does exporting improve matching? evidence from french linked … · rms export (counterfactual) i...

Does Exporting Improve Matching?Evidence from French Linked Firm-Employee Data

M. Bombardini1,2, Gianluca Orefice3, M. D. Tito1

1Vancouver School of Economics (UBC), 2CIFAR, 3CEPII

February 27, 2015

M.D. Tito (VSE) Trade and Sorting February 27, 2015 1 / 31

Research Questions

Does trade influence the sorting patterns of workers across firms?

What are the welfare implications of the changes in sorting due to internationaltrade?


The importance of matching between workers & firms

Sorting of workers across firms has important implications for:

Efficient output production when there are complementarities orsubstitutabilities

I Becker (1973): in a frictionless economy, complementarities ⇒ positiveassortative matching.

I In presence of search frictions, generally inefficient worker-to-firm assignment.

Wage inequality and segregation

I Card, Heining and Kline (2013): 35% increase in wage inequality in WestGermany 1985-2009 explained by increased assortative matching.


Motivation: some stylized facts

Fact # 1: Within-firm wage inequality accounts for a significant share ofoverall wage inequality

I Helpman et al. (2014): within-firm wage inequality 45% of overall wageinequality in Brazil in 1990

I within-firm wage inequality in France in 1995: 62.7% of overall wageinequality.

Fact # 2: Changes in sorting patters

I Card, Heining and Kline (2013): correlation between employee andestablishment fixed effects in Germany goes from 0.034 in 1985-1991 to 0.249in 2002-2009.

I Hakanson et al. (2013): within-firm variance in cognitive skills falls from 0.802in 1986 to 0.697 in 2008 in Swedish firms; between-firm variance increasedover the same period (from 0.134 to 0.176)


Explaining the increase in sorting

Technology, stronger complementarities (Hakanson et al. (2013)) and increasedmobility likely played a role in increased sorting.

But could globalization have something to do with this pattern of increasedsorting?

Information Frictions induce suboptimal partnerships: firms and workers agree tomatch as soon as they find a partner productive enough ⇒ Matching Sets.

In presence of information frictions, trade modifies the incentives to match

1 Access to foreign markets expands revenues; then, potential value from anideal match is higher.

2 Opportunity cost from a suboptimal partnership is higher

3 Smaller deviations relative to the optimal assignment ⇒ Smaller normalizedMatching Sets ⇒ smaller output losses.


Outline and Preview of Results

What we do:1 Theory

I a dynamic model with costly search and shocks to export opportunities

2 Empirical MethodologyI Construct a measure of variation of worker types within firm

3 Regression AnalysisI Findings:

F Exporters have 9% sd’s lower dispersion of worker types, compared to similarnon-exporters

4 General Equilibrium AnalysisI two country general equilibrium version of the model, calibrated to French

momentsI gains from trade are increasing in search frictions


Related Literature

Assignment and Trade: Grossman and Maggi (2000), Bombardini, Gallipoli,Pupato (2013), Davidson, Matusz and Shevchenko (2008), Davidson,Heyman, Matusz, Sjoholm and Zhu (2012), Ohnsorge and Trefler (2007).

Wages and export status: Amiti and Davis (2012), Amiti and Cameron(2012), Schank, Schnabel and Wagner (2007), Helpman, Itskhoki andRedding (2010), Helpman, Itskhoki, Muendler, Redding (2013), Akerman,Helpman, Itskhoki, Muendler and Redding (2013), Sampson (2014).

International trade and wage inequality: Feenstra and Hanson (1996),Yeaple (2005), Verhoogen (2008),Helpman, Itskhoki and Redding (2010),Bustos (2011), Monte (2011), Burstein and Vogel (2012).


Which Theoretical Framework?

Possible existing candidates

Sampson (2014): frictionless positive assortative matching (PAM) ⇒ nowithin-firm variation in worker types.

Helpman, Itskhoki and Redding (2010) and Helpman, Itskhoki, Muendler andRedding (2010)

I Workers are not ex-ante heterogeneous.

I Addition of heterogeneity requires a dynamically-consistent framework


Costly Search and Imperfect PAM

We follow Eeckhout and Kircher (2011) and Atakan (2006)

Two groups of heterogeneous agents, workers and firms.

I Worker type θ distributed g (θ) over [0, 1].I Firm type ψ distributed h (ψ) over [0, 1].

Supermodular production function.

f (θ, ψ) = (θψ)σ

σ > 0


Domestic sales and exportingEmbed in a model of monopolistic competition with Dixit-Stiglitz CESpreferences with elasticity of demand η:

Rd (θ, ψ) = (θψ)σ(η−1)η E

1η

Exporting decision: ( export cut-off )I heterogeneous fixed costs of exporting (Helpman, Itskhoki, Redding, 2013) ⇒

compare exporters and non-exporters of similar productivity Evidence

I fixed cost heterogeneity is not essential to the resultsF version with homogeneous fixed export cost a la Melitz ⇒ only most productive

firms export (counterfactual)

I exporting matches allocate output between domestic and foreign market(equate marginal revenues across markets).

Total revenues for an exporting firm:

Rx (θ, ψ) = (θψ)σ(η−1)η

(E + E∗τ1−η

) 1η

Small Open Economy & Partial equilibrium analysis (only to derive analyticalresults)


Exporting as a positive productivity shockRewriting domestic firm and exporting firm revenues,

Rd (θ, ψ) = (Adθψ)σ(η−1)η

Rx (θ, ψ) = (Axθψ)σ(η−1)η

where Ax > Ad

Remark 1 If looking at revenues, changes in productivity have the same impactas changes in market access.

Reformulate the problem in terms of adjusted productivity Aiψ ≡ ϕRank firms in terms of ϕ and normalize their distribution on [0, 1].

Assume that θ and ϕ are uniformly distributed, g (·) on [0, 1]. (thisassumption is required to derive analytical results).

Rewrite revenues asR (θ, ϕ) = (θϕ)

α

where α ≡ σ(η−1)η

Who are the Exporters?


SearchTime Horizon: Two periods, no discounting

abstract from search frictions a la Shimer and Smith (2000).

First Period: Random Meeting between a firm and a worker. Upon meeting,

If they both accept to match, they produce and split the surplus according toNash bargainingIf they do not match, they both pay a cost c to search in the second period(Atakan, 2006 and Chade, 2001)

Second Period: matching occurs according to competitive and frictionlessassignment.

Why a Two period Model:second period pins down outside options of the agents.

I results are not due to frictionless assignment in the second period

focus on first period allocationQualitatively similar to infinite horizon version (used later in the calibration).

Infinite Horizon: Setting , Infinite Horizon: Trade Equilibrium

Equilibrium


Solving the model

Second Period

Guess the distribution of the unmatched and the matching patterns

Determine firms and workers’ pay-offsI workers receive their marginal productI firms get the residual, after wages are paid to the worker

First Period

Outside options: pay-off net of search costs

Acceptance decision: if revenues in a match are larger than the outsideoption of both agents

Verify that the measures of the unmatched is compatible with the matchingsets


Matching RangeMatching range d (ϕ) for firm ϕ:

d (ϕ) = u (ϕ)− l (ϕ)

where

l (ϕ): lowest worker type to match with firm ϕ.

u (ϕ): highest worker type to match with firm ϕ.

Eeckhout and Kircher (2011) and Atakan (2006) show that boundaries ofacceptance set, l (ϕ) and u (ϕ), are increasing in ϕ.

Prediction 1: Higher types of firms match on average with higher types ofworkers ⇒ Exporters hire better workers.

Two considerations on the matching range:

dispersion measure d (ϕ) is scale dependent

higher ϕ match with higher average worker type.

interested in comparing not where the matching range is located, butconditional on the location how large is the matching range

Matching Set Characterization


Normalized measures of worker type variation by firmWe normalize the dispersion measure by the average worker type hired by firm ϕ, i.e. a (ϕ)

d1 (ϕ) = u1 (ϕ)− l1 (ϕ) , where u1 (ϕ) =u (ϕ)

a (ϕ), l1 (ϕ) =

l (ϕ)

a (ϕ)

similar implications if constructing the dispersion measure on a logarithmic scale

Normalized matching range is decreasing in firm type. Intuition

Prediction 2: Exporters have smaller dispersions of worker types compared to nonexporters, conditioning on average worker type

u1HjLl1HjL

0.0 0.2 0.4 0.6 0.8 1.0j

1

2

3

4

5

Θ

a HjL

Matching Bounds normalized by averageworker type (firm productivity on x-axis)


Measuring the cost of FrictionsLoss in a match (θ, ϕ)

Deviation from the efficient allocation Losses

L (θ, ϕ) =1

2

(ϕ2α + θ2α − 2 (ϕθ)α

)

Note: more productive firms have higher revenues ⇒ larger absolute losseswe construct a firm-level measure of revenues losses, normalizing by theoptimal allocation

RL =

∫ u(ϕ)l(ϕ)

12

(ϕ2α + θ2α − 2 (ϕθ)α

)dθ

12

∫ u(ϕ)l(ϕ)

(ϕ2α + θ2α) dθ

firm-level revenue losses, relative to the optimal allocation, are decreasing in the firm type

0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8RL(ϕ)

ϕ

Normalized losses by productivity level. Firm productivity level on x-axis.


Measuring the cost of FrictionsLoss in a match (θ, ϕ)

Deviation from the efficient allocation Losses

L (θ, ϕ) =1

2

(ϕ2α + θ2α − 2 (ϕθ)α

)Note: more productive firms have higher revenues ⇒ larger absolute losses

we construct a firm-level measure of revenues losses, normalizing by theoptimal allocation

RL =

∫ u(ϕ)l(ϕ)

12

(ϕ2α + θ2α − 2 (ϕθ)α

)dθ

12

∫ u(ϕ)l(ϕ)

(ϕ2α + θ2α) dθ

firm-level revenue losses, relative to the optimal allocation, are decreasing in the firm type

0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8RL(ϕ)

ϕ

Normalized losses by productivity level. Firm productivity level on x-axis.


From Theory to Empirics

Theory focuses on ϕ ≡ A · ψ

disentangle the effect of ψ from the effect of A

I identify the firm type ψ.

I differences in market access A: exporters vs non-exporters.

Predictions for the empirical analysis

Cross-sectional:I Exporters have smaller matching sets than similar (conditional on ψ)

non-exporters, conditioning on average worker type.I Exporters have better workers than similar (conditional on ψ) non-exporters.

(confirming previous predictions)

Variation across sectors and over-time: In presence of larger shocks toexport opportunities ⇒ larger differences in matching sets between exportersand non-exporters

Theoretical Extensions


Empirical Strategy

Empirical strategy - Two conceptual steps:

1 Construct workers’ types.

2 Construct average worker type and measures of dispersion of worker type atthe firm level


French DataMerging three sources:

Matched Employer-Employee Data (DADS)I Panel on Employed Workers (all workers born in the month of October).I Information on annualized real earnings, total number of hours worked,

gender, year and place of birth, occupation, experience, department ofresidence, industry of the employing firm.

Firm Level Data (EAE)I All firms with at least 20 employees.I Information on value added, sales, total employment, industry

Customs DataI Exports by country-HS6 level.

Additional Sources

WITS Dataset ⇒ Information on Tariffs.

COMTRADE Dataset ⇒ Information on World Imports .

Years: 1995-2007.

Institutional Context


Workers Types

Average lifetime wage of worker i : wiI from the model: average lifetime wage strictly increasing in worker type θ

(imperfect positive assortative matching)

Fixed Effects from a wage regression a la Abowd, Kramarz and Margolis(AKM) ( Identification ) - Standard specification:

lnwit = x′itβ + θi + ψj(i,t) + εit

I wit is the wage of worker i in year tI θi is a worker i dummyI ψj(i,t) is a firm dummy =1 if worker i is employed at firm j at t

F Eeckhout and Kircher (2011): ψj(i,t) has no systematic relationship with the

true firm type. ( Fixed Effects as Firm Types )F firm pay-offs are better proxies for firm type.

I xit is a set of observable characteristics (quartic polynomial in experience,Ile-de-France, department of residence, gender interacted with experience andyear dummies)

I Random Mobility?


Constructing the Dependent Variables

AvWorkerTypejt =1

njt

∑i∈Ijt

wi

Measures of Disperion

SdWorkerTypejt =1

njt

√∑i∈Ijt

(wi − AvWorkerTypejt

)2IQRWorkerTypejt = wj,75th − wj,25th


Empirical specification 1

Pooled cross-section

SdWorkerTypejt = β0 + β1Exportjt + β2Firm Typejt +Dst + ujt

AvWorkerTypejt = β′0 + β′1Exportjt + β′2 Firm Typejt +Dst + u′jt

Exportjt= 1 if firm j exports at t

Firm Typejt is one of three proxies: V Apwjt, logEmpjt and DomSharejt

Other controls: N.occjt, white sharejt and log Productsjt, quadratic in thenumber of observations

Sector-year fixed effects Dst

Standard errors clustered at firm level


Standard Deviation: Regression ResultsTable 6: Pooled Cross-Section Regressions: Standard Deviation of Life-time Wage, more than 5 workers

(1) (2) (3) (4) (5) (6)Variables Standard Deviation of Lifetime Wage, more than 5

Export -0.035a -0.020c -0.039a -0.053a -0.024b -0.037a

(0.011) (0.011) (0.011) (0.011) (0.011) (0.013)N.Occ. 0.030a 0.013a 0.011a 0.029a 0.025a

(0.002) (0.001) (0.001) (0.002) (0.002)log empl -0.095a -0.095a -0.091a

(0.005) (0.005) (0.005)log dom.share -0.007a 0.001 -0.0001

(0.002) (0.002) (0.002)log VA per worker 0.038a 0.036a 0.024a

(0.006) (0.006) (0.006)white share 0.154a

(0.016)log N. Products 0.008b

(0.003)Avg. Lifetime Wage -0.087a

(0.005)Sector-Year y y y y y y

Obs. 57,996 57,996 57,996 57,996 57,996 57,996R2 0.070 0.091 0.074 0.075 0.093 0.124

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zerofor non-exporters.Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm.Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: Cross-Sectional Regressions for firms with more than 5 workers, years 1995-2007. Different specifications in the columns. Standard errors, clustered at the level ofthe firm, are reported in parenthesis. All specifications but the first include a quadraticin the number of sampled workers, to control for the precision of the left-hand sidevariable.

6


Average Worker’s Type: Regression Results

Standard Prediction: Exporters tend to match with better workers.Table 5: Pooled Cross-Section Regressions: Average Lifetime Wage,more than 5 workers

(1) (2) (3) (4) (5) (6)Variables Average Lifetime Wage, more than 5

Export 0.167a 0.073a 0.078a 0.097a 0.050a 0.034b

(0.013) (0.012) (0.013) (0.012) (0.012) (0.014)N.Occ. 0.016a 0.035a 0.037a 0.011a -0.003

(0.002) (0.002) (0.002) (0.002) (0.002)log empl 0.135a 0.133a 0.139a

(0.007) (0.007) (0.007)log dom.share 0.027a 0.004b 0.003


(0.009) (0.009) (0.009)white share 0.496a



Obs. 58,541 58,541 58,541 58,541 58,541 58,541R2 0.119 0.179 0.164 0.183 0.208 0.254

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable iszero for non-exporters.Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: Cross-Sectional Regressions for firms with more than 5 workers, years 1995-2007. Different specifications in the columns. Standard errors, clustered at the levelof the firm, are reported in parenthesis. All specifications but the first include aquadratic in the number of sampled workers, to control for the precision of theleft-hand side variable.

5


Interpretation and Robustness

Take column 6 with all controls: coefficient on export is -0.037

Standard deviation of dependent variable is 0.41. Summary Statistics

Exporters have tighter matching sets: reduction in standard deviation by 9%standard deviations

Exporters have better workers: increase in average worker type by 3.9%standard deviations

Robustness Checks

Workers Fixed Effects

Blue and White Collars , Blue and White Collars, with Fixed Effects

Interquartile Range

Stayers vs newly hired workers

GLS regressions

IV Regressions


An Alternative Test: Correlation of TypesSmaller matching sets ⇔ Better Sorting.

Exporters should display better sorting.

Strength of sorting: correlation between firm and worker types.

compare strength of sorting between exporters vs non-exporters

Specification 1B

RCorr(AvWorkerTypejt,FirmTypejt

)st

= β0 + β1Exportst +Ds +Dt + εst

where FirmTypejt is DomSharejtTable 11: Sectoral Rank Correlations

(1) (2) (3) (4) (5) (6) (7) (8)Variables Rank Correlation

Export 0.042a 0.029a 0.023b 0.017c 0.042a 0.037a 0.026a 0.027c

(0.008) (0.010) (0.010) (0.010) (0.008) (0.014) (0.010) (0.014)log empl 0.009c 0.004 0.003 -0.001

(0.005) (0.005) (0.009) (0.009)log VA per worker 0.077a 0.075a 0.064a 0.064a

(0.017) (0.017) (0.023) (0.024)Sector,Year y1 y1 y1 y1 y2 y2 y2 y2

Obs. 3,836 3,836 3,836 3,836 3,836 3,836 3,836 3,836R2 0.041 0.042 0.049 0.049 0.195 0.195 0.198 0.198

1 2 digit sector dummies.2 4 digit sector dummies.log empl. log-employment.logVA per worker: log-value added per worker.Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995-2007. Different spec-ifications in the columns. Standard errors, clustered at the level of the firm, are reported in parenthesis.All specifications but the first include a quadratic in the number of sampled workers, to control for theprecision of the left-hand side variable.

Table 12: GLS Regressions: Sectoral Rank Correlations

(1) (2) (3) (4) (5) (6) (7)Variables Rank Correlation

Export 0.037a 0.033a 0.018b 0.024a 0.035a 0.011 0.022b

(0.009) (0.009) (0.009) (0.009) (0.011) (0.007) (0.011)log empl 0.002 -0.004 -0.001 -0.008


(0.014) (0.015) (0.020) (0.021)Sector,Year y1 y1 y1 y1 y2 y2 y2

Obs. 3,812 3,812 3,812 3,812 3,812 3,812 3,812R2 0.082 0.082 0.094 0.094 0.333 0.343 0.343

1 2 digit sector dummies.2 4 digit sector dummies.log empl. log-employment.logVA per worker: log-value added per worker.Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995-2007.Different specifications in the columns. Standard errors, clustered at the level of the firm, arereported in parenthesis. All specifications but the first include a quadratic in the number ofsampled workers, to control for the precision of the left-hand side variable.

11


Empirical specification 2

Exploit shocks in the export market for sector s:

SdWorkerTypejt = β0 + β1Mkt Accessst · Exportjt +

+β2Mkt Accessst + β3Exportjt + εjt

AvWorkerTypejt = β′0 + β′1Mkt Accessst · Exportjt +

+β′2Mkt Accessst + β′3Exportjt + ε′jt

where

MktAccessst = ln∑r

tariffsr ×French exportssr,t−1French exportss,t−1

MktAccessst = ln∑r

Importssr ×French exportssr,t−1French exportss,t−1


Market Access Results

Import Demand ShocksI average reduction (β1 ¯Mkt Access + β3) in worker type dispersion for exporters

by −3.4% sd’s. Import Shock

I significant effect on average worker type for exporters in sectors with higherimport demand (β1); no increase in worker type dispersion for exporters, onaverage. Average Type

TariffsI average reduction (β1 ¯Mkt Access + β3) in worker type dispersion for exporters

by −13.7% sd’s. Tariffs

I no significant effect on average worker type for exporters in sectors with lowertariffs. Average Type

Robustness Checks

Removing firms switching status over 2 years (continuous exporters vscontinuous non-exporters)


Welfare AnalysisGeneral equilibrium analysis with two countries. At opening:

I Exporting firms: positive shock (tighten matching range)

I Import-competing firms: negative shock (loosen matching range)

I Welfare depends on degree of mismatch across these two kinds of firmsF welfare might decrease if the import-competing effect dominates

Evaluate welfare numerically: opening to trade with a symmetric country

Infinite Horizon framework with endogenous evolution of the unmatchedInfinite Horizon Condition

I Calibration to moments of the French data

I Numerical characterization of the steady state (open economy).

I Numerical characterization of the steady state equilibrium under autarky.F Compare open economy steady state equilibrium to autarky


Welfare MeasuresLook at

Changes in Real Expenditure: 22% (higher compared to autarky)I variety and worker selection effects

Changes in Real Revenue Losses: −1.36% (lower compared to autarky)I Losses under autarky −87.44% vs Losses under Trade −86.08%I worker selection effect (keeping constant the number of varieties)

Both measures are increasing in the cost of search cReal Expenditureα = 0.75 α = 1 α = 1.25

cH = 0.025 22.0% 27.2% 34.1%cM = 0.005 15.6% 16% 16.1%cL = 0.001 15.4% 15.2% 15.9%

Real revenue lossesα = 0.75 α = 1 α = 1.25

cH = 0.025 -1.36% -1.11% -1.01%cM = 0.005 -1.12% -0.95% -0.85%cL = 0.001 -1.05% -0.95% -0.82%

ci search cost, i ∈ {H,M,L}α demand elasticity


Concluding Remarks

Large effect of export status on matching behaviour between firms andworkers

Implications for welfare

I Increase in the number of variety does not account for the entire gains

I Gains from opening to trade are higher when the cost of search is higher.F Trade opening and frictions substitutes


Evidence on Matching FrictionsUS Market Size for talent acquisition: $ 124 billion.

Employer Search:

Cost per HireSize Cost per Hire

100 − 999 3, 665

1, 000 − 9, 999 3, 632

more than 10, 000 1, 949

Source: K. O’Leonard, The Talent Acquisi-ation Factbook, Bersin & Associates, 2011.

Cost per ApplicantSize Hours for Interviews N. Applications Cost per Applicant

1 − 9 6.17 5.19 1.19

10 − 25 7.14 6.27 1.14

26 − 250 9.35 6.97 1.34

251 − 4751 12.74 8.26 1.54

Source: Table from Barron, Bishop and Dulkenberg (1985).

Barron and Bishop (1985): barely significant effect of size on cost perapplicant (T-stat 1.67).

Barron, Black Loewestein (1987): larger employers devote more resources onsearch, but no effect on hours spent on recruiting per applicant

Back


AKM Regression: Identification

Wage Equationwit = ψi + θj(i,t) + εit

2 Firms, A and B, and 3 workers, 1, 2 and 3

𝐴

𝐵

1

2

3

𝐸�𝑤2,𝑡� = 𝜃2 + 𝜓𝐴


AKM Regression: IdentificationWage Equation

wit = ψi + θj(i,t) + εit

2 Firms, A and B, and 3 workers, 1, 2 and 3

𝐴

𝐵

1

2

3

𝐸�𝑤2,𝑡+1� = 𝜃2 +𝜓𝐵

E [w2,t+1]− E [w2,t] = ψB − ψABack


Empirical Methodology: Firms’ Types

Firms’ fixed effects: difference between the wage the firm pays and the averagewage the worker receives.

They capture:

the variation in wages across the pool of workers belonging to a firm’smatching set (wage effect)

the variation of the matching bands (matching set effect)

The total effect depends on the agents’ distributions: both are zero if workers andfirms are distributed uniformly. Thus, zero correlation between firms’ fixed effectsfrom AKM decomposition and firms’ true type.

Back


Distribution of Agents’ Types

Distribution of Workers Fixed Effects.Distribution of Firm Types - percentiles

of Domestic Market Share.

Back


Random Mobility?Positive and Negative Changes when moving to a different job

Sign PercentagePositive 54.82%Negative 45.18%

Back


Correlation between Worker Types and proxies for FirmTypes

Table 2: Measuring Sorting Patterns, Manufacturing Sectors

(4) (5) (6) (7)ψ, Avg. Avg.Share,T ype Avg.Wage

NAF Industry Label No Firms ρS1 p-val2 ρS

1 p-val2

10 Food 9 -0.96 0.00 - -11 Beverage 8 -1 - - -12 Tobacco prods - - - - -13 Textiles - - - - -14 Clothing 270 -0.84 0.00 0.18 0.0015 Leather/shoes - - - - -17 Paper 1317 -0.85 0.00 0.14 0.0018 Printing 1286 -0.86 0.00 0.14 0.0019 Refining 402 -0.88 0.00 0.42 0.0020 Chemical 666 -0.86 0.00 0.17 0.0021 Pharma 780 -0.79 0.00 0.30 0.0122 Plastics 2070 -0.76 0.00 0.13 0.0023 Non-metallic prods 59 -0.64 0.00 0.13 0.3324 Metalworking 1565 -0.72 0.00 0.33 0.0025 Metal prods 1987 -0.83 0.00 0.25 0.0026 Info/elec/opt 947 -0.82 0.00 0.27 0.0027 Elec equip 595 -0.84 0.00 0.14 0.0028 Machinery 5433 -0.81 0.00 0.21 0.0029 Automotive 2898 -0.82 0.00 0.28 0.0030 Other trans equip 126 -0.74 0.00 0.16 0.0731 Furniture 969 -0.81 0.00 0.25 0.0032 Other mfg 878 -0.71 0.00 0.13 0.0033 Repairs 1197 -0.79 0.00 0.23 0.00

Manufacturing 23388 -0.80 0.00 0.20 0.00

1 Spearman correlation coefficient.2 p-value from testing independence between the variables.Notes: Columns (4)-(5): Rank correlation and significance level between the average

worker type, (Avg.Worker), and the firm fixed effect (ψ) from an AKM decompositionincluding a quartic polynomial in experience, a dummy for workers residing in Ile-de-France, time dummies and all the interactions with the gender dummy.Columns (6)-(7): Rank correlation and significance level between the average lifetime

wage of workers, (Avg.Wage), and the firm type, proxied by the average domesticmarket share in 4-digit sectors Avg.Share.

2

Back


Montecarlo Simulation

Dependent Variable Bias

α = 0.75 α = 5Average St. Dev. Length St. Dev.

n = 5Non-Exporters 95.71% 68.68% 94.02% 7.51%Exporters 95.46% 68.60% 93.89% 7.33%



Back


Summary Statistics

Table 2: Pooled Cross-sectional Regressions: Standard Deviation of Wages, at least4 workers

(1) (2) (3) (4) (5) (6)Variables Standard Deviation of Wages within a Firm, at least 4 workers

Export -0.0111 0.00339 -0.0187b -0.0341a -0.00145 -0.00111(0.00771) (0.00785) (0.00787) (0.00774) (0.00790) (0.00669)

N.Occ. 0.0409a 0.0199a 0.0166a 0.0397a 0.0317a

(0.00167) (0.00141) (0.00136) (0.00165) (0.00124)log empl -0.101a -0.101a -0.0145a

(0.00443) (0.00462) (0.00351)log dom.share -0.00844a 0.000335 0.00213*

(0.00147) (0.00153) (0.00120)logVA per worker 0.0432a 0.0395a 0.126a

(0.00588) (0.00589) (0.00506)white share 0.530a

(0.0106)Avg Worker Type -0.783a

(0.00732)logN. Products 0.0122a

(0.00223)Constant 0.568a 0.764a 0.454b 0.306 0.583a 7.276a

(0.209) (0.225) (0.214) (0.209) (0.224) (0.185)

Obs. 88,813 88,813 88,813 88,813 88,813 88,813R2 0.029 0.048 0.034 0.035 0.050 0.546

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters.Avg Worker Type: average worker fixed effect, estimated by the AKM decomposition, by firm.Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: Cross-sectional Regressions for firms with at least 4 workers, years 1995-2007. Differentspecifications in the columns. Standard errors, clustered at the level of the firm, are reported inparenthesis. All specifications but the first include a quadratic in the number of sampled workers,to control for the precision of the left-hand side variable.

Table 3: Summary Statistics

Mean Median Std Deviation

Avg. Worker Type -0.04 -0.02 0.86Std Dev. Worker Fixed Effects 0.62 0.52 0.41Std Dev. Worker Fixed Effects, White Collars 0.55 0.47 0.36Std Dev. Worker Fixed Effects, Blue Collars 0.50 0.36 0.41Num. Occupation 4.90 4.00 2.44Domestic Market Share 0.03 0.01 0.08Employment 290.48 134.00 715.65Products 8.57 9.01 4.22Share of Non Production Worker 0.34 0.29 0.25Value Added per worker 70.76 45.71 161.35

2

Back


Average Worker Type measured as Average of Workers’Fixed Effects

Table 3: Pooled Cross-sectional Regressions: Average, more than 5workers

(1) (2) (3) (4) (5) (6)Variables Average of Workers’ Fixed Effects, more than 5 workers

Export 0.087a 0.045c 0.047c 0.052b 0.037 0.019(0.025) (0.026) (0.026) (0.026) (0.026) (0.028)

N. Occ 0.011a 0.017a 0.018a 0.009a -0.002(0.004) (0.003) (0.003) (0.004) (0.004)

log empl 0.045a 0.045a 0.048a

(0.012) (0.013) (0.013)log dom.share 0.008a 0.000 -0.000

(0.004) (0.004) (0.004)logVA per worker 0.065a 0.065a 0.019

(0.014) (0.014) (0.014)white share 0.405a

(0.035)logN. Products 0.009


Observations 56,938 56,938 56,938 56,938 56,938 56,938R-squared 0.021 0.027 0.026 0.027 0.028 0.040

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable iszero for non-exporters.Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995-2007. Different specifications in the columns. Standard errors, clustered at thelevel of the firm, are reported in parenthesis. All specifications but the first includea quadratic in the number of sampled workers, to control for the precision of theleft-hand side variable.

3


Standard Deviation of Workers’ Fixed Effects

Table 4: Pooled Cross-sectional Regressions: Standard Deviation, more than 5workers

(1) (2) (3) (4) (5) (6)Variables Standard Deviation of Workers’ Fixed Effects, more than 5 workers

Export -0.033a -0.018c -0.037a -0.050a -0.023b -0.035a

(0.011) (0.011) (0.011) (0.010) (0.011) (0.011)N. Occ 0.029a 0.014a 0.011a 0.028a 0.024a

(0.001) (0.001) (0.001) (0.001) (0.001)log empl -0.093a -0.092a -0.088a

(0.005) (0.005) (0.005)log dom.share -0.007a 0.000 -0.000


(0.006) (0.006) (0.006)white share 0.154a





N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zero fornon-exporters.Avg Worker Type: average worker fixed effect, estimated by the AKM decomposition, byfirm.Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995-2007.Different specifications in the columns. Standard errors, clustered at the level of the firm, arereported in parenthesis. All specifications but the first include a quadratic in the number ofsampled workers, to control for the precision of the left-hand side variable.

4

Back


Standard Deviation of Worker Types: White Collar

Table 7: Pooled Cross-sectional Regressions: Standard Deviation whitecollar workers, at least 4 workers

(1) (2) (3) (4) (5) (6)Variables Standard Deviation of Workers’ Fixed Effects, at least 4

Export -0.056b -0.044c -0.055b -0.062a -0.048b -0.056b

(0.024) (0.024) (0.024) (0.024) (0.024) (0.026)N. Occ 0.013a -0.000 -0.001 0.013a 0.018a

(0.002) (0.002) (0.002) (0.002) (0.002)logVA per worker 0.011 0.006 -0.002

(0.008) (0.008) (0.008)log dom.share -0.004b 0.003 0.003

(0.002) (0.002) (0.002)white share 0.200a

(0.022)log empl -0.058a -0.060a -0.041a

(0.006) (0.006) (0.007)logN. Products 0.006


(0.008)Constant 0.530a 0.722a 0.478a 0.462a 0.728a 0.570a

(0.104) (0.134) (0.105) (0.113) (0.143) (0.128)Sector-Year y y y y y y

Obs. 30,186 30,186 30,186 30,186 30,186 30,186R2 0.131 0.141 0.134 0.134 0.141 0.159

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zerofor non-exporters.Avg Worker Type: average worker fixed effect, estimated by the AKM decomposi-tion, by firm.Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: Cross-sectional Regressions for firms with at least 4 workers, years 1995-2007.Different specifications in the columns. Standard errors, clustered at the level of thefirm, are reported in parenthesis. All specifications but the first include a quadraticin the number of sampled workers, to control for the precision of the left-hand sidevariable.

7


Standard Deviation of Worker Types: Blue Collar

Table 8: Pooled Cross-sectional Regressions: Standard Deviation bluecollar workers, at least 4 workers

(1) (2) (3) (4) (5) (6)Variables Standard Deviation of Workers’ Fixed Effects, at least 4

Export -0.046a -0.028a -0.042a -0.056a -0.028a -0.032a

(0.008) (0.009) (0.009) (0.009) (0.009) (0.011)N. Occ 0.022a 0.006a 0.003b 0.021a 0.022a

(0.002) (0.001) (0.001) (0.002) (0.002)log empl -0.077a -0.075a -0.071a

(0.005) (0.005) (0.006)log dom.share -0.009a -0.003 -0.003c


(0.006) (0.006) (0.006)white share 0.005

(0.022)logN. Products 0.005


(0.005)Constant 0.578a 0.677a 0.456a 0.428a 0.551a 0.613a

(0.111) (0.145) (0.133) (0.118) (0.142) (0.180)Sector-Year y y y y y y

Obs. 62,522 62,522 62,522 62,522 62,522 62,522R2 0.033 0.045 0.035 0.034 0.045 0.072

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zerofor non-exporters.Avg Worker Type: average worker fixed effect, estimated by the AKM decomposition,by firm.Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: Cross-sectional Regressions for firms with at least 4 workers, years 1995-2007.Different specifications in the columns. Standard errors, clustered at the level of thefirm, are reported in parenthesis. All specifications but the first include a quadraticin the number of sampled workers, to control for the precision of the left-hand sidevariable.

8

Back


Standard Deviation of Lifetime Wage: Executives

Table 7.A Executives

(1) (2) (3) (4) (5) (6)Variables Standard Deviation of Average Lifetime Wage, more than 5

Export -0.137a -0.105c -0.115b -0.123b -0.101c -0.016(0.052) (0.054) (0.054) (0.053) (0.053) (0.027)

N.Occ. 0.003 -0.005c -0.007b 0.003 0.003(0.003) (0.003) (0.003) (0.003) (0.002)

log empl -0.054a -0.053a 0.025a

(0.009) (0.010) (0.007)log dom.share -0.008a -0.001 0.002

(0.003) (0.003) (0.002)log VA per worker -0.017c -0.016 0.052a

(0.010) (0.010) (0.007)white share 0.043b

(0.020)log N. Products 0.005



Obs. 11,732 11,732 11,732 11,732 11,732 11,732R2 0.153 0.164 0.158 0.157 0.165 0.586

Table 7.B Managers


Export 0.237a 0.231a 0.235a 0.226a 0.226a 0.093b

(0.056) (0.054) (0.054) (0.054) (0.053) (0.042)N.Occ. 0.004 -0.009a -0.010a 0.004 0.009a

(0.004) (0.003) (0.003) (0.004) (0.003)log empl -0.068a -0.070a 0.007

(0.012) (0.012) (0.010)log dom.share -0.00561 0.00344 0.00521

(0.005) (0.004) (0.004)log VA per worker 0.011 0.007 0.044a

(0.014) (0.014) (0.010)white share 0.079b



(0.020)

Obs. 7,440 7,440 7,440 7,440 7,440 7,440R2 0.273 0.289 0.280 0.279 0.289 0.578

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zero

for non-exporters.Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm.Notes: Cross-sectional Regressions for firms with at least 4 workers, years 1995-2007.

Different specifications in the columns. Standard errors, clustered at the level of thefirm, are reported in parenthesis. All specifications but the first include a quadratic inthe number of sampled workers, to control for the precision of the left-hand side variable.

7


Standard Deviation of Lifetime Wage: Managers

Table 7.A Executives


Export -0.137a -0.105c -0.115b -0.123b -0.101c -0.016(0.052) (0.054) (0.054) (0.053) (0.053) (0.027)

N.Occ. 0.003 -0.005c -0.007b 0.003 0.003(0.003) (0.003) (0.003) (0.003) (0.002)

log empl -0.054a -0.053a 0.025a

(0.009) (0.010) (0.007)log dom.share -0.008a -0.001 0.002

(0.003) (0.003) (0.002)log VA per worker -0.017c -0.016 0.052a

(0.010) (0.010) (0.007)white share 0.043b




Obs. 11,732 11,732 11,732 11,732 11,732 11,732R2 0.153 0.164 0.158 0.157 0.165 0.586

Table 7.B Managers


Export 0.237a 0.231a 0.235a 0.226a 0.226a 0.093b

(0.056) (0.054) (0.054) (0.054) (0.053) (0.042)N.Occ. 0.004 -0.009a -0.010a 0.004 0.009a

(0.004) (0.003) (0.003) (0.004) (0.003)log empl -0.068a -0.070a 0.007

(0.012) (0.012) (0.010)log dom.share -0.00561 0.00344 0.00521

(0.005) (0.004) (0.004)log VA per worker 0.011 0.007 0.044a

(0.014) (0.014) (0.010)white share 0.079b



(0.020)

Obs. 7,440 7,440 7,440 7,440 7,440 7,440R2 0.273 0.289 0.280 0.279 0.289 0.578

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zero

for non-exporters.Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm.Notes: Cross-sectional Regressions for firms with at least 4 workers, years 1995-2007.

Different specifications in the columns. Standard errors, clustered at the level of thefirm, are reported in parenthesis. All specifications but the first include a quadratic inthe number of sampled workers, to control for the precision of the left-hand side variable.

7


Standard Deviation of Lifetime Wage: Blue Collar

Table 8: Pooled Cross-sectional Regressions: Standard Deviation blue collar work-ers, more than 5 workers

(1) (2) (3) (4) (5) (6)Variables Standard Deviation of Average Lifetime Wage, more than 5 workers

Export -0.088a -0.069a -0.083a -0.099a -0.070a -0.024b

(0.014) (0.014) (0.014) (0.014) (0.014) (0.011)N.Occ. 0.021a 0.006a 0.002 0.020a 0.009a

(0.002) (0.002) (0.002) (0.002) (0.002)log empl -0.092a -0.092a 0.024a

(0.007) (0.008) (0.006)log dom.share -0.010a -0.003 0.002


(0.008) (0.008) (0.008)white share 0.004




Obs. 38,835 38,835 38,835 38,835 38,835 38,835R2 0.051 0.066 0.054 0.053 0.068 0.616

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters.Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm.Notes: Cross-sectional Regressions for firms with at least 4 workers, years 1995-2007. Differentspecifications in the columns. Standard errors, clustered at the level of the firm, are reportedin parenthesis. All specifications but the first include a quadratic in the number of sampledworkers, to control for the precision of the left-hand side variable.

8

Back


Interquartile Range of Lifetime WageTable 10: Pooled Cross-sectional Regressions: Inter-quartile Range, morethan 5 workers

(1) (2) (3) (4) (5) (6)Variables Inter-quartile of Lifetime Wage, more than 5

Export -0.083a -0.010 -0.049a -0.073a -0.021 -0.024b

(0.015) (0.015) (0.015) (0.015) (0.015) (0.012)N.Occ. 0.019a -0.012a -0.016a 0.016a 0.005a

(0.002) (0.002) (0.002) (0.002) (0.002)log empl -0.178a -0.179a -0.068a

(0.007) (0.007) (0.006)log dom.share -0.011a 0.003 0.004a


(0.010) (0.010) (0.007)white share 0.789a

(0.019)log N. Products 0.019a



Obs. 57,469 57,469 57,469 57,469 57,469 57,469R2 0.056 0.094 0.062 0.066 0.099 0.493

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zerofor non-exporters.Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm.Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995-2007. Different specifications in the columns. Standard errors, clustered at the level ofthe firm, are reported in parenthesis. All specifications but the first include a quadraticin the number of sampled workers, to control for the precision of the left-hand sidevariable.

10


Interquartile Range of Worker Fixed EffectTable 9: Pooled Cross-sectional Regressions: Inter-quartile Range, morethan 5 workers

(1) (2) (3) (4) (5) (6)Variables Inter-quartile of Workers’ Fixed Effects, more than 5

Export -0.071a -0.0075 -0.041b -0.063a -0.016 -0.040b

(0.016) (0.016) (0.016) (0.016) (0.016) (0.018)N.Occ. 0.020a -0.007a -0.011a 0.018a 0.011a

(0.002) (0.002) (0.002) (0.002) (0.002)log empl -0.162a -0.163a -0.157a

(0.007) (0.008) (0.008)log dom.share -0.011a 0.002 0.001


(0.010) (0.010) (0.010)white share 0.300a




Obs. 54,933 54,933 54,933 54,933 54,933 54,933R2 0.058 0.086 0.062 0.064 0.089 0.121

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zerofor non-exporters.Avg Worker Type: average worker fixed effect, estimated by the AKM decomposi-tion, by firm.Notes: Cross-sectional Regressions for firms with at least 4 workers, years 1995-2007.Different specifications in the columns. Standard errors, clustered at the level of thefirm, are reported in parenthesis. All specifications but the first include a quadraticin the number of sampled workers, to control for the precision of the left-hand sidevariable.

9

Back


StayersTable 2: Pooled Cross-sectional Regressions: Standard Deviation of cur-rent workers

(1) (2) (3) (4) (5) (6)Variables Standard Deviation of lifetime wage, stayers

Export 0.020b 0.010 0.002 -0.003 0.006 -0.014(0.009) (0.009) (0.009) (0.009) (0.009) (0.010)

N.Occ. 0.025a 0.020a 0.018a 0.024a 0.018a

(0.001) (0.001) (0.001) (0.001) (0.001)log empl -0.032a -0.033a -0.017a

(0.004) (0.004) (0.004)log dom.share -0.001 -8.06e−5 0.001


(0.005) (0.005) (0.005)white share 0.381a




Obs. 40,579 40,579 40,579 40,579 40,579 40,579R2 0.043 0.071 0.066 0.072 0.077 0.253

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zerofor non-exporters.Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm.Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995-2007. Different specifications in the columns. Standard errors, clustered at the level ofthe firm, are reported in parenthesis. All specifications but the first include a quadraticin the number of sampled workers, to control for the precision of the left-hand sidevariable.

2

Back


Newly Hired WorkersTable 1: Pooled Cross-sectional Regressions: Standard Deviation of newly hiredworkers

(1) (2) (3) (4) (5) (6)Variables Standard Deviation of lifetime wage, hired

Export -0.025 -0.048b -0.057a -0.063a -0.056a -0.057a

(0.020) (0.020) (0.020) (0.020) (0.020) (0.017)N.Occ. 0.031a 0.024a 0.022a 0.030a 0.0198a

(0.00289) (0.00234) (0.00223) (0.00289) (0.00209)log empl -0.028a -0.031a -0.023a

(0.007) (0.008) (0.006)log dom.share -0.0002 0.002 0.004c


(0.010) (0.010) (0.008)white share 0.332a




Obs. 14,971 14,971 14,971 14,971 14,971 14,971R2 0.154 0.168 0.166 0.168 0.169 0.483

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters.Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm.Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995-2007. Differentspecifications in the columns. Standard errors, clustered at the level of the firm, are reported inparenthesis. All specifications but the first include a quadratic in the number of sampled workers,to control for the precision of the left-hand side variable.

1

Back


GLS Regressions: Standard Deviation of Lifetime Wage

Table 5: Pooled GLS Regressions: Standard Deviation of Lifetime Wage

(1) (2) (3) (4) (5) (6)Variables Standard Deviation of Lifetime Wage

Export -0.017 -0.017 -0.038a -0.050a -0.025b -0.035a

(0.011) (0.012) (0.012) (0.012) (0.012) (0.010)N.Occ. 0.024a 0.012a 0.010a 0.024a 0.017a

(0.003) (0.002) (0.002) (0.003) (0.003)log empl -0.055a -0.060a -0.004

(0.009) (0.008) (0.006)log dom.share -0.004 0.004c 0.006a


(0.008) (0.009) (0.007)white share 0.508a




Obs. 88,790 88,790 88,790 88,790 88,790 88,790R2 0.099 0.119 0.108 0.111 0.123 0.553

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zerofor non-exporters.Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm.Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995-2007. Different specifications in the columns. Standard errors, clustered at the level ofthe firm, are reported in parenthesis. All specifications but the first include a quadraticin the number of sampled workers, to control for the precision of the left-hand sidevariable.

5

Back


Correlation of Types: a counterpartSmaller matching sets ⇔ Better Sorting.

Strength of Sorting: rank correlation between workers’ and firms’ types.

Firm’s type: ranking of average domestic market share.

Exporters should display better sorting.

Table 11: Sectoral Rank Correlations

(1) (2) (3) (4) (5) (6) (7) (8)Variables Rank Correlation

Export 0.042a 0.029a 0.023b 0.017c 0.042a 0.037a 0.026a 0.027c

(0.008) (0.010) (0.010) (0.010) (0.008) (0.014) (0.010) (0.014)log empl 0.009c 0.004 0.003 -0.001


(0.017) (0.017) (0.023) (0.024)Sector,Year y1 y1 y1 y1 y2 y2 y2 y2

Obs. 3,836 3,836 3,836 3,836 3,836 3,836 3,836 3,836R2 0.041 0.042 0.049 0.049 0.195 0.195 0.198 0.198

1 2 digit sector dummies.2 4 digit sector dummies.log empl. log-employment.logVA per worker: log-value added per worker.Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995-2007. Different spec-ifications in the columns. Standard errors, clustered at the level of the firm, are reported in parenthesis.All specifications but the first include a quadratic in the number of sampled workers, to control for theprecision of the left-hand side variable.

Table 12: GLS Regressions: Sectoral Rank Correlations

(1) (2) (3) (4) (5) (6) (7)Variables Rank Correlation

Export 0.037a 0.033a 0.018b 0.024a 0.035a 0.011 0.022b

(0.009) (0.009) (0.009) (0.009) (0.011) (0.007) (0.011)log empl 0.002 -0.004 -0.001 -0.008


(0.014) (0.015) (0.020) (0.021)Sector,Year y1 y1 y1 y1 y2 y2 y2

Obs. 3,812 3,812 3,812 3,812 3,812 3,812 3,812R2 0.082 0.082 0.094 0.094 0.333 0.343 0.343

1 2 digit sector dummies.2 4 digit sector dummies.log empl. log-employment.logVA per worker: log-value added per worker.Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: Cross-sectional Regressions for firms with more than 5 workers, years 1995-2007.Different specifications in the columns. Standard errors, clustered at the level of the firm, arereported in parenthesis. All specifications but the first include a quadratic in the number ofsampled workers, to control for the precision of the left-hand side variable.

11

Back


Export Status and Correlation

0.0 0.2 0.4 0.6 0.8

0.5

1.0

1.5

2.0


Export Status and Correlation

0.0 0.2 0.4 0.6 0.8

0.5

1.0

1.5

2.0

Back


Conditional Export Cut-OffA firm of productivity ϕ exports iff

Rx (h, ϕ)− f − w (h) ≥ Rd (h, ϕ)− w (h)

Conditional Export Cut-off

ϕ (h) =

f[

E + τ− 1

1−θ E∗]1−θ

− E1−θ

1θ

1

h

0.125 0.25 0.375 0.5 0.625 0.75 0.875 1

0.125

0.25

0.375

0.5

0.625

0.75

0.875

1

Conditional Export Cut-offSimulation with f = 1, c = 0.25,θ = 0.75, E = E∗ = 0.077

Note: ϕ (h) ↑ if

f, τ ↑.E∗ ↓


Firm Type Space

Firm’s type space

Non-Exporters

Conditional Exporters (exporting depends on matching with a sufficientlyproductive worker)

Exporters

𝜑�ℎ�� 𝜑�ℎ�

Non Exporters Conditional

Exporters Exporters

Back


Who are the exporters?Defining the adjusted productivity ϕ ≡ Aiψ allows us to compare firms onlyalong a single dimension of heterogeneity.

The adjusted productivity contains differences in the export status.

Consider two firms, A and B of equal productivity ψI A is an exporter: ϕA = Axψ

I B is a non exporter: ϕB = Adψ

I Conditional on equal initial productivity, an exporter faces a larger market ⇒an exporter has a higher adjusted productivity

I Exporters are relatively to the right compared to non-exporter

𝐴𝑥𝜓 𝐴𝑑𝜓

𝜑𝐴 𝜑𝐵

Back


Distribution of Value Added per Worker by Export Status

Back


Infinite Horizon vs Two Period Model

Qualitative equivalence of results based upon

pay-offs strictly increasing in the agents’ types

∂w (θ)

∂θ> 0,

∂π (ϕ)

∂ϕ> 0

pay-off capture average productivity of the partner

∂w (θ)

∂θ∝ E [ϕ|ϕ ∈M (θ)] ,

∂π (ϕ)

∂ϕ∝ E [θ|θ ∈M (ϕ)]

pay-offs increasing faster than marginal contribution to revenue (benefit froma mismatch)

Back


Search and Matching

Meeting between workers and firms occurs at random - workers’ and firms’characteristics are observed only after a meeting occurs.

Constant cost c > 0 to be paid for searching one additional period Evidence

Upon meeting, two optionsI keep searching and get outside option (w (θ) for workers, π (ϕ) for firms)I matching if surplus, revenues net of outside options, is non-negative,

ϕ′ ∈M (θ) ⇔ s(θ, ϕ′

)= R

(θ, ϕ′

)− w (θ)− π

(ϕ′)≥ 0

θ′ ∈M (ϕ) ⇔ s(θ′, ϕ

)= R

(θ′, ϕ

)− w

(θ′)− π (ϕ) ≥ 0

If matching, net revenues after compensations are split according to NashBargaining (γ → share of the surplus accruing to workers).


Unmatched Agents

Endogenous evolution of the unmatched

each period agents meet potential partners at the rate ρ (normalize ρ ≡ 1).

matches are destroyed at the rate λ.

once matched, the agents leave the market.

In steady state the measure of separations should be balanced by the measureof newly formed matches, (steady state flow conditions),

λ [g (θ)− u (θ)] = u (θ)

∫M(θ)

u (y) dy for worker-type θ

λ [g (ψ)− u (ψ)] = u (ψ)

∫M(ψ)

u (x) dx for firm-type ψ

Back


Equilibrium in the Two Period Model

Definition

A search equilibrium consists of a pair of outside options functions w∗ : [0, 1]→ R,π∗ : [0, 1]→ R, a pair of matching strategies M (θ), θ ∈ [0, 1], M (ϕ), ϕ ∈ [0, 1], a pair ofdistributions (of the unmatched), u (θ) ≤ g (θ), u (ϕ) ≤ g (ϕ) such that

given w∗ (·), π∗ (·), first period matching conditions

ϕ ∈M (θ) iff (ϕ · θ)α − w∗ (θ)− π∗ (ϕ) + 2c ≥ 0

θ ∈M (ϕ) iff (ϕ · θ)α − w∗ (θ)− π∗ (ϕ) + 2c ≥ 0

given M (θ) and M (ϕ), measures of the unmatched in the second period

u (θ) = g (θ)

[1−

∫M(θ)

g (t) dt

], u (ϕ) = g (ϕ)

[1−

∫M(ϕ)

g (t) dt

]

given u (θ) and u (ϕ), outside option determination

w∗ (θ) :∂w∗ (θ)∂θ

=∂R (θ, ϕ)

∂θ

∣∣∣∣ϕ=µ(θ)

π∗ (ϕ) = R(µ−1 (ϕ) , ϕ

)− w∗

(µ−1 (ϕ)

)where µ (θ) :

∫ θ0 u (t) dt =

∫ ϕ0 u (t) dt

Back M.D. Tito (VSE) Trade and Sorting February 27, 2015 63 / 31

Trade Search Equilibrium

Definition

A Trade search equilibrium (SE) consists of a pair of functions w : [0, 1]→ R, π : [0, 1]→ R, apair of strategies MX (h), h ∈ [0, 1], M (ϕ), ϕ ∈ [0, 1], a pair of distributions, u (θ) ≤ g (θ),u (ϕ) ≤ g (ϕ) and a cut-off rule ϕ (h) such that

given M (h) and M (ϕ), w (·) and π (·) solve

w (h) =

∫ 1

0max

{−c+ w (h) +

max{sD (h, ϕ) , sX (h, ϕ)

}γ

,−c+ w (h)

}uϕ (ϕ) dϕ

π (ϕ) =

∫ 1

0max

{−c+ π (ϕ) +

max{sD (h, ϕ) , sX (h, ϕ)

}1− γ

,−c+ π (ϕ)

}Uh (h) dh

given w (h) and π (ϕ),

ϕ ∈M (h) iff max{sD (h, ϕ) , sX (h, ϕ)

}≥ 0

h ∈M (ϕ) iff max{sD (h, ϕ) , sX (h, ϕ)

}≥ 0

given M (h) and M (ϕ), the steady state flow conditions for the unmatched, for uϕ (ϕ)and uh (h), are satisfied.

conditional on h ∈M (ϕ), firms with ϕ ≥ ϕ (h) exports; firms with ϕ < ϕ (h) serve onlythe domestic market.

Back M.D. Tito (VSE) Trade and Sorting February 27, 2015 64 / 31

Variation of Matching BoundsDetermination of the Matching Range: trade-off between

paying a fixed cost for further search

deviating from the optimal assignment

Willingness to deviate from the optimal assignment

Strength of complementarity (cross-partial derivative).I Contribution to revenues of workers and firms depends on the shape of the

revenue function.

𝜑 𝜑𝐿

𝜑𝐻

𝜃 = 𝜇(𝜑)

𝜑 𝜑𝐿

𝜑𝐻

𝜃 = 𝜇(𝜑)


Shape of Matching SetsShape of matching sets depends on shape of revenue function ( Intuition )

α = 1: Linear and Parallel Matching Bounds.

α < 1: Larger matching bounds for more productive agents

α > 1: Larger matching bounds for less productive agents

Matching Bounds with α = 1 Matching Bounds with α = 0.75

Back


Matching Set ConditionsMarginal Losses from Deviation (by the firm productivity level)

0.2 0.4 0.6 0.8 1.0

1.0

1.5

2.0

2.5

3.0

3.5

α < 1 ⇒ Concave Revenues0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

α > 1 ⇒ Convex Revenues

Conditions:

α = 1: constant cross-partial ⇒ Linear and Parallel Matching Bounds.

α < 1: decreasing cross-partial ⇒ Larger matching bounds for moreproductive agents (concave revenue function)

α > 1: increasing cross-partial ⇒ Larger matching bounds for less productiveagents (convex revenue function)

Back



Table 1: Rank Correlation Matrix, proxies for firms’ types

ψAvg. Avg. Avg.Dom. Avg.VA Avg.Type Wage Share per w. Empl.

ψ 1Avg. Worker Type by Firm -0.80 1Avg. Wage by Firm 0.13 0.35 1Avg. Dom. Share 0.01 0.08 0.20 1Avg. VA per worker 0.001 0.05 0.13 0.64 1Avg. Empl. -0.01 0.06 0.12 0.78 0.72 1

ψ: Firms’ fixed effects, from the AKM decomposition.Avg. Wage by Firm: average of the workers’ wages overAvg. Worker Type by Firm: Average of workers’ fixed effects by firm, from the AKM decomposition.Avg. VA per worker: Average value added per worker, normalized by 4-digit industries.Avg. Dom. Share: Average domestic market share at a 4-digit level.Avg. Empl.: Average employment, normalized by 4-digit industries.Notes: Rank correlation between proxies of firms types. We do not report the p-values but all rank

correlations are significantly different from zero.

1

Back



Table 2: Measuring Sorting Patterns, Manufacturing Sectors

(4) (5) (6) (7)ψ, Avg. Avg.Share,T ype Avg.Wage

NAF Industry Label No Firms ρS1 p-val2 ρS

1 p-val2

10 Food 9 -0.96 0.00 - -11 Beverage 8 -1 - - -12 Tobacco prods - - - - -13 Textiles - - - - -14 Clothing 270 -0.84 0.00 0.18 0.0015 Leather/shoes - - - - -17 Paper 1317 -0.85 0.00 0.14 0.0018 Printing 1286 -0.86 0.00 0.14 0.0019 Refining 402 -0.88 0.00 0.42 0.0020 Chemical 666 -0.86 0.00 0.17 0.0021 Pharma 780 -0.79 0.00 0.30 0.0122 Plastics 2070 -0.76 0.00 0.13 0.0023 Non-metallic prods 59 -0.64 0.00 0.13 0.3324 Metalworking 1565 -0.72 0.00 0.33 0.0025 Metal prods 1987 -0.83 0.00 0.25 0.0026 Info/elec/opt 947 -0.82 0.00 0.27 0.0027 Elec equip 595 -0.84 0.00 0.14 0.0028 Machinery 5433 -0.81 0.00 0.21 0.0029 Automotive 2898 -0.82 0.00 0.28 0.0030 Other trans equip 126 -0.74 0.00 0.16 0.0731 Furniture 969 -0.81 0.00 0.25 0.0032 Other mfg 878 -0.71 0.00 0.13 0.0033 Repairs 1197 -0.79 0.00 0.23 0.00

Manufacturing 23388 -0.80 0.00 0.20 0.00

1 Spearman correlation coefficient.2 p-value from testing independence between the variables.Notes: Columns (4)-(5): Rank correlation and significance level between the average

worker type, (Avg.Worker), and the firm fixed effect (ψ) from an AKM decompositionincluding a quartic polynomial in experience, a dummy for workers residing in Ile-de-France, time dummies and all the interactions with the gender dummy.Columns (6)-(7): Rank correlation and significance level between the average lifetime

wage of workers, (Avg.Wage), and the firm type, proxied by the average domesticmarket share in 4-digit sectors Avg.Share.

2

Back


Mkt Access: Tariffs - Effect on Average TypeTable 11: Tariff Regressions: Average, more than 5 workers

(1) (2) (3) (4) (5) (6)Variables Average Lifetime Wage, more than 5 workers

Weighted Tariff*Export 0.002 0.001 0.001 -0.001 -0.001 -0.004(0.004) (0.003) (0.003) (0.003) (0.003) (0.003)

Weighted Tariff 0.001 0.002 0.002 0.00395 0.006c 0.012a

(0.004) (0.003) (0.003) (0.003) (0.003) (0.003)Export 0.128a 0.082a 0.045b 0.050b 0.071a 0.039c

(0.023) (0.021) (0.020) (0.020) (0.021) (0.021)N.Occ. 0.039a 0.016a 0.033a 0.035a -0.002

(0.001) (0.002) (0.001) (0.001) (0.001)log empl 0.123a 0.124a

(0.005) (0.005)log dom.share 0.031a 0.005a

(0.002) (0.002)white share 0.512a

(0.021)log VA per worker 0.161a 0.099a

(0.008) (0.007)log N. Products 0.004



N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zero fornon-exporters.Notes: Cross-sectional Regressions for firms with at least 4 workers, years 1995-2007.Different specifications in the columns. Standard errors, clustered at the level of the firm,are reported in parenthesis. All specifications but the first include a quadratic in thenumber of sampled workers, to control for the precision of the left-hand side variable.

11

Back


Mkt Access: Import Shocks - Effect on Average TypeTable 13: Pooled Cross-sectional Regressions: Average, more than 5 workers

(1) (2) (3) (4) (5) (6)Variables Average Lifetime Wage, more than 5 workers

Market Access*Export 0.014a 0.012a 0.011a 0.012a 0.013a 0.013a

(0.003) (0.003) (0.003) (0.003) (0.003) (0.003)Market Access -0.016a -0.014a -0.013a -0.012a -0.015a -0.018a

(0.004) (0.004) (0.003) (0.004) (0.004) (0.003)Export -0.052 -0.078 -0.106b -0.114b -0.108b -0.168a

(0.051) (0.050) (0.047) (0.050) (0.050) (0.050)N.Occ. 0.039a 0.015a 0.032a 0.035a -0.002

(0.002) (0.002) (0.001) (0.001) (0.001)log empl 0.125a 0.125a

(0.005) (0.005)log dom.share 0.031a 0.004b

(0.002) (0.002)log VA per worker 0.158a 0.096a

(0.008) (0.006)white share 0.500a




N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zero fornon-exporters.Notes: Cross-sectional Regressions for firms with at least 4 workers, years 1995-2007.Different specifications in the columns. Standard errors, clustered at the level of the firm,are reported in parenthesis. All specifications but the first include a quadratic in thenumber of sampled workers, to control for the precision of the left-hand side variable.

13

Back


Mkt Access: Tariffs - Effect on Standard DeviationTable 12: Pooled Cross-sectional Regressions: Standard Deviation, more than5 workers

(1) (2) (3) (4) (5) (6)Variables Standard Deviation of Lifetime Wages, more than 5 workers

Weighted Tariff*Export 0.007b 0.007b 0.007b 0.007b 0.006b 0.002(0.003) (0.003) (0.003) (0.003) (0.003) (0.002)

Weighted Tariff -0.013a -0.012a -0.012a -0.013a -0.011a -0.001(0.003) (0.003) (0.003) (0.003) (0.003) (0.002)

Export -0.059a -0.069a -0.037b -0.062a -0.073a -0.032b

(0.017) (0.017) (0.017) (0.017) (0.017) (0.013)N.Occ. 0.011a 0.031a 0.013a 0.010a 0.025a

(0.001) (0.001) (0.001) (0.001) (0.001)log empl -0.108a -0.022a

(0.004) (0.003)log dom.share -0.007a 0.005a

(0.002) (0.001)white share 0.480a

(0.010)log VA per worker 0.047a 0.103a

(0.006) (0.004)log N. Products 0.014a

(0.002)avg lwage -0.727a



N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zero fornon-exporters.Avg Worker Type: average worker fixed effect, estimated by the AKM decomposition, byfirm.Notes: Cross-sectional Regressions for firms with at least 4 workers, years 1995-2007.Different specifications in the columns. Standard errors, clustered at the level of the firm,are reported in parenthesis. All specifications but the first include a quadratic in the numberof sampled workers, to control for the precision of the left-hand side variable.

12

Back


Mkt Access: Import Shocks - Effect on Standard DeviationTable 14: Pooled Cross-sectional Regressions: Standard Deviation, more than 5 workers

(1) (2) (3) (4) (5) (6)Variables Standard Deviation of Workers’ Fixed Effects, more than 5 workers

Market Access*Export -0.009a -0.009a -0.009a -0.009a -0.009a -0.009a

(0.00324) (0.00317) (0.00305) (0.00320) (0.00312) (0.00279)Market Access 0.011a 0.012a 0.011a 0.011a 0.012a 0.011a

(0.003) (0.003) (0.003) (0.003) (0.003) (0.003)Export 0.096b 0.089c 0.113b 0.096b 0.080c 0.094b

(0.048) (0.047) (0.046) (0.048) (0.046) (0.041)N.Occ. 0.011a 0.031a 0.012a 0.010a 0.026a

(0.001) (0.001) (0.001) (0.001) (0.001)log empl -0.107a -0.105a

(0.004) (0.004)log dom.share -0.006a 0.002

(0.002) (0.002)log VA per worker 0.050a 0.033a

(0.006) (0.005)white share 0.158a




Obs. 44,728 44,728 44,728 44,728 44,728 44,552R2 0.068 0.071 0.094 0.072 0.075 0.143

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variable is zero for non-exporters.Avg Worker Type: average worker fixed effect, estimated by the AKM decomposition, by firm.Notes: Cross-sectional Regressions for firms with at least 4 workers, years 1995-2007. Different speci-fications in the columns. Standard errors, clustered at the level of the firm, are reported in parenthesis.All specifications but the first include a quadratic in the number of sampled workers, to control for theprecision of the left-hand side variable.

14

Back


CalibrationParameter Model Data Moment

η = 4 Demand Elasticity Average trade elasticityσ = 0.653 Production Curvature Worker type elasticityτ = 1.513 Variable trade cost Average foreign to domestic shipmentsλ = 0.8 Share of exporters Average share of exporters

δ = 1.7% Destruction rateAverage separation probabilityHairault et al. (2012)

ρ = 13.5% Meeting rateAverage number of new hiresHairault et al. (2012)

c = 0.025 Search cost Within-firm wage dispersionB (αθ = 39.92, βθ = 28.96) Worker distribution Empirical distributionB(αψ = 0.89, βψ = 1.09

)Firm distribution Empirical distribution

Normalize fixed trade costs, fL = 0, fH →∞.

Model FitMoment Data Model

Average foreign to total shipments 0.28 0.25Average within-firm wage dispersion 0.91 0.92

Back


Institutional context

Since 1950 wage bargaining on three levels

I National level: minimum wages (SMIC) set by governmentI Industry level: employers’ organisations and unions negotiate wages by

occupationI Firm level: employers and unions negotiate wage increases

At end of 1980’s industry-level agreements were still covering 95% of workers

Last 30 years: decentralization

I Auroux laws in 1982: duty to bargain annually on wages at the firm-level(Condition: firms with more than 50 employees and a union representative)

By 2005, 41% of the workers employed in private firms with more than 10employees were covered by a wage agreement signed that very same year(Naboulet and Carlier, 2007)

Back


Second period: Perfect Positive Assortative Matching

Assume same distribution of the unmatched of firms and workers (then verify)

Positive assortative matching =⇒ matching function is ϕ = µ (θ) = θ

Second period pay-offs - in a match,I workers receive their marginal product

w∗ (θ) :∂w∗ (θ)

∂θ=

∂R (θ, ϕ)

∂θ

∣∣∣∣ϕ=µ(θ)

w∗ (θ) =

∫ θ

0

∂R (t, µ (t))

∂tdt =

1

2θ2α

I firms get the residual, after wages are paid to the worker

π∗ (ϕ) = R(µ−1 (ϕ) , ϕ

)− w∗

(µ−1 (ϕ)

)=

1

2ϕ2α

Back


First period: Acceptance SetsAcceptance set in first period determined by matches such that surplus, revenuesnet of outside option, is positive

Outside option for worker is w∗ (θ)− c

Outside option for firm is π∗ (ϕ)− c

Acceptance set condition: surplus from a match is positive,

(θϕ)α − 1

2ϕ2α − 1

2θ2α + 2c ≥ 0

Symmetric surplus conditions and symmetric matching sets ⇒ thedistribution of the unmatched in the second period will be the same forworker and firm types.

Back


Normalized Surplus condition

Simple intuition coming from behaviour of surplus condition

Rewrite surplus as a function of relative worker type θ = θϕ[

θα − 1

2θ2α − 1

2

]ϕ2α︸︷︷︸

S(θ,ϕ)

+ 2c ≥ 0

As type of firm increases ϕ ↑ =⇒sharper drop of surplus on eitherside of optimal matching functionϕ = θ

Figure: Figure 3 - Surplus condition as a function of normalized worker types forα = 1 and c = 0.01.

Bombardini, Orefice, Tito (June 2014) Exporting and Matching – – – — 22 / 51

Simulation with c = 0.01, α = 1

Back


Measuring the Losses: realized vs optimal revenues

𝜃 𝜑

𝜑

𝜃

firm types

wor

ker t

ypes

Mismatched allocation

𝜃 𝜑

𝜑

𝜃

firm types

wor

ker t

ypes

Efficient allocation

Back


Theoretical Extensions

Theory involves one firm and one worker. Possible Extensions:

I Firm as a collection of independent matches with workersR (ϕ, θ1, . . . , θn) = ϕα

∑ni=1 θ

αi

I Allow n (exogenous) workers R (ϕ, θ1, . . . , θn) = ϕα∏ni=1 θ

αi

Back


Average Type by Export Status

Average of Workers Fixed Effects byquartile of Value Added per Worker.

Average of Workers Fixed Effects byquartile of Domestic Market Share.

Back


Firm Types

Eeckhout and Kircher (2011) show that ψj(i,t) has no systematic relationshipwith the true firm type (also Lopez De Melo, 2013)

I Theoretical result: Wage is a non-monotonic function of the employer firmtype. ( Wages and Firm Types )

I Empirical Correlations: Rank Correlations , Ranks Correlation by Sector

Two proxies for Firm Type: average over sample period of

I value added per worker V Apwj

I share of sales in the domestic market (in the firm’s primary industry)DomSharej

I additional control: size (total employment) logEmpj

Back


Infinite Horizon ModelOutside options: flow value that maximizes the expected utility. E.g. aworker receives

I receives its outside option and pays the search cost if unmatchedI in addition, receives a share of the surplus if matched

w (θ) =

∫ 1

0

max

{−c+ w (θ) +

max {s (θ, ϕ) , 0}γ

,−c+ w (θ)

}uϕ (ϕ) dϕ

Endogenous evolution of the unmatchedI each period agents meet potential partners at the rate ρ (normalize ρ ≡ 1).I matches are destroyed at the rate λ.I once matched, the agents leave the market.I In steady state the measure of separations should be balanced by the measure

of newly formed matches, (steady state flow conditions),

λ [g (θ)− u (θ)] = u (θ)

∫M(θ)

u (y) dy for worker-type θ

λ [g (ψ)− u (ψ)] = u (ψ)

∫M(ψ)

u (x) dx for firm-type ψ

Back


Standard Deviation of Types by Export Status.5

8.6

.62

.64

.66

.68

Std

Dev

iatio

n w

orke

rs’ f

ixed

effe

ct

1 2 3 4Firm type − quartile of value added pw

Non Exporters histd_work/lostd_workExporters histd_work/lostd_work

Figure 1: Standard Deviation of Workers’ Fixed Effects, whole sample

.55

.6.6

5.7

Std

Dev

iatio

n w

orke

rs’ f

ixed

effe

ct

1 2 3 4Firm type − quartile of mkt share



1

Standard Deviation of Workers Types byquartile of Value Added per Worker.

.58

.6.6

2.6

4.6

6.6

8S

td D

evia

tion

wor

kers

’ fix

ed e

ffect

1 2 3 4Firm type − quartile of value added pw



.55

.6.6

5.7

Std

Dev

iatio

n w

orke

rs’ f

ixed

effe

ct

1 2 3 4Firm type − quartile of mkt share



1

Standard Deviation of Workers Types byquartile of Domestic Market Share.

Back


IV Regressions

Endogeneity of export status and worker selection ⇒ instrument export statususing tariffs τsrt. ( First Stage )

IVjt =∑r

[ln

(1 +

1

τsrt

)exportjr,t−1exportj,t−1

]

Std Deviation of Lifetime WageVariable OLS GLS IVExport -0.037a -0.035a -0.099b

(0.013) (0.010) (0.042)Obs 57,996 88,790 19,241

Back


First Stage

Table 6: IV Regressions: Standard Deviation of Lifetime Wage, morethan 5 workers


Export -0.001 -0.042a 0.025 -0.035b -0.054a -0.099b

(0.013) (0.015) (0.016) (0.017) (0.014) (0.042)N.Occ. 0.011a 0.026a 0.012a 0.011a 0.023a

(0.002) (0.002) (0.002) (0.002) (0.001)log empl -0.106a -0.016a

(0.006) (0.004)log dom.share -0.003 0.010a

(0.002) (0.002)logVA per worker 0.033a 0.099a

(0.007) (0.005)white share 0.471a




Obs. 19,241 19,241 19,241 19,241 19,241 19,241R2 0.065 0.068 0.088 0.068 0.069 0.549

N.Occ.: number of occupations, based on 2 digit occupational codes for France.log empl. log-employment.logVA per worker: log-value added per worker.log dom.share: log-domestic market share, at the 4 digit sector level.white share: share of non-production worker.logN. Products: log-number of exported products (HS6 codes). This variableis zero for non-exporters.Avg. Lifetime Wage: workers’ lifetime wage, averaged by firm.Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: Cross-sectional Regressions for firms with more than 5 workers, years1995-2007. Different specifications in the columns. Standard errors, clusteredat the level of the firm, are reported in parenthesis. All specifications but thefirst include a quadratic in the number of sampled workers, to control for theprecision of the left-hand side variable.

Table 7: IV Regressions: Standard Deviation of Lifetime Wage, more than 5workers


Export (Second Stage) -0.001 -0.042a 0.025 -0.035b -0.054a -0.099b

(0.013) (0.015) (0.016) (0.017) (0.014) (0.042)Mkt Access (First Stage) 0.128a 0.126a 0.122a 0.114a 0.126a 0.034a

(0.004) (0.004) (0.004) (0.004) (0.004) (0.002)F-stat (First Stage) 1261 1168 1093 994 1143 346

Obs. 19,241 19,241 19,241 19,241 19,241 19,241

Legend : a significant at 1%, b significant at 5%, c significant at 10%.Notes: IV Regressions for firms with more than 5 workers, years 1995-2007. Dif-ferent specifications in the columns. Standard errors, clustered at the level of thefirm, are reported in parenthesis. All specifications but the first include a quadraticin the number of sampled workers, to control for the precision of the left-hand sidevariable.

6

Back


does exporting improve matching? evidence from french linked … · rms export (counterfactual) i...

Documents