Trade and Inequality: From Theory to Estimation

Trade and Inequality:From Theory to Estimation

Elhanan Helpman Oleg Itskhoki Marc Muendler Stephen ReddingHarvard Princeton UC San Diego Princeton

NES 20th Anniversary ConferenceDecember 2012

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Motivation

• Neoclassical trade theory (H-O, SF, R)

— sector-level comparative advantage— focus on “between” effects

• New trade theory

— Krugman: intra-industry trade— Melitz: firm-level comparative advantage— focus on “within” effects

• Trade and inequality

— Heavily influenced by H-O framework— Empirically has limited explanatory power

• “New view” of trade and inequality

— link wages to firm performance— within-industry, between-firm

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This Paper

1 Uses matched employer-employee data from Brazil for1986-1998

— increase in inequality show

— trade liberalization show

2 Documents, for both levels and changes, the importance ofinequality:◦ within sector-occupations◦ for workers with similar observables (residual inequality)◦ between firms

3 Structurally estimates a heterogenous-firm model of firmemployment, wages and export status

— extension of HIR (2010)— a model of within-sector, between-firm residual inequality— reproduces empirical size and exporter wage premia:

wij = α + βhj + δxj + x ′i γ + εij

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Related Literature

• Long and large tradition in labor literature

• “New view” empirics:

◦ Bernard and Jensen (1995). . .◦ Verhoogen (2008)◦ Amity and Davis (2011)◦ AKM (1999) estimation used in trade context

• “New view” theory:

◦ Feenstra and Hanson (1999). . .◦ Yeaple (2005). . .◦ Egger and Kreickemeier (2009)◦ HIR (2010). . .

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Brazilian RAIS Data

• Matched employer-employee data from 1986–1998

— All workers employed in the formal sector— Focus on the manufacturing sector— Observe firm, industry and occupation— Observe worker education (high school, college degree),

demographics (age, sex) and experience (employment history)

• Over the period 1986-1998 as a whole, our sample includesmore than 7 million workers and 100,000 firms in every year

• Trade transactions data from 1986-1998

— Merged with the matched employer-employee data— Observe firm exports and export products and destinations

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Sectors

• Twelve aggregate sectors (IBGE) 1986-1998

Industry Empl’t Rel. mean Fraction Exportershare (%) log wage Exporters Empl’t %

2 Non-metallic mineral products 5.5 −0.12 2.3 32.33 Metallic products 9.8 0.27 6.1 49.94 Machinery, equipment & instr. 6.6 0.38 12.3 54.15 Electrical & telecomm. equip. 6.0 0.37 11.8 56.36 Transport equipment 6.3 0.61 11.2 70.67 Wood products & furniture 6.5 −0.48 3.2 23.58 Paper, publishing & printing 5.4 0.14 2.5 30.69 Rubber, tobacco, leather & fur 7.0 −0.04 8.6 50.810 Chemical & pharma. products 9.9 0.40 11.2 50.611 Apparel & textiles 15.7 −0.32 2.5 34.812 Footwear 4.4 −0.44 12.2 65.713 Food, beverages & alcohol 16.9 −0.30 3.9 38.0

• More than 250 disaggregated industries (CNAE) 1994-1998

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Occupations

• Five aggregate occupations 1986-1998

Occupation Employment Relative meanshare (%) log wage

1 Professional and Managerial 7.8 1.082 Skilled White Collar 11.1 0.403 Unskilled White Collar 8.4 0.134 Skilled Blue Collar 57.4 −0.155 Unskilled Blue Collar 15.2 −0.35

• More than 300 disaggregated occupations (CBO) 1986-1998

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Non-structural EvidenceWithin and Between Inequality

• Decompose overall wage inequality into within and betweensector-occupation components

Tt = Wt + Bt

Tt =1

Nt

∑`

∑i∈` (wit − wt)

2

Wt =1

Nt

∑`

∑i∈` (wit − w`t)

2

Bt =1

Nt

∑` N`t (w`t − wt)

2

◦ i – workers

◦ ` – sectors, occupations or sector-occupation bins

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Within and Between InequalitySector-occupation bins

Level GrowthPanel A (1990) (1986-95)

Within occupation 80% 92%Within sector 83% 73%Within sector–occupation 67% 67%Within detailed-occupation 58% 60%Within sector–detailed-occupation 52% 54%

Panel B (1994) (1994-98)

Within sector–occupation 68% 125%Within detailed-sector–detailed-occupation 47% 140%

Fact 1Within sector-occupation component of wage inequality accountsfor over 2/3 of both level and growth of wage inequality

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Within and Between InequalitySector-occupation bins

.02

.04

.06

.08

.1.1

2In

dex

(198

6=0)

1986 1990 1994 1998Year

Total Within sector-occupationBetween sector-occupation

Log Wage Dispersion (Sector-Occupations)

Jump to Between Firm

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Observable and Residual Inequality

• Mincer regression:

wit = z ′itϑt + νit ,

• Observables: (zit)

◦ Education (high-school, college degree)◦ Age bins and male/female◦ Experience quintiles

• Observable-residual inequality decomposition:

var (wit) = var(z ′it ϑt

)+ var (νit)

• Decompose residual (within-group) inequality into within andbetween sector-occupation inequality

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.02

.04

.06

.08

.1.1

2In

dex

(198

6=0)

1986 1990 1994 1998Year

Total ObservablesWithin-Group

Log Wage Dispersion Decomposition

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.02

.04

.06

.08

Inde

x (1

986=

0)

1986 1990 1994 1998Year

Overall Within Sector-OccupationBetween Sector-Occupation

Within-Group Wage Inequality Decomposition (Sector-Occupations)

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Level GrowthOverall wage inequality (1990) (1986-95)

Observables inequality 43% 52%Residual wage inequality 57% 48%

— within sector–occupation 88% 91%

Fact 2(i) Residual inequality is at least as important as workerobservables for both level and growth of wage inequality(ii) Almost all residual inequality is within sector-occupations

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Between-firm Inequality

• Mincer log-wage regression with firm fixed effect:

wit = z ′itϑ`t + ψj`t + νit

— i worker— j firm— ` sector-occupation bin

• ψj`t firm fixed effect includes:— Returns to unobserved skill (workforce composition)— Worker rents (differences in wage for same workers)— Match effects

• Decomposition of within inequality:◦ Observables: var

(z ′it ϑ`t

)◦ Between-firm component: var

(ψj`t

)◦ Covariance: cov

(z ′it ϑ`t , ψj`t

)◦ Within-firm component: var

(νit)

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Between-firm InequalityWithin sector-occupation bins

Level GrowthA. Unconditional (1990) (1986-1995)

Between-firm wage inequality 55% 115%Within-firm wage inequality 45% −15%

B. Controlling for Worker ObservablesBetween-firm wage inequality 38% 86%Within-firm wage inequality 34% −11%Worker observables 17% 2%Covariance observables and firm effects 11% 24%

Fact 3Between-firm component account for about half of level and themajority of growth of within sector-occupation wage inequality

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Between-firm InequalityWithin sector-occupation bins

-.02

0.0

2.0

4.0

6.0

8In

dex

(198

6==0

)

1986 1990 1994 1998Year

Total Worker Obs CovarianceBetween-Firm Within-Firm

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Between-firm InequalitySize and exporter wage premia

ωj`t = λo`t + λs`thj`t + λx`tιjt + νj`t

ωj`t ∈ {wj`t , ψj`t}

◦ Size premium: λs`t = 0.12

◦ Exporter premium: λx`t = 0.20

◦ Residual variation: R2 = 0.12 more

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Between-firm InequalitySize and exporter wage premia

worker observablesunconditional firm-occupation-year

average wage, wj`t fixed effect, ψj`t

Cross-Section Panel Cross-Section Panel1990 1986-1998 1990 1986-1998

Firm Size 0.126∗∗∗ −0.003∗ 0.118∗∗∗ 0.048∗∗∗

(0.008) (0.002) (0.006) (0.001)

Firm Export Status 0.202∗∗∗ 0.216∗∗∗ 0.088∗∗∗ 0.012∗∗∗

(0.046) (0.004) (0.027) (0.002)

Industry Fixed Effects yes no yes noFirm Fixed Effects no yes no yesWithin R-squared 0.164 0.007 0.146 0.013Observations 93, 392 1, 229, 133 93, 392 1, 229, 133

Fact 4Larger firms on average pay higher wages; exporters on averagepay higher wages even after controlling for size. This holds both inthe cross-section and for a given firm over time.

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Non-structural EvidenceSummary

1 Within sector-occupation component accounts for 2/3 ofoverall wage inequality

2 Residual inequality is at least as important as workerobservables

3 Between-firm component accounts for majority of growth ofwithin sector-occupation inequality

Regional robustness

4 Trade participation correlates with the between-firm wagecomponent

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Structural Exercise

• Empirical model of (h,w , ι):h = αh + µhι+ u,w = αw + µw ι+ ζu + v ,ι = I{z ≥ f },

where (u, v , z) is a firm-specific draw

• Reproduce size and exporter wage relationship:

w = λo + λsh + λx ι+ ν

• Explore the link between trade and (h,w) distribution:— Selection effect: cov(u, z), cov(v , z) > 0— Market access effect: µh, µw > 0

• Model-based structural counterfactuals— reduction in trade costs: joint movement in (µh, µw , f )

Jump to estimation results

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Structural ModelExtension of HIR

• Melitz (2003) product market:

R = ΥAyβ, Υ ∈ {1,Υx > 1}• Complementarity between productivity and worker ability

y = eθHγ a, γ < 1

• Unobserved heterogeneity and costly screening

e−ηCaδc/δ ⇒ a =k

k − 1ac

• DMP frictional labor market and wage bargaining

W =βγ

1 + βγ

R

H= ba

k/δc

• Heterogeneity in fixed cost of exports

eεFx

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Model Predictions• A firm with idiosyncratic shock {θ, η, ε}:

R(θ, η, ε) = κrΥ1−β

Γ

(eθ) β

Γ

(eη) β(1−γk)

δΓ

H(θ, η, ε) = κhΥ(1−β)(1−k/δ)

Γ

(eθ) β(1−k/δ)

Γ

(eη) β(1−γk)(1−k/δ)

δΓ − kδ

W (θ, η, ε) = κwΥk(1−β)δΓ

(eθ) βkδΓ

(eη) kδ (1+ β(1−γk)

δΓ )

• Market access variable

Υ = 1 + Ix(Υx − 1

), Υx = 1 + τ−

β1−β

Ax

Ad

• Selection into exporting

Ix =

{κπ

(Υ

1−βΓ

x − 1

)(eθ) β

Γ

(eη) β(1−γk)

δΓ ≥ Fxeε

}15 / 25

Econometric Model• Empirical model of Xj = {hj ,wj , ιj}j : hj = αh + µhιj + uj ,

wj = αw + µw ιj + ζuj + vj ,ιj = I{zj ≥ f }

• Distributional assumption

(uj , vj , zj)′ ∼ N (0,Σ), Σ =

σ2u 0 ρuσu

0 σ2v ρvσv

ρuσu ρvσv 1

• Parameter vector Θ = {αh, αw , ζ, σθ, ση, ρθ, ρη, µh, µw , f }

f =1

σ

(αf + log Fx − log

(Υ

1−βΓ

x − 1

))µh + µw = Υ

1−βΓ

x

• Theoretical restrictions: µh, µw > 0. Likelihood function

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Econometric ModelAdditional Restrictions

1 Positive premia (market access) and selection:

µh, µw , ρu, ρv > 0

2 Orthogonal structural shocks:

ρu/ρv = (1 + ζ)σu/σv

3 Orthogonal productivity shocks:

µw ≥ ζµh

4 No effects of trade on wage distribution

µh = µw = ρu = ρv = 0

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Shape of the Likelihood Function

−0.50

0.51 −1

−0.50

0.51−0.44

−0.435

−0.43

−0.425

−0.42

−0.415

ρv

logL

µw

Show ML Estimates

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Shape of the Likelihood Function

−3.98

−3.98

−3.98

−3.98

−3.98

−3.98

−3.97

−3.97

−3.97

−3.97

−3.97

−3.97

−3.96

−3.96

−3.96

−3.96

−3.96

−3.96

−3.96

−3.96

−3.95

−3.95

−3.95

−3.95

−3.95

−3.95

−3.95

−3.95−3.94

−3.94

µw

ρv

−0.5 −0.25 0 0.25 0.5 0.75 1−0.75

−0.5

−0.25

0

0.25

0.5

0.75

µw = ζµh

−3.944

µw ≥ 0−3.938

Global Max−3.935

Orthog shocks−3.945

Local Max−3 .939

Show ML Estimates

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Maximum Likelihood and GMM FitUnconstrained and Restricted Models

Specification logL LR Sqrt. GMM Obj.

(i) Unconstrained −39,349.6 — 0.013

(ii) µh, µw > 0 −39,381.0 62.8 0.021

(iii) µw = ζµh −39,441.3 183.4 0.034

(iv) Orthogonal structural shocks −39,445.2 191.1 0.035

(v) No trade effects −49,543.6 20,387.9 0.370µh = µw = ρu = ρv = 0

• No premia (µh = µw = 0) strongly rejected

• No selection (ρθ = ρη = 0) NOT strongly rejected

• Pure noise in wages strongly rejected

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ParametersStructural specification

86 88 90 92 94 96 980.06

0.08

0.1

0.12ζ

86 88 90 92 94 96 981.3

1.4

1.5

1.6

f

86 88 90 92 94 96 981

1.1

1.2σu

86 88 90 92 94 96 980.35

0.4

0.45σv

86 88 90 92 94 96 980

0.02

0.04

ρu

86 88 90 92 94 96 980.05

0.1

0.15

0.2

0.25ρv

86 88 90 92 94 96 981.8

2

2.2

2.4

2.6µh

86 88 90 92 94 96 980.1

0.2

µw

86 88 90 92 94 96 982.6

2.7

2.8

2.9αh and αw

−0.4

−0.35

−0.3

−0.25

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Model Fit: Firm-level Moments

Data ModelUnconstrained Structural

A. Full SampleMean Employment 2.97 2.97 2.97

Mean Wages −0.340 −0.341 −0.341

St. Dev. Employment 1.27 1.27 1.27

St. Dev. Wages 0.424 0.424 0.423

Covar Empl’t and Wages 0.352 0.354 0.352

Fraction of Exporters 5.5% 5.5% 5.5%

B. Non-exportersMean Employment 2.83 2.83 2.83

Mean Wages −0.359 −0.360 −0.360


St. Dev. Wages 0.419 0.419 0.416

Covar Empl’t and Wages 0.306 0.309 0.304

C. ExportersMean Employment 5.28 5.29 5.29

Mean Wages −0.010 −0.010 −0.006


St. Dev. Wages 0.366 0.373 0.417

Covar Empl’t and Wages 0.322 0.289 0.30420 / 25

Model Fit: Worker-level Moments

Data ModelUnconstrained Structural

A. First and Second MomentsMean Wage 0.000 −0.085 −0.072

Non-exporters −0.122 −0.213 −0.215

Exporters 0.152 0.109 0.140

St. dev. Wages 0.404 0.429 0.450

Non-exporters 0.407 0.415 0.416

Exporters 0.345 0.374 0.414

Empl’t Share of Exporters 44.6% 40.0% 40.3%

B. Wage Inequality MeasuresGini 0.215 0.236 0.250

90/10 2.77 3.00 3.18

90/50 1.54 1.70 1.79

50/10 1.80 1.76 1.78

C. Size and Exporter Wage PremiaSize premium 0.111 0.112 0.111

Exporter premium 0.077 0.075 0.082

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Employment and Wage Distributions

−2 0 2 4 6 8 100

0.25

0.5Log Employment

−2 −1 0 10

0.5

1Log Firm Wages

−2 0 2 4 6 8 100

0.25

0.5Exporters vs Non-Exporters

−2 −1 0 10

0.5

1

Exporters vs Non-Exporters

Data (non-exp) Data (exporters) Model (non-exp) Model (exporters)

Data

Model

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Worker Wage Distribution

−2 −1 0 1 20

0.5

1

Log Worker Wages

−2 −1 0 1 20

0.5

1

Exporters vs Non-Exporters

Data

Model

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Dynamic FitDispersion of worker Wages

86 88 90 92 94 96 980

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Variance

logworker

wages

Data

Structural Model

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CounterfactualsOut of sample: variation in τ

0 1 2 3 4 5 6 7 80.17

0.18

0.19

0.2

0.21

0.22

log Υ(1−β)/Γx

Variance

logworker

wages

1986

Estimate

1990

Show sensitivity

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Conclusions

• Neoclassical trade theory emphasizes wage inequality betweenoccupations and industries

• In contrast, new theories of firm heterogeneity and trade pointto wage dispersion within occupations and industries

• Using matched employer-employee data for Brazil, we showthat

• Much of the increase in wage inequality since the mid-1980shas occurred within sector-occupations

• Increased within-group wage inequality• Increased wage dispersion between firms• Between-firm wage dispersion related to trade participation

• Develop a framework for the structural estimation of a modelwith firm heterogeneity and wage dispersion across firms

• Use this framework to quantify the contribution of changes intrade openness to wage inequality and to undertakecounterfactuals

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Wage Inequality

.65

.7.7

5V

aria

nce

log

wag

e (U

.S. d

olla

rs)

7.5

88.

5M

ean

log

wag

e (U

.S. d

olla

rs)

1986 1990 1994 1998Year

Mean log wage (left scale) Variance log wage (right scale)

Back to slides

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Trade Openness

.44

.46

.48

.5.5

2.5

4S

hare

of E

mpl

oym

ent

.05

.06

.07

.08

.09

Sha

re o

f Firm

s

1986 1990 1994 1998Year

Share Exporters Exp Employ Share

Panel A: Firm Export Participation

Back to slides

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Regional Robustness

within components overall residualinequality inequality

Level Change Level Change1990 1986–95 1990 1986–95

Sector-occupation 67 67 88 91Sector-occupation, Sao Paolo 66 49 91 71Sector-occupation-state 57 38 73 57Sector-occupation-meso 53 30 69 49

Back to slides

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Between-Firm Wage InequalitySize and Exporter Premia

Level GrowthA. Unconditional (1990) (1986-1995)

Firm Employment 7% 5%Firm Export Status 3% 6%Covar Employment-Export Status 3% 5%Residual 88% 84%

B. Controlling for Worker ObservablesFirm Employment 7% 2%Firm Export Status 2% 4%Covar Employment-Export Status 2% 3%Residual 89% 91%

Back to slides

30 / 25

Likelihood Function

L(Θ|Xj) =∏j

P{(hj ,wj , ιj)|Θ}

P{(hj ,wj , ιj)|Θ} =

1

σuφ(uj

) 1

σvφ(vj) [

Φ

(f − ρu uj − ρv vj√

1− ρ2u − ρ2

v

)]1−ιj [1− Φ

(f − ρu uj − ρv vj√

1− ρ2u − ρ2

v

)]ιj

uj =hj − αh − µhιj

σu,

vj =(wj − αw − µw ιj)− ζ(hj − αh − µhιj)

σv

back to slides

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Unconstrained and Restricted Models

αh αw ζ σu σv f1990 2.84 −0.35 0.11 1.14 0.40 1.601994 2.75 −0.35 0.10 1.08 0.41 1.35

1990 1994ρu µh ρv µw ρu µh ρv µw

(i) Maximum, µw <0 0.14 2.11 0.53 −0.16 0.07 1.91 0.48 −0.06(ii) µh, µw ≥ 0 0.09 2.24 0.39 0.00 0.06 1.94 0.42 0.00

(iii) µw = ζµh 0.02 2.40 0.10 0.27 0.02 2.02 0.20 0.20(iv) Orthogonal shocks 0.00 2.45 0.00 0.35 0.00 2.07 0.00 0.36(v) Maximum, ρv <0 −0.03 2.53 −0.48 0.78 0.03 2.01 −0.55 0.82

back to slides

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CounterfactualsOut of sample

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.425

0.43

0.435

0.44

0.445

0.45

0.455

0.46

Exporter Employment Share

Standard

DeviationofLogWages

Counterfactual

Data

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Sensitivity of CounterfactualOut of sample: variation in τ

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.15

0.16

0.17

0.18

0.19

0.2

0.21

0.22

0.23

0.24

0.25

Exporter Employment Share

Var

ianc

e lo

g w

orke

r w

ages

back to slides

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Trade and Inequality: From Theory to Estimation

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