price, productivity and wage dispersion in german
TRANSCRIPT
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Price, Productivity and Wage Dispersion in
German Manufacturing
(Firm Dynamics with Frictional Product and
Labor Markets)
Leo Kaas Bihemo Kimasa
University of Konstanz
AFiD-Nutzerkonferenz
29. Marz 2017
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Motivation
ā® Firm heterogeneity matters for the labor market and for the
macroeconomy (e.g. hires, separations, wages, productivity).
ā® Macro literature considers shocks to revenue productivity to
account for firm dynamics
ā® But supply and demand affect firms differently.
ā® Foster, Haltiwanger and Syverson (2008, 2016):
ā® Demand is important for firm growth and firm survival.ā® Price dispersion: younger firms are more demand constrained
and charge lower prices.
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Research question
Examine the respective roles of demand and productivity for
1. Firm-level dynamics of prices, output, employment and wages
2. Aggregate dynamics
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Contribution
ā® Develop an equilibrium model of firm dynamics with
ā® product and labor market frictionsā® costly recruitment and salesā® wage and price dispersionā® separate roles for demand and productivity shocks
ā® Quantitative evaluation using firm-level data on prices,
output, employment and wages for German manufacturing
(1995ā2014).
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Literature
Firm dynamics and the labor market
Hopenhayn & Rogerson 1993, Smith 1999, Cooper, Haltiwanger & Willis
2007, Veracierto 2007, Elsby & Michaels 2013, Fujita & Nakajima 2013,
Acemoglu & Hawkins 2014, Kaas & Kircher 2015
Search in product markets
Gourio & Rudanko 2014, Kaplan & Menzio 2014, Den Haan 2013,
Michaillat & Saez 2015, Petrosky-Nadeau & Wasmer 2015, Huo &
Rios-Rull 2015
Price and productivity dispersion
Abbott 1992, Foster, Haltiwanger & Syverson 2008, 2012, Smeets &
Warzynski 2013, Kugler & Verhoogen 2012, Carlson & Skans 2012,
Carlson, Messina & Skans 2014
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Data
ā® Administrative Firm Data (AFiD), Panel Industriebetriebe and
Module Produkte.
ā® All establishments in manufacturing (& mining, quarrying)
with ā„ 20 employees.
ā® Restriction to one-establishment firms.
ā® 1995ā2014 (annual).
ā® Sales value and quantity for nine-digit products.
ā® Employment, working hours, wages.
ā® ā 400, 000 firm-years.
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Firm dynamics
ā® Measure firm i ās output growth:
Qi ,t+1
Qi ,t=
āj PjitQji ,t+1āj PjitQjit
.
ā® Log sales growth is split into log output growth and log
growth of the firmās Paasche price index:
Si ,t = Qi ,t + Pi ,t .
ā® Further consider log growth rates of employment E , hours H
and hourly wage w .
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Firm dynamics
Std. dev.
S 0.20
P 0.18
Q 0.26
E 0.10
H 0.14
w 0.10
Correlation
(P , Q) -0.54
(Q, E ) 0.25
(Q, H) 0.29
Fraction [ā2%,+2%]
P 0.35
Q 0.11
E 0.25
Data statistics are averages of yearly residuals after controlling for industry and region.
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Dispersion of firm growth (1996ā2014)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1996 1998 2000 2002 2004 2006 2008 2010 2012 2014
Standard deviations
Sales growth Price growth Quantity growth Hours growth
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Skewness (1996ā2014)
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
1996 1998 2000 2002 2004 2006 2008 2010 2012 2014
Skewness: (P90+P10-2*P50)/(P90-P10)
Price growth (Skewness) Quantity growth (Skewness)
Employment growth (Skewness) Sales growth (Skewness)
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Price and productivity dispersion
ā® Consider subsample of homogeneous goods (measured in
length, area, volume, or weight). Examples
ā® P j quantity-weighted mean price of good j (in a given year).
ā® Firm i ās relative price index:
Pi =
āj PjiQjiāj P jQji
ā® Revenue and quantity labor productivity (per hour):
RLPi =
āj QjiPji
Hi
, QLPi =
āj QjiP j
Hi
, RLPi = Pi Ā· QLPi .
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Wage dispersion
ā® Matched employer-employee data for subsample (ā 15%) of
establishments in 2001, 2006, 2010 and 2014.
ā® Regress hourly wages on worker observables and job
characteristics: logwki = Ī²Xki + Īµki .
ā® Firm i ās relative wage index:
Wi =
āk wkihkiāk e
Ī²Xkihki
Wage decomposition
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Price, productivity and wage dispersion
Std. dev.
log(RLP) 0.639
log(QLP) 1.032
log(P) 0.727
log(W ) 0.210
Correlation
log(QLP), log(P) -0.769
log(QLP), log(W ) 0.282
log(RLP), log(W ) 0.422
Data statistics are averages of yearly residuals after controlling for industry and region.
ļæ½
ļæ½
ļæ½
ļæ½Negative relation between QLP and P ā Ļ(RLP) < Ļ(QLP).
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The model
ā® General equilibrium model of firm dynamics with search
frictions in product and labor markets.
ā® Firms build customer base B and workforce L via costly sales
and recruitment activities.
ā® Firms react to idiosyncratic productivity (cost) shocks x and
demand shocks y .
ā® Dispersion of wages and prices, reflecting differences in x , y
(and firm age).
Model details
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Response to firm-level shocks
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Quantitative analysis
ā® Calibrate the model to evaluate the respective roles of
productivity and demand for firm dynamics.
ā® Patterns of price, wage and productivity dispersion.
ā® Business-cycle analysis (impulse responses)
More
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Productivity and demand shocks
ā® Idiosyncratic productivity and demand shocks
log(xt+1) = Ļx log(xt) + ĻxĪµxt+1 ,
log(yt+1) = Ļy log(yt) + ĻyĪµyt+1 .
ā® Set Ļx = 0.125, Ļy = 0.130, Ļx = ā0.34, Ļy = 0.78 to match
volatility and persistence of firm-level price and output
dynamics.
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Firm dynamics
Productivity and demand shocks calibrated to match
Data Model Only x shocks Only y shocks
Ļ(P) 0.18 0.18 0.03 0.17
Ļ(Q) 0.26 0.27 0.24 0.10
P ā [ā2%,+2%] 0.35 0.36 0.47 0.72
Q ā [ā2%,+2%] 0.11 0.14 0.31 0.32Data statistics are averages of yearly residuals after controlling for industry and region.
ļæ½
ļæ½
ļæ½
ļæ½Demand shocks are important for dispersion of price growth.
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Employment, hours and wages
Data Model Only x shocks Only y shocks
Ļ(E ) 0.10 0.15 0.02 0.15
Ļ(H) 0.136 ā ā ā
E ā [ā2%,+2%] 0.25 0.31 0.870 0.24
Ļ(W /E ) 0.09 0.08 0.01 0.07
Ļ(W /H) 0.10 ā ā āData statistics are averages of yearly residuals after controlling for industry and region.
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Price, productivity and wage dispersion
Data Model Only x shocks Only y shocks
Ļ(RLP) 0.639 0.220 0.132 0.178
Ļ(QLP) 1.032 0.312 0.147 0.115
Ļ(P) 0.727 0.259 0.018 0.257
Ļ(W ) 0.210 0.077 0.015 0.073
Ļ(QLP , P) -0.769 -0.550 -0.859 -0.803
Ļ(QLP , W ) 0.282 -0.023 0.332 -0.315
Ļ(RLP , W ) 0.422 0.820 0.336 0.893
Data statistics are averages of yearly residuals after controlling for industry and region.
ļæ½
ļæ½
ļæ½
ļæ½Model accounts for ā¼ 1/3 of price, productivity and wage dispersion.
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Model impulse responses
Aggregate shocks:
1. Mean productivity (decrease of x by 5%).
2. Mean demand (decrease of y by 5%).
3. Productivity uncertainty (increase of Ļx by 20%).
4. Demand uncertainty (increase of Ļy by 20%).
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Impulse response to lower mean productivity/demand
More
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Impulse response to lower mean productivity/demand
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Impulse response to uncertainty shocks
More
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Impulse response to uncertainty shocks
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Conclusions
ā® Firm dynamics with product and labor market frictions:
separate roles for demand & productivity.
ā® Quantitative analysis: calibrate productivity and demand
shocks to capture price and output dynamics.
ā® Implications for wage and price dispersion
ā® Mean productivity/demand shocks cannot account for
counter-cyclical firm dispersion.
ā® Demand uncertainty shocks generate sizeable reactions of
output and employment.
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Examples of nine-digit products
ā® āHomogeneousā goods:
ā® 1720 32 144 Fabric of synthetic fibers (with more than 85%
synthetic) for curtains (measured in m2).ā® 2112 30 200 Cigarette paper, not in the form of booklets,
husks, or rolls less than 5 cm broad (measured in t).ā® 2125 14 130 Cigarette paper, in the form of booklets or husks
(measured in kg).
ā® Other goods
ā® 1740 24 300 Sleeping bags (measured in āitemsā).ā® 2513 60 550 Gloves made of vulcanized rubber for housework
usage (measured in āpairsā).ā® 2971 21 130 Vacuum cleaner with voltage 110 V or more
(measured in āitemsā).
Back
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Wage dispersion
ā® Firm i ās relative wage index:
Wi =
āk wkihkiāk e
Ī²Xkihki
ā® Decomposition of log hourly wage:
log(wi ) = log(Wi ) + log( ā
k eĪ²Xkihkiāk hkiļøø ļø·ļø· ļøø
=w i (Predicted wage)
).
ā® Variance decomposition:
8.6%ļøø ļø·ļø· ļøøvar(log(w))
= 3.2%ļøø ļø·ļø· ļøøvar(log(w))
+ 4.4%ļøø ļø·ļø· ļøøvar(log(W ))
+ 1.0%ļøø ļø·ļø· ļøø2Ā·covar(log(w),log(W ))
.
Back
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The Model
ā® Canonical model of firm dynamics with trading frictions in
product and labor markets.
ā® Representative household with
ā® L worker members, each supplying one unit of labor per period.ā® Endogenous measure of shopper members (cost c), each
buying up to one unit of a good per period.
ā® Preferences
ā
tā„0
Ī²t[et + u
(ā«yt(f )Ct(f )dĀµt(f )
)].
et consumption of a numeraire good,
yt(f ) firm-specific demand state ,
Ct(f ) consumption of firm f ās output,
Āµt(.) measure of active firms in period t.
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Firms
ā® Consider a firm with L workers and B customers.
ā® Output xF (L) with F ā² > 0, F ā²ā² < 0. x is firm-specific
productivity.
ā® The firm sells min(B , xF (L)) units of output.
ā® z = (x , y ) follows a Markov process.
ā® Recruitment and sales costs r(R , L) and s(S , L).
ā® Costs are increasing & convex in effort R , S and possibly
declining in size L (scale effects).
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Search and matching
ā® Firms offer long-term wage contracts to new hires and price
discounts to new customers.
ā® Directed search: Matching rates vary across firms.
ā® Firm hires m(Ī»)R where Ī» are unemployed workers per unit of
recruitment effort (mā² > 0, mā²ā² < 0).
ā® Firm attracts q(Ļ)S new customers where Ļ are unmatched
shoppers per unit of sales effort (qā² > 0, qā²ā² < 0).
ā® Matching rate for workers: m(Ī»)/Ī».
ā® Matching rate for shoppers: q(Ļ)/Ļ.
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Separations, entry and exit
ā® New firms enter at cost K , draw initial state (x0, y0),
(L0,B0) = (0, 0).
ā® Firms exit with probability Ī“.
ā® Exogenous quit rates Ī“w and Ī“b.
ā® Firms choose customer and worker separation rates Ī“b ā„ Ī“b,
Ī“w ā„ Ī“w .
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Stationary competitive search equilibrium
Value functions for workers U , W , shoppers V , Q, firms J, firm policies
Ī», R , Ļ, S , Ī“b, Ca = (w a(.), Ī“aw (.)), (L
Ļ )aĻ=0, L, B, p, p
R , entrant firms
N0, aggregate consumption C , and workersā search value Ļā such that
(a) Workers search optimally.
(b) Shoppers search optimally.
(c) Firmsā value functions J and policy functions solve the recursive
firm problem. more
(d) Free entry:
K =ā
z0
Ļ0(z0)J(0, z0)
(e) Aggregate resource feasibility:
L =ā
za
N(za){L(za) + [Ī»(za)ām(Ī»(za))]R(za)
}.
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Social optimality
Recursive planning problem: Maximize the social firm value
G(Lā,Bā, x , y) = max
{uā²(C )yB ā bLā r(R , Lā(1ā Ī“w ))ā s(S , Lā(1ā Ī“w ))
ā Ļ[L+ (Ī»ām(Ī»))R ] ā c[B + (Ļā q(Ļ))S ] + Ī²(1 ā Ī“)Ex,yG(L,B, x+, y+)
},
subject to
L = Lā(1ā Ī“w ) +m(Ī»)R ,
B = Bā(1ā Ī“b) + q(Ļ)S ,
B ā¤ xF (L) , Ī“w ā„ Ī“w , Ī“b ā„ Ī“b .
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Firm policies
ā® Recruitment expenditures and job-filling rates are positively
related. If R > 0,
r ā²1(.) = Ļ[m(Ī»)mā²(Ī»)
ā Ī»]
ā® Sales expenditures and customer acquisition rates are
positively related. If S > 0,
s ā²1(.) = c[q(Ļ)qā²(Ļ)
ā Ļ]
ā® Faster growing firms offer higher salaries to workers and
greater discounts to customers.
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Prices and revenue
ā® Discount price p = uā²(C )y ācĻq(Ļ)
falls in Ļ (and S).
ā® Reservation price pR = uā²(C )y ā c .
ā® Younger firms charge lower prices to build a customer base.
ā® Revenue
pRBā(1ā Ī“b) + pq(Ļ)S
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Calibration
ā® Functional forms:
F (L) = LĪ± , r(R , L0) =r0
1 + Ī½
( R
L0
)Ī½
R , s(S , L0) =s0
1 + Ļ
( S
L0
)Ļ
S ,
m(Ī») = m0Ī»Āµ , q(Ļ) = q0Ļ
Ī³ .
ā® Parameters
Ī± = 0.7, Ī½ = Ļ = 2, Āµ = Ī³ = 0.5 ,
Ī“w = 0.02 , Ī“b = 0.43 , Ī“ = 0.02 , Ī² = 0.96 .
ā® m0, q0 such that matching rates for workers (shoppers) are
0.45 (0.5).
ā® Expenditures for recruitment (sales) are 1% (2%) of output.
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Impulse response to lower mean productivity/demand
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Impulse response to uncertainty shocks
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