technology-specific production functions · technology-specific production functions michele...

Technology-specific production functions

Michele Battisti1 Filippo Belloc2 Massimo Del Gatto3

1University of Palermo, CeLEG LUISS Guido Carli and RCEA

2“G.d’Annunzio” University

3“G.d’Annunzio” University and CRENoS

Battisti, Belloc, Del Gatto Tech-specific production functions May 11, 2018 1 / 57

Introduction Motivation

Motivation

Focus: productivity (VA/L) differences associated to within-industrytechnological heterogeneity ⇒ disentangling between “pure TFP” and“Technology” at the firm-level.

Early 2000 ⇒ growing attention to firms’ heterogeneity:

heterogeneity in TFP: Melitz, 2003; Melitz-Ottaviano, 2008 andsubsequent;

heterogeneity in Technology: Sampson (QJE, 2015), Perla andTonetti (JPE, 2014), Perla, Tonetti and Waugh (2015), Benhabib,Perla, Tonetti (2015), Luttmer (QJE, 2007).

Different strands of literature: Technology Adoption, ProductivityEstimation, Trade Models with Firm-Selection, Misallocation . . .



Related literature

Technology Adoption/Diffusion.

Parente and Prescott (1994): Barriers to Technology Adoptionaccount for the great disparities in income across countries.

Barro and Sala-i Martin (1997): imitation in technology diffusion.

Acemoglu and Zilibotti (2001), Desmet and Rossi-Hansberg (2013):relationship between economic development and technology diffusion.

Desmet and Parente (2010): relationship between market size andtechnological upgrading.

⇒ Aggregate perspective



Related literature (cont.)

New Trade Models with Technology Adoption. Trade Models withHeterogenous firms and Technology Adoption focus on the process oftechnology adoption at the firm-level ⇒ effects of integration onaggregate productivity (and growth) through the technological upgrading.

Sampson (QJE, 2015). Key role for ENTRANT FIRMS: tradeintegration ⇒ firm-selection ⇒ tfp distribution of incumbent firms up⇒ entrants draw from a better distribution ⇒ tech diffusion. NB:heterogeneity in the tfp distribution of entrants because they do notnecessarily adopt the frontier tech.

Perla and Tonetti (JPE, 2014). Key role for the LEASTPRODUCTIVE FIRMS: diffusion of tech from the more to the lessproductive ⇒ tfp distribution ’evolves’ endogenously even without theintroduction of new technologies.




New Trade Models with Technology Adoption (cont.)

Perla, Tonetti and Waugh (2015). Firms choose whether to adopt abetter tech or not. Trade integration increases the incentives to adoptbetter tech ⇒ growth rate up.Benhabib, Perla, Tonetti (2015). Firms choose to keep producingwith their existing tech, adopt a new tech, or innovate. Tech adoincreases growth, but only innovation ⇒ long run growth.Luttmer (QJE, 2007). The small size of entrants must indicates thatimitation is difficult.Alvarez, Buera and Lucas (2014). Idea flows: firms get new tech bylearning from the people they do business with. Trade ⇒ moremeetings ⇒ tech diffusion ⇒ growth rate up.Bloom, Draca and Van Reenen (REStat, 2015). Import competition(from low cost countries) forces firms to innovate more thanotherwise (mainly because of the within-firm costly adjustment ofproduction factors).




Misallocation

Atkinson and Stiglitz (EJ, 1969): ”localized” technological progress;

Restuccia and Rogerson (Rew Econ Dynamics, 2013). Definition ofmisallocation: lower aggregate TFP due to distortions in theallocation of inputs across units (given firms’ technology and TFP)

Tai Hsieh - Klenow (QJE, 2009), model of misallocation with mktdistorsions (i.e. credit mkt)

Asker, Collard-Wexler and De Loecker (JPE, 2014): dynamic inputchoice can explain the dispersion of static measures of Kmisallocation (MRPK)

Collard-Wexler and De Loecker (2013): productivity and reallocationassociated to the ”minimill” technology.

Gopinath, Kalemli-Ozcan, Karabarbounis and Villegas-Sanchez(2015): Capital Allocation and Productivity in South Europe.



Definition of terms: TFP estimation

AMBIGUITY: “TFP”, “productivity” and “technology” are often usedinterchangeably. Actually, these concepts are not equivalent. Sometimesthe focus is on “technology”.

Log Cobb-Douglas usually assumed:

yi = ai + βKki + βLli + ui

i=firm; Ai = TFP (firm-specific); ui = iid term.

TFP usually estimated as the Solow residual

ai = yi −(βKki + βLli

)Simultaneity issue: Cov(Ki ,Ai ) 6= 0 and Cov(Li ,Ai ) 6= 0 ⇒ OLS distorted[Olley and Pakes (1996), Levinsohn and Petrin (2003), Ackerberg et al.(2006), Wooldridge (2009), and Doraszelski and Jaumandreu (2012).Surveys by: Del Gatto et al. (JoES, 2011), Van Beveren (JoES, 2012)].


Introduction Definition of terms

Definition of terms

In our world, the production function is technology-specific:

yi = ai + αm + βmki + ui

yi = ln(Yi/Li ) and ki = ln(Ki/Li )

m=technology, with m = 1, . . . ,M(M = number of available technologies - exogenous)

different production functions identify different technologies bydiffering in (αm, βm).

several technologies are available in each sector-industry, with anumber of firms using each technology.



Technology-specific production functions

Y/L

K/L

m2

kA kB

m3

m1

m3 m2 m1 for k < kAm3 m1 m2 for kA < k < kBm1 m3 m2 for kB < k



Technology-specific production functions (cont)

Atkinson and Stiglitz (EJ, 1969): ”localized” technological progress

A NEW VIEW OF TECHNOLOGICAL CHANGE I

THE recent literature on technological progress has almost entirely been based on the assumption that its effect can be represented as shifting the production function outwards-as illustrated in Fig. 1. Technical advance is assumed to raise output per head for all possible techniques. The advocates of this approach seem, however, to have forgotten the origins of the neo-classical production function: as the number of production processes increases (in an activity analysis model), the production possibilities can be more and more closely approximated by a smooth, differentiable curve. But the different points on the curve still represent different processes of production, and associated with each of these processes there will be certain technical knowledge specific to that technique. Indeed, both supporters and critics of the neoclassical theory seem to have missed one of the most important points of the activity analysis (Mrs. Robinson's blue- print) approach: that if one brings about a technological improvement in one of the blue-prints this may have little or no effect on the other blue- prints. If the effect of technological advance is to improve one technique of production but not other techniques of producing the same product, then the resulting change in the production function is represented by an outward movement at one point and not a general shift-see Fig. 2. This figure

Output Output' per man per man - -

Capital per man Capital per man

FIG. 1. FIG. 2.

shows the extreme case where technical progress is completely " localised" to one technique: there are no spillover improvements in other techniques. It reality we should expect that a given technical advance would give rise to some spillovers and that several techniques would be affected. However, we would reach the traditional position only if there were spillovers to every technique. This means that a technical advance would have to be

1 The authors are very grateful to G. de Menil, P. A. Diamond, R. S. Eckaus, F. H. Hahn, M. Piore, M. Rothschild, K. Shell andJ. H. Williamson for their helpful comments on an earlier draft. Stiglitz's research was supported in part by the United States-United Kingdom Educational Commission and the National Science Foundation.

This content downloaded from 192.167.14.32 on Tue, 25 Nov 2014 11:49:15 AMAll use subject to JSTOR Terms and Conditions


Introduction Contribution

Methodological Contribution

We show how mixture models can be used to unbundle Technology andTFP at the firm-level by estimating technology-specific productionfunctions

I avoiding any type of ex-ante assumption on the degree of technologicalsharing across firms and countries (the number of available technologiesis endogenously determined by the mixture estimation algorithm ⇒ thedistribution of technologies across firms is observed ex-post)

I controlling for simultaneity



Methodological Contribution (cont)

Mixture models unable us to disentangle between

I firm productivity relative to the other firms in the same technologygroup (i.e. Within-technology TFP - WTFP) ⇒ a firm’s ability toexploit a given technology (compared to the other firms using the sametechnology)

I firm productivity relative to the labour productivity that the firm couldhave reached, given its capital-labour ratio, had it chosen the frontiertechnology (i.e. Between-technology TFP - BTFP) ⇒ aquantification of the labour productivity gap associated with thetechnological choice.



Methodological Contribution (cont)

Figure: Definition of TFP with one technology (panel a) and two technologies(panel b).

ln yi

single technology

ln ki

. firm

ai

panel a

∧

yi

yi ∧

ln yi

m1

ln ki

. firmm2

m2

panel b

localized fron2er technology

yi;m ∧

yi

yi;m ∧

H

WtTFP

BtTFP



Methodological Contribution (cont.)

...neglecting the presence of different (within-sector) technologies resultsin overstating the TFP of the firms that adopt relatively more productivetechnologies (due to underestimation of their input coefficient - i.e.βm > β - and overestimation of the intercept - i.e. αm > 0):

yi = ai + α + βki

yi = ai ,m + αm + βmki

ai = ai ,m + (αm − α) + (βm − β)ki



...back to the motivation of the paper.

If one believes in such a world, the ”ambiguity” is evident. For example:

Sampson (2015): what firms draw is basically ”tech” (tech diffusion),BUT selection takes place on the basis of tfp and technology.

Perla and Tonetti (2014), Perla, Tonetti and Waugh(2015), Benhabib,Perla, Tonetti (2015): diffusion of tech from the more to the lessproductive firms. BUT it might well be the case that a firm using thefrontier technology lies on the left tail of the TFP distributionbecause of a low ”ability in using that technology” (low TFP).

Alvarez, Buera and Lucas (2014). Idea flows. Do business contactshelp firms in getting the best tech or in learning how to best exploitthe tech in use (i.e. tfp)?



Contribution (cont)

Empirical Contribution: we use international firm-level data (Orbisdatabase - Bureau van Dijk) ' 73.000 worldwide distributedmanufacturing firms (2012-2014) to:

identify, for each industry, the number M of available technologiesand, for each firm, the probability of using each technology(technology clusters)

quantify the firm-level productivity (VA/L) gaps in terms of WTFP(not being able to use the technology as well as the best users) andBTFP (not adopting the best technology)

look at key aggregate correlations and firm-level markers of WTFPand BTFP


Analysis Analysis: main steps

Analysis: steps

1 - Production function(s) estimationI 1.1 - Empirical model of Technology AdoptionI 1.2 - Mixture regressions to identify:

- M (# of technologies),- production function parameters (for each technology),- probability to belong to each technology group (for each firm)

2 - Quantification of WTFP and BTFP

3 - Quantification of WTFP and BTFP Gaps

4 - Aggregate correlations and firm-level markers of WTFP andBTFP


Analysis Production function estimation

Step 1 - Production function estimation

We want to estimate:

lnYi ,t = αm + lnAi ,t + βKm lnKi ,t + βLmlnLi ,t

with an endogenous finite set M of available technologies indexed by m

⇒ OLS distorted because of ”simultaneity”:

Cov(Ki ,t ,Ai ,t) 6= 0 and/or Cov(Li ,t ,Ai ,t) 6= 0

In our M > 1 case, also potential simultaneity stemming from thetechnological choice:

Cov(Ki ,t ,mi ,t) 6= 0 and/or Cov(Li ,t ,mi ,t) 6= 0

⇒ An ”empirical model” of Technology Adoption is needed


Analysis Empirical model of Technology Adoption

Step 1.1 - Empirical model of Technology Adoption

Production function:

lnYi ,t = αm + lnAi ,t + βKm lnKi ,t + βLmlnLi ,t

Finite set M of available technologies m = (αm, βKm , β

Lm)

One period time-to-build (i.e. the new technology is productive oneperiod after its acquisition)

TFP term ai ,t = ai ,t(mi ,t): evaluated wrt the other firms usingtechnology m ⇒ differences (not associated to K , L) in the ability toexploit the given technology

TFP follows a first order Markov process:

ai ,t = E [ai ,t |ai ,t−1] + ξm,i ,t

where ξm,i ,t is innovation in either the adopted technology(mi ,t 6= mi ,t−1) or the ability to exploit it (mi ,t = mi ,t−1)




Use terminology X [t] to remember that variable X is chosen at time [t]

Timing:

end of period t: firm chooses Ki ,t+1[t] and mi ,t+1[t]

beginning of period t + 1: ai ,t+1 (i.e. firm’s tfp) and Zt+1 (i.e. avector of exogenous mkt-level state vars) are observed⇒ firm adjusts L (freely) => Li ,t+1[t + 1]

end of period t + 1: firm chooses Ki ,t+2[t + 1] and mi ,t+2[t + 1] onthe basis of ai ,t+1 and Zt+1




In each period t, firm i solves:

max(Ki,t+1,mi,t+1)

Et

∞∑j=t

δj−tPi ,j |Ωi ,j

where the net profit Pi ,j given by

Pi ,j = πi ,j(Ki ,j , ai ,j ,mi ,j ,Zj)︸︷︷︸gross profit

−C (Ki ,j+1,Ki ,j ,mi ,j+1)

with

C (Ki ,j+1,Ki ,j ,mi ,j+1) = C Ii ,j(Ii ,j)︸︷︷︸

Inv. cost

+ CDi ,j(Di ,j)︸︷︷︸

Disinv. cost

+CAi ,j ,mI(mi ,j+1 6= mi ,j)(Ii ,j)︸︷︷︸

tech Adjustment cost

with Ii ,j = Ki ,j+1 − Ki ,j + Di ,j , with Di ,j = εi ,jKi ,j and 0 ≤ εi ,j ≤ 1




K accumulates according to

Ki ,j+1 = Ki ,j − δKi ,j + Ii ,j − Di ,j

Bellman equation:

Vi ,t(Ωi ,t) = max(Ki,t+1,mi,t+1)

(Pi ,t + δEt [Vi ,t+1|Ωi ,t ])




Solution (K∗i ,t+1[t],m∗i ,t+1[t])

- policy function for K:

K ∗i ,t+1(m∗i ,t+1,Ki ,t , ai ,t ,Zt)

- and the firm will choose the m∗i ,t+1 that maximizes:

[δEt

(Vi ,t+1|Ωi ,t)− C (K ∗i ,t+1,Ki ,t ,m

∗i ,t+1)

]|m = m∗i ,t+1

among all possible m ∈ M.


Analysis Production function(s) estimation

Step 1.2 - Production function(s) estimation

I STAGE. ”Correction factors” estimation

- estimate the K policy function K ∗i ,t+1(m∗i ,t+1,Ki ,t , ai ,t ,Zi ,t) as

lnKi ,t [t − 1] = α0 + α1g(lnKi ,t−1[t − 2]) + Zc,t + ΦKi ,t + ui ,t

- estimate the static condition for L as

lnLi ,t [t] = γ0 + γ1g(lnKi ,t [t − 1]) + Zc,t + ΦLi ,t + ui ,t

with Zc,t = country-year effects. Under the assumption that ui ,t is iid:

ΦKi ,t embodies Cov (Ki ,t [t − 1],mi ,t [t − 1]) and

Cov(Ki ,t [t − 1], ai ,t−1)

ΦLi ,t embodies Cov(Li ,t [t], ai ,t)



Step 1.2 - Production function(s) estimation

II STAGE: Production function estimation.

In each 2-digits sector, we use

yi ,t = αm + βmki ,t + ΦKi ,t + ΦL

i ,t + FEs + εi ,t

where FEs are 4-digits industry fixed effects and the ”correction factors”

ΦKi ,t and ΦL

i ,t are included

⇒ Mixture models



Step 1.2 - Production function(s) estimation:mixture analysis

Write the (implicit) probability distribution function of yi ,t as a weightedaverage of the M specific segment (technology) densities fm(yi ,t |µm, σm),each with proper mean (µm) and variance (σ2

m):

f (yi ,t |µ, σ2) =M∑

m=1

ϕmfm(yi ,t |µm, σ2m)

ϕm = unknown ex-ante probability to belong to the technology-group m.Algorithm (based on WLS regressions with weights given by ϕm): randomstarting points for ϕm ⇒ posterior probabilities through WLS ⇒ updatethe regression coefficients βm (as weights change) ⇒ iteratively alternateWLS and probabilities until a loglikelihood convergence criterion is reached⇒ repeat many times to avoid local optima.



Step 1.2 - Production function(s) estimation:mixture analysis (cont)

Weighted least squares (WLS), sector-by-sector (at the 2-digit level), year2014:

yi = αm + βmkδi,mi + ϕΦ

δi,mi + ψΨ

δi,mi + FEs + εi

where FEs are 4-digits industry fixed effects.



Step 1.2 - Production function(s) estimation:mixture analysis (cont)

Start with random values of ωm ⇒ posterior probability pi ,m that firm ibelongs to group m ⇒ observation weights ωm:

δi ,m =√pi ,m with pi ,m ≡ pr(i ∈ m) =

ωmfmyi |µm;σ2m∑M

m=1 ωmfmyi |µm;σ2m

This set of probabilities is then used to update the regression coefficientsby changing the weights ωm according to

ωm =

∑i pi ,m∑

m

∑i pi ,m

with the following constraints:

ωm ≥ 0 ∀m = 1, . . .M andM∑

m=1

ωm = 1.



Descriptive statistics

Table 1: Descriptive statistics

SECTOR CODE VA K # firms VA/L K/L(% of all sectors) (% of all sectors) (avg) (avg)

Food products Fd 6.7% 7.6% 7601 25.15 37.29Beverages Bv 2.7% 5.1% 1053 45.08 122.99Tobacco products Tb 1.7% 1.7% 32 67.02 102.66Textiles TX 1.1% 1.3% 2253 26.73 30.04Wearing apparel WA 1.0% 0.6% 3438 16.02 10.39Leather and related products LP 0.8% 0.4% 1802 21.93 13.06Wood and of products of wood and cork Wo 0.5% 0.3% 3435 23.79 26.74Paper and paper products Pa 2.7% 3.0% 1237 39.95 61.85Printing and reproduction of recorded media Pr 1.2% 1.4% 2643 30.96 27.95Coke and refined petroleum products PC 1.7% 2.7% 168 83.95 222.14Chemicals and chemical products Ch 6.6% 8.0% 2082 54.38 87.46Basic pharmaceutical products and pharmaceutical preparations Ph 13.5% 15.8% 504 59.90 94.14Rubber and plastic products RP 4.0% 2.8% 3308 36.47 41.98Other non-metallic mineral products NM 5.9% 8.9% 3702 31.13 55.49Basic metals BM 6.4% 7.8% 1355 46.94 75.12Fabricated metal products, except machinery and equipment MP 4.7% 2.6% 11732 34.75 30.04Computer, electronic and optical products EP 11.2% 8.9% 2372 43.00 38.57Electrical equipment El 4.6% 4.0% 2318 38.85 32.56Machinery and equipment nec Ma 12.8% 8.0% 5601 47.04 37.05Motor vehicles, trailers and semi-trailers MV 7.4% 7.1% 1463 35.40 46.24Other transport equipment Tr 2.3% 1.7% 619 37.42 47.50Furniture Fu 0.5% 0.3% 2673 20.60 20.75TOTAL - - 61391 - -

20



Production function estimates

Table 2: Mixture regressions: estimated production function parameters

SECTOR α1 β1 α2 β2 α3 β3 α4 β4 α5 β5

Fd -1.925*** 0.275*** -0.774* 0.719 -0.853 0.677*** 0.131 0.127(0.002) (0.000) (0.054) (n.a.) (0.258) (0.000) (0.528) (n.a.)

Bv -0.001 0.765*** -0.711*** 0.582***(0.981) (0.000) (0.000) (0.000)

TX 1.715*** 0.139*** 1.329* 0.465*** 1.725 0.113(0.005) (0.000) (0.093) (0.000) (0.418) (0.174)

WA -0.075 -0.004 -0.217 0.210*** -0.817*** 0.242*** -0.491 0.545*** -0.039 0.237***(0.672) (0.609) (0.847) (0.000) (0.000) (0.000) (0.518) (0.000) (0.962) (0.000)

LP 0.866 -0.254 -0.507*** 0.722*** 1.139*** 0.251***(0.074) (0.304) (0.000) (0.000) (0.000) (0.000)

Wo -0.374 0.431*** -0.485 0.506*** 0.068 0.095(0.628) (0.000) (0.838) (0.000) (0.866) (n.a.)

Pa -0.473 0.617*** -0.505 0.178***(0.611) (0.000) (0.136) (0.000)

Pr 0.935*** 0.072*** -0.538*** 0.418***(0.000) (0.000) (0.000) (0.000)

Ch 0.997*** 0.217*** 0.238 0.710***(0.000) (0.000) (0.469) (0.000)

Ph 1.529** 0.158 0.324 0.736***(0.043) (0.211) (0.789) (0.000)

RP -0.614 0.581*** -0.133 0.106***(0.233) (0.000) (0.583) (0.000)

NM -0.180 0.282*** -0.705*** 0.739*** -1.020*** 0.687*** 0.918*** 0.146***(0.450) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

BM 1.034*** 0.141*** 0.879* 0.552***(0.000) (0.000) (0.078) (0.000)

MP -1.459** 0.273*** 0.625 0.526*** 0.556* 0.112*** 0.591 0.309***(0.012) (0.000) (0.225) (0.000) (0.100) (0.000) (0.147) (0.000)

EP -1.732*** 0.012 1.024 0.155***(0.000) (0.579) (0.127) (0.000)

El -0.413 0.338*** -0.337 0.105***(0.758) (0.000) (0.530) (0.000)

Ma 0.323 0.328*** 0.639*** 0.115***(0.176) (0.000) (0.000) (0.000)

MV -0.059 0.327*** 1.013*** 0.107***(0.626) (0.000) (0.000) (0.000)

Tr 0.737 0.543*** 0.933 0.152***(0.605) (0.000) (0.116) (0.006)

* p < 0.10, ** p < 0.05, *** p < 0.01. Standard errors are in parenthesis.

Fd: Food products; Bv: Beverages; Tb: Tobacco products; TX: Textiles; WA: Wearing apparel; LP: Leather and related products; Wo:

Wood and of products of wood and cork; Pa: Paper and paper products; Pr: Printing and reproduction of recorded media; PC: Coke and refined

petroleum products; Ch: Chemicals and chemical products; Ph: Basic pharmaceutical products and pharmaceutical preparations; RP: Rubber and

plastic products; NM: Other non-metallic mineral products; BA: Basic metals; MP: Fabricated metal products, except machinery and equipment;

EP: Computer, electronic and optical products; El: Electrical equipment; Ma: Machinery and equipment nec; MV: Motor vehicles, trailers and

semi-trailers; Tr: Other transport equipment; Fu: Furniture.

21



Estimated Production Functions-2

02

4ln

(Y/L

)

0 2 4 6ln(K/L)

Fd

-20

24

6ln

(Y/L

)0 2 4 6

ln(K/L)

Bv

12

34

ln(Y

/L)

0 2 4 6ln(K/L)

TX

-10

12

3ln

(Y/L

)

0 2 4 6ln(K/L)

WA

-10

12

34

ln(Y

/L)

0 2 4 6ln(K/L)

LP

01

23

ln(Y

/L)

0 2 4 6ln(K/L)

Wo

01

23

4ln

(Y/L

)

0 2 4 6ln(K/L)

Pa

-.5

0.5

11.

52

ln(Y

/L)

0 2 4 6ln(K/L)

Pr

01

23

4ln

(Y/L

)

0 2 4 6ln(K/L)

Ch

01

23

4ln

(Y/L

)

0 2 4 6ln(K/L)

Ph

01

23

4ln

(Y/L

)

0 2 4 6ln(K/L)

RP

-10

12

34

ln(Y

/L)

0 2 4 6ln(K/L)

NM1

23

4ln

(Y/L

)

0 2 4 6ln(K/L)

BM

-2-1

01

23

ln(Y

/L)

0 2 4 6ln(K/L)

MP

0.2

.4.6

.81

ln(Y

/L)

0 2 4 6ln(K/L)

EP

0.5

11.

52

ln(Y

/L)

0 2 4 6ln(K/L)

El

0.5

11.

52

ln(Y

/L)

0 2 4 6ln(K/L)

Ma

0.5

11.

52

ln(Y

/L)

0 2 4 6ln(K/L)

MV0

12

34

ln(Y

/L)

0 2 4 6ln(K/L)

Tr



Technology-specific production functions (cont)

Figure: Estimated technology clusters: Chemicals (Ch) and Food (Fd) sectors

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3

3

3

3

1

2

3

34 2

4

3

3

4

4

4

33

3

2

3

3

3

3

4

2

4

2

33

3

3

4

3

3

2

34

2

3

3

4

14

3

4

4

3

2

4

3

2

3

3

1

3

13 3

3

44

3

3

3

3

33

4

2

3

23

3

44

4

3

4

4

1

34

3

1

3

44

3

4 44

2

34

2

3 3

3

1

3

3

4

4

3

3

4

3

3

3

2

3

4

4

1

4 3

4

1

2

4

4

33

3

24

4

3

33

34

4

2

4

1

3

3

4

3

2

3

4

4

3

2

4

4

44

2

42

3

3

2

3

4

44

4

31

43

2

3

44

3

3

4

1

1 4

3

34

2

4

3

4

2

4

3

3

4 2

3

4

2

1

4

3

2

4

34

2

3

1

2

3

4

3

3

22

3

4

3

12

4

31

2

4 43

3

2

4

2

4

3

4

4

3

3

3

33

4

4

1

4

3

4

1

2

4

1

3

3

4

3

44

4

4

3

3

3

43

4

344

2

4

4

2

4

1

3

4

3

1

4

4

34

44

4

3

2

4 2

34

3

3

2

3

3

2

44

3

24

3

3

4

4 43

3

3

34

3

4

3

4

14

3

2

43

33

43

2

3

2

4

44

3

3

4

4

1

4

3

4

1

3

43

1

3

3

4

4

3

4 4

3

2

3

3

3

4

3

4

3 3

3

4

3

3

4

3

3

1 4

3

3

4

2

33

3

2

1

3

3

4

33

3

3

3

3

4

4

34

3

4

4

3

3

44

4

3

4

3

4

1

2

3

43

1

2

2

3

4

3

2

4

3

3

4

4

34

3

3

2

4

3

22

4

4

43

3

4

4

1 3

4

4

4

3

4

4

3

44

2

4

1

4

1

3

4

3

3

1

3

4

2

4

3

3

4

34

2

3

4

4 4

3

2

4

33

4 4

3

4

4

1

4

4

4

3

2

2

4

3

1

4

34

4

3

4

4

3

2

3

44

2

3

4

4

4

13

44

4

3

2

32

2

4

3

4

4

1

24

34

2

4

4

4

4

2

3 2

2

3

3

3

44

4

42

3

1

3

3

2

3

4

3

4

3

3

1

4

3

4 3

3

3

33

4

3

44

3

3

4

34

4

4

3

3

12

3

4

44

4

3

1

3

2

43

4

2

3

3

3

3

4

31

232

344

4 3

4

3

34

42

3

4

4

4

4

2

3

33

2

44

41

3

23

2

3

3

4

41

3

4

3 3

4 3

3

4

3

2

4

3

4

33

2

3

3

3

3

2

33

4

4

4

31

2

4 34

3

4

4

3

3

1

4

3

4

2

3

3

4

1

3

4

3

3

3

33

4

4

4

44

1 3

3

2

4

3

44

3

3

444

4

3

4

2

33

3

4 3

4

44

4 3

34

4

2

3

3

2

2

3

4

4

3

4

3

3

3

4

3

33

34

3

3

2

2

1

1

2

4

4

4

3

4

2

4

4

4

4

3

4

3

3

4

34

3

3

3

2 2

3

4

4

2

3

2

4

33

4

3

1

4

1 4

3

3

4

1

4

4

1

3

4

4

4

3

1

3

4

43

2

4

3

3 2

4

4

14

3

4

31

333

4

3

1

4

3

3

44

1

1

1

3

4

3

4

34

24

4

34

4

3

4

4

3

2

4

4

2

3

33

4

4

133

1

34

3

13

2

4

4

3

4

4

4 4

33

34

13

4

1 3

444

3

444

4

2

2

44

4

44

4 4

3

3 3

4

4

4

4

4

1

41

4

3

2

3

3

31

1

4

3

2

44

2

44 3

4

3

32

44

3

4

3

4

1

4

3

3

3 24

2

4

4

4

4

3

44

3

2

3

3

3

3 33

41

1

3

3

33

33

4

4

1

3

2

3

4

3

3

41

4

3

4

23

3

3

2

1

4

2

4

3

3

3

2

4

3

3

4

4

1

4

1

4

4

3

4

44

3

2

1

3

2

4

4

3

3

3

3

14

3

14

4

4

4

4

3

2

1

4

4

22

3

3

1

3

2

3

44

4

1

3

3

3

43

41

3

43

4

3

4

2

4

3

2

1

4

2

2

4

4

3

4

4

2

3

34

3 3

2

4

4

4

3

2

33

3

4

4

3

4

13

4

4

4

4

3

3

4

3

4

33

4

3

3

4

3 3

3

4

3

41

3

4 4

1

3

4

3

4

4

3

4

3

3

2

34

2

33

34

4

2

3

4

44

2

4

3

2

4

3

1

34

4

44

2

3

2

2

43

3

3

4 4

3

4

4

44

2

3

3

3

4

2

4

3

42

4

2

3

3

3

4

4

4

4

34

4

2

3

3

4 4

4

3

2

3

4

4

3

4

3

4

4

3

4

3

43

1

2

4

3

4

2

3

3

3

4 14

3

4

11

3

4

3

4

3

4

3

3 2

3

33 3

4

4

2

44

4

4

3

4

2

1

4

1

33

4

4

4 3

3

4

33

4

4

3

3

4

3

3

4

1

2

3

4

4

4

3

4 4

4

14

4

3

3

1

3

3

1

3

4

3

1

2

2

3

44

4

2

3

3

4

1

4

3

3

2

33

4

3

3

43

2

4

3

2

4

1

3

4

2

4 3

3

3

4

2

3

3

3

3

3

4

3

3

3

1

2

3

4

2

4 3

3

2

2

4

3

2

3

4

32

3

33

4

3

4

3

3

2

4

3

4

3

4

3

33

1

3

3

3 34

3

2

1

3

3

34

3

34

3

34

3

4

3

3

1

3

4

33

3

2

1

4

42

2

4

4

3

2

2

4

4

3

2

4

3

43

2

4

3

3

3

3

4

4

44

4

3

3

3

3

2

23

34

33

3

4

4

44

2

3

4

33

4

4

3

3

1

4

2

3

4

24

23

2

4

3

1 4

43

4

4

3

1

3

1

4

3

3

4

2

4

3

4

3

4

44

3

3

2

1

4

4

3

34

3

1

4

3

33

3

44

2

3

3

34

4

3

1 3

1

2

4

4

1

3

3

4

3

4

2

3

4

2

3 3

3

4

4

1

4

3

4

2

2

4

4

1

4

4

3

3

4

3

1

4

4

2

3

3

4

3

4

3

4

34

3

2

2

3

3

43

4

2

4

3

3

4

4

3

4

4

3

2

4

3

2

23

3

4

3

4

2

4

4

2

3

3

2

3

4

33

4

4

3

4

1

3 4

3

3

3

4

3

4

4

4

3

4

4

4

2

3

4

2

3

44

2

1 4

3

3

4

4

4

4

3

34

3

3

2

3

31

3

3

3

2

1

1

4

44

3

4

31

4

4

3

1

3

4

2

14

4

4

4

23

2

34

31

3

4

4

3

4

4

2

3

4

4

3

4

3

1

3

4

3

3 2

3

3

3

3

43

3

3

4

3

3

2

11

4

3

4

3

2

1

2

1 3

1

4

3

44

4

4

2

3

44

3

4

3

3 2

3

34

3

33

34

3

4

4

33

4

4

4

34

3

144

4

4

1

2

4

2

44

3

3

4

4

4

3

4

4

3

3

3

1

3

3

4

3

44

4

4

1

1

33

4

3

1

4

2

3 3

3

3

1

4

2

4

2

3

4

3

3

2

2

444

3

4

3

3

4

4

4

1

3

2

3

4

2

3

43

3

4

3

4

3

43

23

3

3

1

4

4

1

4

3

2

4

3

4

3

3

1

3 2 23

4

4

1

3

3

3

2

3

3

43

4

2

4

4

3

4

3

4 44

3

1

4

2

14

2

2

33 32

4

1

1 44

4

3

3

3

4

2

3

34

3

31

3

3

2

4

4

3

4 3

2

3

3

4

3

4

4

3

44

1

3

3

4

3

4

3

33

33

3

3

1

3

3

3

2

3

2

2

3

43

3

34

3

4

3

3

4

3

43

24

3

2

2

2

3

3

4

32

2

4

3

2

4

3

4

3

3

333

2

44

3

4

34

4

34 3

42

3

3

1 3

3

31

3

4 3

4

4

3 3

2

44

1

3

4 4

3

3

3

4

4

2

4

33

4

1

2

3

2

4

4

3

4

4

1

4

44

1

3

4

3

2

3

23

1

3

1

33

4

4

3

4

2

43

4

3

34

33

444

43

1

1

3

3

3

4

3

3

44

3

3

1

3

4

4

3

4

1

3

4

4

4

3

4

4 4

2

3

33

3

3

3

4

1

4 4

3

44

1

3

2

4

2

4

4

3

2

4

2

3

4

3

3 4

3

3

2

3

4

2

4

3

3

4

3

33

33

3

1

3

1

3

3

2

4

4

4

4

3

2

3

4

1

2

44

4

3

4

4

1

2

2

4

3

4

2 2

3

4

43

1

3

3

42

4

3

4

3

3

3

4

1

3

2

3

34

44

1

1

3

23

3

4

13

3

4

2

1

4

1

2

2

3

3

3

3

3

4

2

2

4

2

2

3

4

4

3

2

4 3

33

33

2

2

4

2

3

3

4

3

4

3

2

3

4

2

3

3

2

33

2

4

3

3

3

4

1

3

2

3

4

3

43

4

3

4

2

41

3

3

3

1

4

3

3

3

4 34 4

32

4

4

4

4

4

3

3

3

4

33 3

3

4

343

3

4 2

4

3

3

4

2

4

3

4

3 4

3

3

4

2

3

3

2

4

4

2

3

31

4 3

43

1

1

34

3

2

3

1

2

3

4

4

2

4 2

4

2

3 3

1

4

3

4

4

2

3

4

1

3

1

3

3

2

4

3

3

3

4

34

3

2

4

3

4

3

2

4

3

4

4

44

3

31

4

2

3

3

33

4

434

3

34

44

4

2

23

4

4 44

4

1

3

23

3

2

34 4

4

2

3

4

2

4

4

3

1

4

3

3

1

2

4

3

4

2

4

3

3

3

33

3

13

4

2

11

3

4

3

4

2

2

3

2

1

4

2

3

4

11

2

4 34

3

3

42

4

2

2

4

2

4

2

3

3

1

4

1

43

4

43

1

4 23

3

3

3

4

1

3

3

4

3

2

3

3

2

3

2

4

3

2

3

1

3

4

3

34

3

3

3

4

3

4

2

4 4

2

3

13

4

4

4

4

2

2

4

4

3 3

4

3

2

1

3

43

1

2

4

3

41

2

3

4

2

3

4

3

44

3

2

4

3

4 3

4

22

1

3

4

1

3

3

4

3

3

4

3

3

2

4

2

3

44

2

33 4

41

4

3

2

23

3

3

2

1

2

44

3

3

32

4

3

2

33

2

4

3

4

4 3

3

4

2

4

33

1

2

3

2

4

4

3

3

4

3

4

3

33

4

3

1

3

3

4

3 3

2

3

34

2

1

2

3

4 4

4 3

41

2

3

3

4

1

1

22

1

3

2

2

4

2

44

44

4

3

4

4

3

444

1

2

3

2

4

4

34

4

3

3

4

4

4

4

3

3

2

2

2

4

4

3

3

3

4

333

3

3

4

1

2

4

3

4

4

4

4

34

3

4

33

3

3

2

1

323

3

3

11

4

4

3

4

4

3

4

3

3

4 4

3114

2

4

4

3 3

44

3

2

3

2

243

4

3

4

3

4

3

3

2

3

333

4

4 3

4

4

3

4

3

4

2

1

23

1 1

2

4

4

3

4

3

3

4

3

3

4 2

3

3 3

3

1

2

314

3

3

4

2

3

3

2

22

3

4

3

4

4

3

1

2

3 4

44

4

2

3

33

3

4

2

4

4

42

3 3 3

2

2

4

4

4

14

43

3

1

4

1

2

3

3

2

2

4

4

2

3

14

3

34

4

4

4

3

4

2

1

2

4

3

3

2

3

3

3

1

4

3

3

3

2

3

33

3

3

4

3

4

1

4

3

4

2

3

4

4

3

01

23

45

lny

0 2 4 6lnk

Fd



Mixture regressions: total probability by technology group

SECTOR prob1 prob2 prob3 prob4 prob5 # firmsFd 916 1813 2829 2043 0 7601Bv 648 405 0 0 0 1053TX 526 1214 514 0 0 2253WA 702 487 566 1346 336 3438LP 117 1091 594 0 0 1802Wo 2031 778 626 0 0 3435Pa 770 467 0 0 0 1237Pr 696 1947 0 0 0 2643Ch 990 1092 0 0 0 2082Ph 241 263 0 0 0 504RP 2029 1279 0 0 0 3308NM 838 1100 934 830 0 3702BM 625 730 0 0 0 1355MP 1261 4438 3403 2631 0 11732EP 1144 1228 0 0 0 2372El 1232 1086 0 0 0 2318

Ma 2543 3058 0 0 0 5601MV 1008 455 0 0 0 1463Tr 352 267 0 0 0 619

Total 18668 23199 9466 6850 336 58518


Analysis WTFP and BTFP

Step 2 - Computation of WTFP and BTFP

Use mH to refer to the locally optimal (i.e. ”frontier”) technologyyi ,mH |k = ki > yi ,m|k = ki ∀m 6= mH .

For each firm, we are able to compute the predicted values y and aunder the actual (m) and the frontier tech (mH):

yi ,m = αm + βmki and yi ,mH = αmH + βmHki

ai ,m = yi − yi ,m and ai ,mH = yi − yi ,mH

These map into...



Step 2 - Computation of WTFP and BTFP

BTFP =mH∑m=1

pri ,m · (yi ,m − yi ,mH ) =mH∑m=1

pri ,m · (ai ,mH − ai ,m)

WTFP =mH∑m=1

pri ,m · ai ,m.

ln yi

single technology

ln ki

. firm

ai

panel a

∧

yi

yi ∧

ln yi

m1

ln ki

. firmm2

m2

panel b

localized fron2er technology

yi;m ∧

yi

yi;m ∧

H

WtTFP

BtTFP



Step 3 - Quantification of WTFP and BTFP Gaps

Compute the labour productivity gaps associated with:

being relatively less productive within a given technology group (thatis, displaying a relatively low ability in exploiting the given technology,as measured by the idiosyncratic component ai ,m)

WTFP gapi = WTFPbest 5% −WTFPi

not choosing the frontier technology. This is equivalent to quantifyingthe productivity gain each firm would enjoy by filling the gap with thehighest productivity firms in the same technology group or byswitching to the best available technology in the sector.

BTFP gapi = −BTFPi



Step 3 - Sectoral distribution of BTFP gaps

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Step 3 - Scatterplot of the WTFP and BTFP gaps(sectoral averages)



Aggregate gaps (sectoral averages)

SECTOR WTFP gap BTFP gapFd 70.6 517.4Bv 139.0 1154.3TX 89.8 396.4WA 118.4 159.5LP 108.0 251.2Wo 80.2 37.6Pa 85.7 1286.8Pr 66.0 0.0Ch 103.0 1391.9Ph 67.5 0.0RP 91.0 988.3NM 113.4 1496.7BM 91.3 1346.0MP 90.4 543.8EP 43.3 0.0El 97.2 284.4Ma 85.3 242.7MV 93.9 500.3Tr 110.6 698.2Total 89.0 544.4


Analysis Markers - Correlations

Step 4 - Correlation with Tech Balance of Payments andfirm-level markers of WTFP and BTFP

WTFP and BTFP cross-section regressions using

I OECD Stat (2015) data from the technology balance of payments,measuring international technology receipts - i.e. outcomingtechnology flows (variable Tech Receipts) - and payments - i.e.incoming technology flows (variable Tech Payments). Data coverslicence fees, patents, purchases and royalties paid, know-how, researchand technical assistance.

I firm-level characteristics (age, listed, intangibles, liquidity, MNE)



Step 4 - Correlation with Tech BoP and firm-level markersof WTFP and BTFP (cont)

Table 5: Markers of WTFP and BTFP

WTFP gapi WTFP gapi WTFP gapi BTFP gapi BTFP gapi BTFP gapi(all firms) (> median) (< median) (all firms) (> median) (< median)

Tech Payments cs 32.582 31.480 25.858* 710.963** 1803.711*** -119.367**(20.074) (22.403) (13.793) (326.796) (426.759) (58.826)

Tech Receipts cs -54.449*** -108.717*** -10.855 -567.197* -1764.148*** 148.297**(18.120) (35.637) (11.972) (312.453) (502.529) (60.014)

Firm Age f 1.093*** -0.138 0.779*** 100.117*** 51.610*** 7.387***(0.380) (0.554) (0.255) (7.745) (11.058) (1.430)

Listed f 9.738** 6.588 3.994 -130.738 -321.041** -14.090(4.169) (7.200) (2.861) (91.866) (144.158) (56.233)

Firm Intangibles f -1.117*** 0.130 -0.587*** 8.242*** 7.739* 0.213(0.148) (0.220) (0.095) (3.170) (4.363) (0.520)

Liquidity Ratio f -14.159*** -8.054*** -5.210*** -171.957*** -154.938*** -9.076***(0.461) (0.614) (0.291) (9.727) (13.581) (1.543)

Multinational f -3.051*** -3.857*** 0.328 96.911*** 31.274 21.369***(0.820) (1.188) (0.559) (19.580) (24.406) (4.062)

Constant 19.447*** 77.146*** 35.924*** 144.516*** 646.709*** 76.390***(2.403) (6.205) (1.609) (49.322) (68.108) (10.149)

# obs. 21455 8896 12559 21455 13084 8371Country FE yes yes yes yes yes yesSector FE yes yes yes yes yes yesR2 0.406 0.422 0.245 0.267 0.439 0.442

f firm-level; cs country-sector-level.Median of the WTFP and BTFP distribution referred to in columns 2-3 and 5-6, respectively.Robust standard errors are in parenthesis. All variables are in logs.* p < 0.10, ** p < 0.05, *** p < 0.01.

24



Step 4 - Correlation with Tech BoP and firm-level markersof WTFP and BTFP (cont)

WTFP gaps are lower in country-sectors in which the outcoming flowsof tech are higher

higher incoming (outcoming) flows of technology are associated tohigher (lower) average and dispersion of BTFP gaps.


Analysis Conclusions

Conclusions

Mixture models can be used to estimate technology-specificproduction functions

I avoiding any type of ex-ante assumption on the degree of technologicalsharing across firms and countries (the number of available technologiesis endogenously determined by the mixture estimation algorithm ⇒ thedistribution of technologies across firms is observed ex-post)

I controlling for simultaneityI multiple technologies within-sector

This allows disentangling betweenI firm productivity relative to the other firms in the same technology

group (i.e. Within-technology TFP - WTFP) ⇒ a firm’s ability toexploit a given technology (compared to the other firms using the sametechnology)

I firm productivity relative to the labour productivity that the firm couldhave reached, given its capital-labour ratio, had it chosen the frontiertechnology (i.e. Between-technology TFP - BTFP) ⇒ aquantification of the labour productivity gap associated with thetechnological choice.



Conclusions (cont)

The availability of a large international covarage is key in order topotentially capture all the technologies available worldwide.

Our estimates, based on Orbis (' 73.000 worldwide distributedmanufacturing firms, 2012-2014) point to

I Sectoral number of technologies ranging from 2 to 5, depending on theindustry.

I When evaluated wrt the frontier, we find that

while the WTFP gaps to be much larger than the latter in mostsectors, the relative role of these two dimensions varies considerablyacross firms, being often reversed.

higher incoming (outcoming) flows of technology are associated tohigher (lower) average and dispersion of the between-technology TFPgaps.



Conclusions (cont)

Neglecting the existence of multiple technologies results into:I biased and more dispersed TFP estimatesI uncorrect identification of the TFP markers and distorted policy

implications.

⇒ this stresses the growing importance of the availability ofinternationally comparable data in dealing with the technologicaldimension of firm-level productivity.



Ongoing work and next steps

Use wages to (roughly) purge the estimated technology (and thus theadopted notion of technology) of human capital effects.

Extend the time span to allow firms to change technology:I allow for firm effects in the empirical analysis of TFP and Tech

Adoption markersI see whether the technology distribution of entrants and incumbent

firms move together, as suggested by e.g. Aw et al. (2001) and Fosteret al. (2001) for productivity (not for technology!)

Product/process technology...


Reserve slides

RESERVE SLIDES


Reserve slides The importance of controlling for different technologies.

Production functions: comparison with standard OLS(dashed line)

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TFP densities

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Different TFP estimates



Difference between corrected and non corrected OLS

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Reserve slides Variables

Variables description

Added Value. Log of added value. Added value is defined as profit forperiod + depreciation + taxation + interests paid + cost ofemployees. This is a firm-level variable, covering years from 2012 to2014, which we deflated using the OECD-Stan sector-country specificdeflators (source: Orbis (2015))Labour Input. Log of total number of employees included in thecompany’s payroll. This is a firm-level variable, covering years from2012 to 2014, which we deflated using the OECD-Stan sector-countryspecific deflators (source: Orbis (2015))Capital Input. Tangible assets: buildings, machinery and all othertangible assets. This is a firm-level variable, covering years from 2012to 2014, which we deflated using the OECD-Stan sector-countryspecific deflators. (source: Orbis (2015))Firm Intangibles. Intangible assets: formation expenses, researchexpenses, goodwill, development expenses. 2012-2014 (source: Orbis,2015)


Reserve slides Variables

Variables description (cont)

Firm Size. Log of total number of employees included in thecompany’s payroll. This is a firm-level variable, covering years from2012 to 2014, which we deflated using the OECD-Stan sector-countryspecific deflators (source: Orbis (2015))

Firm Age. Age of the firm (years). This is a firm-level variable,covering years from 2012 to 2014. (source: Orbis (2015))

Listed Firm. Dummy variable (1 = the firm is listed in the stockmarket, 0 = otherwise). This is a firm-level variable, covering yearsfrom 2012 to 2014. (source: Orbis (2015))

Multinational. Dummy variable (1 = the firm is part (as a controlleror controlled enterprise) of multinational group. This is a firm-levelvariable, covering years from 2012 to 2014. (source: Orbis (2015))


Reserve slides Number of technologies

Selection criteria resultsFigure 1: Selection criteria results for the sectoral number of clusters

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Reserve slides Number of technologies

Selection criteria results (cont)

Figure 1: Selection criteria results for the sectoral number of clusters

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technology-specific production functions · technology-specific production functions michele...

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