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GENDER AND RACE IN THE LABOR MARKET

Sponsored by a Grant TÁMOP-4.1.2-08/2/A/KMR-2009-0041 Course Material Developed by Department of Economics,

Faculty of Social Sciences, Eötvös Loránd University Budapest (ELTE) Department of Economics, Eötvös Loránd University Budapest

Institute of Economics, Hungarian Academy of Sciences Balassi Kiadó, Budapest

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2

Author: Anna Lovász Supervised by Anna Lovász

June 2011

Week 5

Measuring discrimination II:

other methods using databases Literature for next week

• Bertrand–Mullainathan 2004

• Goldin–Rouse 2000

• Further recommended reading:

– Heckman 1998

Estimation of group-level relative productivity from production functions

• Unexplained wage gap from wage equations ≠ discrimination, since there may be unobserved group-level differences in productivity.

(3)

3 How can we take these into account?

• Firms differ in output (revenue) and in the demographic composition of their workforces.

• Over time, a given firm’s workforce composition and output varies

Can use to estimate the effect of the ratio of different worker groups on output/productivity

Goal

• Estimate the relative productivities and wages of various worker groups (gender, age, education)

MPn / MP0 ≠ wn / w0

wage discrimination (or efficiency wages, compensating wage differentials)

• Research questions:

• Do differences in the relative productivity of various worker groups explain their wage differentials? (For example, the gender wage gap)

– Kertesi–Köllő (2002): the wage and productivity of young skilled workers increased relative to unskilled worker in Hungary.

• Do firms set relative wages closer to relative productivities since the transition (more efficient wage setting)?

• Increased competition decreased the gender wage gap (Becker)

Benefits of the methodology

• Mincerian wage equations (residual wage gap): estimate of discrimination is consistent if:

• We can measure all differences in group-level productivity.

• Production function augmented with workforce composition → relative productivity

(4)

4 of worker groups

• This relative productivity estimate includes the effect of unobservable and observable differences in productive characteristics

• Makes it possible to take systematic differences in group-level productivity into account

• Literature: Hellerstein–Neumark (1999), Dostie (2006), Van Biesebroek (2007), Hellerstein–Neumark (2005), Zhang és Dong (2009), Lovász–Rigó (2009)

Main steps

• Step 1:

• Estimation of production function augmented with workforce composition → relative productivities

• Step 2:

• Estimation of firm-level wage equation → relative wages

• Step 3:

• Test:

• Relative productivity = relative wage?

Methodology: production function (Hellerstein–Neumark 1999)

lnY = α lnK + β lnM + γ lnQL

• Workers are perfect substitutes:

φ0: productivity of reference group



 





 −

+

= +

=

=

∑ ∑ ∑

=

=

=

N

n

n n n

N

n n n

N

n

n L

L L L L

L QL

1 0

0 1

0 0 0

1

1 ϕ

ϕ ϕ

ϕ ϕ

ϕ

(5)

5

• Estimated equation:

• Can easily calculate relative productivities based on NLS estimates:

φn / φ0 = MPn/MP0

• Z: industry, year, ownership, (firm fixed effects)

Estimation strategy

• Worker groups:

• Gender: male (G), female (F)

• Age: <40, 40<

• Education: elementary or secondary school (E), higher education (U) – 8 worker groups (interactions)

– 7 relative productivity parameters

• Reference group: male, below 40, no diploma

• QL simplification:

• Constant relative productivity:

• For example, gender difference is the same within each age group

• Traditional wage equation estimation also assumes this if there are no interaction terms

• The number of relative productivity parameters decreases to 3

• Equiproportional assumption:

• For example, the ratio of women is the same within each age group

• Number of parameters: 3

• Ratios of worker groups are estimated for larger groups

jt jt N

n jt

n n jt

jt jt

jt Z u

L L L

M K

Y jt + ⋅ +









 −

+ +

+ +

+ +

=

=

ϕ δ γ ϕ

γ ϕ γ β

α α

1 0

0

0 ln ln ln ln ln 1 1

ln

jt jt N

n jt

n n jt

jt jt

jt Z u

L L L

M K

Y jt + ⋅ +









 −

+ +

+ +

+ +

=

=

ϕ δ γ ϕ

γ ϕ γ β

α α

1 0

0

0 ln ln ln ln ln 1 1

ln

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6

• Equation with constraints 1. + 2.:

• Most studies use both constraints (e.g. Hellerstein–Neumark 1999 and 2004;

Hellerstein–Neumark–Troske 1999 , 1999; Van Biesebroeck, 2007; Dostie, 2006)

Production function – problems

• Differences over time or between industries (structural):

• Divide sample:

• into time periods

• by industries

• Measurement of labor inputs (QL)

• Determining worker groups (which characteristics, how many categories)

• Measurement error: we estimate the firm-level ratio of worker groups from the sample of workers in the dataset

• Unobserved productivity shocks

• Firm fixed effects

• Levinsohn and Petrin (2003) method

( ) ( )

( )

jt jt

jt U U

jt O O

jt F F

jt jt

jt jt

u Z L

L

L L L

L

L M

K Y

jt

jt jt

+

+



 + −

+

+



 + −

+



 + −

+

+ +

+ +

=

δ ϕ

γ

ϕ γ

ϕ γ

γ β

α α

1 1

ln

1 1

ln 1

1 ln

ln ln

ln

ln 0

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7

Methodology: firm-level wage equation (Hellerstein–Neumark 1999)

• Aggregation of individual wage equations

• Dependent variable: weighted sum of worker wages, OR firm-level wage bill

• Benefits of firm-level estimation:

• Simultaneous estimation of production and wage equations

• Straightforward hypothesis testing

• Two firm-level variables

• All wage-related costs

Linear estimation

NLS (Stata:nlsur) is slow and difficult to implement, so usually estimate linear approximation

• As long as , the approximation is:

• Estimated equations (Stata: sureg):

jt jt N

n jt

n n jt

jt jt

jt d Z u

L L w

c w L c w c M b K a a

W jt + ⋅ +









 −

+ +

+ +

+ +

=

=1 0 0

0 ln ln ln ln ln 1 1

ln

( 1 ) < 0 . 1

L L

F

ϕ

F

( ) ( )

L L L

L F

F F

F 1 1

1

ln ≈ −





+ ϕ ϕ

jt jt jt

U F jt O O jt F F jt jt

jt

Z u

L L L

L L

L L

K

Y = α + α ⋅ ln + γ ⋅ ln + φ

jt

+ φ

jt

+ φ

jt

+ δ ⋅ +

ln

0

jt jt jt

U F jt O O jt F F jt jt

jt Z u

L L L

L L

L L

K

W =α +α⋅ln +γ ⋅ln +φ jtjtjt +δ⋅ +

ln 0

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8

Data

• Hungarian Wage and Employment Survey

• 1986, 1989, 1992–2005

• Matched employer-employee dataset: worker variables (wage, education, gender, age, occupation) and firm variables (revenue, size, ownership, industry, capital, material and wage costs)

• All firms with at least 20 employees, sample of smaller firms

• 6.5% of blue collar workers, 10% of white collar workers sampled on average

• Panel in terms of firms, not workers

Data – sample restrictions

• Only firms with at least 50 employees

• Only those with at least 5% of their workers included in the sample

• 47,928 firm-years

• 1,245,577 worker-years

• 15,804 firms

• 10,155 with at least 10 workers

• 5,624 with at least 20 workers

Data – variables

• Ratio of worker groups within each firm, each year: from worker-level dataset

• Y (output): value added (VA)

• W (wage): firm’s wage bill

• K (capital)

• Z controls

jt jt jt

U F jt O O jt F F jt jt

jt Z u

L L L

L L

L L

K

Y =α +α⋅ln +γ⋅ln +φ jtjtjt +δ ⋅ +

ln 0

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9

Results – women

(10)

10

Results – by skill level

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11

Results – by age

Summary

• The female-male wage productivity-wage gap decreased after the transition.

• Women are paid in line with their productivity – no evidence of discrimination.

• Highly skilled have a negative gap: they are underpaid.

• Workers above 40 are overpaid

– Productivity decreased compared to younger workers significantly following the transition: skill obsolence

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12

Results: old and new firms

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13

Indirect tests

• Use the implications of discrimination models to test for the presence of discrimination

• For example: the relationship between the ratio of minority workers and profit:

(taste-based) discriminating employers are not profit-maximizing.

• Hellerstein–Neumark–Troske (1995): negative significant relationship between profits and the ratio of female workers

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14

The effect of competition on discrimination – Lovász 2009

The log female-male wage gap decreased from 0.31 to 0.18 following the transition:

The change is mostly unexplained (Campos és Joliffe 2004)

Were discriminating employers forced out of the market due to increased competition?

If yes: empirical evidence of discrimination against women

Becker (1957): an increase in product market competition will decrease discrimination in the long-run

• Empirical testing opportunity:

• Rapid liberalization of Hungarian markets: sudden, large change in the level of competition

• Large, representative matched employer-employee database, long time period:

1986–2005

Statistics

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Year

Relative Wage of Women 1986-2003

Relative Wage

Source: CSO

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15

Gender wage gap in Hungary, 1986–2005

Empirical strategy

Step 1: estimation of unexplained wage gaps:

For every firm j and year t:

lnwijt = αt + βtXijt + δjtFEit + εijt

Xij = worker characteristics (education, experience, occupation) FEi = female dummy

δjt = firm-level residual wage gap = upper-bound estimate of discrimination Step 2: testing the effect of competition:

δjt = αt + β1CMkt + β2Nt + εjt

CMkt: competition measures in industry k and year t Nt: controls (year, region, industry fixed effects) Becker’s implication: β1 < 0

Source: WES database

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16

Competition measures

• Concentration ratio (1-HHI: for ease of evaluation)

– 3 digit industries, based on Tax Authority revenue data – 0=monopoly, 1=perfect competition

• Export share (export revenue/revenue)

– 3 digit industries, based on Tax Authority revenue and export data – 0=no export, 1=all export

• Import penetration ratio (import/revenue+import-export)

– 3 digit industries, based on Tax Authority revenue, Customs import data – 0=no import, 1=all import

• Price Cost Margin (profit/revenue)

– 3 digit industries, based on Tax Authority revenue data All increase as competition increases

Empirical issues

Collective agreements decrease wage discrimination Subsamples based on presence of agreement 2 step estimation: the wage gap

Weighting the second step based on the standard errors from the first step Unobservable industry characteristics

Industry fixed effects: estimate the effect within industries of changes over time Selection bias: exit of low-skilled women

Worker controls, subsamples by skill level

Identification: is there sufficient variation within industries?

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17

Changes in competition over time

0.2.4.6.81

HHI in 1998

0 .2 .4 .6 .8 1

HHI in 1989 1989-1998

Changes in Industry Concentration Ratios

0.2.4.6.81Export share in 1998

0 .2 .4 .6 .8 1

Export share in 1989 1989-1998

Changes in Industry Export Shares

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18

Data

Hungarian WES: 1986, 1989, 1992–2005 Matched employer-employee data Panel in firms, not workers

Worker characteristics: gender, age, education, occupation, potential experience, workplace

Firm characteristics: size, industry, region, ownership Sample:

Firms with at least 20 employees

At least 2 men and 2 women in the sample (for FE) Private sector only

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19

Results: δjt = αt + β1CMkt + β2Nt + εjt

All industries Manufacturing

1 2 3 4

1-HHI

-0.075**

(0.018)

-0.081**

(0.025)

-0.133*

(0.054)

-0.117*

(0.056)

Import penetration

0.094**

(0.036)

0.012 (0.032)

0.129**

(0.027)

0.057 (0.032)

Export share

-0.056 (0.041)

-0.160**

(0.043)

-0.169**

(0.048)

-0.186**

(0.048)

Year dummies Y Y Y Y

Industry FE N Y N Y

Weighted Y Y Y Y

Number of

observations 9312 9312 5274 5274

R squared 0.378 0.597 0.407 0.562

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20

All industries Manufacturing

1 2 3 4

Price Cost Margin

-0.137**

(0.051)

-0.104**

(0.035)

-0.305**

(0.075)

-0.074**

(0.031)

Import penetration

0.014 (0.034)

0.055 (0.036)

-0.095 (0.091)

-0.020 (0.063)

Export share

-0.018 (0.032)

-0.042 (0.045)

-0.059*

(0.026)

-0.056 (0.046)

Year dummies Y Y Y Y

Industry FE N Y N Y

Weighted Y Y Y Y

Number of obs. 9312 9312 5274 5274

R squared .453 .639 .495 .621

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21

Results: by presence of collective agreements

Collective Wage Agreement No Collective Wage Agreement

1 2 3 4

1-HHI

-0.046*

(0.022)

0.061 (0.063)

-0.115**

(0.024)

-0.101 (0.054)

Import penetration

-0.079 (0.053)

0.021 (0.042)

0.013 (0.057)

-0.005 (0.053)

Export share

-0.108 (0.072)

-0.038 (0.091)

-0.161**

(0.049)

-0.070 (0.082)

Year dummies Y Y Y Y

Industry FE N Y N Y

Weighted Y Y Y Y

Number of obs. 2231 2231 2846 2846

R squared 0.152 0.499 0.170 0.468

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22

Results: by skill level

High skilled Medium and low skilled

1 2 3 4

1-HHI

-0.064 (0.036)

-0.044 (0.037)

-0.094**

(0.033)

-0.092*

(0.043)

Import penetration

0.272 (0.157)

-0.019 (0.051)

0.386**

(0.073)

0.023 (0.035)

Export share

-0.390 (0.209)

-0.098 (0.056)

-0.368**

(0.069)

-0.165 (0.054)

Year dummies Y Y Y Y

Industry FE N Y N Y

Weighted Y Y Y Y

Number of obs. 9289 9289 8741 8741

R squared 0.482 0.727 0.873 0.928

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23

Summary

• The results support Becker’s implication that an increase in competition decreases the unexplained wage gap.

• How big is the effect?

• The observed changes in competition levels can explain roughly 26% of the decrease in the gender wage gap.

• Import results contradictory?

Meta-analysis: the effect of competition

• International comparison: relationship between the gender wage gap and the legal/economic environment – Weichselbaumer & Winter-Ebmer

• Method: meta-analysis:

• Dependent variable: wage gap estimates from international studies

• Explanatory variables: competition (Economic freedom index), legislature (equal treatment laws)

• Results:

• Competition decreases the wage gap

• Equal treatment laws do so as well

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