z)

Z Mean Std. Dev. Cov(w,Z) / Var(w) Mean Std. Dev. Cov(w,Z) / Var(w)

Full sample (20,703,609 observations)

w 0.0196 0.1486 0.0221 1.0000 5.2372 0.3072 0.0944 1.0000

θ -0.0780 0.0578 0.0019 0.0868 4.8103 0.2319 0.0543 0.5752

ψ 0.1110 0.0470 0.0009 0.0415 0.2547 0.1107 0.0132 0.1399

Xβ -0.0134 0.0248 0.0005 0.0218 0.1723 0.0940 0.0088 0.0927

ε 0.0000 0.1370 0.0188 0.8499 0.0000 0.1347 0.0181 0.1922

High educated

Men (1,682,834 observations)

w 0.0279 0.1537 0.0236 1.0000 5.6571 0.3354 0.1125 1.0000

θ -0.3121 0.0687 0.0017 0.0739 5.5965 0.2945 0.0645 0.5732

ψ 0.3370 0.0673 0.0018 0.0753 0.1186 0.1392 0.0119 0.1059

Xβ 0.0031 0.0259 0.0005 0.0216 -0.0581 0.1838 0.0141 0.1255

ε 0.0000 0.1400 0.0196 0.8292 0.0000 0.1483 0.0220 0.1954

Women (450,948 observations)

w 0.0297 0.1482 0.0220 1.0000 5.4231 0.3104 0.0963 1.0000

θ 0.0960 0.1130 0.0026 0.1161 5.5190 0.2689 0.0598 0.6208

ψ -0.0581 0.1106 0.0021 0.0961 -0.0851 0.1451 0.0124 0.1289

Xβ -0.0083 0.0217 0.0005 0.0208 -0.0108 0.1315 0.0099 0.1031

ε 0.0000 0.1298 0.0169 0.7670 0.0000 0.1191 0.0142 0.1472

Medium educated


w 0.0181 0.1488 0.0222 1.0000 5.2778 0.2633 0.0693 1.0000

θ -0.0533 0.0582 0.0016 0.0712 4.8230 0.1817 0.0313 0.4513

ψ 0.0931 0.0546 0.0012 0.0558 0.2670 0.1199 0.0134 0.1935

Xβ -0.0218 0.0238 0.0005 0.0220 0.1878 0.0882 0.0071 0.1025

ε 0.0000 0.1373 0.0189 0.8509 0.0000 0.1324 0.0175 0.2527

Women (3,443,791 observations)

w 0.0259 0.1406 0.0198 1.0000 5.0995 0.2546 0.0648 1.0000

θ -0.2304 0.0720 0.0020 0.1024 4.5700 0.1774 0.0277 0.4271

ψ 0.2595 0.0650 0.0013 0.0661 0.3321 0.1104 0.0103 0.1591

Xβ -0.0032 0.0276 0.0006 0.0280 0.1974 0.1181 0.0127 0.1955

ε 0.0000 0.1260 0.0159 0.8036 0.0000 0.1190 0.0141 0.2183

Low educated


w 0.0151 0.1554 0.0241 1.0000 5.1837 0.2447 0.0599 1.0000

θ 0.0051 0.0720 0.0020 0.0841 4.6726 0.1620 0.0211 0.3531

ψ 0.0359 0.0704 0.0019 0.0781 0.3344 0.1432 0.0175 0.2915

Xβ -0.0258 0.0275 0.0006 0.0267 0.1767 0.0783 0.0058 0.0976

ε 0.0000 0.1400 0.0196 0.8111 0.0000 0.1242 0.0154 0.2577

This table continues on the next page.

Note: Z in columns 4, 5, 9 and 10 denotes w, θ, ψ, Xβ or ε depending on the row in question.

18 Chapter 1

Table 6 – continued from previous page.


Cov(w,Z) Cov(w,Z)

Z Mean Std. Dev. Cov(w,Z) / Var(w) Mean Std. Dev. Cov(w,Z) / Var(w)

Women (1,914,928 observations)

w 0.0160 0.1376 0.0189 1.0000 5.0194 0.2277 0.0518 1.0000

θ 0.0526 0.0785 0.0020 0.1063 4.7302 0.1593 0.0178 0.3429

ψ -0.0577 0.0738 0.0016 0.0825 0.1063 0.1420 0.0154 0.2972

Xβ 0.0212 0.0279 0.0005 0.0277 0.1830 0.0853 0.0064 0.1244

ε 0.0000 0.1218 0.0148 0.7836 0.0000 0.1105 0.0122 0.2355

Note: Z in columns 4, 5, 9 and 10 denotes w, θ, ψ, Xβ or ε depending on the row in question.

Our results of the variance decomposition yield much lower estimates of the degree of ex-

planation of the variance in wage levels than those given by most former literature. One ex-

planation of this can be that we use much longer panels than e.g. Abowd et al. (1999) (panel

covering 1976-1987, excluding 1981 and 1983), Abowd et al. (2002) (same panel length as

AKM) and Barth and Dale-Olsen (2003) (panel covering 1989-1997). Figures 2 to 4 show the

variance decomposition (equation (6)) plotted for each subgroup against the number of times

we have observed the individual worker. The development in contribution to the variance of

wages is almost the same for all three subgroups where the worker effects seem to be mostly

negatively affected by the length of the panels while the contributions from firm effects are rel-

atively constant and the covariates experience increasing contribution to the variance of wages

for all subgroups. AKM, Abowd et. al, and Barth and Dale-Olsen all use unbalanced panels

as we do, and they could thus possibly have an upward biased worker effect. It is a subject

for further research whether the estimated worker and firm effects are dependent on the panel

lengths at hand.

Now turning to the main analysis of the wage growth equation. For the full sample the

variation in the worker effect explains 8.7 percent, the firm effect explains 4.2 percent, and

experience and year effects explain 2.2 percent. I.e., as in the regressions on wage levels,

the most important component is the worker fixed effect. When we estimate the model on

the six subgroups of gender and educational level an interesting pattern emerges. It seems

that especially the worker effect, but to some extent also the firm effect, is more important in

explaining women’s wage growth. In all subgroups with an equal amount of education the

explanatory power of both the worker and the firm effect is higher for women than for men.


Figure 2: Degree of explanation given by worker effects, firm effects and covariates according to the variancedecomposition plotted against number of person-years observed.

0.2

.4.6

.81

Degre

e o

f expla

nation

1 5 9 13 17 21 25Number of years observed

Worker effects Firm effects

Covariates Residuals

High educated men

0.2

.4.6

.81

Degre

e o

f expla

nation




High educated women


0.2

.4.6

.81

Degre

e o

f expla

nation




Medium educated men

0.2

.4.6

.81

Degre

e o

f expla

nation




Medium educated women

20 Chapter 1


0.2

.4.6

.81

Degre

e o

f expla

nation




Low educated men

0.2

.4.6

.81

Degre

e o

f expla

nation




Low educated women

The clear pattern from the wage level estimation, where worker effects were most important for

high educated, is nearly not present in wage growth. In general, worker effects explain around 8

to 12 percent, firm effects explain around 4 to 10 percent, and experience and the year dummies

together explain 2 to 3 percent. That is, the most important component of wage growth is worker

specific differences, but it also seems that firm heterogeneity plays a relatively important role

in determining wage growth compared to determining variance in wage levels. We also see that

experience and year dummies explain a very small fraction of the variation in wage growth.

This is not a surprising result though, since (in the Robustness section below (table A1 column

(1))) we find R2 = 0.024 when running a simple OLS regression without including any fixed

effects.

Compared to the model for wage levels the degree of explanation is dramatically smaller

for wage growth. I.e. we cannot explain the variation in wage growth as precisely as we can

explain the variation in the level of wages. Also for wage levels the most important component

is the worker fixed effect, while the firm fixed effect and experience and year dummies seem

to explain an almost equal share. The latter part is in contrast to the model for wage growth

where the covariates constantly contribute with around half the share of the contribution given

by firm fixed effects. A possible explanation of this can simply be that there is a relatively higher

variance in the error term when analyzing wage growth than wage levels. Given the relatively


low contribution by firm effects compared to the worker effects and the residual, one could

doubt the significance of the firm effects. We have tested this for each subgroup using a simple

F-test with the hypothesis that the model with firm effects included does not provide a significant

better fit of wage growth (and levels) than a model without firm fixed effects included. The test

gives a p-value of zero for all subgroups for both wage growth and wage levels.11

Table 7 shows the correlation structure of the two models for wage growth and wage levels.

In levels we see that there is a small but positive correlation between the firm effect and the

worker effect in the full sample, but when we turn to the subsamples we find a negative cor-

relation. This is also found by Sørensen and Vejlin (2009). In the wage growth equation we

find a strong negative correlation between the firm effect and the worker effect. I.e. workers

with high wage growth are on average in firms with low wage growth. One reason could be the

negative bias between worker and firm effects, see e.g. Bagger and Lentz (2008). Furthermore,

Andrews et al. (2008) show that the magnitude of this bias is increasing in the size of the error

term variance which explains our much stronger correlation than earlier studies such as e. g.

Abowd et al. (2002) and Gruetter and Lalive (2004). The negative correlation between worker

and firm effects is consistently stronger for women than for men throughout the educational

subgroups, and does not differ much for men whether they are high, medium or low educated,

whereas the correlation is much higher (in absolute terms) for high educated women than for

low and medium educated women. The difference in the magnitude of the correlation between

worker and firm effects when analyzing wage growth and wage levels can to a large extent be

explained by a much lower standard deviation of worker and firm effects in the wage growth

estimations compared to wage levels.

11The test with the lowest F-statistic is high educated women, wage growth at F = 52, 393. The correspondingcritical value on a significance level of five percent is F (92, 036 − 20, 277; 450, 948 − 20, 277) = 1.009 and thefirm effects are thus highly significant.

22 Chapter 1

Table 7: Correlation structure, full AKM model, wage growth and wage levels.


w θ ψ Xβ ε w θ ψ Xβ ε

Full sample

w 1.0000 0.2232 0.1313 0.1306 0.9219 1.0000 0.7619 0.3883 0.3029 0.4384

θ 0.2232 1.0000 -0.4749 -0.0931 0.0000 0.7619 1.0000 0.0302 -0.0124 0.0000

ψ 0.1313 -0.4749 1.0000 -0.0008 0.0000 0.3883 0.0302 1.0000 0.0169 0.0000

Xβ 0.1306 -0.0931 -0.0008 1.0000 0.0000 0.3029 -0.0124 0.0169 1.0000 0.0000

ε 0.9219 0.0000 0.0000 0.0000 1.0000 0.4384 0.0000 0.0000 0.0000 1.0000

High educated

Men

w 1.0000 0.1652 0.1720 0.1285 0.9106 1.0000 0.6528 0.2551 0.2290 0.4420

θ 0.1652 1.0000 -0.6020 -0.1089 0.0000 0.6528 1.0000 -0.1225 -0.3182 0.0000

ψ 0.1720 -0.6020 1.0000 0.0198 0.0000 0.2551 -0.1225 1.0000 -0.0955 0.0000

Xβ 0.1285 -0.1089 0.0198 1.0000 0.0000 0.2290 -0.3182 -0.0955 1.0000 0.0000

ε 0.9106 0.0000 0.0000 0.0000 1.0000 0.4420 0.0000 0.0000 0.0000 1.0000

Women

w 1.0000 0.1523 0.1288 0.1422 0.8758 1.0000 0.7165 0.2756 0.2434 0.3837

θ 0.1523 1.0000 -0.8131 -0.0229 0.0000 0.7165 1.0000 -0.1768 -0.1589 0.0000

ψ 0.1288 -0.8131 1.0000 0.0178 0.0000 0.2756 -0.1768 1.0000 -0.0911 0.0000

Xβ 0.1422 -0.0229 0.0178 1.0000 0.0000 0.2434 -0.1589 -0.0911 1.0000 0.0000

ε 0.8758 0.0000 0.0000 0.0000 1.0000 0.3837 0.0000 0.0000 0.0000 1.0000

Medium educated

Men

w 1.0000 0.1821 0.1523 0.1379 0.9225 1.0000 0.6540 0.4249 0.3061 0.5027

θ 0.1821 1.0000 -0.5467 -0.0523 0.0000 0.6540 1.0000 -0.0463 -0.0449 0.0000

ψ 0.1523 -0.5467 1.0000 -0.0039 0.0000 0.4249 -0.0463 1.0000 0.0048 0.0000

Xβ 0.1379 -0.0523 -0.0039 1.0000 0.0000 0.3061 -0.0449 0.0048 1.0000 0.0000

ε 0.9225 0.0000 0.0000 0.0000 1.0000 0.5027 0.0000 0.0000 0.0000 1.0000

Women

w 1.0000 0.1999 0.1429 0.1428 0.8964 1.0000 0.6130 0.3668 0.4215 0.4672

θ 0.1999 1.0000 -0.6275 -0.1128 0.0000 0.6130 1.0000 -0.1121 -0.0759 0.0000

ψ 0.1429 -0.6275 1.0000 0.0098 0.0000 0.3668 -0.1121 1.0000 0.0243 0.0000

Xβ 0.1428 -0.1128 0.0098 1.0000 0.0000 0.4215 -0.0759 0.0243 1.0000 0.0000

ε 0.8964 0.0000 0.0000 0.0000 1.0000 0.4672 0.0000 0.0000 0.0000 1.0000

Low educated

Men

w 1.0000 0.1816 0.1723 0.1512 0.9006 1.0000 0.5333 0.4983 0.3048 0.5077

θ 0.1816 1.0000 -0.6030 -0.0478 0.0000 0.5333 1.0000 -0.1693 -0.0927 0.0000

ψ 0.1723 -0.6030 1.0000 -0.0077 0.0000 0.4983 -0.1693 1.0000 0.0786 0.0000

Xβ 0.1512 -0.0478 -0.0077 1.0000 0.0000 0.3048 -0.0927 0.0786 1.0000 0.0000

ε 0.9006 0.0000 0.0000 0.0000 1.0000 0.5077 0.0000 0.0000 0.0000 1.0000



Table 7 – continued from previous page.


w θ ψ Xβ ε w θ ψ Xβ ε

Women

w 1.0000 0.1862 0.1537 0.1366 0.8852 1.0000 0.4901 0.4764 0.3319 0.4853

θ 0.1862 1.0000 -0.6717 -0.1175 0.0000 0.4901 1.0000 -0.2549 -0.1348 0.0000

ψ 0.1537 -0.6717 1.0000 0.0015 0.0000 0.4764 -0.2549 1.0000 0.0826 0.0000

Xβ 0.1366 -0.1175 0.0015 1.0000 0.0000 0.3319 -0.1348 0.0826 1.0000 0.0000

ε 0.8852 0.0000 0.0000 0.0000 1.0000 0.4853 0.0000 0.0000 0.0000 1.0000

4.2 Within- and Between-Firm Wage Growth

So far, all results have been solely focusing on wage growth. Here we distinguish between

within- and between-firm wage growth. We have divided our samples of the full sample, men

and women, into those who have made a transition into a new job and those who have not.

Table 8 shows the results of within- and between-firm wage growth. First, we have included

transition as a dummy in the covariates of the basis regression to see whether transition itself

can help explain wage growth variation. The first five rows of Table 8 contain results from this

exercise. Comparison with Table 6 reveals that inclusion of this transition dummy contributes

no extra explanatory power to the model. Second, we regress the standard model for men

and women together as well as for men and women separately for both the sample of workers

staying at the same employer (within-firm wage growth) and workers making a transition into a

new job (between-firm wage growth). Two very interesting results leap out of Table 8; first, the

overall explanatory power of the model rises for both samples. We are able to explain 20 percent

of the variance in within-firm wage growth and as much as 46 percent of the full sample and

male between-firm wage growth variation and even 58 percent of female between-firm wage

growth variation. Second, the relative firm specific importance in wage growth variation rises

dramatically when analyzing between-firm wage growth.

Table 9 shows the correlation structure of the within- and between-firm wage growth analy-

sis. Comparing with the baseline model, we see that the correlation structure of worker and firm

specific effects changes only very little and it retains its overall structure with worker specific

effects being highly negatively correlated with firm specific effects, although the correlation is

slight lesser in the between-firm wage growth sample than it is in the within-firm sample.

24 Chapter 1

Tabl

e8:

Rob

ustn

ess

chec

ksfo

rwag

egr

owth

;Reg

ress

ion

Res

ults

.

All

Men

Wom

enCov(w,Z

)/Cov(w,Z

)/Cov(w,Z

)/Z

Mea

nSt

d.D

evCov(w,Z

)Var(w

)M

ean

Std.

Dev

Cov(w,Z

)Var(w

)M

ean

Std.

Dev

Cov(w,Z

)Var(w

)

Full

Sam

ple

(20,

703,

609

obs)

Full

Sam

ple

(14,

619,

789

obs)

Full

Sam

ple

(5,9

49,1

55ob

s)w

0.01

960.

1486

0.02

211.

0000

0.01

840.

1514

0.02

291.

0000

0.02

290.

1407

0.01

981.

0000

θ-0

.075

00.

0576

0.00

190.

0866

-0.0

755

0.05

810.

0018

0.07

77-0

.224

80.

0687

0.00

210.

1082

ψ0.

1094

0.04

700.

0009

0.04

150.

1104

0.05

070.

0011

0.04

810.

2537

0.05

940.

0011

0.05

55Xβ∗

-0.0

148

0.02

480.

0005

0.02

21-0

.016

50.

0249

0.00

050.

0213

-0.0

060

0.02

600.

0005

0.02

59ε

0.00

000.

1370

0.01

880.

8499

0.00

000.

1399

0.01

960.

8530

0.00

000.

1267

0.01

600.

8104

Tran

sitio

n=

0(1

7,22

7,14

4ob

s)Tr

ansi

tion

=0

(12,

074,

930

obs)

Tran

sitio

n=

0(4

,976

,707

obs)

w0.

0194

0.13

270.

0176

1.00

000.

0178

0.13

370.

0179

1.00

000.

0235

0.12

890.

0166

1.00

00θ

0.04

130.

0599

0.00

250.

1392

0.06

880.

0592

0.00

230.

1286

-0.0

741

0.07

060.

0027

0.16

14ψ

-0.0

077

0.03

960.

0005

0.02

94-0

.039

80.

0412

0.00

060.

0335

0.11

230.

0540

0.00

070.

0405

Xβ?

-0.0

141

0.02

350.

0005

0.02

64-0

.011

20.

0237

0.00

040.

0250

-0.0

148

0.02

410.

0005

0.03

12ε

0.00

000.

1191

0.01

420.

8050

0.00

000.

1206

0.01

450.

8129

0.00

000.

1129

0.01

270.

7669

Tran

sitio

n=

1(3

,374

,561

obs)

Tran

sitio

n=

1(2

,469

,392

obs)

Tran

sitio

n=

1(8

82,6

27ob

s)w

0.02

080.

2104

0.04

431.

0000

0.02

110.

2168

0.04

701.

0000

0.02

010.

1908

0.03

641.

0000

θ0.

0046

0.13

670.

0128

0.28

890.

0304

0.13

760.

0125

0.26

52-0

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50.

1510

0.01

280.

3512

ψ0.

0731

0.11

400.

0070

0.15

900.

0578

0.12

210.

0084

0.17

840.

9575

0.13

340.

0077

0.21

26Xβ?

-0.0

569

0.03

370.

0009

0.02

07-0

.067

10.

0340

0.00

100.

0207

-0.0

219

0.03

460.

0008

0.02

26ε

0.00

000.

1534

0.02

350.

5314

0.00

000.

1587

0.02

520.

5356

0.00

000.

1227

0.01

510.

4135

∗ Ful

lsam

ple;

Cov

aria

tes

incl

ude:

expe

rien

ce,e

xper

ienc

esq

uare

d,ye

aref

fect

san

da

tran

sitio

ndu

mm

y.?

Tran

sitio

nsa

mpl

es;C

ovar

iate

sin

clud

e:ex

peri

ence

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erie

nce

squa

red

and

year

effe

cts.


Tabl

e9:

Rob

ustn

ess

chec

ksfo

rwag

egr

owth

;Cor

rela

tion

Stru

ctur

e.

All

Men

Wom

enZ

wθ

ψXβ

εw

θψ

Xβ

εw

θψ

Xβ

ε

Full

Sam

ple

(20,

703,

609

obs)

Full

Sam

ple

(14,

619,

789

obs)

Full

Sam

ple

(5,9

49,1

55ob

s)w

1.00

000.

2025

0.14

350.

1296

0.92

361.

0000

0.20

250.

1435

0.12

960.

9236

1.00

000.

2216

0.13

150.

1401

0.90

02θ

0.20

251.

0000

-0.4

978

-0.0

876

0.00

000.

2025

1.00

00-0

.497

8-0

.087

60.

0000

0.22

161.

0000

-0.5

935

-0.0

883

0.00

00ψ

0.14

35-0

.497

81.

0000

-0.0

034

0.00

000.

1435

-0.4

978

1.00

00-0

.003

40.

0000

0.13

15-0

.593

51.

0000

-0.0

038

0.00

00Xβ∗

0.12

96-0

.087

6-0

.003

41.

0000

0.00

000.

1296

-0.0

876

-0.0

034

1.00

000.

0000

0.14

01-0

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3-0

.003

81.

0000

0.00

00ε

0.92

360.

0000

0.00

000.

0000

1.00

000.

9236

0.00

000.

0000

0.00

001.

0000

0.90

020.

0000

0.00

000.

0000

1.00

00

Tran

sitio

n=

0(1

7,22

7,14

4ob

s)Tr

ansi

tion

=0

(12,

074,

930

obs)

Tran

sitio

n=

0(4

,976

,707

obs)

w1.

0000

0.29

050.

1089

0.14

060.

9016

1.00

000.

2905

0.10

890.

1406

0.90

161.

0000

0.29

460.

0968

0.16

700.

8757

θ0.

2905

1.00

00-0

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8-0

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10.

0000

0.29

051.

0000

-0.4

478

-0.0

811

0.00

000.

2946

1.00

00-0

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3-0

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30.

0000

ψ0.

1089

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478

1.00

00-0

.003

30.

0000

0.10

89-0

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81.

0000

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033

0.00

000.

0968

-0.5

883

1.00

000.

0006

0.00

00Xβ?

0.14

06-0

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1-0

.003

31.

0000

0.00

000.

1406

-0.0

811

-0.0

033

1.00

000.

0000

0.16

70-0

.036

30.

0006

1.00

000.

0000

ε0.

9016

0.00

000.

0000

0.00

001.

0000

0.90

160.

0000

0.00

000.

0000

1.00

000.

8757

0.00

000.

0000

0.00

001.

0000

Tran

sitio

n=

1(3

,374

,561

obs)

Tran

sitio

n=

1(2

,469

,392

obs)

Tran

sitio

n=

1(8

82,6

27ob

s)w

1.00

000.

4178

0.31

690.

1323

0.73

191.

0000

0.41

780.

3169

0.13

230.

7319

1.00

000.

4440

0.30

430.

1246

0.64

31θ

0.41

781.

0000

-0.3

813

-0.0

147

0.00

000.

4178

1.00

00-0

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3-0

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70.

0000

0.44

401.

0000

-0.4

884

-0.0

313

0.00

00ψ

0.31

69-0

.381

31.

0000

-0.0

268

0.00

000.

3169

-0.3

813

1.00

00-0

.026

80.

0000

0.30

43-0

.488

41.

0000

-0.0

459

0.00

00Xβ?

0.13

23-0

.014

7-0

.026

81.

0000

0.00

000.

1323

-0.0

147

-0.0

268

1.00

000.

0000

0.12

46-0

.031

3-0

.045

91.

0000

0.00

00ε

0.73

190.

0000

0.00

000.

0000

1.00

000.

7319

0.00

000.

0000

0.00

001.

0000

0.64

310.

0000

0.00

000.

0000

1.00

00∗ F

ulls

ampl

e;C

ovar

iate

sin

clud

e:ex

peri

ence

,exp

erie

nce

squa

red,

year

effe

cts

and

atr

ansi

tion

dum

my.

?Tr

ansi

tion

sam

ples

;Cov

aria

tes

incl

ude:

expe

rien

ce,e

xper

ienc

esq

uare

dan

dye

aref

fect

s.

26 Chapter 1

5 Robustness

To analyze the robustness of our results we have run several different specifications of the

model. First, to check if the low contribution in the wage growth variance decomposition by

covariates results from too few variables added, we have included information on marital status,

children, the size of the firm this period and one period before to the covariates. Second, we

regress seven different variations of the model to see if the results change between them. Table

A1 (in the appendix) shows these robustness checks. Column (3) is the baseline model where

the only difference compared to the full sample part of Table 6 (row 2 - 6) is that a very small

fraction of the worker effect and the residuals has been absorbed by the covariates with the

inclusion of the extra variables. The difference between column (3) and the full sample part

of Table 6 is not significant on any conventional levels, though, and we have thus no reason

to think that excluding the extra covariates alters our results.12 Column (1) is the original OLS

regression and the covariates themselves are seen to explain 2.24 percent of the variance in wage

growth; The same contribution up to four decimals as in the baseline model with both worker

and firm fixed effects added. We thus seem to be able to extract truly unobserved heterogeneity

by including the fixed effects. The importance of the covariates does not alter much if we

include either firm effects (column (2)) or worker effects (column (6)) to the model only, and

lies between 2.1 and 2.9 percent. The contribution from the unobserved worker heterogeneity

on the variance of wage growth is relatively robust over columns (3) to (6) but the importance

of the unobserved firm heterogeneity seems to increase for models with worker fixed effects

included (columns (3) and (5)) than without worker specific effects (columns (2) and (7)). In

the end, our model specification seems to be relatively robust.13

Table A2 and A3 list the same robustness checks as Table A1 but for growth in wages

over two and three periods, respectively. Comparing the baseline model (column (3)) in Table

A2 and A3 with Table 6 shows that the interrelationship between the worker fixed effects,

the firm fixed effects and the covariates remains relatively constant with the firm effects being

twice as important as the covariates and the worker effects again twice as important as the firm

effects. When analyzing higher period wage growth one would expect the different components

to absorb some of the residual explanation compared to one-period wage growth; the covariates12F-test not shown, but available upon request.13One could argue a more important experience measure were firm or industry tenure instead of overall experi-

ence. We have tried several different specifications, letting firm or industry tenure be an extra covariate or replaceexperience and experience squared with tenure and tenure squared. None of these operations led to any significantchanges in regression results or the correlation structure.


because experience increases. the firm effect because firms paying consistently higher than

average period-to-period wage growth will be paying even higher two-period wage growth.

Finally, the worker effect will follow a similar pattern and be more important for describing

the variance in wage growth over two periods than in only one period. Likewise, these effects

would be expected to be even more clear when analyzing wage growth over three periods. Table

A2 and A3 indeed show that the contribution to the variance in wage growth rises when moving

from one-period to two- and three-period wage growth as we would expect. However, it is

important to note that the relative contribution does not change much. Furthermore, Table A2

and A3 support our conjecture that the part of the lack in wage growth variance explanatory

power compared to analysis of wage level variation can be contributed to a higher variance in

the error term as we are able to extract more and more explanatory power from the error term

when using longer period wage growth.

As a final robustness check, one could argue that using size of the firm as the only firm

specific control would not capture wage policies within firms. We have thus regressed the

baseline model with average firm wage growth within each year as covariate together with

worker experience and experience squared to see if this changes the results dramatically. Table

A4 shows the regression results and following correlation structure.

Comparing the results with those of the baseline model (table 6) reveals that including aver-

age firm wage growth in the regression lowers the contribution to the variance of wage growth

by firm effects to 2.6 percent while covariates become much more important. Including average

firm wage growth thus raise the explanatory power of observables from 2.2 percent to 9.6 per-

cent. There is no significant change in the contribution of worker specific effects to the variance

of wage growth. However, it is not surprising that including average firm wage growth in the

regression lowers the importance of firm effects and rises the effect of the covariates. A positive

firm effect firm is characterized by being one that pays higher than average wage growth given

the observables so including exactly the characterization into the observables will automatically

bias the results towards the covariates. The correlation structure does not change much by this

inclusion, and especially the correlation between worker and firm effects remains the same as

for the baseline model.

28 Chapter 1

6 Conclusions

This paper estimates a regression model for individual wage growth incorporating fixed worker

and firm effects. We find that these worker and firm fixed effects influence wage growth very

differently from the way they influence wages in levels. We have decomposed the variance of

wage growth and wage levels into contributions from fixed worker effects, fixed firm effects,

observable experience and year effects and what is left unexplained. We found that while worker

effects could contribute with around 60 percent for high educated workers, around 42 percent

for medium educated workers and around 35 percent for low educated workers of the variance

in wage levels we are only able to attribute around 7 to 12 percent to worker effects for all three

educational groups of the variance in wage growth to fixed worker effects. The same pattern

seems to be the case for firm effects, for which we can attribute from 10 to 30 percent of the

contribution to the variance in wage levels, while they are estimated to explain 4 to 10 percent

of the variance in wage growth. Finally, the amount of variance left unexplained is much higher

for wage growth than it is for wage levels ranging from 76 percent to 85 percent for subgroups

and 85 percent for the full sample in wage growth versus 14 to 25 percent for subgroups and 19

percent for the full sample in wage levels.

However, the amount of variance that we can explain increases from 15 percent to 30 per-

cent, when we use three-period wage growth instead of one-period growth. Importantly, the

interrelationship between the components does not alter considerably when moving from using

one-period wage growth to either two- or three-period wage growth, as the worker effect keeps

having around twice the explanatory power as firm effects which then have almost twice the

explanatory power as observable covariates.

We also find a very strong negative correlation between fixed worker and fixed firm effects

in wage growth, much stronger than usually found for AKM wage level models. Some of

this difference can be attributed to our estimated worker and firm effects having much lower

standard deviation than worker and firm effects in wage levels. However, the major explanation

lies in the high residual variance which Andrews et al. (2008) have shown to be important for

the size of the correlation in worker and firm effects.


ReferencesAbowd, J., H. Finer and F. Kramarz (1999), Individual and Firm Heterogeneity in Compen-

sation: An Analysis of Matched Longitudinal Employer and Employee Data for the State ofWashington, in J. Haltiwanger, J. Lane, J. Spletzer and K. Troske (eds.), The Creation andAnalysis of Employer-Employee Matched Data, North-Holland, 3–24.

Abowd, J. M., R. H. Creecy and F. Kramarz (2002), Computing Person and Firm Effects Us-ing Linked Longitudinal Employer-Employee Data, Technical Paper 2002-06, U.S. CensusBureau.

Abowd, J. M. and F. Kramarz (1999), The Analysis of Labor Markets using Matched Employer-Employee Data , vol. 3 of Handbook of Labor Economics, chap. 40, Elsevier Science B.V.,2629–2710.



Bagger, J., F. Fontaine, F. Postel-Vinay and J.-M. Robin (2007), A Tractable Equilibrium SearchModel with Experience Accumulation, Working Paper.

Bagger, J. and R. Lentz (2008), An Empirical Model of Wage Dispersion with Sorting, WorkingPaper.

Baker, M. (1997), Growth-Rate Heterogeneity and the Covariance Structure of Life-Cycle Earn-ings, Journal of Labor Economics, 15(2): 338–375.

Barth, E. and H. Dale-Olsen (2003), Assortative matching in the labor market? Stylized factsabout workers and plants, Institute for Social Research, Oslo, Norway.

Connolly, H. and P. Gottschalk (2006), Differences in Wage Growth by Education Level: DoLess-Educated Workers Gain Less from Work Experience?, IZA Discussion Papers 2331, In-stitute for the Study of Labor (IZA).

Eeckhout, J. and P. Kircher (2009), Identifying Sorting - In Theory, Working Paper.

Gladden, T. and C. Taber (2009), The Relationship Between Wage Growth and Wage Levels,Journal of Applied Econometrics, 24: 914–932.


Heckman, J. J., L. J. Lochner and P. E. Todd (2003), Fifty Years of Mincer Earnings Regres-sions, NBER Working Papers 9732, National Bureau of Economic Research, Inc.

Kramarz, F., S. Machin and A. Ouazad (2009), What Makes a Test Score? The RespectiveContributions of Pupils, Schools and Peers in Achievement in English Primary Education,CEE Discussion Papers CEEDP0102, CEE.

Lopes de Melo, R. (2008), Sorting In the Labor Market: Theory and Measurement, WorkingPaper, Yale.


Mincer, J. A. (1974), Schooling, Experience, and Earnings, New York: Columbia UniversityPress.

30 Chapter 1

Mortensen, D. T. (2005), Wage Dispersion - Why are similar workers paid differently, First MITPress paperback edition.

Postel-Vinay, F. and J.-M. Robin (2002), Equilibrium Wage Dispersion with Worker and Em-ployer Heterogeneity, Econometrica, 70(6): 2295–2350.

Shimer, R. (2005), The Assignment of Workers in an Economy with Coordination Frictions,Journal of Political Economy, 113(5): 996–1025.

Sørensen, K. L. and R. M. Vejlin (2011), Return to Experience and Initial Wage Level: Do LowWage Workers Catch Up?, Working Paper; School of Economics and Management, AarhusUniversity.

Sørensen, T. and R. Vejlin (2009), The Importance of Worker, Firm and Match Fixed Effectsin the Formation of Wages, Working Paper; School of Economics and Management, AarhusUniversity.

Woodcock, S. (2008), Match Effects, Discussion Papers. Department of Economics, SimonFraser University.


AppendicesA Tables

Table A1: Results from the wage growth variance decomposition for different models.

Degree of contribution to the variance of wage growth

(1) (2) (3) (4) (5) (6) (7)

θ - - 0.0864 0.0890 0.0872 0.0905 -ψ - 0.0352 0.0415 - 0.0436 - 0.0377Xβ 0.0224 0.0292 0.0224 - - 0.0212 -ε 0.9776 0.9356 0.8497 0.9110 0.8692 0.8883 0.9623

Components included

θ no no yes yes yes yes noψ no yes yes no yes no yesXβ yes yes yes no no yes noObservations 20,703,609 20,703,609 20,703,609 20,703,609 20,703,609 20,703,609 20,703,609Workers 2,083,391 2,083,391 2,083,391 2,083,391 2,083,391 2,083,391 2,083,391Firms 295,034 295,034 295,034 295,034 295,034 295,034 295,034Covariates 7 7 7 0 0 7 0

Note: Covariates included are; Experience, experience squared, married, children, firm size, lagged firm sizeand year dummies.

Table A2: Results from the two-period wage growth variance decomposition for different models.

Degree of contribution to the variance of two-period wage growth

(1) (2) (3) (4) (5) (6) (7)

θ - - 0.1231 0.1245 0.1221 0.1327 -ψ - 0.0554 0.0645 - 0.0706 - 0.0601Xβ 0.0269 0.0416 0.0317 - - 0.0297 -ε 0.9731 0.9030 0.7807 0.8755 0.8073 0.8376 0.9399

Components included


Note: Covariates included are; Experience, experience squared and year dummies.

32 Chapter 1

Table A3: Results from the three-period wage growth variance decomposition for different models.

Degree of contribution to the variance of three-period wage growth

(1) (2) (3) (4) (5) (6) (7)

θ - - 0.1712 0.1742 0.1667 0.1868 -ψ - 0.0698 0.0765 - 0.0879 - 0.0774Xβ 0.0397 0.0528 0.0407 - - 0.0382 -ε 0.9603 0.8774 0.7116 0.8258 0.7454 0.7750 0.9226

Components included


Note: Covariates included are; Experience, experience squared and year dummies.

Table A4: Wage growth regression results with average firm wage growth included in the covariates.

Cov(w,Z)Z Mean Std. Dev. Cov(w,Z) /V ar(w)

Full sample (19,758,785 obs)w 0.0193 0.1465 0.0215 1.0000θ 0.0310 0.0567 0.0019 0.0893ψ -0.0135 0.0422 0.0006 0.0259Xβ 0.0017 0.0474 0.0021 0.0964ε 0.0000 0.1301 0.0169 0.7884

Corr. w θ ψ Xβ ε

w 1.0000 0.2307 0.0898 0.2979 0.8879θ 0.2307 1.0000 -0.4903 -0.0467 0.0000ψ 0.0898 -0.4903 1.0000 -0.0261 0.0000Xβ 0.2979 -0.0467 -0.0261 1.0000 0.0000ε 0.8879 0.0000 0.0000 0.0000 1.0000

Chapter 2

Wage Sorting Trends

Wage Sorting Trends∗

Jesper Bagger† Rune Vejlin‡

Royal Holloway College Aarhus University

Kenneth L. Sørensen§

Aarhus University

Abstract

Using a population-wide Danish Matched Employer-Employee panel from 1980-2006,

we document a strong trend towards more positive assortative wage sorting. The correlation

between worker and firm fixed effects estimated from a log wage regression increases from

−.07 in 1981 to .14 in 2001. The nonstationary wage sorting pattern is not due to com-

positional changes in the labor market, primarily occurs among high wage workers, and

comprises 41 percent of the increase in the standard deviation of log real wages between

1980 and 2006. We show that the wage sorting trend is associated with worker reallocation

via voluntary quits.

Keywords: Matched Employer-Employee Data, Firm fixed effects, Worker fixed effects,

Wage sorting, Wage inequality, Voluntary quits.

JEL codes: J30, J31, J62

∗This chapter has been published in a shorter version as: Wage Sorting Trends, Economics Letters, 2013, vol.118(1), pp. 63-67. We would like to thank Juan Pablo Rud, Dan Hamermesh, Michael Svarer, and Francis Kramarzfor helpful comments and suggestions, and The Cycles, Adjustment, and Policy research unit, CAP, Departmentof Economics and Business, Aarhus University, for support and for making the data available. Vejlin greatlyacknowledges financial support from the Danish Social Sciences Research Council (grant no. FSE 09-066745).†Department of Economics, Royal Holloway College, University of London, Egham, Surrey TW20 0EX,

United Kingdom; E-mail: [email protected]‡Department of Economics and Business, Aarhus University, Fuglesangs Alle 4, DK-8210 Aarhus V, Denmark;

E-mail: [email protected].§Department of Economics and Business, Aarhus University, Fuglesangs Alle 4, DK-8210 Aarhus V, Denmark;

E-mail: [email protected].

35

36 Chapter 2

1 Introduction

The seminal paper of Abowd et al. (1999), refined and extended in Abowd et al. (2002), inves-

tigates whether “high wage firms” employ “high wage workers”. The empirical analysis builds

on a log wage regression with fixed worker and firm effects. In this context, a high wage worker

is a worker with a relatively high worker fixed effect. A high wage firm is defined analogously.

Subsequent to estimation on French and US Matched Employer-Employee (MEE) panels, the

authors compute the empirical correlation between worker and firm fixed effects, pooling an-

nual cross sections, and find that it is negative in France (correlation −.28 using data from

1976-1987) and in the US (correlation −.03 using data from 1984-1993).1 Similar studies have

since been conducted on a number of different datasets.2 We refer to the correlation between

worker and firm fixed effects, as estimated from a log linear wage regression, as wage sorting.3

The purpose of this paper is to document and examine trends in wage sorting. We use a

Danish full population MEE panel for 1980-2006. Pooling across annual cross sections, the

correlation between worker and firm fixed effects is .05. We show that this estimate masks

a systematic nonstationarity. By computing cross section specific correlations we find that

the correlation between worker and firm effects increases from a low −.07 in 1981 to a high

.14 in 2001. The trend towards positive assortative wage sorting occurs almost exclusively in

the top quartile of the distribution of worker effects, i.e. among high wage workers, and is

economically important: it comprises 41 percent of the increase in the standard deviation of log

wages between 1980 and 2006.

We ascertain that the nonstationary wage sorting pattern is due to nonstationarity in the

covariance between firm and worker effects, and that it is not driven by compositional changes

in the labor force in terms of education, age, and gender. Further evidence suggests that the trend

towards more positive assortative wage sorting is driven in part by entry and exit of workers,

although this channel is likely to be weak, and in part by voluntary quits.4 The increasing

wage sorting trend in the top quartile of worker effects could be related to high wage workers

1These results are reported in Abowd et al. (2002).2See e.g. Gruetter and Lalive (2004) (1990-1997, correlation−.22, Austria), Andrews et al. (2008) (1993-1997,

correlation −.21 to −.15, Germany), Sørensen and Vejlin (2012) (1980-2006, correlation −.06 to .11, Denmark).3This notion of wage sorting is not linked to economic theory, and is distinct from that of productivity sorting,

i.e. sorting on worker and firm productivity. A number of recent studies of productivity sorting (see e.g. Eeckhoutand Kircher (2011), Bagger and Lentz (2012), and Bartolucci and Devicienti (2012)) find that it is difficult toidentify productivity sorting from wage data alone.

4In our terminology, a worker who is employed in different firms at date t− 1 and t has made a voluntary quitbetween t− 1 and t.

Wage Sorting Trends 37

employed in high wage firms being increasingly likely to transit to another high wage firm, or

to high wage workers employed in low wage firms being increasingly likely to transit to a high

wage firm. Our analysis supports the former relation.

2 Data

Our empirical analysis is based on IDA, a Danish register-based annual MEE panel covering

1980-2006. This data set is unique in an international comparison since it covers 27 years full

labor force population and is perfectly suited for this study. The unit of observation is a given

individual in a given year with measurements generally referring to the last week of November.

Measures of actual labor market experience are available from 1964. For workers entering the

labor market prior to 1964 (born before 1948) we add the potential pre-1964 experience net of

education.5

The raw data consists of 60,847,593 observations. We inflate wages to 2006 levels. We

discard (i) public sector jobs and individuals under education (19,191,599 observations), (ii)

observations with missing data (6,103,607 observations), (iii) observations preceding observed

labor market entry or if the individual enters later than age 35 (13,804,815 observations). We

trim the within-experience-education group wage distribution (top and bottom 1 percent deleted,

503,454 observations) and select the maximal set of connected workers and firms (99,953 ob-

servations deleted).6 The analysis data contains 21,144,165 observations.

Table 1 documents that average (real) log wages and their dispersion are increasing over our

data period. Moreover, average education increases by around 1.5 years over the data period,

the labor force ages due to the general demographic development, average experience is stable,

and female (private sector) labor force participation is increasing.7

5In this specification older workers are assigned too much experience. We have experimented with differentforms of pre-1964 experience, including specifications that assign too little experience to older workers. Our resultsare very robust to these changes.

6See Abowd et al. (2002) for an explanation of the necessity of conditioning on workers and firms beingconnected.

7Potential experience is trending upwards while our actual experience measure is stationary. We ascribe thisto older cohorts being assigned too much experience, and an increased prevalence of sabbaticals from educationduring 1980-2006.

38 Chapter 2

Table 1: Summary Statistics

Avg. S.d. Share Avg. Avg. years Avg.Year Obs. lnw lnw women age of education experience

1980 767,088 5.069 .304 .24 36.43 10.45 21.501985 787,526 5.103 .293 .24 36.47 10.81 20.141990 777,097 5.246 .296 .26 37.09 11.19 19.591995 778,641 5.257 .303 .28 38.82 11.49 19.912000 816,112 5.291 .326 .31 41.44 11.67 21.112005 799,643 5.299 .335 .32 43.06 11.78 21.86

3 Econometric Framework

Let i index individuals, j index employers, and let t index annual cross sections. The function

J(i, t) maps individual observations into employer IDs. Consider a log-linear two-way error

component wage equation

lnwit = x′itβ + θi + ψJ(i,t) + εit, (1)

where lnwit is the log-wage, x′it contains time-varying regressors: experience, experience

squared and a set of year dummies, θi is a time-invariant worker effect, ψJ(i,t) is a time-invariant

firm effect, and εit is the residual log-wage. Throughout we maintain the assumption that

E[εit|x′it, J(·, ·), i, t] = 0.8 Conditioning on workers and firms being connected ensures that

the matrix of regressors in (1) has full column rank.

Abowd and Kramarz (1999) argue that many existing models of wage determination under

two-sided heterogeneity fail to deliver a log-linear wage equation with worker and firm effects.

Estimated worker and firm effects from an OLS regression are therefore complicated functions

of the underlying true (i.e. economically well-defined) worker and firm effects, and in general

do not admit a structural interpretation.9 Nonetheless, for descriptive purposes, (1) is a useful

and widely used representation of log wages.

Wage sorting is measured by Pearson’s correlation coefficient between the estimated worker

and firm effects. As is usual, the correlation is computed by pooling all available cross sections,

and it is here denoted ρ. We are interested in the evolution of wage sorting over time and report

cross section specific estimates of Pearson’s correlation coefficient, a time-varying measure of

8See Abowd et al. (1999) and Postel-Vinay and Robin (2006) for discussions of the economic content of thisassumption.

9Abowd et al. (2012) show how a version of the model developed in Shimer (2005) conditions the structure ofworker and firm effects as estimated from a log linear wage equation, and use this structure to test for assortativematching in the labor market.


wage sorting, which we denote ρt. Formally, let θit = (θi − µθ,t)/σθ,t and ψJ(i,t)t = (ψJ(i,t) −µψ,t)/σψ,t be worker and firm effects standardized with respect to cross section t averages and

standard errors, denoted µθ,t and σθ,t, and µψ,t and σψ,t for worker and firm effects, respectively.

Let N be the total number of observations and let It be the index set of workers present in cross

section t. Then,

ρt =1

|It|N∑

i=1

1(i ∈ It)θitψJ(i,t)t, (2)

where 1(·) is an indicator function.

Part of our analysis involves partitioning each cross section into K groups to investigate

possible sources of trends in ρt. In these cases it will be useful to employ the following decom-

position of ρt,

ρt =K∑

k=1

πktρkt, (3)

where πkt = |Ikt|/|It| is the empirical share of cross section t workers belonging to group

k (Ikt is the index set of workers in group k in cross-section t), and ρkt =∑N

i=1 1(i ∈Ikt)θitψJ(i,t)t/|Ikt| measures the strength of the statistical dependence between θit and ψJ(i,t)t

in group k in cross section t. Note that ρt is not a within-group Pearson’s correlation coefficient

as the worker and firm effects are standardized using cross section specific means and standard

deviations.10 Expression (3) is useful in that it allows us to assert the extent to which changes

to ρt stem from compositional changes, i.e. changes to πkt, and from group changes in wage

sorting, i.e. changes to ρkt.

4 Results

The correlation over pooled cross-sections between the estimated worker and firm fixed effects

is found to be ρ = .05. Figure 1 plots the ρt-profile (solid line) which exhibits a strong upward

trend. This phenomenon has not been documented in previous studies. Overall, the correlation

increases from a low −.07 in 1981 to a high .14 in 2001 at which point the correlation declines

slightly. Conducting the analysis separately for two subperiods, 1980-1993 and 1994-2006, we

obtain estimates of the pooled correlation of −.03 in 1980-1993 and .07 in 1994-2006.

A correlation between two variables may change because the covariance changes or because

10Using Pearson’s correlation coefficient within groups in each cross section has the severe drawback that, if themarginal distributions of worker and firm effects differ across groups, the notions of high wage workers and highwage firms differ across groups, invalidating inter-group comparisons of wage sorting.

40 Chapter 2

Figure 1: Wage Sorting Trends

of changes to the marginal distributions. The dashed line in Figure 1 plots the time profile of ρ∗t ,

which is computed similarly to ρt (cf. (2)), except that worker and firm effects are standardized

using the means and standard errors in the pooled cross-sections. If the marginal distributions

of worker and firm effects are constant over time we have ρ∗t = ρt. Comparing the solid and

dashed lines in Figure 1, we note they are almost coinciding; the rising ρt-profile is driven

exclusively by changes in the covariance between worker and firm effects.

It is well-known that the empirical covariance between estimated worker and firm effects

underestimates the true covariance (cf. Andrews et al. (2008)). The intuition is simple: if a firm

effect is under-estimated, workers at that firm will have over-estimated worker effects, and vice

versa. This could drive the rising ρt-profile if the bias is more pronounced in earlier years. This

could happen if, for example, the number of job movers, firms, worker observations, or firm size

distribution are not stable over the time period considered. To ascertain that this is not the case

we retain the allocation of workers to firms as found in the data, but simulate counterfactual

individual wages by independently and randomly sampling the empirical marginal distributions

of firm and worker effects, and residual wages. This generates a “true” zero correlation between

worker and firm effects, with a flat ρt-profile. The dotted line in Figure 1 shows the ρt-profile

from re-estimating (1) on this simulated data. There is a small negative bias in the estimated

covariance, but the counterfactual ρt-profile is flat.

Partitioning each annual cross section into quartiles of the distribution of worker effects,

we can compute quartile-specific ρkt-profiles according to (3). These are plotted in Figure

2. Wage sorting in the first and third quartile of the worker effect distribution is stationary,

whereas it is weakly increasing in the second and strongly trending among the highest worker


Figure 2: Wage Sorting Trends in Worker Quartiles

effects, increasing from a low−.20 to a high .37. Hence, the economic forces that generated the

nonstationary wage sorting pattern appear to have impacted almost exclusively on high wage

workers.

As many other countries, Denmark has experienced an increase in wage inequality (cf.

Krueger et al. (2010) and Table 1). Ceteris paribus, a rising ρt-profile contributes to this in-

crease. To relate the documented wage sorting trend to wage inequality trends, we compute

the standard deviation of log wages and a counterfactual standard deviation under stationary

wage sorting. Using (1), the (cross section t) counterfactual standard deviation is constructed as√[Var(lnwit) + 2Cov(θi, ψJ(i,t)|t = 1980)− 2Cov(θi, ψJ(i,t))]. The adjustment to Var(lnwit)

ensures that wage sorting, Cov(θi, ψJ(i,t)), is fixed at the 1980 level for all t, and thus stationary.

The standard deviation of log wages increases from .30 to .34 between 1980 and 2006. Nonsta-

tionary wage sorting comprises 41 percent of this increase. We make no attempt at identifying

the direction of causality, but conclude that nonstationary wage sorting is an economically im-

portant phenomenon.

4.1 Compositional Changes in Education, Age, and Gender

Table 1 documented three compositional shifts in the (private sector) labor market: rising ed-

ucation, aging, and rising female labor force participation. These offer potential explanations

for the wage sorting trend. If, for example, the market for highly educated workers exhibits

higher wage sorting than that of workers with low education, a shift towards a more educated

labor force will induce an increase in overall wage sorting, even if wage sorting is stationary

in each education group. We assess these explanations by partitioning the data according to

42 Chapter 2

workers’ education, age, and gender, and decompose the ρt according to (3). The decomposi-

tion in (3) also allows us to construct two alternative ρt-profiles, by holding in turn labor market

composition (the πkts) and group wage sorting (the ρkts) constant at their 1980 level.11

We define three education groups (7-11, 12-14 and 15-20 years of education),12 and four

age groups (≤ 30, 31-40, 41-50, ≥ 51 years). We also split the data according to gender. The

top panel of Figure 3 traces the time profiles of the shares of each of the groups in our data

(i.e. the πkt’s in (3)) related to education (top-left), age (top-middle) and gender (top-right),

respectively. The middle panel of Figure 3 plots the corresponding ρkt-profiles. And finally, the

bottom panel depicts the alternative ρt-profiles.

With respect to education, the share of workers with 7-11 years of education is in decline

while those of workers with 12-14 and 15-20 years of education are on the rise. Turning to the

ρkt-profiles, they are all nonstationary, with the ρkt-profile for high educated workers increasing

more than the rest. This is reminiscent of the result obtained from Figure 2, since highly edu-

cated workers are more likely to have high worker effects. Putting these two results together,

the alternative ρt-profiles in the bottom panel confirms that the increasing wage sorting profile

is not associated with compositional changes in educational attainment.

A similar pattern emerges when partitioning the data according to workers’ age (middle

panel) or gender (right panel). Thus, subgroup wage sorting exhibits nonstationarity similar

to the overall trend: the rising ρt-profile does not appear to be associated with compositional

changes in education, age and gender. Notice that for young workers, our group sorting measure

ρkt drops sharply from around year 2000. Workers who are young towards the end of the data

period are only observed for a short period. This exacerbates the negative bias in the estimated

covariance discussed earlier (cf. Andrews et al. (2008)). Hence, ρkt is likely to be significantly

underestimated for late t’s among young workers. Results not reported also rule out shifts in

industry-level employment as the main driver of the nonstationary wage sorting pattern.

4.2 Worker Reallocation, Entry, and Exit

Having documented a robust nonstationary wage sorting pattern we now consider how this

pattern is related to worker entry and exit over the data period, as well as worker reallocation.

11We deliberately refrain from denoting the alternative profiles counterfactual profiles. They are not counterfac-tual since one cannot, in general, manipulate πkt independent of ρkt, or vice versa.

12These groups correspond roughly to workers with primary school education, workers with high school orvocational education, and workers with some college education.


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44 Chapter 2

Consider the following two partitions of workers in cross section t:

• Entry worker partition: An entering worker is not present in t − k for k ≥ 1, but

present in t. A staying worker remains employed in the same employer in t− 1 and t. A

voluntarily quitting worker changes employer between t and t− 1, while an involuntarily

quitting worker is not present in t− 1, but is present in the data at some date t−k, k ≥ 2.

• Exit worker partition: An exiting worker is present in t, but not present at any date t+k

for k ≥ 1. A staying worker remains employed by the same employer in t and t + 1. A

voluntarily quitting worker changes employer between t and t+1, while an involuntarily

quitting worker is not present in t+1, but is present in the data at some date t+ k, k ≥ 2.

If a worker has a gap (e.g. is present at t − 2, not at t − 1, but again present at t) s/he

most likely experienced a nonemployment or a public sector employment spell. However, with

annual data, being present in two consecutive cross sections does not ensure that the worker

did not undergo an unemployment period. Hence, the terms voluntary and involuntary quits

are imprecise, but reflect the fact that workers who undergo an involuntary quit are more likely

to have experienced an unemployment period in between jobs than workers who undergo a

voluntary quit. Notice also that in the Entry worker partition, a voluntary (involuntary) quitting

worker, is a worker who has just undergone a voluntary (involuntary) quit. In the Exit worker

partition, a voluntary (involuntary) quitting worker, is a worker who is about to undergo a

voluntary (involuntary) quit.

For each of the two partitions we plot, in Figure 4, the share of each group of workers (top

panel), the subgroup wage sorting profile, ρkt (middle panel), and the two alternative profiles

(bottom panel). The shares of the groups are roughly constant over the period we consider in

both partitions (cf. top panel in Figure 4). Hence, composition effects along the worker entry

and exit dimensions are not likely drivers of the increasing ρt-profile. This is confirmed in

the bottom panel. The middle panel in Figure 4 reveals nonstationary subgroup wage sorting

patterns similar to the overall pattern in Figure 1.

Comparing the ρkt-profile of entering workers (middle-left) and exiting workers (middle-

right) we see that the correlation is higher for entering workers in most years except from 2000

onwards where the correlation profile for entering workers is in decline (as is the overall ρt-

profile in Figure 1). Similar to young workers in Figure 3, workers who enter late or exit early

in the data period are only observed for short periods, and ρkt is likely to be downward biased


Figure 4: Wage Sorting Trends and Worker Reallocation

for late t’s among entering workers and for early t’s among exiting workers. Thus, the negative

bias among the entering workers might be part of the explanation of the downward sloping

ρt-profile in the early 2000s. Keeping this potential caveat in mind, entering workers exhibit

stronger wage sorting than exiting workers over most of the data period. This selection process

contributes to the increasing ρt-profile in Figure 1, although the share of workers entering and

exiting every year is too low to generate the wage sorting trend in Figure 1.13

Next we focus on the role of worker reallocations in generating an increasing wage sorting

trend. Considering the Entry worker partition, ρkt is higher for workers who have just undergone

a quit (voluntary or involuntary), than it is for staying (and entering) workers. It also seems that

workers who have undergone a voluntary quit exhibit higher wage sorting than workers who

quit involuntarily, except in a few years in the 1990s.14 In the Exit worker partition, voluntarily

quitting, involuntarily quitting, and staying workers appear similar in terms of ρkt-profiles. That

13Results not reported show that the increasing wage sorting trend is also weakly related to the entry and exit offirms.

14As mentioned earlier, our categorization of quits into voluntary and involuntary is imperfect. This leads to anunderestimation of the difference between the two types of transitions in terms of wage sorting.

46 Chapter 2

is, job outflow seems to be a random sample in terms of wage sorting. Moreover, comparing the

ρkt-profiles of voluntary quitting workers in the Entry and Exit partitions, we see that workers

undergoing a voluntary quit move towards firms where the correlation between worker and firm

effect is higher. In summary: (a) new matches initiated by a voluntary quit exhibit higher wage

sorting than existing matches. In other words, wage sorting is more pronounced in the match

inflow than in the stock. (b) Matches that break up are not different from matches that survive

in terms of wage sorting. In other words, wage sorting in the match outflow and in the stock are

similar. From (a) and (b), the correlation between worker and firm effects in the new match is

higher than in the old match. These facts imply that wage sorting becomes increasingly positive

assortative over time.

4.3 Voluntary Quits

We have shown that wage sorting is trending, that the trend appears mostly in the top quartile

of the distribution of worker effects, and that the trend is associated with voluntary quits. We

now further investigate the association between voluntary quits and the observed wage sorting

pattern.

Let Dθ,t be the decile of the worker effect in an annual cross section t, let Doψ,t be the decile

of the origin firm effect (the firm effect of the firm from which the worker made the transition),

and let Ddψ,t be the decile of the destination firm effect (the firm effect of the worker’s current

firm). Finally, let Vt be an indicator for a voluntary quit in cross section t as defined in the

Entry worker partition above. We now consider the probability of making a voluntary quit that

involves a given worker type moving to a similar firm type.15 That is, we consider

Pr[Ddψ = Dθ, Vt = 1|Dθ, D

oψ] = Pr[Dd

ψ = Dθ|Dθ, Doψ, Vt = 1]× Pr[Vt = 1|Dθ, D

oψ]. (4)

Equation (4) decomposes the object of interest, Pr[Ddψ = Dθ, Vt = 1|Dθ, D

oψ], into the probabil-

ity of Ddψ = Dθ conditional on Dθ, Do

ψ and a voluntary quit, and the probability of a voluntary

quit, conditional onDθ andDoψ. Without an explicit model of the labor market there is no formal

relationship between wage sorting and Pr[Ddψ = Dθ, Vt = 1|Dθ, D

oψ], but it seems plausible that

an increase in Pr[Ddψ = Dθ, Vt = 1|Dθ, D

oψ] is associated with an increase in wage sorting.16

15Using the definitions of voluntary and involuntary quits from the Exit worker partition leads to identicalconclusions.

16It is of course possible to envisage situations where Pr[Ddψ = Dθ, Vt = 1|Dθ, D

oψ] and wage sorting move in


We are interested in the evolution of Pr[Ddψ = Dθ, Vt = 1|Dθ, D

oψ] over time. As it turns out,

Pr[Vt = 1|Dθ, Doψ], does not change systematically over our data period, and its contribution

towards generating increased assortative wage sorting is therefore negligible, and we focus

attention on Pr[Ddψ = Dθ|Dθ, D

oψ, Vt = 1].17

Unconditionally on ranking in the distributions of worker and origin firm effects, Pr[Ddψ =

Dθ|Vt = 1] is increasing over time from .09 in 1980 to .13 in 2002, a 44 percent increase.

This pattern is consistent with an increasing wage sorting trend. Figure 5 shows contour plots

of Pr[Ddψ = Dθ|Dθ, D

oψ, Vt = 1] for nine three-year subperiods. Darker areas indicate higher

probabilities and are predominantly located in the south-west and north-east corners in each

subperiod. Interestingly, the north-east areas (high worker effect, high origin firm effect) appear

to darken further and expand from 1980 to 2000. Hence, during this period, voluntary quits

among high wage workers employed in high wage firms are increasingly likely to involve a

transition to another high wage firm. We cannot detect any other systematic changes over

time in Figure 5. Considering involuntary quits, results not shown, but available upon request,

document that Pr[Ddψ = Dθ|Dθ, D

oψ, It = 1],where It is an indicator for involuntary quits, does

not exhibit systematic changes over the data period.

The increasing wage sorting trend in the top quartile of worker effects could be explained

by two processes: (a) high wage workers employed in high wage firms are increasingly likely

to transit to another high wage firm or (b) high wage workers employed in low wage firms are

increasingly likely to transit to a high wage firm. The above analysis shows that the increased

wage sorting arises (at least in part) because of (a). Ceteris paribus, both explanations result

in increased wage sorting and cross section wage inequality. However, the two processes have

different implications in terms of lifetime wage inequality. (a) is likely to lead to a higher

increase in lifetime wage inequality than (b) as it stifles the transitions between deciles in the

cross sectional wage distribution (simply because Pr[Ddψ = Dθ|Dθ, D

oψ, Vt = 1] increases).18

Notice also that the increase in lifetime inequality generated by (a) is one in which the workers in

the high deciles of the wage distribution benefits, whereas those in the bottom are not adversely

affected.

opposite directions because changes in within-decile wage sorting, or because other decile transition probabilitiesalso change.

17Contour plots of Pr[Ddψ = Dθ, Vt = 1|Dθ, D

oψ] for nine different subperiods are available upon request.

18Flinn (2002) and Bowlus and Robin (2004) study lifetime wage inequality in Italy and the U.S. (Flinn) and inthe U.S. (Bowlus and Robin), but do not use MEE data, and so, do not consider wage sorting.

48 Chapter 2Fi

gure

5:W

age

Sort

ing

Tren

dsan

dVo

lunt

ary

Qui

ts

0.00

0.05

0.10

0.15

0.20

1st2nd3rd4th5th6th7th8th9th

10th

1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

Wor

ker

effe

ct d

ecile

Origin firm effect decile

1980

−19

82

0.00

0.05

0.10

0.15

0.20


10th

1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

Wor

ker

effe

ct d

ecile


1983

−19

85

0.00

0.05

0.10

0.15

0.20


10th

1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

Wor

ker

effe

ct d

ecile


1986

−19

88

0.00

0.05

0.10

0.15

0.20


10th

1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

Wor

ker

effe

ct d

ecile


1989

−19

91

0.00

0.05

0.10

0.15

0.20


10th

1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

Wor

ker

effe

ct d

ecile


1992

−19

94

0.00

0.05

0.10

0.15

0.20


10th

1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

Wor

ker

effe

ct d

ecile


1995

−19

97

0.00

0.05

0.10

0.15

0.20


10th

1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

Wor

ker

effe

ct d

ecile


1998

−20

00

0.00

0.05

0.10

0.15

0.20


10th

1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

Wor

ker

effe

ct d

ecile


2001

−20

03

0.00

0.05

0.10

0.15

0.20


10th

1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

Wor

ker

effe

ct d

ecile


2004

−20

06

Not

e:T

heco

ntou

rsin

dica

tePr[Dd ψ=Dθ|D

θ,D

o ψ,Vt=

1],w

hereDd ψ

isth

ede

cile

ofth

ede

stin

atio

nfir

mef

fect

,Do ψ

isth

ede

cile

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igin

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effe

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θis

the

deci

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the

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t,an

da

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itis

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ion.

Pr[Dd ψ=Dθ|D

θ,D

o ψ,Vt=

1]

istr

unca

ted

at.2

0.


5 Conclusions

Wage sorting is measured by the correlation between worker fixed effects and firm fixed effects,

as estimated from a log-linear wage regression. Using a Danish MEE panel for 1980-2006, this

paper documents a strong trend towards more positive assortative wage sorting. The correlation

between worker and firm fixed effects computed from pooled annual cross sections is .05, but

masks a systematic nonstationarity over the data period. Quantitatively, the correlation ranges

from −.07 in 1981 to .14 in 2001. The nonstationarity is not explained by compositional shifts

in the labor force in terms of education, age, and gender. We provide evidence that is consistent

with the wage sorting trend being associated with entry and exit of workers, although this chan-

nel is likely to be weak, as well as worker reallocation. The latter is consistent with the observed

wage sorting trend because, over the period we consider, wage sorting is more pronounced in

the match inflow than in the stock, while wage sorting in the match outflow and in the stock

are similar. The contribution to the wage sorting trend from the reallocation process is driven

primarily by high wage workers employed in high wage firms. Finally, while it is beyond the

scope of this paper to give a structural interpretation to the documented wage sorting trend, it is

economically important in that it comprises 41 percent of the increase in the standard deviation

of log wages between 1980 and 2006.

References

Abowd, J. M., R. H. Creecy and F. Kramarz (2002), Computing Person and Firm Effects Us-ing Linked Longitudinal Employer-Employee Data, Technical Paper 2002-06, U.S. CensusBureau.

Abowd, J. M. and F. Kramarz (1999), The Analysis of Labor Markets using Matched Employer-Employee Data, vol. 3, chap. 40, Handbook of Labor Economics, Elsevier Science B.V., 2629–2710.


Abowd, J. M., F. Kramarz, S. Perez-Duarte and I. M. Schmutte (2012), A Formal Test of As-sortative Matching in the Labor Market, Working Paper.


50 Chapter 2

Bagger, J. and R. Lentz (2012), An Empirical Model of Wage Dispersion with Sorting, WorkingPaper.

Bartolucci, C. and F. Devicienti (2012), Better Workers Move to Better Firms: A Simple Testto Identify Sorting, Working Paper.

Bowlus, A. and J.-M. Robin (2004), Twenty Years of Rising Inequality in US Lifetime LaborIncome Values, The Review of Economic Studies, 71(7): 709–774.

Eeckhout, J. and P. Kircher (2011), Identifying Sorting - In Theory, The Review of EconomicStudies, 78(3): 872–906.

Flinn, C. (2002), Labour Market Structure and Inequality: A Comparison of Italy and the U.S.,The Review of Economic Studies, 69(3): 611–645.


Krueger, D., F. Perri, L. Pistaferri and G. Violante (2010), Cross-Sectional Facts for Macroe-conomists, Review of Economic Dynamics, 13(1): 1–14.

Postel-Vinay, F. and J.-M. Robin (2006), Microeconometric Search-Matching Models andMatched Employer-Employee Data, chap. 11, in: Blundell, R., Newey, W., Persson, T. (Eds),The Proceedings of the 9th World Congress of the Econometric Society, Cambridge UniversityPress: Cambridge, UK, 279–310.

Shimer, R. (2005), The Assignment of Workers in an Economy with Coordination Frictions,Journal of Political Economy, 113(5).

Sørensen, T. and R. Vejlin (2012), The importance of worker, firm and match fixed effects inwage regressions, Forthcoming in Empirical Economics.

Chapter 3

Return To Experience and Initial Wages:Do Low Wage Workers Catch Up?

Return to Experience and Initial Wage Level:

Do Low Wage Workers Catch Up?∗

Kenneth L. Sørensen†

Aarhus University

Rune Vejlin†

Aarhus University and CAP

Abstract

This paper estimates the relationship between initial wage and return to experience. We use a Mincer-

like wage model to nonparametrically estimate this relationship allowing for an unobservable individual

permanent effect in wages and unobservable individual return to experience. The relationship between

return to experience and unobservable individual ability is negative when conditioning on educational

attainment while the relationship between return to experience and educational attainment is positive.

We link our finding to three main theories of wage growth, namely search, unobserved productivity and

learning, and human capital. We devise several empirical tests in order to separate the theories. We find

evidence in favor of the learning model and mixed evidence regarding the search model. We find no

evidence in support of the human capital model.

Keywords: Wage growth, initial wage, return to experience, nonparametric estimation

JEL codes: J3, J24

∗We thank Michael Svarer, Christopher Taber, Greg Veramendi, participants at the DGPE conference 2010,the Xiamen-Aarhus Labor workshop, Xiamen 2010, CEF 2011, San Francisco, BI-LMDG annual meeting, 2011,Brownbag lunch seminar Aarhus University 2011 and at the annual workshop of the NBER group on micro andmacro perspectives, 2011. We would like to thank The Cycles, Adjustment, and Policy research unit, CAP, Depart-ment of Economics and Business, Aarhus University, for support and for making the data available. Vejlin greatlyacknowledges financial support from the Danish Social Sciences Research Council (grant no. FSE 09-066745).

†Department of Economics and Business, Aarhus University, Building 1322, Bartholins Alle 10, DK-8000Aarhus C, Denmark. Correspondence to: Kenneth Lykke Sørensen, email: [email protected].

53

54 Chapter 3

1 Introduction

Since Mincer (1958, 1974) it has been commonly acknowledged that earnings rise with the

accumulation of experience. Furthermore, one of the most established facts in the literature

is that wage profiles can be ranked by education. The wage-experience profile for workers

with a higher educational level dominates that of workers with a lower educational level. E.g.

Sørensen and Vejlin (2013) show that the return to experience depends on observable measures

of permanent ability such as education, while Bagger, Fontaine, Postel-Vinay and Robin (2011)

show the same in a structural search model with experience accumulation.

It is also widely recognized that workers have permanent abilities that go beyond for in-

stance education. Thus, including education in wage regressions might bias the estimates be-

cause both education and wages are affected by by permanent abilities, and therefore the in-

clusion of an individual worker fixed effect in wage regressions is by now standard. Using for

instance the Abowd, Kramarz and Margolis (1999) decomposition, which decomposes wages

into observed and unobserved fixed effects for workers and firms, one usually finds that observ-

able measures for skills such as detailed educational information only explain a smaller part

of the variation in the estimated worker fixed effect, see e.g. Sørensen and Vejlin (2013) and

Woodcock (2011).

Combining these two empirical regularities, we might suspect that the return to experience

also change with unobservable skills. However, the relationship between unobserved individual

permanent ability and the individual experience profile is greatly understudied in the literature.

One of the contributions of this paper is to nonparametrically estimate the relationship be-

tween an individual permanent component of wages and an individual return to experience. We

thus extend the identification argument developed by Gladden and Taber (2009), who show that

the covariance between the permanent component of wages and a random coefficient on expe-

rience can be estimated from initial wages and later wage growth. We extend this argument

in order to nonparametrically estimate this relationship. Like Gladden and Taber (2009) we

find that workers with high permanent abilities have low individual returns to experience for all

educational groups.

Gladden and Taber (2009) use a sample of the NLSY79 data set to estimate the covariance

between initial wages and later wage growth for low skilled workers. They estimate the rela-

tionship using observations that are sufficiently far apart in time such that they avoid potential

problems with autocorrelation in the error term, which would generate a negative bias in the

Return to Experience and Initial Wage Level 55

estimate. They find only a small and insignificant effect between initial wages (interpreted as

skill level) and future wage growth. Specifically they find that a one standard deviation increase

in permanent skill level reduces future wage growth (interpreted as return to experience) by 0.87

per cent. Gladden and Taber (2009) conduct their analysis using mainly covariances because

of lack of data. Almost all their estimates are only borderline significant, which is a problem

since the limited amount of observations only allows them to estimate a covariance giving them

an estimate of the slope between wage growth and initial wages. Although not the focus of

his paper, Baker (1997) also estimates a similar model and finds a negative covariance between

wage growth and wage level in the PSID data. However, Baker does not emphasize the potential

problem with autocorrelation in the error term.

Connolly and Gottschalk (2006) analyze whether returns to education and experience are

lower for the less educated using the 1986-1993 panels of the Survey of Income and Program

Participation (SIPP) which are comparable to the PSID although its time frame is considerably

shorter than that of the PSID. SIPP’s advantage lies in more frequent interviews and thus more

precise information on income and employer tenure. Connolly and Gottschalk argue that the

number of former successful job matches is more important for job match quality than the num-

ber of former draws from the wage distribution. They analyze all age groups, both men and

women, and find that higher educated do have higher returns to both experience and tenure.

French, Mazumder and Taber (2006) also use the SIPP, but confine themselves to using workers

between the ages of 18-28, in order to analyze the dependence of early career wage growth

from accumulated work experience and job match quality for three different groups of educa-

tion levels. Formally, they would like to test whether labor market policies encouraging job

market experience help low educated workers out of poverty. They find that simple experience

accumulation is important for early career wage growth whereas they on average do not find

support for the importance of job changes in wage growth.

Since we use a much larger data set than both Baker (1997) and Gladden and Taber (2009)

we are able to divide our sample into finer educational groups. For all educational subgroups

(primary/high school, vocational, bachelor, and master) there seems to be a negative relationship

between initial wage and later wage growth. The negative relationship is most pronounced for

those with a vocational education.

Both Baker (1997) and Gladden and Taber (2009) only estimate the covariance. A potential

problem is that the relationship between wage growth and wage level is non-linear. This paper

56 Chapter 3

thus takes the analysis one step further and nonparametrically estimates the return to experi-

ence given permanent skills. We find that the relationship is non-linear for those with only a

primary/high school education and those with a master degree and thus the covariance might

not be a particular good measure to describe the distribution.

Using our rich data set we explore some of the theoretical channels of the negative relation-

ship. One explanation is provided by human capital theory. Human capital theory is based on

the seminal work of Becker (1962), Mincer (1962), and Ben-Porath (1967) and emphasizes the

role of human capital acquirement in school and on the job. While on the job, workers face

a trade-off between earning wages and investing in their human capital in order to earn higher

wages in the future. Thus, human capital theory will predict a negative relationship between ini-

tial wages and return to experience. The second explanation is one of frictions. Standard search

models like Burdett and Mortensen (1998) or Postel-Vinay and Robin (2002) also predict a neg-

ative relationship. In a wage posting model like Burdett and Mortensen workers will gradually

move up the wage ladder. This implies that those who are initially lucky and find a firm with

a high wage will later have lower wage growth, simply because there are fewer firms which

are offering higher wages. Postel-Vinay and Robin (2002) use Bertrand competition among

firms to determine wages. This mechanism actually enhances the negative relationship, since

high productivity firms will be able to pressure workers to start out with a very low wage in

order to later have the potential of very high wage growth as they find outside offers to pressure

the incumbent firm. Like in the human capital theory this will generate a negative relationship

between initial wages and later wage growth. The third explanation is based on unobserved

productivity and learning. The model that we have in mind is inspired by Jovanovic (1979).

The central idea behind this explanation is that workers slowly gets sorted out of the job. The

employer pays the worker his expected productivity and gets noisy signals on the worker’s abil-

ity. As the option value of keeping low productive workers get smaller over time the workers

are fired. Hence, the concave wage profile is driven by low productive workers getting fired.

We concive several empirical tests in order to separate the three competing explanations. We

find suggestive evidence that the learning model might be part of the explanation (especially for

low educated). We find no evidence in the favor of the human capital explanation and mixed

evidence for the search explanation.

Finally, we investigate if the negative relationship between permanent ability and return to

experience is driven by any specific group. We look closer at occupations, industries, time of


labor market entry and finally labor market transitions. We find that none of these observable

features explain the negative relationship.

The rest of this paper is organized as follows. Section 2 goes through our wage model and

the nonparametric estimation approach. In section 3 we discuss the data used for the estimation

and sections 4 and 5 present results and robustness checks. Finally, in section 6, we conclude.

2 Econometric Approach

We use a correlated random effects model inspired by Baker (1997) and Gladden and Taber

(2009). Our goal is to analyze the relationship between initial wages and future wage growth

within the first ten years of a worker’s labor market life. This relationship holds important

information on wage profiles for workers with different skill levels. We assume that the wage

structure is a linear function of worker specific permanent ability and human capital, measured

as experience. Wages have been detrended by a simple OLS regression of year dummies on log

wages such that all year specific effects have been removed. Let detrended log wages be defined

as

wit = θi + γiEit + εit, (1)

where θi and γi are worker specific random effects, Eit is the experience of worker i at time t

and εit is an error term. The linear relationship in (1) necessitates us to be very restrictive with

how many years to include in the sample. The typical experience-wage profile is concave on

its full support, but will be very nearly linear during the first 10 years on the labor market.1 We

thus include observations up until t = 9 only (labor market entry at t = 0 makes it 10 years).

θi and γi represent unobserved individual permanent abilities and the unobserved individual

ability to make use of experience interpreted as the return to experience. The overall goal of

this paper is to gain insights in the relationship between θi and γi from model (1).

We allow workers into our sample only after they have completed their highest education.

The identifying assumption is that no worker has any experience when entering the labor market

or that the experience that he has is not useful, i.e. Ei0 = 0. This assumption is crucial for the

1Gladden and Taber (2009) also use a linear model in experience. They justify this by referring to experienceprofiles in Gladden and Taber (2000), which are very close to linear. Sørensen and Vejlin (2011) estimate experi-ence profiles using the same Danish data as used in this paper and find that the experience profiles are also close tolinear.

58 Chapter 3

identification of the random effects. With the wage specification (1) the initial wage is

wi0 = θi + εi0, (2)

and the wage growth from period t− τ to t becomes

∆τwit = γi∆τEit + ∆τεit, (3)

where ∆τxit = xit − xit−τ . To ensure that we do not measure serial correlation, we discard

all wage growth observations before year 6 on the labor market. A simple transformation of

(3) gives the more convenient representation of wage growth normalized by the growth in ex-

perience as a function of the unobservable individual return to experience and an altered error

term

∆τwit∆τEit

= γi +∆τεit∆τEit

. (4)

As intuition would suggest equations (2) and (4) tell us that the initial wage might be a

good estimate of unobserved permanent ability, while wage growth might be a good estimate

for unobserved ability to learn. We thus use these to estimate the relationship between θ and

γ . Notice, that we do not need to make any assumptions regarding the relationship between

(θi, γi) and Eit for the estimator to work. This is important since any reasonable model would

imply that actual experience is correlated with (θi, γi). However, loosely speaking we need the

error terms in equations (2) and (4) to be uncorrelated. Baker (1997) estimates a model very

close to ours and fits the error term by an ARMA(1,2) process. Gladden and Taber (2009) use

Baker’s estimates to show that the covariance between the error term in equations (2) and (4) is

tiny compared to the estimate and thus the potential bias is very small. Using the data in this

paper we have estimated a corresponding model.2 The results confirm the previous findings by

Gladden and Taber (2009) and Baker (1997) in that the potential bias is negligible compared to

the estimates.

Before we turn to our nonparametric approach we start out analyzing a more simple vari-

2Table 5 contains covariations between initial errors and later changes in errors estimated by assuming theresiduals of equation (1) following an ARMA(1,2) process as assumed by Baker (1997) and Gladden and Taber(2009). All correlations fall dramatically after year three and compared to the estimated covariance between θand γ we find very low covariances between initial errors and later error growth. We thus feel confident using theconservative choice of year six as our first yearly wage growth in our regression analysis.


ant of the relationship between individual permanent abilities (θi) and the individual return to

experience (γi), the covariance. Since θi and γi, by definition, are unobserved, we make use of

the model specification (2) and (4). A simple OLS regression of wage growth normalized by

growth in experience on initial wages gives us a slope coefficient that converges to

Cov(wi0,

∆wit∆Eit

)

V ar(wi0).

By the structure of (2) and (4), the slope coefficient will converge to

Cov(θi, γi)

V ar(wi0),

so the covariance between permanent individual ability and the individual return to experience

can thus fairly easy be estimated using OLS. We distinguish between two types of experience;

potential and actual. Potential experience is initially set equal to zero and then simply grows

one unit per year. Actual experience is an exact measure of experience accumulation each year,

but is also set to zero at labor market entry. If the worker has worked full time all year, actual

experience accumulation is equal to one unit. To eliminate the serial correlation in the error

term, we use yearly wage growth only from period 6 to 9 after entering the labor market. We

are not able to bring in later observations because of the linearity in the experience measure in

(1).

2.1 Nonparametric Estimation Model

Given the structure of our model and the richness of our data we are able to nonparametrically

estimate the joint distribution of γi and θi using initial wages and future wage growth. First, to

estimate the expected level of wage growth for different levels of unobserved worker specific

abilities (i.e. E[γi | θi]) we consider the nonparametric regression model

∆τwit∆τEit

= g(wi0) + ui, i = 1, . . . , N, t = 6, 7, 8, 9, τ = 1, (5)

60 Chapter 3

where the functional form of g is unknown. g can, however, be interpreted as the conditional

mean of ∆wit∆Eit

given Wi0 = wi0.3 E[

∆wit∆Eit| wi0

]= g(wi0) is estimated nonparametrically as

g(wi0) =N∑

i=1

∆wit∆Eit

Xi(wi0), (6)

with

Xi(wi0) =K(wi0−w0

h

)∑N

j=1 K(wj0−w0

h

) .

h is the bandwidth smoothing parameter for initial wages. w0 is the grid point for which we

evaluate the kernel. Optimally h would be chosen to minimize the asymptotic mean integrated

squared error of the kernel estimates, which is the integration of the sum of the approximate

variance and squared bias. Unfortunately, this includes unknown terms such as the second

derivative of the unknown true density function. Instead of the theoretical optimal bandwidth,

we use Silverman’s Rule-of-Thumb bandwidth determined as

h = 2.34σwi0n−1/5. (7)

Alternatively, we could implement a cross-validation method to estimate the bandwidth.

Instead, we have tested the robustness of the Silverman rule of thumb bandwidth and found the

estimates to be very robust to changes in the bandwidth. Indeed, if the true density is normal,

then the rule-of-thumb bandwidth will give the optimal bandwidth, and for g close to normal, h

will be close to optimal.4 K(·) is the second order Epanechnikov kernel given by5

K

(wi0 − w0

h

)=

34

(1−

(wi0−w0

h

)2)

for∣∣wi0−w0

h

∣∣ ≤ 1

0 for∣∣wi0−w0

h

∣∣ > 1

. (8)

The fact that we have chosen an Epanechnikov kernel instead of e.g. a Gaussian, Uniform or

Triangular kernel is of minor importance. Instead, the important factor for the performance of

any nonparametric kernel density estimation is not so much the choice of kernel itself, but rather

the bandwidth smoothing selection (Zhang et al. (2006)). However, the Epanechnikov kernel

3See Li and Racine (2007, Chapter 2 and especially Theorem 2.1).4See e.g. Hansen (2010, Chapter 16).5See Li and Racine (2007, Chapter 1) and Zhang, King and Hyndman (2006)


has the advantage of being relatively fast to compute and it is the most efficient in minimizing

the asymptotic mean squared error (Silverman (1986)).

Second, we take the estimation one step further and nonparametrically estimate the full joint

distribution between initial wages and future wage growth. The estimate of the full joint density

of initial wages and wage growth is given by

f

(wi0,

∆wit∆Eit

)=

1

nhwi0h∆wit∆Eit

n∑

i=1

K

(wi0 − w0

hwi0

)K

∆wit∆Eit−∆w

h∆wit∆Eit

, (9)

where hwi0 and h∆wit∆Eit

are the bandwidth smoothing parameters for initial wages and wage

growth respectively while K(·) remains to be the Epanechnikov kernel from equation (8).6

When turning from a nonparametric regression model to a nonparametric two-variate joint den-

sity model, Silverman’s rule of thumb smoothing bandwidth parameter changes to

hj = 2.20σjn−1/5 for j ∈

{wi0,

∆wit∆Eit

}. (10)

3 Data

This paper uses Danish data to estimate the models specified above. We utilize two different

kinds of data; (1) we use yearly data from the Integrated Database for Labor Market Research

(IDA) and (2) we use weekly spell data. Both data sets are kept by Statistics Denmark. The

data are confidential but our access is not exclusive. IDA is a matched employer-employee

longitudinal database containing socio-economic information on the entire Danish population,

the population’s attachment to the labor market, and at which firms workers are employed.

Both persons and firms can be monitored from 1980 onwards. The reference period in IDA is

given as follows; the linkage of persons and firms refers to the end of November, ensuring that

seasonal changes (such as e.g. shutdown of establishments around Christmas) do not affect the

registration. The creation of jobs within individual firms thus refers to the end of November.

Background information on individuals mainly refers to the end of the year.7

Our gross sample contains all male workers having their main employment at a private firm

in the period of 1987− 2006 and having entered the labor market after 1980.

6Li and Racine (2007) show that this is a MSE consistent estimate of the true joint density.7See a more detailed documentation on IDA:

http://www.dst.dk/HomeUK/Guide/documentation/Varedeklarationer/emnegruppe/emne.aspx?sysrid=1013

62 Chapter 3

The weekly spell data set is a longitudinal data set containing information of labor mar-

ket transitions for each individual in the Danish population. The spell data is constructed by

merging several Danish register data sets. All individuals are at first assigned to one of sixteen

mutually exclusive labor market states in each week over the years 1985-2003 using the dif-

ferent register data sets. These states are then narrowed down to two states; non-employment

and employment. We use the spell data to split the sample into three mutually exclusive sub-

samples. The first sample are those making a Job-to-Job transition within the year where we

measure wage growth. The second sample is those making a Job-to-Nonemployment-to-Job

transition likewise in the year where wage growth is measured. The final sample are those who

have not changed jobs (henceforth denoted stayers).

The advantage of IDA is the detailed socio-economic information on each individual from

year to year while spell data delivers important information on how each individual acts on

the labor market between the last week of November one year to the following last week of

November next year. This information is very important since all we can see from IDA is

whether or not an individual has changed employer or not, not whether he has switched directly

from one job to another or if there has been a spell of un- or nonemployment in between, which

is potentially very important for wage growth. The time period of our analysis is 1987-2006

except when we analyze transitions where spell data forces us to narrow down the sample to

1987-2003.

3.1 Sample Selection

In this section we present how we have chosen to narrow down the sample. The raw data con-

sist of the entire Danish male labor force. First of all, we look only at full-time employment

within the private sector. Second, we are interested only in labor market participation after the

completion of education, so we delete all observations referring to periods before completion

of the highest education as well as observations during education. Furthermore, to eliminate

educational outliers we delete all observations belonging to individuals finishing their highest

education after turning 35. As we are interested in examining the wage structure for the first

ten years on the labor market, this ensures that all individuals will be relatively young workers.

Also, one of the identifying assumptions was that rewardable experience at labor market entry

was zero. This is unlikely to be a valid assumption if labor market entry happens when the

worker is relatively old. We have split the sample into groups of education crossed with expe-


Table 1: Individuals in the sample.

Primary/ Vocational educatedFull sample High school Vocational Bachelor Master Stayers JtJ† JtNtJ∗

1 obs 38,028 10,331 18,980 5,685 3,032 22,609 34,570 5,8362 obs 29,794 7,254 14,971 4,929 2,640 22,432 10,375 3993 obs 25,712 5,893 12,918 4,517 2,384 28,353 2,299 514 obs 146,337 22,999 82,786 28,697 11,855 43,863 287 10Total 239,871 46,477 129,655 43,828 19,911 117,257 47,531 6,296†Job-to-Job transitions.∗Job-to-Nonemployment-to-Job transitions.

rience, and then trimmed the top and bottom percentile of the wage distribution within each of

these groups for each year separately.

This results in a total of 239,871 male workers. Of these, 20 percent have at most a primary

or high school diploma, 54 percent are educated at a vocational level, 18 percent hold a bachelor

and 8 percent carry a master’s degree. 16 percent of all workers are present only once in our

sample, 12 percent are in the sample twice, 11 percent enter three times and 61 percent of all

workers are present four times. This comprises our sample to 760,100 worker observations.8

Tables 1 and 2 describe the sample used. Table 1 shows the number of individuals by

education and by transitions within the vocational educated sample. The reason we have such

a low number of Job-to-Nonemployment-to-Job transitions is that the requirement for being in

this sample is that we observe two consecutive November cross-section job spells. I.e. in order

for the worker to be in the Job-to-Nonemployment-to-Job sample he will need to be employed

at one firm in a given November cross-section, become nonemployed during the year, and then

finally find a job before the next November cross-section. This leaves out a lot of transitions

that do not fulfill these requirements.

Table 2 shows descriptive statistics for initial wage and wage growth by education and type

of transition. Those making a Job-to-Job transition has a little higher initial experience and

much higher wage growth. Workers that experience a Job-to-Nonemployment-to-Job transition

on average have a negative wage growth. There is also a clear pattern across educational groups.

The higher the educational level the higher is the initial wage and the wage growth.

8Note that since we do not use wage growth between the entry on the labor market and year 6 as well as wagegrowth earned later than year 9, we can include a maximum of four observations per individual.

64 Chapter 3

Table 2: Descriptive statistics on initial wages and future wage growth.

Primary/High school Vocational Bachelor Masterw0 ∆w ∆w

∆Ew0 ∆w ∆w

∆Ew0 ∆w ∆w

∆Ew0 ∆w ∆w

∆E

Obs. 134,514 134,514 134,514 418,820 418,820 418,820 143,882 143,882 143,882 62,884 62,884 62,884Mean 4.8170 0.0131 0.0145 5.0592 0.0075 0.0079 5.2769 0.0262 0.0276 5.4007 0.0413 0.0433Std. dev. 0.3799 0.1587 0.2058 0.2711 0.1529 0.1985 0.2357 0.1430 0.1814 0.2127 0.1516 0.1959P5 4.1751 -0.2406 -0.2572 4.6028 -0.2488 -0.2607 4.8809 -0.2064 -0.2101 5.0396 -0.1890 -0.1919P25 4.5282 -0.0625 -0.0657 4.8669 -0.0633 -0.0652 5.1326 -0.0318 -0.0321 5.2676 -0.0203 -0.0204Median 4.8587 0.0113 0.0118 5.0642 0.0077 0.0079 5.2900 0.0233 0.0234 5.4015 0.0356 0.0357P75 5.1012 0.0858 0.0907 5.2487 0.0789 0.0816 5.4335 0.0863 0.0871 5.5316 0.1045 0.1051P95 5.3992 0.2776 0.2990 5.5034 0.2649 0.2792 5.6383 0.2655 0.2730 5.7496 0.2889 0.2963

Vocational educatedFull sample Stayers Job-to-Job Job-to-Nonemployment-to-Job

w0 ∆w ∆w∆E

w0 ∆w ∆w∆E

w0 ∆w ∆w∆E

w0 ∆w ∆w∆E

Obs. 760,100 760,100 760,100 327,984 327,984 327,984 63,365 63,365 63,365 6,827 6,827 6,827Mean 5.0858 0.0148 0.0157 5.0570 0.0059 0.0067 5.0631 0.0182 0.0174 5.0934 -0.0001 -0.0040Std. dev. 0.3296 0.1524 0.1968 0.2709 0.1287 0.1398 0.2742 0.2260 0.2578 0.2673 0.2199 0.3544P5 4.4936 -0.2370 -0.2478 4.6004 -0.2148 -0.2189 4.5993 -0.3629 -0.3992 4.6407 -0.3595 -0.5301P25 4.8824 -0.0536 -0.0551 4.8663 -0.0545 -0.0559 4.8681 -0.1166 -0.1240 4.9095 -0.1270 -0.1689Median 5.1140 0.0142 0.0145 5.0636 0.0065 0.0067 5.0661 0.0226 0.0236 5.0943 -0.0008 -0.0009P75 5.3175 0.0841 0.0866 5.2454 0.0668 0.0685 5.2529 0.1577 0.1656 5.2772 0.1243 0.1628P95 5.5702 0.2691 0.2828 5.4998 0.2254 0.2343 5.5106 0.3815 0.4115 5.5296 0.3635 0.5102

4 The Results

In this section we present the results. We first estimate the covariance of θi and γi in equation

(1) also estimated in Gladden and Taber (2009). Secondly, we move to the nonparametric

estimation. And finally, we present evidence on the degree of wage catch up.

4.1 The Covariance of Initial Wage Level and Return to Experience

In this section we present results similar to those of Gladden and Taber (2009). Table 3 presents

the regression results for both potential and actual experience for each of the four educational

groups. Column (1) contains unweighted estimates of the slope. Column (2) contains weighted

versions such that each individual gets equal weight regardless if they appear one, two, three

or four times in the sample. All groups display significant negative slopes except the weighted

bachelor regressions. There are no significant differences in the weighted vs. unweighted re-

gressions. A result of the descriptive fact that most of our workers are represented by four ob-

servations. Vocational educations see the steepest negative covariances between wage growth

and initial wages followed by workers holding a master’s degree and workers with at most a

primary or high school diploma. Gladden and Taber (2009) calculate similar numbers for low

educated (corresponding to our primary/high school group) and find results of an insignificant

magnitude of -0.005. We estimate a significant covariance for primary/high school workers of

-0.0139. There is a tendency that the coefficients get more negative when using actual experi-

ence, although there is no significant difference.

The important coefficient is the significant negative slope coefficient on initial wage which

reveals that e.g. a worker with a vocational education earning one percent higher initial wage


Table 3: Regression of log wage growth years 6 to 7, 7 to 8, 8 to 9 and 9 to 10 on initial log wages, subsamples.

Primary/High school Vocational Bachelor MasterModel (1) (2) (1) (2) (1) (2) (1) (2)

∆wit = α+ βwi0 + εit -0.0105*** -0.0110*** -0.0318*** -0.0322*** -0.0047*** -0.0025 -0.0169*** -0.0156***(0.0012) (0.0015) (0.0009) (0.0011) (0.0017) (0.0021) (0.0030) (0.0039)

∆wit∆AEit

= α+βwi0+εit -0.0123*** -0.0139*** -0.0337*** -0.0353*** -0.0043** -0.0010 -0.0191*** -0.0193***(0.0015) (0.0021) (0.0011) (0.0019) (0.0020) (0.0030) (0.0035) (0.0049)

Observations 134,514 134,514 418,820 418,820 143,882 143,882 62,884 62,884Individuals 46,477 46,477 129,655 129,655 43,828 43,828 19,911 19,911

The standard errors in parentheses are robust.(1) Unweighted regressions. (2) The regressions are weighted such that each individual have equal weights.***, **, * indicates significance at levels 1, 5 and 10 percent respectively.

will on average have 0.032 percentage point less wage growth than the normalized worker and

0.034 percentage point lower wage growth per actual experience year.

Gladden and Taber (2009) report that a worker with a one standard deviation higher level of

permanent ability have around 0.61 to 0.87 percentage point lower return to experience. If we

calculate the similar number given our sample we find that a primary/high school worker with

a one standard deviation higher level of permanent ability have a 0.40 to 0.53 lower return to

experience. These are very similar results.

4.2 Nonparametric estimation

One might suspect that the relationship between return to experience and initial wage levels is

non-linear. If this is the case, then the covariance will not capture the true relationship. We here

present evidence that the relationship may not be linear on the entire support.

We estimate equation (6), the expected wage growth conditional on initial wages using the

actual experience measure. As shown above, this relationship contains information on the return

to experience we would expect of a worker conditional on his individual permanent ability level.

Figure 1 plots the estimated expected wage growth conditional on initial wage levels with

bootstrapped confidence intervals for the four subsamples. The four figures confirm the results

from the OLS regressions. Vocational educated workers see a steep negative relationship, pri-

mary/high school workers have an overall negative slope, but for lower ability workers the rela-

tionship is insignificant. Workers with a bachelor degree exhibit an almost constant initial wage

- wage growth relationship and master’s degree workers have an overall negative slope. The

figure highlights slope differences within especially the groups of primary/high school workers

and master’s degree holders. The covariance analysis thus only gives an overview over the true

relationship while the nonparametric approach is able to give a more thorough picture.

66 Chapter 3

Figure 1: Expected wage growth over initial wages for educational subgroups.

.01

.01

.03

.05

Expe

cted

wag

e gr

owth

4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7Initial log wage

Primary/High school VocationalBachelor Master

Note how a large fraction of primary/high school workers start out lower than vocational

educated, but for workers starting at the same level between the two groups, primary/high school

workers can expect a higher wage growth than vocational educated workers. All workers with

a bachelor and a master’s degree can, on the other hand, expect even higher wage growth for all

permanent worker types.

Another very important conclusion from Figure 1 is that if we had estimated the model on

the entire sample we would get a U-shape of growth by initial wages. This is done in figure 2

However, the U-shape is simply a composition effect from estimating the model on all edu-

cational groups at the same time. In general, both initial wages and wage growth is increasing

in educational attainment. This leads to the U-shape which was observed in Figure 2. Wage

growth is thus increasing in observed permanent ability (education), while it is decreasing in

unobserved permanent ability (initial wage).

4.3 Catching Up or Not?

Given the non-parametric estimations presented above we are able to calculate the expected

log wage levels any permanent ability type worker can on average expect at any point in time

during his early labor market career. The calculations are based on the results presented in

figure 1. From this figure we can find the average wage growth for each group in the initial

wage distribution. However, though we can calculate the expected wage increase for each year

of extra experience, it is harder to find out how the level should be. We have chosen to use the


Figure 2: Expected wage growth over initial wages for the full sample.

.01

.015

.02

.025

.03

Exp

ecte

d w

age

grow

th

4.4 4.6 4.8 5.0 5.2 5.4Initial log wage

fifth year wage. E.g. for the fifth percentile (P5) the level is set to the average fifth year wage

for all workers within a 0.1 log wage distance of the fifth percentile initial wage and likewise

for the other percentiles.

Figure 3 depicts the graphical estimated wage paths for five initial wage distributional

groups in each of our educational subgroups. These graphs are interesting in at least two ways;

(1) they show how the wage paths are expected to evolve for each subgroup and (2) they give

a better picture of the robustness of our estimations. Imagine that the DGP is equation (1) and

that all workers have the same permanent ability (θi = θ), and when entering the labor market

they each draw an error term, εi0. Some workers draw a high value of εi0 and therefore a high

initial wage while some workers draw a low εi0 and receive a low initial wage. Given that all

are the same and the errors are iid, these random draws should be neutralized by time and all

workers should see wage paths converging to the same level.9

Primary/high school workers below the 75th percentile initial wage in fact do seem to follow

a pattern like the example of homogeneous workers. The average fifth year wage is the same

for the 5th, 25th and 50th percentile while higher initial wage workers with a primary/high

school degree still have a higher wage after five years on the labor market. Because of the

steep negative slope in the nonparametric analysis, wee see that the lower wage workers are

not only catching up to the higher wage workers, but are overtaking them. Workers with a

vocational education see some of the same pattern, only not as clear. As both the covariance

and nonparametric analysis indicated, workers with a bachelor degree do not show any kind

9This is confirmed by our ARMA estimations presented in table 5.

68 Chapter 3

Figure 3: Estimated mean log wages per year after entry. Percentiles P5 to P95 refer to the respective initial wagedistributions.

5.1

5.2

5.3

5.4

5.5

5.6

Expe

cted

wag

e le

vel

5 6 7 8 9Years after entry

P5 P25 P50P75 P95

Primary/High school

55.

25.

45.

65.

8

Expe

cted

wag

e le

vel


P5 P25 P50P75 P95

Vocational

5.2

5.4

5.6

5.8

66.

2

Expe

cted

wag

e le

vel


P5 P25 P50P75 P95

Bachelor

5.5

66.

57

Expe

cted

wag

e le

vel


P5 P25 P50P75 P95

Master

of catching up for any of the distributional groups, although the median initial wage percentile

does have a higher wage growth rate than the 75th percentile. Low initial wage workers holding

a master’s degree stay at the bottom while the 25th percentile and median workers overtake the

top initial wage workers after year seven.

One might be suspicious that these results are an artifact of the estimation procedure, which

puts some restrictions on the functional form. Figure 4 shows experience profiles for different

groups of the initial wage distribution estimated by log wages on experience and experience

squared.

Looking at figure 4 the qualitative results regarding catching up seems to be related to the

data and not just be spurious. Especially for those with either primary/high school or a voca-

tional education it seems that the 5th percentile almost catches up to the 95th percentile. For

those with a bachelor or a master’s degree there seems to be very little catch up. This is true in

particular for the bachelor group. However, there are also differences. Note that there are dif-

ferences on the scale of the x-axis between Figure 3 and 4. In particular, since Figure 3 is based

on a linear model we can never replicate the inverted U-shape that Figure 4 has. Therefore it

also only makes sense to compare the first 10 years of the graphs.


Figure 4: OLS estimates of log wage-experience profiles for different initial wages groups.

44.

55

5.5

Log

wag

es

0 5 10 15 20 25Experience years after labor market entry

P0 P5 P5 P25 P25 P50P50 P75 P75 P95 P95 P100

Primary/High school

4.8

55.

25.

45.

6Lo

g w

ages


P0 P5 P5 P25 P25 P50P50 P75 P75 P95 P95 P100

Vocational

4.8

55.

25.

45.

65.

8Lo

g w

ages


P0 P5 P5 P25 P25 P50P50 P75 P75 P95 P95 P100

Bachelor

55.

25.

45.

65.

86

Log

wag

es

0 5 10 15 20 25Experience y ears after labor market entry

P0 P5 P5 P25 P25 P50P50 P75 P75 P95 P95 P100

Master

5 Relation to Theory

Our main finding is that initial wages and later wage growth have a negative relationship. In

this section we will relate this finding to the three main theories relating initial wages to later

wage growth, namely search theory, unobserved productivity and learning, and finally human

capital theory. All three theories predict the negative relationship, so in order to try to shed light

on which of the theories are consistent with the data we will devise empirical implications that

hold only for a subset of theories and then test these implications. Since many versions of these

theories exist we start by presenting our view of the fundamental theories.

5.1 Search Theory

One of the theories that explain the negative correlation between individual return to experience

and initial wages is job search theory. The models that we have in mind are search models like

Burdett and Mortensen (1998) or Postel-Vinay and Robin (2002). However, the implications

of how wage posting models and second price auctions model wages are different in a number

of ways as we will show later. In a wage posting model like Burdett-Mortensen workers will

gradually move up the wage/productivity ladder. This implies that those who are initially lucky

and find a firm with a high wage will later have lower wage growth. This happens because

70 Chapter 3

there are simply fewer firms offering higher wages. In Postel-Vinay and Robin (2002) this

mechanism is actually enhanced. In the Postel-Vinay and Robin model wages are set in Bertrand

competition between firms. High productivity firms will be able to pressure workers to start out

with a very low wage in order to later have the potential of very high wage growth as they find

outside offers. However, the one to one correspondence between wages and productivity, as

was present in the wage posting model, is now broken.

5.2 Unobserved Productivity, Job Matching, and Learning

The theory of unobserved productivity and learning is centered around the assumption of im-

perfect information within the job match. In job search theory transitions and wage changes

happen because of arrival of new information about alternative matches. In the theory of job

matching new information arrives in the form of information about the current job match. One

of the seminal papers in the literature regarding unobserved productivity, job matching, and

learning is Jovanovic (1979). In this model workers and firms have match specific unobserved

productivity. True match specific productivity is an experience good and is slowly recovered

from noisy signals. Workers receive a wage equal to their expected output. One of the key

predictions is that it delivers a concave wage-tenure profile. This is loosely speaking caused

by selection, since workers with a low match quality slowly separate and thus only high match

workers are left. The separated workers move to another firm and start the process again. One

implication of this is a negative relationship between initial wages and later wage growth in

general. The reason for this negative relationship is that workers who initially receive a high

wage are more likely to be of a high match quality and therefore more likely to stay at the same

firm. Since this profile is concave it gives on average higher wage growth at low tenure values.

The main difference between the job search theory and the theory of job matching is that in

the search theory the main determinants of wage growth are outside offers while in job matching

it is based on new information of the match. Thus, one way to try to separate the theories is to

look at wage growth within and between the original job match.

5.3 Human Capital Theory

The final theory that we want to relate our results to is human capital theory. This is based

on the seminal work of Becker (1962), Mincer (1962), and Ben-Porath (1967) and emphasizes

the role of human capital acquirement in school and on the job. What we have in mind here


is a Ben-Porath type model where workers face a trade-off on the job between earning higher

wages and investing in their human capital, thereby increasing their earnings potential in the

future. In order to invest in human capital the worker will have to take a job with a lower wage.

Thus, human capital theory will predict a negative relationship between the initial wages and

individual wage growth (return to experience). For a survey on this literature see Weiss (1986).

The model can be extended to incorporate workers with scholastic abilities, see e.g. Rubin-

stein and Weiss (2006). If we allow for individuals to have different abilities to learn (scholastic

ability) one of the predictions is that those with high ability will stay longer in school. However,

they will then do less investment on the job.

The driving force behind the negative relationship between initial wages and later wage

growth according to human capital theory is different investment strategies by otherwise identi-

cal workers. This is contrary to both of the two previous explanations that focused on informa-

tional frictions.

5.4 Key Predictions and Testable Outcomes

In order to try to differentiate between the three theories we have two possible paths. The first

is to write down a fully structural model encompassing all three explanations. However, this is

well beyond the scope of this paper. Thus, our approach is to devise different testable outcomes

of the three theories presented. The goal is to try to find suggestive evidence for or against each

for them.

Unemployment A feature of almost all search models is that unemployment acts as a resetting

device. If a worker becomes unemployed, search models like those mentioned above, dictate

that he will be searching on the grounds of his unemployment benefit and not his former wage,

eliminating the link between his former (initial) wage and later wage growth. We can thus test

if search is the main explanation by looking at workers who have been unemployed between

entry on the labor market and year six and workers who have not.10 In order to do this we make

use of the weekly spell data previously described. An insignificant relationship between initial

wages and future wage growth for those who have been unemployed would thus confirm the

search theory explanation, while a significant slope contradicts it.

10We categorize unemployed to be only those with more than 12 weeks of unemployment to get rid of possi-ble bias from workers with only short-term unemployment in between jobs. The results do not depend on thisassumption.

72 Chapter 3

Figure 5: Expected wage growth divided on workers experiencing at least one 12 weeks unemployment spellbetween entry on the labor market and his 6th year.

.01

0.0

1.0

2.0

3

Expe

cted

wag

e gr

owth

4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5Initial log wage

Some U spells > 12 weeks No U spells > 12 weeks

Primary/high school

.01

0.0

1.0

2.0

3

Expe

cted

wag

e gr

owth

4.5 4.7 4.9 5.1 5.3 5.5Initial log wage


Vocational

.02

.025

.03

.035

.04

.045

Expe

cted

wag

e gr

owth

4.8 5 5.2 5.4 5.6Initial log wage


Bachelor

.02

.03

.04

.05

.06

.07

Expe

cted

wag

e gr

owth

5 5.2 5.4 5.6 5.8Initial log wage


Master

Figure 5 indicates that in general, there seems to be very little difference between the groups

that experienced an unemployment spell and those that did not. Note, that for the Primary/high

school group we find some indicative evidence that search theory might be an explanation, since

workers that have experienced an unemployment spell have a flatter relationship.

We take this to indicate that the search model might explain some of the negative relationship

for low educated but not for high and medium educated.

Job to Job transitions Both Learning models and Burdett and Mortensen (1998) imply a

negative relationship between initial wages and the number of job to job transitions. How-

ever, Postel-Vinay and Robin (2002) implies a positive relationship. Figure 6 shows the yearly

average number of job to job transitions by educational group and initial wage.

The pattern is quite different for the four educational groups. For primary/high school and

vocational educations the relationship is negative, while it is clearly positive for master degree

holders. For workers with a bachelor degree it is hard to say anything, but the mass of the data

seems to be on the upward sloping part.

Note, that this mixed pattern is consistent with the results in Postel-Vinay and Robin (2004).

They show that in an environment, where workers choose search intensity and firms have the

possibility to commit to never match an outside offer, a plausible labor market pattern is one


Figure 6: Average Yearly Job to Job transitions by educational group and initial wages.

0.2

.4.6

.81

CD

F (g

rey

lines

)

.05

.1.1

5.2

.25

.3Av

g. #

of J

ob−t

o−Jo

b tra

nsiti

ons

4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0Initial log wage

Primary VocationalBachelor Master

where bad jobs exist at low-productivity, non-matching firms and good jobs exist at high-

productivity, matching firms. Thus, the Postel-Vinay and Robin (2002) offer matching game

is mostly likely to arise in high-productive jobs, whereas ’ordinary’ wage search is most likely

to arise in low productive jobs. Since education is a very good proxy for productivity, this is in

accordance with the results in figure 6. E.g. the negative slope for low educated as predicted by

the wage search and the positive slope for high educated as predicted by the Postel-Vinay and

Robin (2002) model.

We take this as suggestive evidence that the Learning model is not the main driver behind

the negative relationship for high educated, but it might be a part of the explanation for low

educated.

Cyclical variation In search models, wage growth is due to the arrival of outside offers. Thus,

if the search model is the primary driving force we would expect to see a less negative slope in

recessions, since job offers in recessions are fewer. The learning explanation is essentially an

argument about recovering unobserved productivity from noisy signals. It is hard to imagine

that this has much to do with cyclical variation. Figure 7 shows the profile separated into years

of high and low GDP growth.11

In general we observe lower growth in times of low GDP growth which is not surprising.

For bachelor degree holders it seems that the relationship is more flat, but the differences are

only marginally significant. For the three other educational groups the estimated negative rela-

11We divide growth by the median.

74 Chapter 3

Figure 7: Expected wage growth given initial wages. Divided into high and low GDP growth years.

−.01

.01

.03

.05

Expe

cted

wag

e gr

owth

4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6Initial log wage

Low GDP growth years High GDP growth years

Primary/high school

−.01

.01

.03

.05

Expe

cted

wag

e gr

owth

4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6Initial log wage


Vocational

−.01

.01

.03

.05

Expe

cted

wag

e gr

owth

4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6Initial log wage


Bachelor

−.01

.01

.03

.05

Expe

cted

wag

e gr

owth

4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6Initial log wage


Master

tionship seems to have almost the same slope. We conclude that there is little evidence here to

support the search explanation.

Separations and shocks All reasonable theories would predict that if a firm is hit by a pro-

ductivity shock it should lay-off workers. However, theories differ in which workers the firm

should lay-off. The learning model predicts that if a firm is hit by a shock it should lay-off

relatively more high tenure workers compared to a firm that has not been hit by a shock. The

mechanism is that older workers have no option value, so it matter more for those workers.

However, the human capital model would predict that if human capital investments are to some

extent firm-specific then the firm should lay-off younger workers since these workers have lit-

tle firm-specific human capital. The argument is more formally presented in Nagypal (2007),

where a structural model is estimated using this identification argument.

It is hard to define firm shocks, but we define it as a firm losing more than 50 % of its

employees during a year.12 Figure 8 presents the job destruction hazard rate for different tenure

levels in firms that are hit by a shock and firms that are not.

We see that for all educational groups high tenure workers are laid off relatively more when

the firm is hit by a shock. We take this as suggestive evidence in favor of the learning explanation

12We limit this analysis for firms with more than 10 employees and workers aged less than 55


Figure 8: Job termination hazard rate for workers below the age of 55 and working in firms with more than 10employees by years of tenure.

0.0

5.1

.15

.2.2

5.3

.35

.4.4

5.5

Haz

ard

rate

1 3 5 7 9 11 13 15 17 19 21 23 25Tenure (years)

Low separation rate High separation rate

Primary/high school

0.0

5.1

.15

.2.2

5.3

.35

.4.4

5.5

Haz

ard

rate

1 3 5 7 9 11 13 15 17 19 21 23 25Tenure (years)


Vocational0

.05

.1.1

5.2

.25

.3.3

5.4

.45

.5H

azar

d ra

te

1 3 5 7 9 11 13 15 17 19 21 23 25Tenure (years)


Bachelor

0.0

5.1

.15

.2.2

5.3

.35

.4.4

5.5

Haz

ard

rate

1 3 5 7 9 11 13 15 17 19 21 23 25Tenure (years)


Master

and in disfavor of the human capital explanation.

Training We add to our data on individuals data on intensity of government co-sponsored

training for the Danish adult population. On average each worker in our sample gets around

one week of government co-sponsored training per year of employment.13 The training courses

consist both of basic courses (literacy and basic skills training), vocational and technical courses

(cooperation courses and industry-specific courses), and post-secondary courses (college courses).

Admittedly this training is only the part that is co-sponsered by the government. However, we

suspect that a very large fraction of total training is government co-sponsored.

Figure 9 show the non-parametric estimates of the average number of yearly course weeks

for years 0 to 5 since entry.

The different educational groups display very different patterns. For those with primary/high

school and vocational educations we see that those taking more courses are those with a low

to medium initial wages (except for those with primary/high school education with really low

initial wages). For bachelor degree holders there are no clear pattern, but for those in the master

group it is those with high initial wages that takes more training. Hence, it seems that the human

capital explanation might have some merit for those with a low level of education, while it has

13For a more thorough description of the institutional features consult Simonsen and Skipper (2008).

76 Chapter 3

Figure 9: Average number of course weeks in years 0 to 5 after entering the labor market.

.4.6

.81

1.2

1.4

Expe

cted

# o

f cou

rse

wee

ks

4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7Initial log wage

expected # of course weeks

Primary

.4.6

.81

1.2

1.4

Expe

cted

# o

f cou

rse

wee

ks

4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7Initial log wage


Vocational

.4.6

.81

1.2

1.4

Expe

cted

# o

f cou

rse

wee

ks

4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7Initial log wage


Bachelor

.4.6

.81

1.2

1.4

Expe

cted

# o

f cou

rse

wee

ks

4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7Initial log wage


Master

less for those with higher levels.

Figure 10 shows average wage growth by initial wages for each of the four educational

subgroups divided into the categories ’No Courses’ (which means no government co-sponsored

training) and ’Some Courses’ (which means they have taken some government co-sponsored

training).14

Even though we in Figure 9 found differences in the amount of training that different groups

received, we find in Figure 10 that there are no significant differences between those taking

courses and those taking no courses. This is consistent with previous estimates, see Kristensen

and Skipper (2009). However, it might be that we do not have the correct measure for human

capital accumulation. Even though we believe that we have a good measure of more formal

training activities these might not be the most important ones. If human capital accumulation is

more of a learning-by-doing mechanism then formal training might be a bad way of measuring

this.15

In total the evidence using training data is at best mixed. We find some evidence that indi-

viduals with lower levels of education and low initial wages get more training. However, these

14Training is measured in years 0 to 5 after labor market entry.15We have experimented with many different measures such as courses measured in year t and wage growth

from t to t + 1 for different years since labor market entry. All results indicate that training does not affect wagegrowth.


Figure 10: Expected wage growth per initial wage by acquiring job training or not.

−.01

.01

.03

.05

Expe

cted

wag

e gr

owth

4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7Initial log wage

No courses Some courses

Primary/high school

−.01

.01

.03

.05

Expe

cted

wag

e gr

owth

4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7Initial log wage


Vocational

−.01

.01

.03

.05

Expe

cted

wag

e gr

owth

4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7Initial log wage


Bachelor

−.01

.01

.03

.05

Expe

cted

wag

e gr

owth

4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7Initial log wage


Master

individuals do not have higher wage growth compared to those with similar initial wages and

education.

Summary of Tests The empirical tests above show little evidence to support the human cap-

ital explanation. Both the indirect test via the job hazard and the more direct test using training

data found no support. The learning model did relatively better. The test using separations

found in favor of the learning model, since high tenure workers were fired relatively more when

the firm experienced a negative shock. Also, the negative relationship between job-to-job tran-

sitions and initial wages for low educated support the learning explanation, while the positive

relationship between job-to-job transitions and initial wages for high educated goes against it.

Regarding the search explanation, we find mixed evidence. Using unemployment spells we find

some evidence that support the search explanation for low educated. Also, the test using job to

job transitions give some, but limited, support to the search explanation.

6 Robustness

Imagine that the labor market consists of two groups. The first group has a positive covariance

between initial wage and return to experience, while the second has a negative covariance.

78 Chapter 3

Table 4: Regression of log wage growth years 6 to 7, 7 to 8, 8 to 9 and 9 to 10 on initial log wages for vocationaleducated, labor market transitions.

Stayers JtJ† JtNtJ∗

Model (1) (2) (1) (2) (1) (2)

∆wit = α+ wi0 + εit -0.0261*** -0.0259*** -0.0551*** -0.0543*** -0.0255** -0.0265**(0.0008) (0.0010) (0.0033) (0.0040) (0.0100) (0.0124)

∆wit∆AEit

= α+wi0 + εit -0.0259*** -0.0261*** -0.0586*** -0.0578*** -0.0352** -0.0384**(0.0009) (0.0012) (0.0038) (0.0049) (0.0155) (0.0186)

Observations 327,984 327,984 63,365 63,365 6,827 6,827Individuals 117,257 117,257 47,531 47,531 6,296 6,296

The standard errors in parentheses are robust.(1) Unweighted regressions. (2) The regressions are weighted such that each individual have equal weights.***, **, * indicates significance at levels 1, 5 and 10 percent respectively.†Job-to-Job transitions.∗Job-to-Nonemployment-to-Job transitions.

Estimating the joint covariance using both groups could potentially result in a zero covariance

estimate. This highlights the importance of estimating on a homogeneous group of workers.

This was one of the reasons to separate by educational groups in the above analysis as we saw

that we estimated a U-shape when using the entire sample.

In this section we look for other possible explanations for the negative relationship. We

restrict the analysis to those with a vocational education, since this is the largest group and the

one with the clearest negative relationship. We look at labor market transitions, differences

in industries, differences in occupation, time of labor market entry, and minimum wages. In

general we find that none of these explain the negative relationship.

Labor Market Transitions It is a common result that much wage growth can be attributed

to job change (see e.g. Altonji and Williams (1992), Topel and Ward (1992), Neal (1995), and

Dustmann and Meghir (2005)).

Table 4 and figure 11 show the covariance analysis and the non-parametric estimates for

the vocational educated divided into stayers, Job-to-Job and Job-to-Nonemployment-to-Job

transitions.16 Generally, those with Job-to-Job transitions have a much stronger negative co-

variance between return to experience and initial wages than the stayer sample. This result

carries through no matter which measure of experience we use. Workers making a Job-to-

Nonemployment-to-Job have a more negative covariance if we use real experience, but not if

we use potential experience. Comparing to the main results in table 3 the stayer sample has a

less negative covariance of about three quarters of what it was before, but it is still very sig-

nificant. From this it is clear that the negative relationship is not driven by differences in labor

16The transitions refer to the year where wage growth is measured.


Figure 11: Expected wage growth over initial wages for stayers, job-to-job switchers, and job-to-nonemployment-to-job switchers, vocational education.

.05

.03

.01

.01

.03

.05

Expe

cted

wag

e gr

owth

4.6 4.8 5.0 5.2 5.4 5.6Initial log wage

Stayers Job to Job Job to Non to Job

market transitions in the year where wage growth is measured.

Industry One could imagine that different industries have different relationships between ini-

tial wages and return to experience. Figure 12 shows the results for the four largest industries for

vocational educated workers; the financial sector, wholesale, construction and manufacturing.17

There are level differences as one would expect. The financial sector enjoys higher wage

growth than the others. Wholesale come next, and then the manufacturing industry while con-

struction sees the lowest levels of wage growth for fixed permanent ability types, but all four

industries maintain the downward sloping relationship for the vocational educated group as a

whole.

Occupations Figure 12 also shows results where we have split the vocational workers into

occupations. Once more, there are level differences corresponding to what one would expect,

but again the overall pattern of the downward sloping relationship does not seem to be explained

by differences between occupations.18

Labor Market Entry; 80’ies vs. 90’ies Finally, although wages have been controlled for

year effects, one could imagine that entry in different periods of time could play a role in the

17We measure industry at the time of wage growth. We have also tried to measure it at labor market entry. Thismakes little difference.

18We measure occupation at the time of wage growth. We have also tried to measure it at labor market entry.This makes little difference.

80 Chapter 3

Figure 12: Expected wage growth over initial wages. Vocational educated workers divided into industries (upperpanel), occupations (lower left panel) and entry (lower right panel).

.01

.01

.03

.05

Expe

cted

wag

e gr

owth

4.6 4.8 5.0 5.2 5.4 5.6Initial log wage

Wholesale ConstructionFinance Manufacturing

.01

.01

.03

.05

Expe

cted

wag

e gr

owth

4.6 4.8 5 5.2 5.4 5.6Initial log wage

Manager Executive Some managementSalaried worker Skilled Unskilled

.01

0.0

1.0

2.0

3.0

4

Expe

cted

wag

e gr

owth

4.6 4.8 5 5.2 5.4 5.6Initial log wage

Entry 1980 1989 Entry 1990 2000

relationship between permanent observable ability and the return to experience. The lower right

panel of figure 12 divides the vocational educated workers into whether they entered the labor

market in the eighties or in the nineties. There seems to be a slight difference in the magnitude

of the slopes as the relationship for eighties-enters displays a steeper negative slope, but their

overall pattern does not reveal much difference.

Minimum Wages One potential problem with the above specifications is that e.g. minimum

wages could enforce a negative relationship. Denmark does not have an official fixed minimum

wage level but nevertheless, there are unofficial lower thresholds for wages within occupations

negotiated by the trade unions and the employer association.

Think of a very low permanent ability type worker (i.e. a worker with a very low initial

wage). He would gain wage increases simply because his wage could only go up. If this sign

went through over the entire initial wage support we would see a negative sloping relationship

as the ones above. However, we would also see a much lower variance in wage growth for

low permanent ability types than for high permanent ability types as there is no such thing as

an upper ceiling of wages. In order to address such an issue we have nonparametrically calcu-

lated the variance of wage growth conditional on initial wages. Figure 13 shows the estimated

conditional variance.

The variance for low permanent ability types is actually higher than for high permanent


Figure 13: Nonparametrically estimated variance of normalized wage growth conditional on initial log wages,vocational educated workers.

.03

.04

.05

.06

Varia

nce

of n

orm

aliz

ed w

age

grow

thco

nditi

onal

on

initi

al lo

g w

age

4.4 4.6 4.8 5 5.2 5.4 5.6Initial log wage

ability types and the suspicion that minimum wages were driving the result does not seem to

hold.

7 Conclusion

The main goal of this paper was to estimate the relationship between wage levels and wage

growth. We have estimated a Mincer type wage equation allowing for an individual unobserved

permanent effect and an individual unobserved return to experience. We have extended previous

analysis of this relationship to cover the entire sample of male workers. We have also extended

it to go beyond a covariance analysis.

We find an overall negative relationship between initial wages and return to experience, but

a positive relationship between return to experience and educational level (observable individ-

ual characteristics). We have done the analysis on several educational subgroups, and find that

the negative relationship between unobserved individual permanent ability and individual unob-

served return to experience is most clear for lower levels of education (primary/high school and

vocational) while higher levels of education (bachelor and master’s degrees) see an only bor-

derline significant relationship. In general, and especially for the group of vocational educated

individuals, the catching up effect in wages is relatively large.

We have connected the empirical findings with three main theories; search, unobserved

productivity and learning, and human capital. Using several empirical tests we find evidence in

82 Chapter 3

favor of the learning model, but no evidence in support of the human capital model. We find

mixed evidence for the search explanation.

Finally, we tested if we could find any observable characteristics that would explain the

negative relationship. We found that neither job transitions, industry, occupation, labor market

entry time or minimum wages could explain the pattern.

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Postel-Vinay, F. and J.-M. Robin (2002), Equilibrium Wage Dispersion with Worker and Em-ployer Heterogeneity, Econometrica, 70(6): 2295–2350.

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84 Chapter 3

A Tables

Table 5: Covariations between initial errors and future error growth from an ARMA(1,2) model.

Primary /Coefficients High school Vocational Bachelor Master

µ 0.7308 0.6865 0.6835 -0.4017ρ1 -0.6994 -0.7801 -0.7759 0.6354ρ2 -0.0393 -0.3128 -0.3202 0.1314σ2ν 0.0127 0.0102 0.0086 0.0120

Cov(ε0,∆ε1) -0.01229 -0.01120 -0.00944 -0.00923Cov(ε0,∆ε2) -0.00061 -0.00290 -0.00251 -0.00236Cov(ε0,∆ε3) 0.00006 0.00121 0.00105 -0.00063Cov(ε0,∆ε4) 0.00004 0.00083 0.00072 0.00025Cov(ε0,∆ε5) 0.00003 0.00057 0.00049 -0.00010Cov(ε0,∆ε6) 0.00002 0.00039 0.00033 0.00004

Cov(θ, γ)∗ -0.00201 -0.00248 -0.00006 -0.00087

ε is the error term estimated from equation (1).Model: εt = µεt−1 + νt + ρ1νt−1 + ρ2νt−2.∗Calculated from the estimates in table 3.

Chapter 4

Effects of Intensifying Labor MarketPrograms on Post-Unemployment Wages:Evidence From a Controlled Experiment

Effects of Intensifying Labor Market Programs on

Post-Unemployment Wages:

Evidence From a Controlled Experiment

Kenneth L. Sørensen∗

KORA and Aarhus University, CAP and CAFE

Abstract

This paper investigates effects on wages from a Danish field experiment intensifying Active La-

bor Market Policies (ALMP). We link unemployed workers who participated in an ALMP experiment

called “Quickly Back” carried out by the Danish Ministry of Employment 2005-2006 in two counties to

matched employer-employee and public transfer register data up to 2008 enabling us to analyze exact

labor market transitions and jobs of the participants. Men in one of the counties experienced significant

higher probability of earning higher medium and long term wages after treatment. Treated men in the

other county encountered a higher probability of earning lower wages in the short term and higher wages

in the long term than non-treated. Women in one county saw positive short term and negative long term

treatment effects and in the other county negative treatment effects both in the short and long term.

Keywords: Active Labor Market Policies, controlled experiment, wages, Mixed Proportional Hazard model.

JEL codes: C41, J31, J64,

∗I wish to thank Michael Svarer, Henning Bunzel, Rune Vejlin and Mark Kristoffersen for valuable comments.Additionally, I thank participants at the DGPE conference 2011, seminar participants at Aarhus University, theannual meeting of the Danish Econometric Society, Sandbjerg, participants at the annual BI-CAP meeting, Osloand at the CAFE workshop, Børkop 2012 for comments. I wish to thank the Cycles, Adjustment, and Policyresearch unit, CAP, Department of Economics and Business, Aarhus University sponsored by the Danish NationalResearch Foundation for support and for providing the data. Correspondence to; Kenneth Lykke Sørensen, email:[email protected]. KORA, Danish Institute for Local and Regional Government Research, Købmagergade 22, DK-1150 København K, Denmark.

87

88 Chapter 4

1 Introduction

Many welfare states are characterized by a flexible labor market for firms and a generous social

safety net for workers made redundant. For a system with a large public sector, high social

benefits and easy access to lay off workers to be sustainable, a necessary condition is to main-

tain a low unemployment rate and a high participation rate. However, frictions (caused by e.g.

incomplete information of supply and demand) and human capital depreciation in the labor

market induce difficulties for unemployed workers to find jobs. Therefore, most western coun-

tries have a wide range of Active Labor Market Policies (ALMP) consisting of, among other

things, training, activation, wage subsidies, monitoring and sanctions. Active labor market poli-

cies are meant to reduce these frictions and rebuild human capital of the unemployed worker

by adding skills and knowledge, and by offering job search assistance, resume guidance, etc.

to the unemployed as well as inducing him/her to actively search for a new job. This exercise

is very expensive, though, and a natural question arises: does it provide value for the money?1

The direct and short term outcome of ALMP is quite simple: Does it increase the exit-rate

out of unemployment and/or decrease the re-entering rate into unemployment? The long term

outcome of ALMP is less clear. First, ideally, after participating in ALMP, the unemployed

worker should have gained new or updated skills securing a good and sustainable worker-firm

match. Second, if, on the other hand, ALMP send unemployed workers into unsustainable or

bad worker-firm matches, policy makers should rethink the setting of the ALMP system. Third,

by guidance from a case worker or by participating in activation, the unemployed worker can be

updated with the state of the labor market and might choose to lower his/her reservation wage

in order to accept a job. If so, we would see workers entering lower paid jobs than if s/he had

not been treated by ALMP.

In this paper, we analyze short, medium and long term post-unemployment outcomes (wages

one, two and three years after leaving unemployment) from participating in an intensive active

labor market policy program using a mixed proportional hazard framework (see Abbring and

van den Berg (2003)).2 We explore a field experiment carried out in two Danish counties,

Storstroem and Southern Jutland, during the winter of 2005/2006. The experiment randomly

assigned a fraction of all newly unemployed individuals to a treatment group with an intensive1Denmark spends more than 1.5% of GDP every year on active measures of ALMP. Germany spends 0.9%,

France 0.9%, The Netherlands 1.2%, Sweden 1.1%, Switzerland 0.7%, United Kingdom 0.4% and the UnitedStates spends 0.1% of GDP on active measures of labor market policies (2005 numbers, OECD.StatExtracts).

2Following the definition of Card, Kluve and Weber (2010), wages one, two and three years after leavingunemployment relate to short, medium and long term outcomes, respectively.

Effects on Post-Unemployment Wages 89

ALMP scheme compared to the current system.3 The purpose of the experiment was to test

whether an early effort could help treated newly unemployed back to work faster than non-

treated. The intensification mainly consisted of increasing the frequency of meetings between

the unemployed worker and a case worker and by advancing the time of activation. We use

unique Danish administrative register data that allow us to measure labor market histories of the

unemployed workers, both before they entered the experiment and up to three years after in a

duration model setting. From these registers, we construct average hourly wages by following

each of their post-unemployment employment spells. This is the first paper to our knowledge

that link intensification of ALMP and post-unemployment wages using Danish data.

Our findings in terms of wage outcomes from treatment are ambiguous. We find signifi-

cant negative long term outcomes for women in both counties and find treated men in Southern

Jutland to have a significantly higher probability of earning higher long term wages than non-

treated. Treated men in Storstroem county experience a higher probability of earning lower

short term wages than non-treated. Treated women in Southern Jutland have a higher proba-

bility of earning higher short term wages than non-treated while treated women in Storstroem

have a higher probability of earning lower wages than non-treated women. This indicates that

the intensification of ALMP may have had an impact on (short term) reservation wages as well

as on long term wages.

Following the seminal works of Heckman and Singer (1984a,b) and Ham and Lalonde

(1996) many studies have looked into various effects of Active Labor Market Policies. Often, in

the duration model setting, data restrict the focus to the effectiveness of ALMP on the exit rate

out of unemployment into different labor market states such as other public transfers (inactivity)

or self-support (mainly interpreted as employment) (see Heckman, Lalonde and Smith (1999),

Lalive, Zweimuller and van Ours (2005), Rosholm and Svarer (2008), and Kluve (2010)), or

the return rate into unemployment (e.g. Crepon, Dejemeppe and Gurgand (2005), Doiron and

Gørgens (2008), and Blasco and Rosholm (2011)).4

Most of these studies look at the labor market spell after leaving the unemployment pool

when participating in an ALMP program ignoring long term effects. Authors looking into

long term effects often evaluate these on the basis of length of employment or self support. In a

meta analysis of 97 ALMP studies (totaling 199 program estimates) Card et al. (2010) show that

3The assignment to treatment was conducted by day of birth. See section 2 for a more thorough description.4See Kluve (2010) for a meta analysis of European ALMP studies and Card et al. (2010) for an extensive meta

analysis of ALMP evaluations in general.

90 Chapter 4

many programs with insignificant or negative short term impacts (within a year) have significant

positive medium and long term impacts (after 2 to 3 years), and we thus argue that analyzing

the short term as well as medium and long term impacts is important.

The field experiment used in this paper has previously been used to analyze ALMP in a

Danish context. Graversen and van Ours (2008a,b) find that treated individuals experience

shorter unemployment durations. They use a mixed proportional hazard model and find a 30%

higher job finding rate for treated participants compared to control group members. Rosholm

(2008) finds a similar estimate on the exit rate out of unemployment, but also shows that when

controlling for time-varying indicators of treatment all positive effects vanish and some even

become negative, the so-called lock-in effect. He finds that the estimated risks of meetings and

being activated drive the difference in the job finding rates between treated and non-treated in-

dividuals. Vikstrom, Rosholm and Svarer (2011) use non-parametric methods to separate the

sub-treatment effects on the exit rate out of unemployment. They find that job search assistance,

frequent meetings and activation threats have positive impacts on the exit rate. Gautier, Muller,

van der Klaauw, Rosholm and Svarer (2012) examine the outcomes for non-treated unemployed

workers and compare these with unemployed workers in different counties of Denmark unaf-

fected by the experiment to measure general equilibrium effects on the job finding rates. They

find evidence of negative spillovers from treatment. Specifically, they find that estimating ef-

fects of treatment without accounting for externalities will result in an upward biased estimate.

Finally, Blasco and Rosholm (2011) analyze long term effects on post-unemployment employ-

ment stability in terms of duration on self support after leaving the unemployment pool. They

find that treatment increases the post-unemployment self support duration by ten percent for

men while treated women show no post-unemployment stability effects. Decomposing the ef-

fect, they show that 20-25 percent is due to lagged duration dependence. Still, we know very

little about post-unemployment labor market participation other than the duration of self sup-

port. To further elaborate on the knowledge of long term ALMP effects on post-unemployment

employment, this paper contributes by adding another and very important dimension of out-

comes, namely wages.

ALMP schemes are designed to both increase the exit rate out of unemployment and to equip

the unemployed better for a return to employment and thus enhance the quality of the worker-

firm match. Studies of ALMP should not only evaluate exit and return rates but also take into

account post-unemployment labor market outcomes such as wages and employment stability


(see Crepon et al. (2005)). Analysis in these dimensions is important to tell the full story of

potential successes or failures of ALMP programs. This paper contributes to the literature with

research in post-unemployment wages.

Other studies have examined wage gains/losses from participating in labor market schemes.

Most authors analyzing labor market programs use either a duration or a matching framework

to handle problems of selection into different programs. In the matching model literature, a

number of studies have analyzed the impact of labor market programs on post-unemployment

wages.5 Using propensity score matching, Jespersen et al. (2008) analyse cost and benefits of

labor market programs in Denmark. They find both public and especially private job training to

have positive earnings effects, even after correcting for costs of training. For two Swedish labor

market programs on practice and labor market training targeting young unemployed, Larsson

(2003) finds zero or negative short term effects and zero or slight positive long term effects of

participation in the programs. Within the duration framework, Gaure, Røed and Westlie (2012)

examine effects of unemployment benefits and ALMP participation on unemployment duration

together with short term post-unemployment employment stability and earnings in Norway.

They find that participation in ALMP lengthens the unemployment duration, i.e. the time until

finding a job. However, they estimate ALMP to induce a higher probability of finding a job,

and once the job is found, expected earnings have increased as well. Examining young workers

being unemployed for more than nine months after finishing school, Cockx and Picchio (2012)

find that prolonging the unemployment lowers the chance of getting a job but has no effect on

starting wages earned once a job is found. Recently, literature has studied the effect of sanctions

on the quality of post-program employment. In a study of sanctions on Swedish data, van den

Berg and Vikstrom (2009) measure the effect on post-unemployment wages and hours worked.

They find sanctioned workers to experience a 23 percent increase in the exit rate to employment,

but with lower wages and fewer hours worked than non-sanctioned. On top of this, they find

sanctioned workers to incur a higher level of human capital loss than non-sanctioned. Using rich

Swiss unemployment and employment register data, Arni, Lalive and van Ours (2012) analyze

the effect of monitoring and sanctions (full benefit reduction) on post-unemployment duration

and earnings. They find that increasing monitoring increases the exit rate to employment with

reduced earnings while durations are unaffected. Arni et al. (2012) show that sanctions also

5See e.g. Jespersen, Munch and Skipper (2008), Sianesi (2004), Larsson (2003), Raaum, Torp and Zhang(2002) using nordic data and Lechner (1999) using swiss data. See Heckman, Ichimura and Todd (1997) on themethod of matching.

92 Chapter 4

increase the exit rate, but with both lower earnings and lower post-unemployment employment

durations as the result. For a US ALMP experiment, targeting unemployed believed to have a

low probability of re-entering employment before benefit exhaustion, Berger, Black, Noel and

Smith (2003) find that program participation decreases expected unemployment by 2.2 weeks,

but more importantly, it increases subsequent earnings by $1,000.

The rest of this paper is laid out as follows: Section 2 sketches the social experiment

“Quickly Back”, section 3 presents the data we utilize, section 4 review the econometric frame-

work, and in section 5 we present our empirical results. Finally, section 6 concludes.

2 The Experiment

The controlled field experiment “Quickly Back” (henceforth denoted QB) was conducted by

The National Labor Market Authority under the Danish Ministry of Labor in two Danish coun-

ties: Southern Jutland and Storstroem. QB was the first in a series of experiments conducted

by the National Labor Market Authority testing the effects of intensifying ALMP in several

dimensions. We use QB, partly because of a good setup related to measuring precise treat-

ment and, partly because adequate time has passed since the beginning of the experiment such

that we now are able to link post-unemployment employment spells to the participants. The

experiment consisted of an intensification in multiple dimensions of the 2005 ALMP system.

The experiment setting was constructed by randomly assigning a fraction of newly unemployed

(UI benefit eligible) individuals to a treatment group. If a newly unemployed worker was born

between the 1st and the 15th of any given month, he or she was assigned to the treatment group.

Importantly, there were no publicly announced description of the experiment before it was

implemented. The participants in the control group were not told they were put into a control

group of an experiment and individuals in the treatment group were only notified that they

participated in a “pilot study”, not in an experiment, a week and a half after registering as

unemployed.

Individuals in both groups were sent to a CV/basic registration meeting within the first four

weeks of their unemployment spell. In the period of the experiment (first week of November

2005 to the last week of February 2006), the labor market program (i.e. for the control group)

further consisted of:6

6C is for Control group.


C-1 After four and twelve weeks of unemployment (receiving benefits), the unemployed should

attend a meeting with a case worker.

C-2 Hereafter, the unemployed had to attend a meeting with a case worker every 13 weeks.

C-3 After a year of unemployment, the unemployed should participate in an unspecified pro-

gram of at least one week duration.

C-4 For the rest of the unemployment spell, the unemployed worker had to participate in pro-

grams at least once every six month.

The intensification of the existing labor market program consisted of exposing the treatment

group to:7

T-1 1.5 weeks after entering unemployment (receiving benefits) a letter informing the partici-

pant that s/he has been drawn as a member of a “labor market pilot study” and the entire

course of the intense study was sent to the individual in the treatment group.

T-2 A two-week Job Search Assistance (JSA) program was mandatory after five or six weeks

of unemployment.

T-3 During week 9 to 15 of unemployment, the treatment participant should (ideally) meet fre-

quently with a case worker to ensure active job search and to provide JSA. The frequency

was once a week in Storstroem and once every other week in Southern Jutland.

T-4 After week 18, an unspecified mandatory program lasting at a minimum of 13 weeks

would start. There were four different possible programs of different lengths. (i) Private

sector temporary job (subsidized by the authorities, lasting up to 6 months). (ii) Public

sector temporary job (6-12 months). (iii) Classroom training (often less than 13 weeks

each) and (iv) vocational training programs within firms (a couple of months).

T-5 The experiment ended and individuals still unemployed were transferred into the ordinary

labor market program.

Note that the although the experiment was conducted at the same time in the two counties,

it was not identical between them. The meeting frequency differed between the two counties

(cf. T-3). In Storstroem county the treatment participant were to meet with a case worker once

every week between week 9 and 15 of receiving benefits while the treatment participants from

7T is for Treatment group. See Table B1 (in the appendix) for an overview of the time schedule of treatedversus non-treated individuals.

94 Chapter 4

Southern Jutland should only met with their case worker once every other week between week

9 and 15. This difference between the counties de-facto means that QB was not one but two

experiments, and the analysis in this paper is carried out for each of the counties separately.

This particular experiment setting constitutes a good background for the analysis in this pa-

per as the setting of random assignment by birthdays eliminates selection into treatment groups

and justifies the ex-ante assumptions on unobserved heterogeneity of our mixed proportional

hazard model (see Abbring and van den Berg (2003)). Further, it allows us to follow the in-

dividual worker throughout the experiment and, by linkage to register data, through his or her

labor market transitions up to three years after leaving the experiment. Lastly, the treatment

group member was imposed to a much more intense search scheme during his/her unemploy-

ment spell than the control group member. Other studies have already shown QB to have mixed

positive and negative short term effects for men and women in terms of the exit rate out of un-

employment and lowering the probability of re-entering unemployment (see Graversen and van

Ours (2008a,b), Blasco and Rosholm (2011), Vikstrom et al. (2011)). In continuation of Card

et al. (2010), who find that studies of labor market policies with zero or negative short term

effects can have positive long term effects, it would be very interesting to analyze the long term

effects of such an intensification of ALMP.

The down side of QB is the impossibility of distinguishing between the three dimensions of

intensified treatment, (i) the two-week JSA program, (ii) the intensive meeting schedule, (iii)

the faster entry into an activation scheme. The treatments came sequentially and we can thus not

identify whether e.g. it was the meetings with a case worker having an impact or it simply was

that the JSA program had a delayed effect. However, we argue, analyzing whether a general

intensification of treatments has long term labor market outcome effects constitute important

knowledge and insight into the full impacts of ALMP schemes. The division of individual

effects of treatment is an important topic of further research but is beyond the scope of this

paper.8

8In a later experiment named QB II, the National Labor Market Authority assigned each of the treatmentdimensions to different counties such that explicit analysis of types of treatment in time could be conducted. Weare thus in some years (when the participants of QB II have had the opportunity to experience post-unemploymentoutcomes) able to take the analysis from this paper further into dividing up the treatment effects.


3 Data

We use three administrative register databases in this paper; (i) Quickly Back collected by the

National Labor Market Board, (ii) weekly Spell data containing all labor market transitions and

(iii) yearly data from the Integrated Database for Labor Market Research (IDA). All databases

are maintained by Statistics Denmark. The QB data contain information on individuals par-

ticipating in the field experiment carried out in two Danish counties, Storstroem and Southern

Jutland, during the winter of 2005−2006. The information covers participation in the treatment

or control group, spells of unemployment (in terms of which week it started and which week it

ended) prior, during and after the experiment, type of activation if the unemployed experienced

any such and several socio-economic variables on the individual. The weekly Spell data is a

longitudinal data set containing information of labor market transitions for each individual in

the Danish population including wages from employment spells. IDA is a matched employer-

employee longitudinal database containing socio-economic information on the entire Danish

population, the population’s attachment to the labor market, and at which firms the worker is

employed. Both workers and firms can be monitored from 1980 − 2008. The reference period

in IDA is given as follows: the linkage of workers and firms refers to the end of November,

ensuring that seasonal changes (such as e.g. shutdown of establishments around Christmas) do

not affect the registration. Background information on individuals mainly refers to the end of

the year.9 The key feature of these three databases is the unique link between them given by

individual id and firm id that are common across QB, Spell and IDA.

We construct hourly wages by accumulating wages net of public transfers from all employ-

ment spells during a year and normalizing by hours worked. Hours worked are measured by

payments to the Danish mandatory public pension scheme. Payments to the pension scheme are

determined by a step-function of hours worked.

3.1 Descriptive Summary

Here we present descriptives on the counties, QB, the Spell data and on IDA.

9See a more detailed documentation on IDA:http://www.dst.dk/HomeUK/Guide/documentation/Varedeklarationer/emnegruppe/emne.aspx?sysrid=1013.

96 Chapter 4

Figure 1: Map of Denmark with Storstroem and Southern Jutland shaded in black.

3.1.1 The Two Counties

QB was conducted in the two Danish counties, Storstroem and Southern Jutland. They are both

counties without larger cities.10 Both Storstroem and Southern Jutland lie in the geographically

outer regions of Denmark as a whole and should thus not be considered representative of Den-

mark as a whole (Figure 1 shows Storstroem and Southern Jutland shaded in black). However,

as Table 1 shows, West and South Zealand (which contain Storstroem county) saw similar un-

employment rates as the Danish average after 2004. Southern Jutland had lower unemployment

rates than Denmark on average from 2001 to 2008. In both counties as for Denmark, men had a

lower unemployment rate than women. Notice, Table 1 shows that pooling the counties together

should be done carefully, as they face two different labor markets. Southern Jutland participants

face a lower local unemployment rate than their Storstroem counterparts and an assumption that

treated and non-treated in one county have the same employment possibilities as in the other

could very easily be violated. These facts, on top of the difference in the experimental nature

with more frequent meetings in Storstroem than in Southern Jutland, are the reason that we will

not be pooling the counties together, but instead do the full analysis on each county separately

as well as for men and women.

10The largest cities (2006) in Storstroem and Southern Jutland were Næstved (41,158 residents) and Sønderborg(27,391 residents) ranked 15th and 23rd in Denmark, respectively, in terms of residents.


Table 1: Net unemployment rates in percent.

2001 2002 2003 2004 2005 2006 2007 2008

Denmark 4.7 4.8 5.8 5.8 5.1 3.9 2.7 1.9West and South Zeeland∗ 5.1 5.2 6.1 6.0 5.2 3.9 2.9 2.0Southern Jutland 4.5 4.5 5.5 5.3 4.6 3.1 2.0 1.3Men

Denmark 4.1 4.4 5.4 5.4 4.5 3.3 2.3 1.8West and South Zeeland∗ 4.4 4.6 5.6 5.4 4.5 3.2 2.3 1.9Southern Jutland 3.7 3.8 4.8 4.5 3.7 2.4 1.6 1.2

WomenDenmark 5.2 5.2 6.1 6.3 5.7 4.5 3.2 2.0West and South Zeeland∗ 6.0 5.8 6.7 6.6 5.9 4.7 3.5 2.1Southern Jutland 5.5 5.3 6.4 6.4 5.6 4.0 2.6 1.5

∗Covers Storstroem county and more.Source: Statistics Denmark (statistikbanken.dk/AUL06).

3.1.2 The Treatment Group vs. the Control Group

Table 2 shows descriptive statistics on the estimation samples. Storstroem county contains

1,169 observations in the treatment group and 1,217 in the control group. Southern Jutland

county consists of 1,060 observations in the treatment group and 1,064 observations in the con-

trol group. The fraction of women in the Storstroem control group is slightly, but insignificantly,

larger than in the treatment group. In Southern Jutland there is no difference. There are no ma-

jor differences between treatment and control groups in the two counties with respect to week

of entering the experiment. The only significant difference is entry in weeks 49-50 with a larger

fraction of newly unemployed individuals being allocated to the treatment groups. There are

only small educational differences between treatment and control groups in Storstroem county

and none in Southern Jutland. Storstroem has a slightly larger fraction of vocational and smaller

fraction of primary/high school graduates in the treatment than in the control group. Both coun-

ties have a higher fraction of nonwestern immigrants being treated than non-treated. There are

only very few nonwestern immigrants, however, and the significant difference is very unlikely

to cause major selection issues between the groups, if any. Treatment and control groups do not

display any major differences with respect to age, experience, marital status, lagged unemploy-

ment duration or post-unemployment transition to employment.

Treated individuals in Southern Jutland seem to be heading into slightly more stable em-

ployment spells than non-treated in the sense that in 2007 a larger fraction of treated holds only

one job than non-treated. The opposite is the case in Storstroem in 2006 and 2008. There are

only small insignificant differences in the fraction seeing one or more un- or non-employment

spells after leaving QB.

98 Chapter 4

Table 2: Summary statistics.

Storstroem county Southern Jutland

Treatment Control Diff. Treatment Control Diff.

Pre-experiment characteristics

Individual Characteristics

Women 0.381 0.404 0.464 0.453

Married 0.466 0.474 0.499 0.477

Age 40.93 40.65 39.59 39.75

Experience 14.47 14.51 12.92 13.19

Danish 0.928 0.952 0.911 0.925

Western immigrant 0.021 0.015 0.047 0.044

Nonwestern immigrant 0.052 0.034 ** 0.042 0.031 *

Level of education, 2005

Primary and high school 0.397 0.429 0.419 0.428

Vocational 0.491 0.463 * 0.456 0.446

Bachelor 0.093 0.097 0.111 0.109

Master and above 0.020 0.012 * 0.014 0.017

Occupation in the last week of November 2005

Management level 0.031 0.041 0.027 0.026

Skilled level 0.470 0.467 0.450 0.453

Unskilled level 0.304 0.293 0.305 0.303

Unemployed 0.121 0.121 0.133 0.137

Non-employed 0.074 0.077 0.083 0.077

Accumulated unemployment duration 3 years before entering QB

≤ 6 weeks 0.477 0.505 0.517 0.508

7-8 weeks 0.015 0.012 0.015 0.024

9-16 weeks 0.073 0.072 0.068 0.071

17-28 weeks 0.079 0.076 0.068 0.069

29-52 weeks 0.122 0.118 0.125 0.122

> 52 weeks 0.234 0.219 0.208 0.207

Week of entry into QB

43-44, 2005 0.123 0.118 0.148 0.149

45-46, 2005 0.062 0.054 0.053 0.061

47-48, 2005 0.082 0.107 0.127 0.121

49-50, 2005 0.119 0.082 *** 0.097 0.069 ***

51-52, 2005 0.111 0.110 0.108 0.111

01-02, 2006 0.199 0.210 0.190 0.207

03-04, 2006 0.122 0.107 0.093 0.100

05-06, 2006 0.125 0.151 0.143 0.126

07-08, 2006 0.058 0.061 0.041 0.057

Average hourly wages (DKK), men

Earned during 2004 179.0 181.4 172.8 173.3

Earned during 2005 186.4 192.0 ** 180.0 181.5

Average hourly wages (DKK), women

Earned during 2004 157.0 157.5 151.8 153.3

Earned during 2005 165.7 166.9 161.3 164.9

*: Indicates statistical significant difference at the 10% level. **: At the 5% level. ***: At the 1% level.



Table 2: Continued from previous page.

Storstroem county Southern Jutland

Treatment Control Diff. Treatment Control Diff.

Post-experiment characteristics

QB characteristics

Treated ≤ 30 weeks 0.888 0.000 *** 0.861 0.000 ***

Treated > 30 weeks 0.112 0.000 *** 0.139 0.000 ***

Transition QB, U→ E 0.895 0.886 0.876 0.879

Number of different employers after QB

2006, zero employers 0.074 0.092 0.077 0.116

2006, 1 employer 0.416 0.441 0.419 0.406

2006, 2 employers 0.283 0.288 0.287 0.288

2006, 3 or more employers 0.228 0.179 *** 0.217 0.191 *

2007, zero employers 0.125 0.126 0.105 0.123

2007, 1 employer 0.511 0.518 0.571 0.513 ***

2007, 2 employers 0.241 0.241 0.204 0.243

2007, 3 or more employers 0.123 0.116 0.121 0.120

2008, zero employers 0.169 0.167 0.145 0.160

2008, 1 employer 0.483 0.536 0.536 0.522

2008, 2 employers 0.222 0.198 * 0.211 0.205

2008, 3 or more employers 0.126 0.099 ** 0.108 0.114

Experiences unemployment spells after QB

During 2006 0.329 0.303 0.326 0.322

During 2007 0.367 0.377 0.339 0.372

During 2008 0.295 0.310 0.259 0.279

Experiences non-employment spells after QB

During 2006 0.418 0.397 0.450 0.429

During 2007 0.519 0.533 0.556 0.593

During 2008 0.537 0.563 0.583 0.607

Average hourly wages (DKK), men

Earned during 2006 185.2 191.1 ** 179.7 181.4

Earned during 2007 189.3 190.3 185.3 180.0 **

Earned during 2008 194.5 191.1 191.5 185.4 **

Average hourly wages (DKK), women

Earned during 2006 160.0 170.1 *** 165.2 166.0

Earned during 2007 163.1 164.0 161.0 161.9

Earned during 2008 164.8 167.6 164.9 172.6 **

Individuals 1,169 1,217 1,060 1,064

*: Indicates statistical significant difference at the 10% level. **: At the 5% level. ***: At the 1% level.

For average hourly wages we see no significant differences before QB in all samples but

men in Storstroem county in 2005. They display a 5 percent significantly higher average hourly

100 Chapter 4

Figure 2: Evolution of average earnings (2008 prices) and average employment rate for the male treatment andcontrol group members 2004-2008.

200,0

00

220,0

00

240,0

00

260,0

00

Avg. earn

ings

2004 2005 2006 2007 2008Year

Treatment Control

Storstroem, men

.65

.7.7

5.8

.85

Avg. em

plo

ym

ent ra

te

2004 2005 2006 2007 2008Year

Treatment Control

Storstroem, men180,0

00

200,0

00

220,0

00

240,0

00

260,0

00

Avg. earn

ings

2004 2005 2006 2007 2008Year

Treatment Control

Southern Jutland, men

.65

.7.7

5.8

Avg. em

plo

ym

ent ra

te

2004 2005 2006 2007 2008Year

Treatment Control


wage rate. Treated men in Southern Jutland have significantly higher average hourly wages in

2007 and 2008, while no significant differences after the experiment are present in Storstroem

county. Southern Jutland treated women see a significant lower average wage level in 2008 than

non-treated.

The outcome of interest in this paper is average hourly wages earned in the years after

participating in the experiment QB. Of course average hourly wages is a measure of wages

earned by the amount of hours worked. If one individual earns 150,000 Dkk in 2007 working

1,000 hours (just below 2/3 of a full time work-year) he will see the same average hourly wage

as another individual earning 200,000 Dkk in 2007 working at a higher paying job putting in

1,333 hours. They are in reality not equal off however. To examine the evolution of both total

wages earned and hours worked, Figure 2 and 3 show the descriptives of these over the years

2004 to 2008.

There are clearly differences between the treated and non-treated in both counties and es-

pecially so for men. Comparing average earnings and employment rates within groups reveal,

however, that it does not seem that it is only the employment rate or the earnings that change

after participating in QB. Both seem to be affected in a comparable manner.


Figure 3: Evolution of average earnings (2008 prices) and average employment rate for the female treatment andcontrol group members 2004-2008.

140,0

00

160,0

00

180,0

00

200,0

00

Avg. earn

ings

2004 2005 2006 2007 2008Year

Treatment Control

Storstroem, women

.55

.6.6

5.7

.75

Avg. em

plo

ym

ent ra

te

2004 2005 2006 2007 2008Year

Treatment Control

Storstroem, women140,0

00

160,0

00

180,0

00

200,0

00

Avg. earn

ings

2004 2005 2006 2007 2008Year

Treatment Control

Southern Jutland, women

.5.5

5.6

.65

.7A

vg. em

plo

ym

ent ra

te

2004 2005 2006 2007 2008Year

Treatment Control


Table B2 (in the appendix) shows the fraction of individuals in different occupational levels

recorded by the last week of November in the years 2004 to 2008. None of the employment

occupational groups differ significantly between treatment and control groups in either county in

any of the years 2004 and 2005. Only workers employed at unskilled level in Storstroem county

in 2005 that have a 10% level significantly larger fraction in the control than in the treatment

group. In 2006 we see, not surprisingly, that a significantly larger fraction of control group

members are unemployed. More interestingly, a larger fraction within the treatment groups is

now employed at the unskilled level than in the two control groups.

The other employment groups do not display any significant differences. Thus, it seems that

it is lower occupational jobs that differ between the treatment groups and the control groups

in 2006. In 2007 this difference has vanished in Storstroem county while it remains the same

in Southern Jutland with a larger part of individuals from the treatment group employed at

unskilled level than from the control group. The fraction of unemployed in Storstroem by 2007

has grown larger within the treated versus non-treated and equal by 2008. In Southern Jutland

it remains to be a smaller fraction of treated than non-treated being unemployed during the last

week of November 2007 and 2008 (at the 10 percent significance level).

102 Chapter 4

Table 3: Number of QB participants in different unemployment duration categories.

Unemployment Storstroem Southern Jutlandduration (weeks) Treatment Control Diff. Treatment Control Diff.

1 - 4 0.232 0.200 ∗ 0.205 0.1945 - 8 0.203 0.170 ∗∗ 0.194 0.160 ∗∗

9 - 15 0.244 0.222 0.249 0.209 ∗∗

16 - 30 0.209 0.239 ∗ 0.213 0.248 ∗

31 + 0.112 0.169 ∗∗∗ 0.139 0.189 ∗∗∗

Individuals 1,169 1,217 1,060 1,064

*: Indicates statistical significance at the 10% level. **: At the 5% level. ***: At the 1% level.

3.1.3 QB Durations

Several papers have shown that QB increased the exit rate out of unemployment (Graversen

and van Ours (2008a,b), Rosholm (2008)). Table 3 contains the fraction of individuals leaving

the benefit system within each of the experiment schemes (cf. Table B1). As expected, a

higher fraction of treated individuals leaves unemployment before week 16 than non-treated.

During the activation program scheme, this is circumvented and a larger fraction of non-treated

individuals leaves unemployment.

3.1.4 Post-Unemployment Wages

Table B3 holds summary statistics of average hourly wages for men and women. Over all

samples, the is no clear picture from the median and different percentiles of hourly wage. Note,

however, that treated men in Southern Jutland 2008 dominates non-treated in terms of hourly

wages at all percentiles.

Figure 4 shows the cumulative average hourly wage distribution function (CDF) for treated

individuals subtracted the CDF for non-treated at given wage levels.11 A difference of zero at

wage level w∗ indicates an equal fraction of individuals earning w∗ or less between treated and

non-treated. If the difference is positive at wage levelw∗, a higher fraction of treated individuals

earns w∗ or less than non-treated and vice versa. A common feature of all samples is that the

2004 and 2005 differences are close to zero for all wage levels. 2005, Storstroem men being

an outlier. For 2006 wages (triangles), Storstroem women display positive CDF differences

for all wage levels and Storstroem men for all wages higher than 150 Dkk. Men and women

in Southern Jutland see negative or zero differences. The CDF differences for average 2007

wages (circles) of men in Southern Jutland lie below zero with a minimum of 4 percentage

11Note that, by construction, Ftreated(w) − Gnon-treated(w) → 0 for w → ∞ where F and G are the CDF’s oftreated and non-treated respectively.


Figure 4: Plots of treatment group CDF subtracted the control group CDF for given hourly wage levels.

−.0

6−

.04

−.0

20

.02

.04

.06

CD

F t

rea

tme

nt

− C

DF

co

ntr

ol

100 150 200 250 300 350+Hourly wage (DKK)

2004 2005

2006 2007

2008

Storstroem, men

−.0

6−

.04

−.0

20

.02

.04

.06

CD

F t

rea

tme

nt

− C

DF

co

ntr

ol

100 150 200 250 300 350+Hourly wage (DKK)

2004 2005

2006 2007

2008


−.0

6−

.04

−.0

20

.02

.04

.06

CD

F t

rea

tme

nt

− C

DF

co

ntr

ol

100 150 200 250 300 350+Hourly wage (DKK)

2004 2005

2006 2007

2008

Storstroem, women

−.0

6−

.04

−.0

20

.02

.04

.06

CD

F t

rea

tme

nt

− C

DF

co

ntr

ol

100 150 200 250 300 350+Hourly wage (DKK)

2004 2005

2006 2007

2008


points lower fraction of treated paid an hourly wage of 150 Dkk than non-treated.12 Women

in Southern Jutland also see an overall negative difference in 2007 wages, but not as strong as

men. Neither men or women have any differences in the CDF of 2007 wages in Storstroem.

Finally, for 2008 wages (diamonds) men in both counties have a negative difference in CDFs

of roughly 1.5 percentage points in Storstroem and as high as 5 percentage point in Southern

Jutland. Figure A1 and A2 hold the levels of all the CDFs. Most masses are located below 200

DKK for men and 150 Dkk for women. None of the samples has single mass points and the

distributions all seem to be nice and smooth.

We have performed Kolmogorov-Smirnov tests for equal hourly wage distributions between

treated and non-treated. Table 4 presents both one- and two-sided p-values from these tests.13

Using one-sided tests, we cannot reject the null hypothesis of different underlying wage distri-

butions on a 5 percent significance level for men in Southern Jutland 2006-2008 and borderline

12Figure A1 (in the appendix) shows that roughly 50 percent in the control group have a wage less than 150DKK.

13In the one-sided test, if at the point of the largest difference, the CDF of treated is greater than the CDF ofnon-treated, the null is H0 : Ftreated(w) ≤ Gnon-treated(w) versus H1 : Ftreated(w) > Gnon-treated(w), and vice versaif the CDF of treated is smaller than the CDF of non-treated. The null in the two-sided test is H0 : Ftreated(w) =Gnon-treated(w) versus H1 : Ftreated(w) 6= Gnon-treated(w). F and G are the cumulative wage distributions that treatedand non-treated draw their wages from respectively.

104 Chapter 4

Table 4: p-values from Kolmogorov-Smirnov tests for equal hourly wage distributions between treated and non-treated individuals.

Men WomenStorstroem Southern Jutland Storstroem Southern Jutland

Year (1) (2) (1) (2) (1) (2) (1) (2)

2004 0.449 0.818 0.632 0.976 0.334 0.644 0.542 0.9192005 0.256 0.504 0.555 0.930 0.522 0.902 0.649 0.9822006 0.178 0.355 0.022 0.044 0.057 0.114 0.368 0.7002007 0.480 0.857 0.006 0.012 0.343 0.659 0.140 0.2792008 0.580 0.948 0.039 0.078 0.122 0.244 0.102 0.204

(1) One-sided tests. (2) Two-sided tests. Bold numbers are those ≤ 0.05.

for women in Storstroem 2006. The two-sided test also rejects equal hourly wage distribu-

tions between treated and non-treated in the male Southern Jutland sample for the years 2006

and 2007. In 2008 the two-sided test rejects equal distribution on a 10 percent significance

level. None of the samples (including men, 2005 in Storstroem county) rejects the null of equal

pre-experiment wage distributions.

3.2 Observables included

In the model estimation, we include a number of observables. These observables cover individ-

ual characteristics perceived to influence the transition out of unemployment and the explana-

tion of wages. They are personal variables (married, origin, education and age), labor market

variables (experience, occupation, all measured last week of November 2005 and lagged unem-

ployment duration) and experiment-specific variables (treatment and week of entry into unem-

ployment). In the wage specification we have dropped time of entry into the experiment and

lagged unemployment duration. Instead we control for the level of average log hourly wages

earned in 2004 and 2005 prior to the experiment. The observables chosen for the transition out

of unemployment are almost identical to those used by Blasco and Rosholm (2011), although

they also control for UI fund, but not for experience and education. In our wage specification,

we have chosen to include prior wages as well as the other observables partly because it is by

now common knowledge that former wages are important for future wages and partly to follow

in the footsteps of Arni et al. (2012). Ideally, we would have liked to include the precise wage

earned in the very last job before entering QB, but unfortunately the data is not rich enough to

give us this information.

The estimation is carried out using a mixed proportional hazard model (see section 4 below),

and one of the identifying assumptions is that the baseline hazards are piecewise-constant and

that the effect of the covariates affect them in a linear manner. This has been frequently used


in the transition out of unemployment, but treating wages as a hazard is not that common.

However, given the outlook of the hazard specification, if wages are perfectly log normal (which

is assumed in e.g. Mincer type log wage equations) then MPH wage estimates will boil down

to those of a linear log wage equation.

4 Econometric Framework

Analyzing treatment from active labor market programs in general requires that one controls for

the fact, that in general, it is not random who is allocated to which labor market program. This

can be done in several ways, but as we have access to a controlled experiment with randomized

allocation to treatment, the identification of treatment effects on our outcomes is secured under

some mild identifying restrictions.

We use a Mixed Proportional Hazard (MPH) framework to capture the effect of treatment

on post-unemployment wages. The first two key identifying assumptions are that participants

could not anticipate to be included in the experiment and that there are no general equilibrium

effects, i.e. that the potential outcome of any worker is independent of the treatment status of

any other worker. The third key assumption is that both hazards of leaving unemployment and

wage hazards follow a mixed proportional hazard structure. In section 4.1 below, we discuss

potential problems with the first identifying assumption. Concerning the no general equilib-

rium assumption, there could be reasons to suspect it would be violated. E.g. if control group

members were neglected by the case workers during the experiment simply because they had

to spend more time on the treatment group. Fortunately, the counties participating in the ex-

periment were given extra man-hours to cover the extra workload, minimizing this potential

threat. However, Gautier et al. (2012) examine potential general equilibrium effects of the QB

experiment by using comparison counties not in the experiment. They find that the job finding

rate for the control group was affected negatively because of the experiment.

Wages are measured by use of the same MPH structure as transitions from unemployment

to either employment or non-employment and will thus be capturing a treatment effect on the

probability of receiving a wage w∗ conditional on receiving at least a wage w∗. In this section,

we will discuss selection problems and go through the econometric methods used to address

these issues and estimate the average treatment effects on post-unemployment wages.

106 Chapter 4

4.1 Selection Bias

Even though the experiment analyzed here has a treatment and control group formed on the basis

of birthday (i.e. almost as random and exogenous treatment placement as we can get) it is only

random until after the first week and a half of the experiment. Hereafter, the treatment group

members have received the letter sketching out the entire “pilot study” course. It would be a very

strict assumption to assume that awareness of the program would not affect the behavior of the

treatment group members. Thus, if we do not control for this fact, there will be a selection bias

in the observed transition rates out of unemployment and into different jobs or other spells. In

other words, when the experiment starts and no individuals know anything about the experiment,

the hazard rate out of unemployment θ(t | x, ν, d), where x is observable covariates, d ∈ {0, 1}denotes membership of the treatment group and ν is unobserved heterogeneity, will be the same

for both groups in weeks t = {0, 1}. I.e.

θ(t = 0 | x, ν, d = 0) = θ(t = 0 | x, ν, d = 1) and

θ(t = 1 | x, ν, d = 0) = θ(t = 1 | x, ν, d = 1).

However, when treatment group members receive the information letter, dynamic selection

kicks in as the observed duration now depends on whether or not the individual was a mem-

ber of the treatment or control group. This is because the treatment group members now hold

better, or at least more, timing information on their future labor market program. It would be

too harsh an assumption not to allow for different types of individuals to select themselves into

different states. Since we only observe individuals leaving the experiment at a specific point in

time if they actually stayed in the experiment up until that point in time, the observed hazard

rate out of unemployment at time t ≥ 2 will be dependent on the unobserved heterogeneity and

conditional on staying at least until t. So

θ(t | x, d) = Eν [θ(t | x, ν, d) | T ≥ t],

will be the observed hazard out of unemployment at time t with T measuring realized unem-

ployment duration. In other words, without explicitly controlling for dynamic selection, it is not

possible to evaluate the effect of the experiment by comparing transition rates for the treatment

group and for the control group as this would capture both the direct effect and the dynamic


selection effects so we would have trouble identifying true effects. An appealing strategy to

account for dynamic selection is to model the selection out of unemployment simultaneously

with the hazard into post-unemployment outcomes.

4.2 The Mixed Proportional Hazard Model

4.2.1 Baseline Model

The MPH framework is attractable for this analysis for several reasons. First, the approach has

already been extensively used in the field experiment literature.14 Secondly, the MPH model

specifically captures the dynamic selection effects by controlling for the fact that observed dura-

tion depends on participation (See Abbring and van den Berg (2003) for proof of identification).

Let tue and tun denote duration in the experiment until leaving unemployment for employ-

ment and non-employment, respectively. The instantaneous hazard for an individual out of

unemployment into employment or non-employment at time t is then given by

θh(th | xh, d, νh) = λh(th) exp(x′hβh + d′δh) exp(νh), h ∈ {ue, un}, (1)

where xh is observed individual characteristics used in the instantaneous hazard of h, the base-

line hazard λh(th) is duration dependence, d = (1(treated≤ 30 weeks),1(treated> 30 weeks))

is a vector of two treatment dummies and νh is unobserved heterogeneity.15

Following the literature on duration analysis, the duration dependence parameter, λh, is

modeled as a step function to allow for a more flexible duration dependence,

λh(th) = exp

[∑

k

λh,k1(th ∈ k)

], (2)

with k a subscript for time intervals. 1(th ∈ k) is the index function indexing time intervals.

We normalize the duration dependence around one week of unemployment and allow for seven

levels of duration dependence in weeks, k ∈ {2−3, 4−5, 6−8, 9−16, 17−30, 31−52, 53+}.

Our baseline model jointly estimates the parameters in a maximum likelihood setting as

14See e.g. van den Berg and van der Klaauw (2006), Rosholm (2008) and Blasco and Rosholm (2011).15In practice, the treatment for an individual i is di = (1, 0) during the first 30 week-observations. If individual

i is still unemployed after week 30, the dummy switches to di = (0, 1) for the rest of his week-observations.

108 Chapter 4

(indexing by individuals instead of writing out the conditioning on x, d and ν)

L =I∏

i=1

∫

ν

θcue,iue,i (tue)Sue,i(tue)θ

cun,i

un,i (tun)Sun,i(tun)dG(ν), (3)

with ch,i’s are censoring variables indicating whether individual i goes to spell h or not, i.e.

cue,i = 1(individual i moves to employment). In this way we account for both right-censoring

of the unemployment spell and the employment/non-employment competing risks. ν = (νue, νun)

is a vector of unobserved heterogeneity with G(ν) its cumulative joint distribution. We include

two mass points in the distribution of each transition out of unemployment and in the wage

specification. This means we allow for eight different types in total. Optimally, Gaure, Røed

and Zhang (2007) lay out a recipe of looking for the best number of mass points in a model set-

ting like the one used in this paper. However, this is a fairly tedious process and with two mass

points in each transition and wages we end up having very few significant types, not suggesting

that we lack mass points, but rather indicating that the observables describe our samples rather

well.

Sh,i(th) = exp

[−∫ th

0

θh,i(z | xh, d, νh)dz], (4)

is the time-to-event specific survivor function. In the baseline model, we let ν have two support

points in each transition totaling four mass points (αj for j = 1, 2, . . . , J) that are allowed to be

freely correlated across transitions. For identification purposes, we normalize one mass point to

zero (here αJ ≡ 0). The mass point probabilities are given by

Pr(αj) =exp(αj)∑i exp(αi)

. (5)

Below, this model will be extended to capture post-unemployment wage dynamics.

4.2.2 Post-Unemployment Wages

Wages enter the model in the same mixed proportional hazard framework as duration in un-

employment, i.e. as a continuous wage hazard. The method of modeling wages as a hazard

goes back to Donald, Green and Paarsch (2000) while Cockx and Picchio (2012) and Arni et al.

(2012) extend it to a setting like the one used in this paper. Since wages are modeled by a

hazard approach, we are estimating the average treatment effect on the probability of earning


exactly w∗ conditional on earning at least w∗. I.e. the interpretation of treatment effects on

wages is upward. There are several advantages of including wages in the mixed proportional

hazard setting. First, the dynamic selection problem is incorporated in the MPH model. Second,

in this setting we do not have to impose any parametric distribution on wages. Notice, however,

if hourly wages are exponentially distributed, this setting would imply log wages to be linear in

observables and unobservables. If hourly wages are not exponential, we will through the MPH

structure be modeling proportionate shifts in the integrated hourly wage hazards (see Arni et al.

(2012)). Third, short term results have an upper estimate reservation wage interpretation which

we will elaborate on below.

We estimate the model for average hourly wages within the first, second and third year after

entering the QB experiment, wi,2006, wi,2007 and wi,2008. The instantaneous hazard into a given

wage level is composed as

θwm(wm | xwm , d, νwm) = λwm(wm) exp(x′wmβwm + d′wm

δwm) exp(νwm), (6)

for m ∈ {2006, 2007, 2008}. dwm is a dummy variable indicating treatment. Unlike in the

hazard out of unemployment where treatment were divided into treatment in the first 30 weeks

or later, the dummy for treatment in the wage hazard is simply treatment or not. λwm is the

baseline wage hazard, modeled piecewise constant (normalized around average hourly wages

below 100 Dkk.) to allow for a more flexible wage setting as

λwm(wm) = exp

[∑

l

λwm,l1(wm ∈ l)], (7)

with l being wage intervals, l ∈ {100− 140, 140− 180, 180− 220, 220− 240, 240− 280, 280−350, 350+}. When specifying wages in terms of a piecewise constant hazard, the wage distri-

bution will only be identified up the levels of these hazard terms. Obviously this restricts the

wage distribution considerably and is a strict assumption. One way to overcome the strictness

of the piecewise constant assumption is to include a large number of hazard intervals measuring

a histogram over wages (see e.g. Donald et al. (2000)). However, to do this, your need a lot of

observations since each interval is only identified if there are actually realized wages within the

interval. Given the size of the samples used in this paper, we have been forced to restrict the

wage intervals to the above mentioned.

110 Chapter 4

The wage “survivor” function is composed by16

Swm(wi,m) = exp

[−∫ wi,m

0

θwm(z | xwi,m, dwi,m

, νwi,m)dz

], (8)

which leads to three models with likelihoods given by

Lw2006 =I∏

i=1

∫

ν


cun,i

un,i (tun)Sun,i(tun)θcwi,2006w2006 (wi,2006)Sw2006(wi,2006)dG(ν),

(9)

Lw2007 =I∏

i=1

∫

ν


cun,i


(10)

Lw2008 =I∏

i=1

∫

ν


cun,i


(11)

where ν = (νue, νun, νwm). Again, each entry in νh, h ∈ {ue, un, wm}, has two points of

support so the total number of mass points in the unobserved heterogeneity distribution is eight

with α8 ≡ 0, and cwm = 1(wm > 0) is the average hourly wage censoring variable. xwm include

information on wages 2004 and 2005, experience, marriage, occupation and educational level

pre-QB, origin and age. The observable heterogeneity in the transition out of unemployment is

in the shape of experience, marriage, occupation and educational level pre-QB, week of entry

into QB, origin, age and lagged unemployment duration.

5 Results

In this section we present our findings of average treatment effects by participating in the inten-

sified ALMP scheme on post-unemployment wages.

5.1 Post-Unemployment Wages

Table 5 contains the estimated δwm parameters for m ∈ {2006, 2007, 2008} from equations

(9) to (11) on the male samples while Table 6 holds the female sample estimates (Table B4 to

16For the wage transition, the survivor function S(wm) measures individuals who have not exited into a wagelevel lower than wm. I.e. those who have not accepted (if offered) a job with a wage w∗∗ < wm.


Table 5: Wage specification estimation results for men (treatment effects singled out).

Men 2006 wages 2007 wages 2008 wagesAverage treatment effects St. S.J. St. S.J. St. S.J.

Treatment 0.090*** 0.001** 0.000 -0.106*** -0.036*** -0.091***(0.004) (0.001) (0.004) (0.002) (0.003) (0.002)

Percentage effect 0.094 0.001 0.000 -0.101 -0.035 -0.087

Observable heterogeneity yes yes yes yes yes yesUnobservable heterogeneity yes yes yes yes yes yesAvg. log likelihood -9,283 -7,434 -9,085 -7,345 -8,892 -7,254Individuals 1,446 1,150 1,446 1,150 1,446 1,150

*: Indicates statistical significance at the 10% level. **: At the 5% level. ***: At the 1% level.Percentage change is calculated as ∆ = exp(δ)− 1.All parameter estimates can be found in Table B4 and B5 in the appendix.St.: Storstroem county. S. J. Southern Jutland county.Note: The numbers presented here are average treatment effects on the wage hazard. I.e. a positive estimatecause an increase in the wage hazard which means that the probability of “exiting” earlier in the wagedistribution increases. A positive estimate on the wage hazard thus causes a lower expected wage level.

B7 present all parameter estimates). Remember, these estimates are effects on wage hazards.

A positive estimate increases the probability of “exiting” the wage distribution early, i.e. you

are more likely to receive a lower average hourly wage rate. For male individuals in Storstroem

county, treatment has significantly increased the probability of earning lower wages in 2006 than

non-treated. Participation in the experiment increased the 2006 wage hazard by 9.4 percent. For

Southern Jutland men, treatment has only slightly increased the 2006 wage hazard. In the short

term, men in both counties have thus seen negative or almost zero effects on their wage levels.

For women, the short term effects are more clear. Treated women in Southern Jutland have a

strong negative average treatment effect on the wage hazard of 1.3 percent. I.e. treatment have

increased their probability of earning higher wages than non-treated. Storstroem county treated

women, on the other hand, are affected by an increase of 12 percent in the 2006 wage hazard.

Treatment has increased their probability of earning lower wages than non-treated.

In the medium term, the 9 percent increase of the Storstroem male wage hazard from treat-

ment has vanished and has become insignificant. Treated men from Southern Jutland have also

gained in terms of a 10 percent decrease in the wage hazard in the medium term. The exact

opposite is the case for women. In storstroem, treatment has lowered the wage hazard by 3.7

percent and has had no effect on the Southern Jutland female wage hazard.

Moving to long term impacts of the intensified labor market program, for both Storstroem

and Southern Jutland men, treatment has significantly increased the probability of receiving

higher wages in 2008 than if there had been no treatment. The size of the gains from treatment

is a factor of more than double between the counties, with Southern Jutland men gaining most

from treatment both in the short, medium and long term. Women, on the other hand, reveal

112 Chapter 4

significant increases in the wage hazard in both counties, indicating that the long term wage

effects of treatment are negative. In storstroem, treatment increase the wage hazard by just

below two percent while the wage hazard in Southern Jutland is increased by 8.6 percent. The

long term wage effects for women are thus negative, and most so in Southern Jutland.

Estimating short term treatment effects of ALMP on wages by a hazard delivers an inter-

esting economic interpretation caused by its upward looking characteristic. Imagine an unem-

ployed worker searching for a job, receives an offer with a wage w∗. S/he will then, according

to standard search theory, accept the offer if and only if the wage offered is higher than his/her

reservation wage (see e.g. Burdett and Mortensen (1998)). For the pool of QB participants who

hold a job in year Y , the wage hazard delivers the probability that the average wage earned

during year Y is w∗ given that it is at least w∗. In other words, the wage hazard describes the

fraction of workers who are willing to work for wage w∗ but not necessarily for any wages

w∗∗ < w∗. Thus, we are also contributing with an upper estimate of revealed reservation wages

for those who actually accept a job offer. The short term average treatment effect reveals if

treatment conditional on everything else being equal has had an impact on the upper level of

reservation wages or not. Donald et al. (2000) discuss how one has to be careful interpreting

estimates of the hazard function for wages since it is not straightforward to say that a 200 Dkk

hourly wage job was at risk of being only a 150 Dkk hourly wage job. What we can conclude,

however, is that when we observe a 200 Dkk hourly wage job the worker has revealed to be

willing to accept at least an offer of a wage of 200 Dkk. Turning back to Table 5 and 6, we

see that especially Storstroem male short term estimates reveal large positive significant aver-

age treatment effects on the wage hazard. Southern Jutland female estimates are significantly

negative. Treated men and women in Storstroem county have thus lowered the upper estimate

of their reservation wages by increasing the wage hazard by 9.4 and 12.3 percent respectively.

Using the same field experiment as this paper, Gautier et al. (2012) analyze general equi-

librium effects by comparing the control group of the experiment to other newly unemployed

individuals living in other counties of Denmark. They find negative spill-overs from treatment

on the control group and show that outcomes from the experiment will be upward biased if not

accounting for externalities. They look at the exit rate out of unemployment, but it is very likely

their result of negative spill-overs transfers to wage outcomes as well. If so, then the significant

negative parameter estimates in the Southern Jutland samples are even stronger results.

To sum up, we find male post-unemployment wages to be overall more affected than female


Table 6: Wage specification estimation results for women (treatment effects singled out).

Women 2006 wages 2007 wages 2008 wagesAverage treatment effects St. S.J. St. S.J. St. S.J.

Treatment 0.116*** -0.013*** -0.038*** 0.000 0.020*** 0.083***(0.003) (0.004) (0.004) (0.002) (0.004) (0.003)

Percentage effect 0.123 -0.013 -0.037 0.000 0.021 0.086

Observable heterogeneity yes yes yes yes yes yesUnobservable heterogeneity yes yes yes yes yes yesAvg. log likelihood -6,410 -6,634 -6,263 -6,540 -6,142 -6,419Individuals 936 974 936 974 936 974

*: Indicates statistical significance at the 10% level. **: At the 5% level. ***: At the 1% level.Percentage change is calculated as ∆ = exp(δ)− 1.All parameter estimates can be found in Table B6 and B7 in the appendix.St.: Storstroem county. S. J. Southern Jutland county.Note: The numbers presented here are average treatment effects on the wage hazard. I.e. a positive estimatecause an increase in the wage hazard which means that the probability of “exiting” earlier in the wagedistribution increases. A positive estimate on the wage hazard thus causes a lower expected wage level.

wages. Within the male samples, Storstroem treated workers experience a short term negative

effect on wages which hereafter dies out in the medium term and becomes significant positive

in the long term. Treatment causes the Southern Jutland wage hazard to increase slightly in

the short term, and the decline rapidly in the medium term and stays on decreasing the wage

hazard in the long term. For females, Storstroem workers have a sharp short term increase in

the wage hazard, a decrease in the medium term wage hazard and a slight increase in the long

term hazard followed from treatment. In Southern Jutland, treatment caused a decrease in the

short term wage hazard, had no effect in the medium term and increased the long term wage

hazard. These results should be considered with Table 1 displaying regional unemployment

rates in mind. Storstroem workers face a higher local unemployment rate than Southern Jutland

workers do. In fact, the unemployment rate of Southern Jutland falls as low as to 1.3 percent in

2008 while Storstroem has unemployment rates of 3.9 in 2006 and 2.0 in 2008. These figures

will ceteris paribus put less pressure on wages in Southern Jutland than in Storstroem county or

if e.g. the unemployment rates had been at 2003 level of 6.1 percent.

5.1.1 Relating to the Literature

Our findings of men being more affected than women are consistent with those of Blasco and

Rosholm (2011) analyzing post-unemployment employment (self support) stability effects by

participating in QB. They find no significant treatment effects for women but find treated men

to experience a reduction of 9 percent in the transition rate back into unemployment. They

do not estimate their model on counties separately but include a dummy identifying Southern

Jutland. This approach does not give any significant effect on self support stability. Rosholm

114 Chapter 4

(2008) shows differences in the treatment effect on exit rates for the two counties (pooling men

and women together) with Southern Jutland increasing the exit rate out of unemployment more

than Storstroem, consistent with the 2006 unemployment rates (cf. Table 1) and our Southern

Jutland short term estimates of wages being less affected than Storstroem short term wages.

In relation to the international literature on the effects of labor market programs on post-

unemployment wages our findings are in line with Gaure et al. (2012) examining impacts of

(among other things) ALMP on earnings associated with the first job after unemployment. They

find participation in ALMP to raise the expected post-unemployment earnings level (i.e. in the

short term). Specifically, they find that for a typical worker, participation in very short ALMP

programs (one month) have an effect of -5 percent on post-unemployment wages while partici-

pation in long programs (nine) months increase wages by up to 10 percent. The findings in this

paper is thus comparable with those found in Norway despite the differences in the data settings.

As this paper, they model ALMP as one treatment independent of which type of program the

individual is being assigned to. They deviate from this paper in the measurement however. They

measure participation in ALMP or not, whereas this paper measures an intensification of ALMP

versus normal ALMP. Cockx and Picchio (2012) find that prolonging unemployment for young

school-leavers who have already been unemployed for nine months lowers the probability of

them finding a job, but have no effect on the subsequent starting wages. In the literature ana-

lyzing the effect of sanctions on post-unemployment wages, the typical finding is a reduction in

reservation wages and earnings in the short term (see Arni et al. (2012) and van den Berg and

Vikstrom (2009)).

The primary goal of setting up the QB experiment by the National Labor Market Authority

was to help newly unemployed individuals back to work faster through guidance and early

activation than would otherwise be achieved. Graversen and van Ours (2008a,b) and Rosholm

(2008) showed that the experiment did lead to a higher exit rate for treated than non-treated.

It is therefore interesting to analyze how the treatment has affected the post-unemployment

outcomes for these participants. We have now shown that for individuals participating in the

experiment, the average treatment effects on post-unemployment wages are ambiguous. In

Southern Jutland women see a positive treatment effect on short term wage levels and negative

treatment effects on their long term wage levels. Men have a small negative short term average

treatment effect and a large positive long term treatment effect on wages. In Storstroem county,

however, both men and women experience a negative short term treatment effect on wages.


Men have had no treatment effect on medium term wages, while women gained from treatment

in the medium term but lost in the long term. Men in Storstroem had a gain of around three

percent decrease in the wage hazard in the long term. The main difference in the setting of the

experiment between the counties was the meeting schedule. A newly unemployed worker in

Storstroem was supposed to meet with a case worker every week while the schedule was only

every other week in Southern Jutland. This can most likely explain some of the differences in

the results between the counties. In 2006, the local labor market tightness in Storstroem and

Southern Jutland was 0.23 and 0.26 respectively (cf. Table 7), and one could imagine, that if

Storstroem participants every week in contrast to Southern Jutland participants only every other

week, was told by the case worker that it is a tough labor market right now, he should be more

prone to lower his reservation wage, which would case the wage hazard to increase more in

Storstroem than in Southern Jutland.

5.1.2 State of the Labor Market

A primary difference between the economical setting during the experiment, however, was the

local unemployment rates (cf. Table 1). Nonetheless, unemployment in both counties was still

at historically low rates during the experiment, and it is plausible that they have not been the

driving force behind our results, and at the least both the treatment and control groups within

counties faced the same local labor market.

Of course, the unemployment rate is only showing one side of the state of the labor market

the unemployed workers are situated in. If e.g. there are no open jobs for the unemployed to

apply for, then a low unemployment rate will not indicate easy access to employment. The term

of labor market tightness (the ratio of vacant jobs and unemployed workers) reveals how many

open positions per unemployed are available and give a broader picture of the state of the labor

market. Table 7 holds labor market tightness for the two counties. In 2006 there are 0.23 and

0.26 vacant jobs per unemployed in Storstroem and Southern Jutland, respectively, a difference

of 14 percent. However, the tightness is still very low in both counties and we would not expect

the difference in the labor market tightness to solely explain the difference between short term

treatment effects in Storstroem versus Southern Jutland. We do, on the other hand, think that the

labor market tightness difference together with the difference in the experiment setting across

the counties can explain much of the difference in the treatment effect (cf. the discussion in

section 5.1.1). In the long term, however, there is a stronger difference in the labor market

116 Chapter 4

Table 7: Labor market summary.

Average # of vacancies Average # of unemployed Labor market tightness∗

County 2006 2007 2008 2006 2007 2008 2006 2007 2008

Storstroem 1,394 1,356 1,195 6,208 4,306 3,107 0.225 0.315 0.385Southern Jutland 1,458 1,361 1,339 5,680 3,748 2,352 0.257 0.363 0.569∗Labor market tightness calculated as the average number of vacancies divided by the average number of unemployed.Note: The number of vacant jobs is collected by the National Labor Market Board by gathering information fromthe local job centers.

tightness between the two counties with 0.39 vacant jobs per unemployed worker in Storstroem

and 0.57 vacant jobs per unemployed worker in Southern Jutland (a difference of 47 percent).

In other words, there are thus, all else equal, easier access to vacant jobs in Southern Jutland

than in Storstroem county in 2008. Given these market tightnesses, we would expect workers

in Southern Jutland, generally, to have better outside options than workers in Storstroem, and

if treatment has either increased the human capital of the treated individuals or taught them the

true state of the labor market, treated workers should be able to extract more rent, resulting in

higher treatment effects, in Southern Jutland than in Storstroem. This is also what we find, at

least for men (cf. Table 5).

5.2 Robustness – Log Wages

Modeling hourly wages by an MPH structure is appealing because of the dispensable assump-

tion of a specific distribution on wages. If, on the other hand, we assume hourly wages to be

log-normal the individual likelihood contribution of log hourly wages is

φ

(lnwi,m − x′i,wm

βwm − d′i,wmδwm − νi,wm

σwm

)ci,wm

, (12)

with φ(·) being the p.d.f. of the standard normal distribution and σwm is the standard deviation of

log wages in yearm. By incorporating this likelihood contribution in the baseline model instead

of the average hourly wage MPH structure above, we can estimate the effect of treatment on the

log hourly wage. If hourly wages are exactly exponentially distributed then this specification

should yield the exact same estimates as in the MPH structure model. We have incorporated (12)

and estimated it simultaneously with the baseline likelihood function. Table 8 shows selected

parameter estimates from this exercise. We only present parameter estimates on wages in the

short and long term for men (the samples with the most clear results above). Comparison of

average treatment effects on wage hazards and log wages in Table 8 shows that, as expected,

a negative effect on the hazard is followed by a positive effect on log wages and vice versa.


Table 8: Hourly wage and log hourly wage specification average treatment effects.

2006 wages 2008 wagesMen Hourly wages Log hourly wages Hourly wages Log hourly wages

StorstroemTreatment 0.090*** -0.005*** -0.036*** 0.003***

(0.004) (0.000) (0.003) (0.001)Southern Jutland

Treatment 0.001** -0.004*** -0.091*** 0.011***(0.001) (0.000) (0.002) (0.001)

*: Indicates statistical significance at the 10% level. **: At the 5% level. ***: At the 1% level.Note: Hourly wage estimates are average treatment effects on the hourly wage hazard. Log hourly wage estimatesare average treatment effects on the log hourly wage rate.Parameter estimates from log wages equations are not shown. Can be delivered upon request.

In terms of significance, the two approaches seem to deliver the same results. Assuming log

normal hourly wages also results in the conclusion that treated men in Storstroem county are hit

by significantly lower short term wages wages than non-treated, while treatment affects wages

positively in the long term. Likewise, for men in Southern Jutland treatment lowers the short

term wages and increases long term wages. If average hourly wages were perfectly log normal

distributed, we should have seen the exact same parameter estimates (with opposite signs).

Differences between hourly and log hourly wage estimates indicate that average hourly wages

are not exactly log normal, and we thus prefer using our wage hazard specification without the

assumption of a specific wage distribution.17

6 Conclusions

This paper uses a controlled field experiment of intensifying active labor market policies in

Denmark to analyze post-unemployment wages. The experiment was carried out to test whether

an early effort could help treated newly unemployed back to work faster than non-treated. The

primary treatments were frequent meetings with a case worker and faster entry into activation.

Previous studies analyzing the experiment have shown treatment to have positive effects on

the exit rate out of unemployment and to have lowered the re-entry rate into unemployment

for men. To take the analysis on post-unemployment outcomes further, we link the experiment

to Danish employment register data and construct hourly wages pre- and post-unemployment.

Using a mixed proportional hazard framework we control for dynamic selection and estimate

the average treatment effect on the wage hazard. We find male post-unemployment wages to

be overall more affected by treatment than female post-unemployment wages. Within the male

17Kolmogorov-Smirnov, Anderson-Darling and Shapiro-Wilk tests for normality (not shown, but available uponrequest) rejects the null hypothesis of normally distributed log wages for all samples.

118 Chapter 4

samples there are significant differences between the two counties Storstroem and Southern

Jutland. Men in Storstroem have a negative short term effect of treatment on wages resulting

in a 9 percent higher expected hourly wage hazard in 2006 but no significant medium effects

and a 3.7 percent lower expected wage hazard than non-treated in the long term. In Southern

Jutland, men have zero to moderate negative short term and large positive medium and long term

average treatment effects on wage levels, decreasing their expected 2008 hourly wage hazard

by 9.5 percent. Treated Southern Jutland women display a decrease in the wage hazard in the

short term but have no effects in the medium term and negative wage level effects in the long

term. Finally, treated women in Storstroem have a large increase in the expected hazard in the

short term, a decrease in the medium term and a slight increase of the wage hazard in the long

term.

ALMPs are meant to update or teach skills of the unemployed worker and to help him/her

realize the state of the labor market. The outcome on wages from these measures is not straight-

forward. If ALMP build on the human capital of the worker the resulting worker-firm match

should reflect the updated skills and the wage could very well be higher than if no treatment

were conducted. If the treatment effect on the other hand goes through guidance of the state of

the labor market resulting in advice to accept lower paying jobs than the worker would be will-

ing to without such guidance we would see lower wages as the outcome of ALMP. Our results

point to the latter in the Storstroem samples. Relating to standard search theory, unemployed

workers will accept a job if and only if the offer is better than their reservation wage. In this

framework, short term wages can be thought of as a revealed upper estimate of the worker’s

reservation wage. We thus find evidence towards that treatment has lowered the upper estimate

of the reservation wage of especially men in Storstroem county.

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AppendicesA Figures

Figure A1: Cumulative distribution graphs of average hourly wages, men.

0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage

Treatment group Control group

2004 Storstroem, men

0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage


2004 Southern Jutland, men

0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage



0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage



0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage



0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage



0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage



0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage



0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage



0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage



Figure A2: Cumulative distribution graphs of average hourly wages, women.

.2.4

.6.8

1

CD

F

100 150 200 250 300Hourly wage


2004 Storstroem, women

.2.4

.6.8

1

CD

F

100 150 200 250 300Hourly wage


2004 Southern Jutland, women .2.4

.6.8

1

CD

F

100 150 200 250 300Hourly wage


2005 Storstroem, women .2.4

.6.8

1

CD

F

100 150 200 250 300Hourly wage


2005 Southern Jutland, women

0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage



0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage



0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage



0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage



0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage



0.2

.4.6

.81

CD

F

100 150 200 250 300Hourly wage



122 Chapter 4

B Tables

Table B1: Outline of the treatments.

Weeks after registering for un-employment benefits


1.5 Letter of ’pilot study’ notification received1 CV/basic registration meeting with case

workerCV/basic registration meeting with caseworker2

34 Meeting with case worker5

Two-week JSA programme6789

Frequent meetings with case worker

101112 Meeting with case worker13141516 Between programs1718

Activation program


Post-treatment, transferred to normalscheme after week 39


Dashed lines separate treatment group programs. Solid lines separate control group programs.


Table B2: Occupational level in the last week of November each year.

Storstroem Southern JutlandOccupation Treatment Control Diff. Treatment Control Diff.

2004Management level 0.064 0.065 0.076 0.063Skilled level 0.070 0.082 0.068 0.063Unskilled level 0.740 0.730 0.740 0.735Unemployed 0.092 0.085 0.075 0.084Outside the labour force 0.033 0.038 0.042 0.055 *2005Management level 0.050 0.056 0.052 0.043Skilled level 0.059 0.070 0.061 0.064Unskilled level 0.712 0.690 * 0.692 0.695Unemployed 0.144 0.145 0.153 0.154Outside the labour force 0.035 0.039 0.042 0.0442006Management level 0.044 0.052 0.049 0.050Skilled level 0.089 0.086 0.079 0.077Unskilled level 0.728 0.690 ** 0.737 0.682 ***Unemployed 0.092 0.123 ** 0.099 0.146 ***Outside the labour force 0.048 0.048 0.036 0.045 *2007Management level 0.054 0.065 0.057 0.062Skilled level 0.084 0.085 0.075 0.088Unskilled level 0.667 0.689 0.728 0.679 **Unemployed 0.099 0.079 * 0.067 0.082 *Outside the labour force 0.096 0.082 0.074 0.089 *2008Management level 0.072 0.086 0.060 0.075 *Skilled level 0.078 0.083 0.101 0.092Unskilled level 0.591 0.577 0.637 0.601 *Unemployed 0.098 0.103 0.075 0.095 *Outside the labour force 0.162 0.151 0.127 0.137

Individuals 1,169 1,217 1,060 1,064

*: Indicates statistical significance at the 10% level. **: At the 5% level. ***: At the 1% level.

124 Chapter 4

Tabl

eB

3:D

escr

iptiv

eson

aver

age

hour

lyw

ages

,men

inth

eto

ppa

nela

ndw

omen

inth

ebo

ttom

pane

l.

Men

Trea

tmen

tC

ontr

olSt

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Obs

Ave

rage

S.D

.P1

0P2

5P5

0P7

5P9

0O

bsA

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D.

P10

P25

P50

P75

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2004

683

179.

053

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8.1

147.

517

0.2

198.

824

5.4

691

181.

457

.113

1.6

149.

716

8.9

199.

224

7.2

2005

698

186.

451

.913

5.1

154.

417

7.6

206.

624

9.2

694

192.

056

.713

9.5

157.

218

0.4

213.

325

9.3

2006

683

185.

257

.013

6.6

152.

317

3.3

200.

224

8.1

669

191.

163

.613

8.1

155.

417

6.6

210.

525

6.9

2007

646

189.

354

.814

0.5

158.

117

8.6

209.

825

8.2

639

190.

351

.813

8.8

158.

118

1.1

210.

525

9.4

2008

606

194.

557

.814

2.0

159.

818

1.6

213.

526

5.1

610

191.

154

.013

9.8

159.

218

1.7

211.

125

3.9

Sout

hern

Trea

tmen

tC

ontr

olJu

tland

Obs

Ave

rage

S.D

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0P2

5P5

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bsA

vera

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D.

P10

P25

P50

P75

P90

2004

529

172.

853

.012

1.6

143.

816

4.2

193.

523

4.5

545

173.

358

.111

8.8

145.

116

3.0

193.

023

2.9

2005

533

180.

052

.212

8.9

150.

517

0.5

200.

523

9.2

552

181.

555

.113

1.4

150.

417

0.3

198.

924

1.0

2006

536

179.

750

.613

3.7

151.

016

9.9

196.

323

8.9

533

181.

463

.913

3.8

146.

016

9.3

197.

222

7.8

2007

526

185.

352

.113

7.7

154.

217

5.0

207.

224

8.7

513

180.

045

.613

6.9

153.

517

2.2

200.

423

3.8

2008

502

191.

557

.614

0.2

155.

917

7.3

214.

425

9.3

495

185.

451

.513

6.9

154.

317

3.6

206.

825

0.0

Wom

enTr

eatm

ent

Con

trol

Stor

stro

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bsA

vera

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D.

P10

P25

P50

P75

P90

Obs

Ave

rage

S.D

.P1

0P2

5P5

0P7

5P9

0

2004

407

157.

061

.085

.712

9.2

148.

817

4.1

214.

944

815

7.5

6210

2.9

127.

914

8.5

173.

721

3.2

2005

410

165.

756

.497

.013

1.8

157.

919

0.4

233.

845

016

6.9

58.6

109.

413

2.2

158.

018

9.1

230.

820

0639

616

0.0

50.7

109.

813

3.7

152.

017

6.8

208.

743

617

0.1

64.1

120.

613

8.6

158.

918

1.4

222.

420

0737

316

3.1

48.3

118.

513

5.9

153.

918

3.1

229.

642

516

4.0

50.9

116.

313

7.0

154.

617

9.4

219.

020

0836

216

4.8

45.9

121.

013

5.4

159.

718

6.1

219.

540

416

7.6

47.5

125.

114

0.3

158.

118

3.3

225.

3

Sout

hern

Trea

tmen

tC

ontr

olJu

tland

Obs

Ave

rage

S.D

.P1

0P2

5P5

0P7

5P9

0O

bsA

vera

geS.

D.

P10

P25

P50

P75

P90

2004

446

151.

850

.198

.112

4.8

146.

116

9.4

206.

944

015

3.3

51.7

98.9

125.

514

6.9

171.

820

4.1

2005

448

161.

356

.710

2.3

130.

215

5.5

180.

621

8.9

428

164.

957

.710

3.8

132.

515

4.5

184.

222

9.5

2006

442

165.

268

.411

2.5

133.

415

1.1

177.

622

4.4

408

166.

061

.512

0.4

135.

015

2.1

174.

722

7.0

2007

423

161.

050

.511

4.0

133.

915

2.4

179.

921

8.1

420

161.

948

.011

9.0

134.

315

5.5

177.

920

7.7

2008

404

164.

948

.411

9.2

137.

715

6.0

185.

221

6.7

399

172.

660

.112

3.7

138.

715

9.2

185.

922

7.0


Table B4: Men, Storstroem county.

2006 wages 2007 wages 2008 wagesEstimate S.D. Estimate S.D. Estimate S.D.

Transition U→ EExperience 0.030 0.000 0.037 0.000 0.041 0.000Experience squared/100 -0.068 0.000 -0.086 0.001 -0.102 0.002Treatment (U ≤ 30 weeks) 0.269 0.002 0.283 0.000 0.284 0.003Treatment (U > 30 weeks) 0.377 0.016 0.408 0.008 0.383 0.014Married 0.059 0.004 0.049 0.001 0.052 0.003Occupation, top 2005 -0.171 0.012 -0.168 0.016 -0.112 0.014Occupation, middle 2005 0.536 0.002 0.609 0.004 0.624 0.003Occupation, base 2005 0.359 0.002 0.404 0.004 0.425 0.002Occupation, unempl. 2005 -0.338 0.007 -0.269 0.008 -0.269 0.007Education, vocational 2006 0.127 0.002 0.117 0.004 0.113 0.003Education, bachelor 2006 -0.191 0.008 -0.247 0.003 -0.240 0.010Education, master 2006 -0.112 0.016 -0.231 0.008 -0.244 0.021Entry week, 45 - 46, 2005 -0.035 0.008 0.035 0.008 0.039 0.015Entry week, 47 - 48, 2005 -0.321 0.004 -0.261 0.007 -0.262 0.007Entry week, 49 - 50, 2005 -0.271 0.008 -0.199 0.004 -0.203 0.006Entry week, 51 - 52, 2005 -0.071 0.004 -0.012 0.003 -0.022 0.005Entry week, 01 - 02, 2006 -0.165 0.004 -0.075 0.008 -0.094 0.005Entry week, 03 - 04, 2006 0.528 0.004 0.612 0.008 0.607 0.005Entry week, 05 - 06, 2006 -0.189 0.006 -0.057 0.004 -0.042 0.007Entry week, 07 - 08, 2006 0.242 0.008 0.314 0.008 0.329 0.012Western immigrant 0.146 0.002 0.031 0.002 0.052 0.002Non-western immigrant -0.370 0.006 -0.512 0.016 -0.495 0.014Age 25 - 29 -0.235 0.002 -0.165 0.005 -0.173 0.006Age 30 - 39 -0.351 0.004 -0.325 0.004 -0.318 0.005Age 40 - 49 -0.474 0.004 -0.436 0.004 -0.441 0.003Age 50 + -0.525 0.004 -0.468 0.002 -0.469 0.005Lagged Uempl. duration, 7 - 8 weeks 0.382 0.016 0.314 0.016 0.327 0.013Lagged Uempl. duration, 9 - 16 weeks 0.279 0.007 0.232 0.008 0.233 0.011Lagged Uempl. duration, 17 - 28 weeks 0.148 0.004 0.080 0.008 0.080 0.007Lagged Uempl. duration, 29 - 52 weeks 0.072 0.004 0.025 0.004 0.018 0.006Lagged Uempl. duration, 52 + weeks -0.319 0.003 -0.378 0.004 -0.373 0.005Baseline hazard 2 - 3 weeks 0.914 0.008 0.955 0.004 0.967 0.006Baseline hazard 4 - 5 weeks 1.117 0.004 1.161 0.004 1.177 0.001Baseline hazard 6 - 8 weeks 0.997 0.008 1.050 0.008 1.068 0.006Baseline hazard 9 - 16 weeks 1.310 0.004 1.377 0.000 1.404 0.003Baseline hazard 17 - 30 weeks 1.631 0.004 1.817 0.007 1.853 0.003Baseline hazard 31 - 52 weeks 1.554 0.002 1.953 0.008 2.008 0.012Baseline hazard 53 + weeks 1.325 0.012 1.961 0.008 1.942 0.014νe1 -3.919 0.000 -4.040 0.004 -4.101 0.002νe2 -5.339 0.003 -5.908 0.016 -5.914 0.014

Transition U→ NExperience 0.118 0.001 0.124 0.000 0.130 0.001Experience squared/100 -0.513 0.002 -0.541 0.001 -0.563 0.002Treatment (U ≤ 30 weeks) -0.079 0.008 -0.072 0.008 -0.072 0.007Treatment (U > 30 weeks) 0.200 0.032 0.218 0.016 0.236 0.022Married 0.396 0.008 0.403 0.008 0.392 0.014Occupation, top 2005 -0.923 0.026 -0.909 0.016 -0.956 0.058Occupation, middle 2005 -0.190 0.008 -0.175 0.008 -0.174 0.014Occupation, base 2005 0.038 0.003 0.054 0.008 0.055 0.007Occupation, unempl. 2005 -1.605 0.032 -1.576 0.028 -1.538 0.028Education, vocational 2006 0.686 0.006 0.686 0.008 0.680 0.013Education, bachelor 2006 0.975 0.032 0.977 0.016 0.998 0.038Education, master 2006 -0.181 0.032 -0.061 0.032 -0.063 0.076Entry week, 45 - 46, 2005 -0.813 0.032 -0.797 0.032 -0.712 0.028Entry week, 47 - 48, 2005 -0.749 0.012 -0.730 0.016 -0.671 0.028Entry week, 49 - 50, 2005 0.013 0.016 0.045 0.016 0.087 0.034Entry week, 51 - 52, 2005 -0.771 0.016 -0.762 0.016 -0.715 0.028Entry week, 01 - 02, 2006 -1.383 0.006 -1.378 0.004 -1.319 0.014Entry week, 03 - 04, 2006 -0.762 0.032 -0.756 0.016 -0.707 0.028Entry week, 05 - 06, 2006 -1.312 0.032 -1.279 0.016 -1.215 0.012Entry week, 07 - 08, 2006 -1.449 0.032 -1.425 0.020 -1.364 0.016Western immigrant 0.993 0.002 1.122 0.002 1.127 0.007Non-western immigrant 0.692 0.064 0.835 0.032 0.837 0.008Age 25 - 29 0.673 0.016 0.710 0.016 0.736 0.028

Table continues on next page.Bold face numbers indicate statistical significance at the 5 % level.

126 Chapter 4

Table B4 continued: Men, Storstroem county.


Age 30 - 39 0.121 0.016 0.135 0.030 0.178 0.024Age 40 - 49 0.555 0.012 0.587 0.016 0.626 0.014Age 50 + 0.137 0.008 0.194 0.000 0.236 0.015Lagged Uempl. duration, 7 - 8 weeks 2.095 0.128 2.219 0.064 2.135 0.024Lagged Uempl. duration, 9 - 16 weeks -0.079 0.026 -0.079 0.028 -0.100 0.028Lagged Uempl. duration, 17 - 28 weeks 0.871 0.025 0.870 0.028 0.871 0.024Lagged Uempl. duration, 29 - 52 weeks -0.631 0.013 -0.613 0.012 -0.611 0.028Lagged Uempl. duration, 52 + weeks -0.380 0.012 -0.394 0.016 -0.392 0.025Baseline hazard 2 - 3 weeks -1.323 0.032 -1.316 0.032 -1.314 0.028Baseline hazard 4 - 5 weeks -1.558 0.032 -1.558 0.032 -1.525 0.055Baseline hazard 6 - 8 weeks -0.491 0.016 -0.497 0.016 -0.505 0.028Baseline hazard 9 - 16 weeks -0.526 0.006 -0.523 0.016 -0.522 0.014Baseline hazard 17 - 30 weeks -0.378 0.014 -0.365 0.004 -0.365 0.014Baseline hazard 31 - 52 weeks -0.601 0.016 -0.583 0.016 -0.598 0.035Baseline hazard 53 + weeks -0.420 0.016 -0.406 0.016 -0.416 0.014νn1 -2.958 0.510 -4.763 0.128 -4.186 0.220νn2 -3.289 0.008 -3.518 0.004 -3.625 0.007

WagesExperience 0.013 0.000 0.009 0.000 0.002 0.000Experience squared/100 -0.056 0.000 -0.029 0.001 -0.033 0.000Treament 0.090 0.004 0.000 0.004 -0.036 0.003Married -0.053 0.002 -0.085 0.002 -0.015 0.003Occupation, top 2005 0.100 0.016 0.744 0.008 0.580 0.017Occupation, middle 2005 0.535 0.008 0.896 0.001 0.878 0.003Occupation, base 2005 0.575 0.004 0.927 0.008 0.913 0.003Occupation, unempl. 2005 0.740 0.002 1.004 0.007 0.935 0.007Education, vocational 2006 -0.156 0.001 -0.066 0.002 -0.102 0.003Education, bachelor 2006 -0.436 0.016 -0.319 0.004 -0.463 0.011Education, master 2006 -0.494 0.016 -0.456 0.012 -0.766 0.028Western immigrant -0.310 0.016 -0.351 0.003 -0.233 0.028Non-western immigrant 0.065 0.008 0.214 0.014 0.287 0.010Age 25 - 29 0.045 0.001 -0.109 0.008 -0.093 0.007Age 30 - 39 0.041 0.001 -0.060 0.000 0.001 0.001Age 40 - 49 0.129 0.002 0.121 0.004 0.202 0.002Age 50 + 0.017 0.004 0.066 0.004 0.221 0.001Log Wage 2004 -0.081 0.001 -0.130 0.000 -0.080 0.000Log Wage 2005 -0.216 0.000 -0.165 0.001 -0.181 0.001Baseline wage hazard 100 - 140 dkk. 3.272 0.004 2.839 0.001 2.716 0.005Baseline wage hazard 140 - 180 dkk. 4.477 0.001 4.205 0.001 4.107 0.000Baseline wage hazard 180 - 220 dkk. 4.573 0.004 4.399 0.004 4.403 0.008Baseline wage hazard 220 - 240 dkk. 4.460 0.001 4.466 0.016 4.321 0.002Baseline wage hazard 240 - 280 dkk. 4.594 0.002 4.144 0.008 4.120 0.014Baseline wage hazard 280 - 350 dkk. 4.478 0.006 4.493 0.016 4.209 0.011Baseline wage hazard 350 + dkk. 4.270 0.016 4.701 0.012 4.533 0.003νw1 -5.401 0.001 -5.578 0.002 -5.648 0.006νw2 -5.259 0.008 -5.132 0.002 -5.283 0.001

α1 -11.693 1.020 -15.138 2.040 -16.321 2.200α2 -8.362 2.040 -8.175 0.510 -8.066 1.100α3 2.753 0.016 2.476 0.008 2.374 0.028α4 -6.725 1.020 -7.583 1.020 -8.136 1.100α5 -5.785 0.765 -8.592 0.765 -10.257 2.860α6 -5.445 2.040 -6.253 0.128 -5.755 0.275α7 -0.880 0.032 -7.253 0.510 -6.748 1.100α8 0.000 0.000 0.000Pr(α1) 0.000 0.000 0.000Pr(α2) 0.000 0.000 0.000Pr(α3) 0.917 0.922 0.914Pr(α4) 0.000 0.000 0.000Pr(α5) 0.000 0.000 0.000Pr(α6) 0.000 0.000 0.000Pr(α7) 0.024 0.000 0.000Pr(α8) 0.059 0.078 0.085

Average log likehood -9283.37 -9084.75 -8892.02Individuals 1,446 1,446 1,446

Bold face numbers indicate statistical significance at the 5 % level.


Table B5: Men, Southern Jutland county.


Transition U→ EExperience 0.059 0.000 0.052 0.000 0.051 0.000Experience squared/100 -0.184 0.001 -0.159 0.001 -0.154 0.000Treatment (U ≤ 30 weeks) 0.124 0.004 0.127 0.003 0.126 0.001Treatment (U > 30 weeks) 0.418 0.008 0.459 0.011 0.455 0.004Married 0.194 0.001 0.194 0.003 0.194 0.001Occupation, top 2005 0.445 0.012 0.483 0.008 0.453 0.004Occupation, middle 2005 0.645 0.002 0.689 0.003 0.680 0.000Occupation, base 2005 0.478 0.004 0.521 0.002 0.507 0.002Occupation, unempl. 2005 -0.134 0.005 -0.126 0.006 -0.145 0.000Education, vocational 2006 0.086 0.003 0.107 0.002 0.104 0.002Education, bachelor 2006 -0.170 0.006 -0.164 0.006 -0.160 0.002Education, master 2006 -0.141 0.016 -0.115 0.012 -0.126 0.004Entry week, 45 - 46, 2005 -0.274 0.008 -0.295 0.006 -0.289 0.002Entry week, 47 - 48, 2005 -0.676 0.004 -0.697 0.004 -0.703 0.000Entry week, 49 - 50, 2005 -0.569 0.006 -0.598 0.008 -0.597 0.002Entry week, 51 - 52, 2005 -0.303 0.004 -0.327 0.005 -0.326 0.001Entry week, 01 - 02, 2006 -0.297 0.004 -0.312 0.004 -0.319 0.002Entry week, 03 - 04, 2006 0.080 0.004 0.071 0.004 0.062 0.002Entry week, 05 - 06, 2006 -0.344 0.007 -0.357 0.007 -0.366 0.002Entry week, 07 - 08, 2006 0.189 0.000 0.171 0.007 0.170 0.002Western immigrant -0.305 0.002 -0.315 0.001 -0.327 0.000Non-western immigrant -0.566 0.006 -0.613 0.008 -0.632 0.002Age 25 - 29 -0.468 0.004 -0.465 0.007 -0.473 0.002Age 30 - 39 -0.590 0.005 -0.577 0.004 -0.589 0.001Age 40 - 49 -0.491 0.004 -0.471 0.003 -0.488 0.002Age 50 + -0.737 0.003 -0.738 0.003 -0.752 0.002Lagged Uempl. duration, 7 - 8 weeks 0.647 0.008 0.635 0.009 0.639 0.002Lagged Uempl. duration, 9 - 16 weeks 0.195 0.006 0.204 0.006 0.198 0.002Lagged Uempl. duration, 17 - 28 weeks 0.049 0.007 0.058 0.004 0.050 0.004Lagged Uempl. duration, 29 - 52 weeks 0.078 0.004 0.070 0.004 0.070 0.001Lagged Uempl. duration, 52 + weeks -0.178 0.004 -0.176 0.003 -0.177 0.001Baseline hazard 2 - 3 weeks 0.824 0.001 0.806 0.004 0.798 0.002Baseline hazard 4 - 5 weeks 1.003 0.006 0.989 0.003 0.979 0.004Baseline hazard 6 - 8 weeks 1.083 0.004 1.076 0.004 1.069 0.001Baseline hazard 9 - 16 weeks 1.126 0.004 1.132 0.004 1.124 0.002Baseline hazard 17 - 30 weeks 1.362 0.004 1.396 0.009 1.393 0.002Baseline hazard 31 - 52 weeks 0.660 0.008 0.739 0.006 0.732 0.001Baseline hazard 53 + weeks 0.683 0.006 0.837 0.008 0.824 0.004νe1 -4.341 0.004 -4.492 0.008 -4.419 0.004νe2 -3.367 0.002 -3.347 0.004 -3.297 0.001

Transition U→ NExperience -0.060 0.000 -0.045 0.000 -0.032 0.001Experience squared/100 0.115 0.001 0.076 0.001 0.033 0.001Treatment (U ≤ 30 weeks) 0.282 0.008 0.238 0.010 0.250 0.002Treatment (U > 30 weeks) 0.034 0.016 -0.046 0.019 -0.026 0.008Married 0.234 0.006 0.228 0.010 0.221 0.004Occupation, top 2005 0.912 9.180 1.067 11.220 1.501 15.300Occupation, middle 2005 0.358 0.008 0.294 0.004 0.299 0.004Occupation, base 2005 1.451 0.008 1.342 0.008 1.325 0.008Occupation, unempl. 2005 -1.150 0.012 -1.168 0.016 -1.220 0.008Education, vocational 2006 1.544 0.006 1.491 0.008 1.476 0.004Education, bachelor 2006 1.683 0.016 1.612 0.016 1.596 0.008Education, master 2006 0.802 0.032 0.733 0.064 0.818 0.008Entry week, 45 - 46, 2005 0.493 0.016 0.565 0.022 0.512 0.016Entry week, 47 - 48, 2005 -0.792 0.012 -0.722 0.016 -0.759 0.008Entry week, 49 - 50, 2005 1.152 0.016 1.148 0.032 1.061 0.008Entry week, 51 - 52, 2005 -0.690 0.012 -0.635 0.016 -0.647 0.008Entry week, 01 - 02, 2006 -0.932 0.012 -0.896 0.011 -0.952 0.002Entry week, 03 - 04, 2006 0.499 0.016 0.522 0.028 0.460 0.008Entry week, 05 - 06, 2006 -1.833 0.016 -1.725 0.016 -1.775 0.008Entry week, 07 - 08, 2006 -0.187 0.016 -0.185 0.016 -0.268 0.004Western immigrant 1.129 0.004 0.991 0.002 1.043 0.002Non-western immigrant -0.566 0.016 -0.617 0.022 -0.519 0.016Age 25 - 29 0.800 0.016 0.632 0.016 0.600 0.004Age 30 - 39 0.989 0.008 0.845 0.016 0.813 0.004


128 Chapter 4

Table B5 continued: Men, Southern Jutland county.


Age 40 - 49 0.853 0.008 0.709 0.016 0.630 0.008Age 50 + -0.302 0.008 -0.431 0.008 -0.467 0.004Lagged Uempl. duration, 7 - 8 weeks -0.331 0.032 -0.329 0.032 -0.385 0.008Lagged Uempl. duration, 9 - 16 weeks -1.842 0.016 -1.748 0.032 -1.732 0.016Lagged Uempl. duration, 17 - 28 weeks -0.956 0.008 -0.915 0.012 -0.941 0.016Lagged Uempl. duration, 29 - 52 weeks 0.181 0.012 0.154 0.012 0.133 0.004Lagged Uempl. duration, 52 + weeks -0.066 0.012 -0.095 0.016 -0.092 0.008Baseline hazard 2 - 3 weeks -1.564 0.016 -1.584 0.024 -1.584 0.008Baseline hazard 4 - 5 weeks -2.070 0.032 -2.078 0.056 -2.085 0.032Baseline hazard 6 - 8 weeks -1.747 0.008 -1.766 0.032 -1.789 0.016Baseline hazard 9 - 16 weeks -0.675 0.012 -0.709 0.014 -0.711 0.004Baseline hazard 17 - 30 weeks -0.889 0.010 -0.926 0.014 -0.936 0.008Baseline hazard 31 - 52 weeks -0.078 0.016 -0.130 0.016 -0.163 0.008Baseline hazard 53 + weeks 2.007 0.012 1.920 0.016 1.865 0.004νn1 -3.741 0.007 -3.479 0.004 -3.481 0.004νn2 -7.951 0.016 -7.569 0.016 -7.523 0.008

WagesExperience 0.030 0.000 0.032 0.000 0.054 0.000Experience squared/100 -0.087 0.001 -0.134 0.000 -0.163 0.000Treatment 0.001 0.001 -0.106 0.002 -0.091 0.002Married -0.041 0.002 -0.088 0.004 -0.138 0.002Occupation, top 2005 -0.016 0.008 -0.258 0.016 -0.172 0.004Occupation, middle 2005 0.232 0.004 0.222 0.001 0.351 0.002Occupation, base 2005 0.210 0.004 0.227 0.001 0.264 0.001Occupation, unempl. 2005 0.312 0.004 0.265 0.008 0.431 0.001Education, vocational 2006 -0.160 0.004 -0.160 0.003 -0.210 0.002Education, bachelor 2006 -0.229 0.004 -0.356 0.008 -0.340 0.004Education, master 2006 -0.458 0.016 -1.069 0.014 -0.206 0.004Western immigrant 0.117 0.008 -0.001 0.006 0.145 0.002Non-western immigrant 0.007 0.008 0.182 0.009 0.042 0.004Age 25 - 29 -0.183 0.007 0.077 0.004 0.041 0.002Age 30 - 39 -0.408 0.004 -0.120 0.004 -0.158 0.002Age 40 - 49 -0.248 0.004 0.049 0.008 -0.004 0.002Age 50 + -0.262 0.004 0.203 0.002 0.131 0.001Log Wage 2004 -0.047 0.000 -0.055 0.001 -0.100 0.000Log Wage 2005 -0.103 0.000 -0.085 0.000 -0.056 0.000Baseline wage hazard 100 - 140 dkk. 3.458 0.004 2.932 0.001 2.643 0.002Baseline wage hazard 140 - 180 dkk. 4.437 0.001 4.036 0.004 3.983 0.000Baseline wage hazard 180 - 220 dkk. 4.595 0.003 4.288 0.001 4.100 0.002Baseline wage hazard 220 - 240 dkk. 4.286 0.008 4.343 0.016 4.097 0.002Baseline wage hazard 240 - 280 dkk. 4.301 0.008 4.433 0.003 4.165 0.004Baseline wage hazard 280 - 350 dkk. 3.891 0.000 3.882 0.016 3.966 0.002Baseline wage hazard 350 + dkk. 3.726 0.016 4.689 0.012 4.184 0.004νw1 -5.548 0.000 -5.450 0.004 -5.557 0.000νw2 -5.570 0.004 -5.173 0.008 -5.378 0.008

α1 -9.242 0.510 -7.431 0.128 -10.410 1.020α2 -4.281 1.020 -2.614 0.195 -1.026 0.004α3 -3.748 0.510 -4.598 0.255 -3.482 0.128α4 1.347 0.008 1.349 0.016 1.232 0.002α5 3.750 0.016 3.728 0.002 3.639 0.008α6 -4.248 4.080 -4.949 0.510 -5.343 0.510α7 -0.822 0.255 -3.062 0.367 -1.082 0.255α8 0.000 0.000 0.000Pr(α1) 0.000 0.000 0.000Pr(α2) 0.000 0.002 0.008Pr(α3) 0.001 0.000 0.001Pr(α4) 0.080 0.083 0.079Pr(α5) 0.889 0.893 0.881Pr(α6) 0.000 0.000 0.000Pr(α7) 0.009 0.001 0.008Pr(α8) 0.021 0.022 0.023

Average log likehood -7434.00 -7344.58 -7254.15Individuals 1,150 1,150 1,150



Table B6: Women, Storstroem county.


Transition U→ EExperience -0.033 0.000 -0.033 0.000 -0.030 0.000Experience squared/100 0.159 0.001 0.162 0.001 0.151 0.000Treatment (U ≤ 30 weeks) 0.186 0.003 0.187 0.005 0.188 0.001Treatment (U > 30 weeks) -0.016 0.008 -0.012 0.010 -0.016 0.004Married 0.081 0.003 0.080 0.005 0.079 0.001Occupation, top 2005 -0.132 0.008 -0.130 0.012 -0.130 0.008Occupation, middle 2005 0.281 0.002 0.285 0.005 0.287 0.000Occupation, base 2005 0.136 0.004 0.141 0.006 0.142 0.002Occupation, unempl. 2005 -0.116 0.004 -0.107 0.006 -0.104 0.004Education, vocational 2006 0.095 0.002 0.094 0.006 0.092 0.002Education, bachelor 2006 0.003 0.004 0.003 0.007 0.004 0.002Education, master 2006 0.015 0.010 0.019 0.015 0.029 0.008Entry week, 45 - 46, 2005 0.089 0.007 0.090 0.010 0.090 0.004Entry week, 47 - 48, 2005 -0.065 0.005 -0.063 0.009 -0.059 0.004Entry week, 49 - 50, 2005 -0.026 0.008 -0.023 0.010 -0.020 0.004Entry week, 51 - 52, 2005 0.146 0.006 0.152 0.009 0.160 0.004Entry week, 01 - 02, 2006 -0.076 0.004 -0.072 0.006 -0.068 0.002Entry week, 03 - 04, 2006 0.009 0.007 0.014 0.009 0.018 0.004Entry week, 05 - 06, 2006 -0.124 0.004 -0.118 0.007 -0.116 0.002Entry week, 07 - 08, 2006 -0.224 0.008 -0.220 0.008 -0.218 0.004Western immigrant 0.197 0.002 0.229 0.005 0.265 0.001Non-western immigrant -0.210 0.008 -0.180 0.010 -0.138 0.004Age 25 - 29 -0.033 0.006 -0.028 0.008 -0.029 0.002Age 30 - 39 -0.017 0.003 -0.009 0.006 -0.014 0.002Age 40 - 49 -0.251 0.004 -0.241 0.004 -0.245 0.002Age 50 + -0.431 0.004 -0.423 0.006 -0.426 0.002Lagged Uempl. duration, 7 - 8 weeks -0.366 0.018 -0.369 0.026 -0.377 0.008Lagged Uempl. duration, 9 - 16 weeks 0.152 0.008 0.150 0.012 0.152 0.002Lagged Uempl. duration, 17 - 28 weeks 0.039 0.008 0.038 0.009 0.035 0.004Lagged Uempl. duration, 29 - 52 weeks -0.121 0.004 -0.120 0.007 -0.123 0.004Lagged Uempl. duration, 52 + weeks -0.086 0.003 -0.088 0.006 -0.091 0.002Baseline hazard 2 - 3 weeks 0.563 0.008 0.575 0.010 0.591 0.004Baseline hazard 4 - 5 weeks 0.445 0.007 0.459 0.008 0.473 0.004Baseline hazard 6 - 8 weeks 0.526 0.005 0.540 0.008 0.552 0.004Baseline hazard 9 - 16 weeks 0.806 0.004 0.822 0.005 0.831 0.001Baseline hazard 17 - 30 weeks 0.750 0.004 0.764 0.008 0.779 0.001Baseline hazard 31 - 52 weeks 0.379 0.004 0.393 0.008 0.406 0.004Baseline hazard 53 + weeks 0.514 0.006 0.529 0.008 0.543 0.004νe1 -3.786 0.001 -3.845 0.002 -3.904 0.001νe2 0.179 2.040 0.520 6.120 2.227 22.440

Transition U→ NExperience 0.055 0.000 0.063 0.001 0.077 0.000Experience squared/100 -0.327 0.002 -0.354 0.003 -0.399 0.002Treatment (U ≤ 30 weeks) -0.091 0.008 -0.089 0.010 -0.082 0.004Treatment (U > 30 weeks) -0.421 0.012 -0.420 0.015 -0.413 0.008Married -0.211 0.004 -0.200 0.009 -0.196 0.004Occupation, top 2005 -0.018 0.032 -0.038 0.040 -0.066 0.016Occupation, middle 2005 -0.406 0.006 -0.423 0.009 -0.445 0.004Occupation, base 2005 -0.105 0.010 -0.118 0.016 -0.133 0.008Occupation, unempl. 2005 -0.730 0.010 -0.740 0.014 -0.733 0.008Education, vocational 2006 0.199 0.007 0.198 0.009 0.193 0.004Education, bachelor 2006 0.262 0.012 0.267 0.016 0.274 0.008Education, master 2006 0.232 0.032 0.226 0.056 0.241 0.016Entry week, 45 - 46, 2005 -0.003 0.016 -0.018 0.020 -0.031 0.008Entry week, 47 - 48, 2005 -0.312 0.016 -0.308 0.020 -0.282 0.008Entry week, 49 - 50, 2005 -0.116 0.012 -0.109 0.020 -0.090 0.008Entry week, 51 - 52, 2005 0.790 0.016 0.778 0.026 0.785 0.008Entry week, 01 - 02, 2006 -0.439 0.009 -0.441 0.014 -0.425 0.008Entry week, 03 - 04, 2006 -0.402 0.012 -0.401 0.016 -0.381 0.008Entry week, 05 - 06, 2006 -0.780 0.008 -0.787 0.015 -0.776 0.008Entry week, 07 - 08, 2006 -0.002 0.016 -0.006 0.024 0.008 0.008Western immigrant 0.518 0.005 0.485 0.007 0.451 0.004Non-western immigrant 0.475 0.016 0.459 0.024 0.447 0.008Age 25 - 29 -0.340 0.010 -0.368 0.015 -0.392 0.004Age 30 - 39 -0.660 0.007 -0.696 0.014 -0.736 0.004


130 Chapter 4

Table B6 continued: Women, Storstroem county.


Age 40 - 49 -0.373 0.012 -0.429 0.013 -0.492 0.008Age 50 + -0.914 0.008 -0.972 0.012 -1.031 0.008Lagged Uempl. duration, 7 - 8 weeks -0.329 4.080 0.377 4.080 -0.444 6.120Lagged Uempl. duration, 9 - 16 weeks 0.563 0.016 0.558 0.028 0.557 0.008Lagged Uempl. duration, 17 - 28 weeks -1.058 0.032 -1.050 0.042 -1.029 0.016Lagged Uempl. duration, 29 - 52 weeks 0.306 0.016 0.309 0.024 0.313 0.008Lagged Uempl. duration, 52 + weeks -0.086 0.008 -0.084 0.011 -0.085 0.004Baseline hazard 2 - 3 weeks -1.827 0.026 -1.839 0.030 -1.841 0.016Baseline hazard 4 - 5 weeks -1.537 0.016 -1.540 0.032 -1.541 0.016Baseline hazard 6 - 8 weeks -1.272 0.016 -1.276 0.020 -1.281 0.008Baseline hazard 9 - 16 weeks -0.785 0.008 -0.790 0.012 -0.791 0.004Baseline hazard 17 - 30 weeks -0.813 0.009 -0.818 0.012 -0.815 0.008Baseline hazard 31 - 52 weeks -0.180 0.010 -0.184 0.012 -0.175 0.002Baseline hazard 53 + weeks -0.201 0.016 -0.197 0.022 -0.192 0.008νn1 -0.636 8.160 0.781 8.160 -1.141 14.280νn2 -1.599 0.004 -1.561 0.005 -1.560 0.002

WagesExperience 0.004 0.000 0.004 0.000 0.017 0.000Experience squared/100 -0.005 0.001 -0.041 0.001 -0.086 0.001Treatment 0.116 0.003 -0.038 0.004 0.020 0.004Married 0.126 0.002 0.051 0.003 0.047 0.002Occupation, top 2005 -0.297 0.008 -0.431 0.012 -0.201 0.004Occupation, middle 2005 0.148 0.002 0.132 0.004 0.229 0.002Occupation, base 2005 0.195 0.004 0.188 0.006 0.142 0.002Occupation, unempl. 2005 0.493 0.004 0.277 0.008 0.247 0.004Education, vocational 2006 -0.095 0.002 -0.064 0.004 -0.214 0.001Education, bachelor 2006 -0.258 0.005 -0.338 0.008 -0.425 0.001Education, master 2006 -0.524 0.014 -0.441 0.016 -0.696 0.004Western immigrant -0.084 0.014 -0.126 0.018 -0.301 0.008Non-western immigrant -0.093 0.008 0.019 0.011 0.051 0.004Age 25 - 29 -0.145 0.005 -0.050 0.007 0.099 0.004Age 30 - 39 -0.099 0.004 -0.221 0.004 -0.105 0.002Age 40 - 49 -0.161 0.005 -0.144 0.005 -0.132 0.001Age 50 + -0.242 0.004 -0.155 0.005 0.106 0.002Log Wage 2004 -0.066 0.000 -0.012 0.001 -0.013 0.001Log Wage 2005 -0.042 0.001 -0.044 0.001 -0.033 0.000Baseline wage hazard 100 - 140 dkk. 2.538 0.003 2.736 0.004 2.778 0.000Baseline wage hazard 140 - 180 dkk. 3.290 0.004 3.366 0.004 3.596 0.001Baseline wage hazard 180 - 220 dkk. 3.277 0.006 3.386 0.009 3.597 0.001Baseline wage hazard 220 - 240 dkk. 3.264 0.008 3.765 0.016 3.629 0.008Baseline wage hazard 240 - 280 dkk. 2.492 0.014 3.124 0.018 3.702 0.004Baseline wage hazard 280 - 350 dkk. 2.563 0.012 2.784 0.024 3.507 0.004Baseline wage hazard 350 + dkk. 2.880 0.012 3.802 0.020 3.643 0.016νw1 -4.494 0.002 -4.671 0.003 -5.068 0.001νw2 -3.909 2.550 -4.621 10.200 -4.733 2.040

α1 -1.711 3.060 -1.765 3.443 -2.446 4.080α2 -1.757 3.060 -2.189 6.598 -0.969 2.040α3 14.576 1.020 14.654 1.913 14.856 0.510α4 1.370 2.678 1.467 7.841 1.074 3.060α5 -0.310 1.785 -0.864 2.805 -0.029 2.040α6 -3.386 4.590 -2.683 4.686 -2.553 4.080α7 -3.002 4.335 -4.331 6.534 -3.878 5.100α8 0.000 0.000 0.000Pr(α1) 0.000 0.000 0.000Pr(α2) 0.000 0.000 0.000Pr(α3) 1.000 1.000 1.000Pr(α4) 0.000 0.000 0.000Pr(α5) 0.000 0.000 0.000Pr(α6) 0.000 0.000 0.000Pr(α7) 0.000 0.000 0.000Pr(α8) 0.000 0.000 0.000

Average log likehood -6410.41 -6262.69 -6142.44Individuals 936 936 936



Table B7: Women, Southern Jutland county.


Transition U→ EExperience -0.019 0.000 -0.009 0.000 -0.006 0.000Experience squared/100 0.128 0.001 0.093 0.000 0.085 0.001Treatment (U ≤ 30 weeks) 0.321 0.004 0.312 0.002 0.313 0.004Treatment (U > 30 weeks) -0.064 0.009 -0.066 0.008 -0.067 0.007Married -0.041 0.003 -0.042 0.002 -0.043 0.003Occupation, top 2005 0.056 0.014 0.015 0.008 0.007 0.008Occupation, middle 2005 0.237 0.004 0.184 0.002 0.172 0.003Occupation, base 2005 0.340 0.003 0.287 0.001 0.274 0.003Occupation, unempl. 2005 -0.093 0.008 -0.163 0.004 -0.179 0.006Education, vocational 2006 -0.075 0.003 -0.083 0.002 -0.085 0.003Education, bachelor 2006 0.170 0.007 0.160 0.004 0.157 0.006Education, master 2006 -0.049 0.020 -0.063 0.014 -0.066 0.016Entry week, 45 - 46, 2005 -0.204 0.003 -0.224 0.008 -0.229 0.007Entry week, 47 - 48, 2005 -0.205 0.008 -0.228 0.004 -0.234 0.006Entry week, 49 - 50, 2005 -0.159 0.010 -0.186 0.005 -0.194 0.007Entry week, 51 - 52, 2005 0.222 0.008 0.198 0.007 0.190 0.008Entry week, 01 - 02, 2006 -0.239 0.004 -0.263 0.004 -0.270 0.004Entry week, 03 - 04, 2006 -0.181 0.008 -0.220 0.008 -0.229 0.008Entry week, 05 - 06, 2006 -0.213 0.007 -0.243 0.004 -0.251 0.004Entry week, 07 - 08, 2006 -0.098 0.008 -0.143 0.008 -0.154 0.009Western immigrant 0.243 0.002 0.164 0.002 0.142 0.002Non-western immigrant 0.008 0.017 -0.049 0.008 -0.068 0.011Age 25 - 29 -0.381 0.002 -0.418 0.004 -0.426 0.006Age 30 - 39 -0.396 0.004 -0.452 0.004 -0.462 0.004Age 40 - 49 -0.521 0.004 -0.582 0.001 -0.594 0.004Age 50 + -0.714 0.004 -0.773 0.004 -0.783 0.004Lagged Uempl. duration, 7 - 8 weeks 0.036 0.028 0.022 0.012 0.023 0.020Lagged Uempl. duration, 9 - 16 weeks 0.189 0.008 0.188 0.006 0.187 0.008Lagged Uempl. duration, 17 - 28 weeks -0.003 0.011 -0.015 0.006 -0.013 0.008Lagged Uempl. duration, 29 - 52 weeks 0.218 0.010 0.214 0.004 0.212 0.006Lagged Uempl. duration, 52 + weeks -0.018 0.005 -0.019 0.004 -0.020 0.005Baseline hazard 2 - 3 weeks -0.084 0.008 -0.161 0.008 -0.183 0.008Baseline hazard 4 - 5 weeks 0.112 0.004 0.034 0.008 0.012 0.008Baseline hazard 6 - 8 weeks -0.035 0.004 -0.114 0.005 -0.136 0.006Baseline hazard 9 - 16 weeks 0.477 0.005 0.401 0.002 0.380 0.003Baseline hazard 17 - 30 weeks 0.416 0.008 0.339 0.004 0.318 0.004Baseline hazard 31 - 52 weeks 0.293 0.010 0.214 0.008 0.190 0.006Baseline hazard 53 + weeks 0.371 0.004 0.293 0.008 0.269 0.008νe1 -3.255 0.001 -3.024 0.001 -2.967 0.004νe2 -3.015 0.510 -3.163 0.510 -0.999 1.020

Transition U→ NExperience 0.047 0.000 0.059 0.001 0.064 0.001Experience squared/100 -0.196 0.002 -0.237 0.002 -0.259 0.002Treatment (U ≤ 30 weeks) 0.230 0.009 0.220 0.004 0.210 0.008Treatment (U > 30 weeks) 0.040 0.016 0.036 0.008 0.028 0.012Married -0.080 0.008 -0.088 0.004 -0.093 0.008Occupation, top 2005 0.376 0.044 0.381 0.016 0.388 0.032Occupation, middle 2005 -0.010 0.008 -0.038 0.004 -0.043 0.008Occupation, base 2005 -0.414 0.013 -0.448 0.006 -0.457 0.015Occupation, unempl. 2005 -0.272 0.016 -0.300 0.005 -0.312 0.010Education, vocational 2006 -0.022 0.008 -0.022 0.004 -0.021 0.008Education, bachelor 2006 -0.077 0.014 -0.071 0.006 -0.070 0.014Education, master 2006 -0.079 0.044 -0.049 0.012 -0.050 0.036Entry week, 45 - 46, 2005 -0.591 0.008 -0.591 0.008 -0.595 0.016Entry week, 47 - 48, 2005 -0.364 0.021 -0.375 0.008 -0.389 0.016Entry week, 49 - 50, 2005 -0.855 0.016 -0.869 0.011 -0.885 0.018Entry week, 51 - 52, 2005 -0.295 0.021 -0.315 0.016 -0.336 0.022Entry week, 01 - 02, 2006 -0.243 0.010 -0.253 0.002 -0.269 0.010Entry week, 03 - 04, 2006 1.539 0.020 1.525 0.012 1.505 0.018Entry week, 05 - 06, 2006 -0.295 0.017 -0.312 0.006 -0.329 0.014Entry week, 07 - 08, 2006 -0.336 0.016 -0.341 0.012 -0.353 0.024Western immigrant 0.506 0.008 0.441 0.004 0.406 0.006Non-western immigrant 0.385 0.032 0.364 0.010 0.346 0.022Age 25 - 29 0.196 0.014 0.152 0.004 0.136 0.009Age 30 - 39 0.315 0.008 0.254 0.005 0.229 0.010


132 Chapter 4

Table B7 continued: Women, Southern Jutland county.


Age 40 - 49 0.335 0.018 0.267 0.008 0.240 0.015Age 50 + -0.836 0.010 -0.872 0.005 -0.886 0.011Lagged Uempl. duration, 7 - 8 weeks -0.508 0.054 -0.527 0.020 -0.526 0.048Lagged Uempl. duration, 9 - 16 weeks -0.500 0.032 -0.520 0.016 -0.518 0.026Lagged Uempl. duration, 17 - 28 weeks 0.378 0.016 0.386 0.016 0.388 0.022Lagged Uempl. duration, 29 - 52 weeks -0.556 0.022 -0.549 0.008 -0.551 0.016Lagged Uempl. duration, 52 + weeks 0.105 0.013 0.109 0.006 0.106 0.011Baseline hazard 2 - 3 weeks -1.704 0.024 -1.728 0.016 -1.742 0.028Baseline hazard 4 - 5 weeks -1.605 0.032 -1.631 0.016 -1.645 0.024Baseline hazard 6 - 8 weeks -0.833 0.015 -0.849 0.008 -0.865 0.016Baseline hazard 9 - 16 weeks -0.635 0.013 -0.654 0.008 -0.669 0.008Baseline hazard 17 - 30 weeks -0.617 0.013 -0.637 0.006 -0.652 0.008Baseline hazard 31 - 52 weeks -0.519 0.017 -0.544 0.006 -0.559 0.014Baseline hazard 53 + weeks 0.177 0.008 0.159 0.002 0.145 0.011νn1 -2.884 0.446 -0.670 0.510 -2.516 1.403νn2 -2.857 0.004 -2.743 0.008 -2.670 0.007

WagesExperience 0.015 0.000 0.007 0.000 0.018 0.000Experience squared/100 -0.085 0.001 -0.081 0.001 -0.134 0.001Treatment -0.013 0.004 0.000 0.002 0.083 0.003Married 0.058 0.004 0.102 0.001 0.143 0.003Occupation, top 2005 -0.170 0.016 -0.252 0.008 -0.506 0.016Occupation, middle 2005 0.164 0.005 0.144 0.002 -0.035 0.003Occupation, base 2005 0.125 0.004 0.117 0.004 -0.038 0.002Occupation, unempl. 2005 0.341 0.004 0.219 0.004 -0.062 0.006Education, vocational 2006 -0.060 0.004 -0.120 0.002 -0.052 0.003Education, bachelor 2006 -0.418 0.010 -0.323 0.004 -0.350 0.005Education, master 2006 -0.374 0.016 -0.535 0.010 -0.131 0.018Western immigrant 0.115 0.008 0.159 0.004 0.275 0.010Non-western immigrant -0.127 0.014 -0.351 0.005 -0.242 0.011Age 25 - 29 -0.214 0.008 0.087 0.005 -0.047 0.005Age 30 - 39 -0.120 0.001 0.116 0.004 -0.017 0.004Age 40 - 49 -0.163 0.002 0.187 0.003 0.004 0.006Age 50 + -0.370 0.007 -0.073 0.002 -0.169 0.005Log Wage 2004 -0.004 0.000 -0.014 0.000 0.020 0.000Log Wage 2005 -0.043 0.001 -0.050 0.000 0.007 0.001Baseline wage hazard 100 - 140 dkk. 2.760 0.001 2.832 0.008 3.115 0.001Baseline wage hazard 140 - 180 dkk. 3.381 0.001 3.471 0.004 3.733 0.008Baseline wage hazard 180 - 220 dkk. 3.189 0.011 3.494 0.003 3.858 0.009Baseline wage hazard 220 - 240 dkk. 2.959 0.018 3.326 0.016 3.509 0.013Baseline wage hazard 240 - 280 dkk. 2.848 0.016 3.217 0.016 3.034 0.016Baseline wage hazard 280 - 350 dkk. 2.392 0.016 2.508 0.012 3.163 0.014Baseline wage hazard 350 + dkk. 2.491 0.012 3.510 0.015 3.761 0.016νw1 -4.676 0.255 -4.640 0.510 -4.602 1.020νw2 -4.710 0.004 -4.901 0.004 -5.517 0.001

α1 -4.483 2.725 -4.239 2.040 -3.069 3.315α2 0.195 2.040 -0.377 1.020 3.463 4.399α3 -0.909 3.060 -0.096 1.020 -2.598 4.208α4 11.187 1.403 12.076 0.510 13.202 0.462α5 3.301 0.064 1.041 0.510 0.515 0.829α6 -0.414 1.020 -0.171 1.020 0.093 1.785α7 -3.111 2.040 -2.222 2.486 0.462 1.020α8 0.000 0.000 0.000Pr(α1) 0.000 0.000 0.000Pr(α2) 0.000 0.000 0.000Pr(α3) 0.000 0.000 0.000Pr(α4) 1.000 1.000 1.000Pr(α5) 0.000 0.000 0.000Pr(α6) 0.000 0.000 0.000Pr(α7) 0.000 0.000 0.000Pr(α8) 0.000 0.000 0.000

Average log likehood -6633.78 -6539.92 -6418.88Individuals 974 974 974


DEPARTMENT OF ECONOMICS AND BUSINESS AARHUS UNIVERSITY

SCHOOL OF BUSINESS AND SOCIAL SCIENCES www.econ.au.dk

PhD Theses since 1 July 2011 2011-4 Anders Bredahl Kock: Forecasting and Oracle Efficient Econometrics 2011-5 Christian Bach: The Game of Risk 2011-6 Stefan Holst Bache: Quantile Regression: Three Econometric Studies 2011:12 Bisheng Du: Essays on Advance Demand Information, Prioritization and Real Options

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2012-11 Mateusz P. Dziubinski: Essays on Financial Econometrics and Derivatives Pricing 2012-12 Jens Riis Andersen: Option Games under Incomplete Information 2012-13 Margit Malmmose: The Role of Management Accounting in New Public Management Reforms: Implications in a Socio-Political Health Care Context 2012-14 Laurent Callot: Large Panels and High-dimensional VAR 2012-15 Christian Rix-Nielsen: Strategic Investment 2013-1 Kenneth Lykke Sørensen: Essays on Wage Determination

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