GENDER AND RACE
IN THE LABOR MARKET
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
GENDER AND RACE
IN THE LABOR MARKET
Author: Anna Lovász
Supervised by Anna Lovász June 2011
ELTE Faculty of Social Sciences, Department of Economics
GENDER AND RACE
IN THE LABOR MARKET
Week 5
Measuring discrimination II:
other methods using databases
Anna Lovász
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.
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 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
• Estimated equation:
• Can easily calculate relative productivities based on NLS estimates:
φn / φ0 = MPn/MP0
• Z: industry, year, ownership, (firm fixed effects)
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
jt jt
N
n jt
n n jt
jt jt
jt Z u
L L L
M K
Y jt
1 0
0
0 ln ln ln ln ln 1 1
ln
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
jt jt
N
n jt
n n jt
jt jt
jt Z u
L L L
M K
Y jt
1 0
0
0 ln ln ln ln ln 1 1
ln
Estimation strategy
• QL simplification:
1. 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
2. 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
Estimation strategy
• 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)
jt jtjt U U
jt O O
jt F F
jt jt
jt jt
u L Z
L
L L L
L
L M
K Y
jt
jt jt
1 1
ln
1 1
ln 1
1 ln
ln ln
ln
ln 0
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
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
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
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
jt U F jt
O O jt
F F jt
jt
jt Z u
L L L
L L
L L K
Y ln ln jt jt jt
ln 0
1
0.1L LF
F
L L L
L F
F F
F 1 1
1
ln
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 ln ln jt jt jt
ln 0
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 ln ln jt jt jt
ln 0
Results – women
-3,0 -2,0 -1,0 0,0 1,0 2,0 3,0 4,0
1986, 1989 1992-1995 1996-2000 2001-2005
Female-male productivity wage
Gap
Results – by skill level
-6,0
-4,0 -2,0 0,0 2,0 4,0 6,0 8,0
1986, 1989 1992-1995 1996-2000 2001-2005
Diploma - no diploma productivity wage
Gap
Results – by age
-0,2
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
1986, 1989 1992-1995 1996-2000 2001-2005
Above 40 - below 40 productivity wage
Gap
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
Results: old and new firms
-0,2 -0,1 0,0 0,1 0,2 0,3 0,4 0,5
1992-1995 1996-2000 2001-2005 Female-male wage-productivity gap, FE
pooled old new
0,6 0,7 0,8 0,9 1,0 1,1 1,2
1992-1995 1996-2000 2001-2005
Female-male estimates, pooled sample, FE
rel wage rel prod
0,6 0,7 0,8 0,9 1,0 1,1 1,2
1992-1995 1996-2000 2001-2005
Female-male estimates, old firms, FE
rel wage rel prod
Results: old and new firms
-1,2 -1,0 -0,8 -0,6 -0,4 -0,2 0,0
1992-1995 1996-2000 2001-2005
Degree - no degree, wage-productivity gap, FE
pooled old new
0,8 1,0 1,2 1,4 1,6 1,8 2,0
1992-1995 1996-2000 2001-2005 Degree-no degree estimates, pooled
sample, FE
rel wage rel prod
0,8 1,0 1,2 1,4 1,6 1,8 2,0
1992-1995 1996-2000 2001-2005
Degree-no degree estimates, old firms, FE
rel wage rel prod
Results: old and new firms
-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3
1992-1995 1996-2000 2001-2005
Above 40 - below 40, wage-productivity gap, FE
pooled old new
0,8 0,9 1,0 1,1 1,2
1992-1995 1996-2000 2001-2005
Above 40-below 40 estimates, pooled sample, FE
rel wage rel prod
0,8 0,9 1,0 1,1 1,2
1992-1995 1996-2000 2001-2005
Above 40-below 40 estimates, old firms, FE
rel wage rel prod
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
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
Relative Wage of Women 1986-2003
0 0.2 0.4 0.6 0.8 1
1986 1989 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Year
Relative Wage
Source: CSO
Gender wage gap in Hungary, 1986–2005
Source: WES database
Empirical strategy
Step 1: estimation of unexplained wage gaps:
For every firm j and year t:
lnw
ijt= α
t+ β
tX
ijt+ δ
jtFE
it+ ε
ijtXij = 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:
δ
jt= α
t+ β
1CM
kt+ β
2N
t+ ε
jtCMkt: competition measures in industry k and year t Nt: controls (year, region, industry fixed effects)
Becker’s implication: β
1< 0
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?
Changes in competition over time
0.2.4.6.8 1
HHI in 1998
0 .2 .4 .6 .8 1
HHI in 1989 1989-1998
Changes in Industry Concentration Ratios
Changes in competition over time
0.2.4.6.8 1
Export share in 1998
0 .2 .4 .6 .8 1
Export share in 1989 1989-1998
Changes in Industry Export Shares
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
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
Results: δjt = αt + β1CMkt + β2Nt + εjt
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
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
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
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