Does Exporting Improve Matching? Evidence from French Linked Firm-Employee Data M. Bombardini 1, 2 , Gianluca Orefice 3 , M. D. Tito 1 1 Vancouver School of Economics (UBC), 2 CIFAR, 3 CEPII February 27, 2015 M.D. Tito (VSE) Trade and Sorting February 27, 2015 1 / 31
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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?
M.D. Tito (VSE) Trade and Sorting February 27, 2015 2 / 31
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.
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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)
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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.
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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.
M.D. Tito (VSE) Trade and Sorting February 27, 2015 5 / 31
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
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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).
M.D. Tito (VSE) Trade and Sorting February 27, 2015 7 / 31
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)
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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?
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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).
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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
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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
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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
M.D. Tito (VSE) Trade and Sorting February 27, 2015 14 / 31
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)
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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)
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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.
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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.
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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
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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
M.D. Tito (VSE) Trade and Sorting February 27, 2015 17 / 31
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
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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
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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
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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?
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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
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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
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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
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
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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
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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 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.
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
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M.D. Tito (VSE) Trade and Sorting February 27, 2015 27 / 31
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)
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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
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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
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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
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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
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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
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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
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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
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Distribution of Agents’ Types
Distribution of Workers Fixed Effects.Distribution of Firm Types - percentiles
of Domestic Market Share.
Back
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Random Mobility?Positive and Negative Changes when moving to a different job
Sign PercentagePositive 54.82%Negative 45.18%
Back
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Correlation between Worker Types and proxies for FirmTypes
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
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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
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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
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
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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
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
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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
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
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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
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
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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
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
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Standard Deviation of Lifetime Wage: Managers
Table 7.A Executives
(1) (2) (3) (4) (5) (6)Variables Standard Deviation of Average Lifetime Wage, more than 5
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
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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
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
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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
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
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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
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.
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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
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
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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
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
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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
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
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M.D. Tito (VSE) Trade and Sorting February 27, 2015 52 / 31
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.
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.
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.
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M.D. Tito (VSE) Trade and Sorting February 27, 2015 53 / 31
Export Status and Correlation
0.0 0.2 0.4 0.6 0.8
0.5
1.0
1.5
2.0
M.D. Tito (VSE) Trade and Sorting February 27, 2015 54 / 31
Export Status and Correlation
0.0 0.2 0.4 0.6 0.8
0.5
1.0
1.5
2.0
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M.D. Tito (VSE) Trade and Sorting February 27, 2015 55 / 31
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∗ ↓
M.D. Tito (VSE) Trade and Sorting February 27, 2015 56 / 31
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
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M.D. Tito (VSE) Trade and Sorting February 27, 2015 57 / 31
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
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M.D. Tito (VSE) Trade and Sorting February 27, 2015 58 / 31
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
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M.D. Tito (VSE) Trade and Sorting February 27, 2015 58 / 31
Distribution of Value Added per Worker by Export Status
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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)
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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).
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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
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M.D. Tito (VSE) Trade and Sorting February 27, 2015 62 / 31
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.
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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)
M.D. Tito (VSE) Trade and Sorting February 27, 2015 65 / 31
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
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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: increasing cross-partial ⇒ Larger matching bounds for less productiveagents (convex revenue function)
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Correlation between Worker Types and proxies for FirmTypes
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
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Correlation between Worker Types and proxies for FirmTypes
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
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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
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
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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
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
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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
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
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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
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
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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)
Average foreign to total shipments 0.28 0.25Average within-firm wage dispersion 0.91 0.92
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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)
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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
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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.
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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.
M.D. Tito (VSE) Trade and Sorting February 27, 2015 78 / 31
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
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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
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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.
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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
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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
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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
Non Exporters histd_work/lostd_workExporters histd_work/lostd_work
Figure 2: Standard Deviation of Workers’ Fixed Effects, whole sample
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
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
Non Exporters histd_work/lostd_workExporters histd_work/lostd_work
Figure 2: Standard Deviation of Workers’ Fixed Effects, whole sample
1
Standard Deviation of Workers Types byquartile of Domestic Market Share.
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IV Regressions
Endogeneity of export status and worker selection ⇒ instrument export statususing tariffs τsrt. ( First Stage )
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
(1) (2) (3) (4) (5) (6)Variables Standard Deviation of Lifetime Wage, more than 5
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.
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