card lemieux 2001

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1Empirical Labor Economics

Changes in the Wage

Structure: Explanations

Empirical Labor Economics


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Explanations

2

1. Educational Production

2. Immigration

3. Biased Technical Change and Organizational Change

4. International Trade and Outsourcing

5. Institutions and Wage Compression


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Educational Production

David Card and Thomas Lemieux (2001, QJE): Can falling supply explain the

rising return to college for younger men? A cohort-based analysis

Comparison of U.S., U.K. and Canada.

Cohort-based analysis: Comparing college-high school gap for different agegroups (young vs. old).

Authors argue that the changing structure of the college-high school gap is

a reflection of intercohort shifts in the relative supply of highly educated

workers.

Driving force is the slowdown of the rate of growth in educational attainmentbeginning with cohorts born in the early 1950s.

Basic ingredient: imperfect substitution between younger and older workers.


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Estimated College-High School Wage

Differentials for Younger and Older Men


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Theoretical framework

Aggregate output depends on two CES subaggregates of high-school and

college labor:

(1)

(2)

where is a function of the partial elasticity of substitution

between different age groupsjwith the same level of education ;

and relative efficiency parameters.

1/[ ( )]t j jt j

H H =

1/[ ( )]t j jt j

C C =

1 > A

( 1 1/ )A =

j j


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Aggregate output in period t, yt,is a function of high school labor, college

labor, and the technical efficiency parameters and .

(3)

Aggregate production function:

(4)

where is a function of the elasticity of substitution

between the two education groups ;

( , ; , )t t t ht ct

y f H C =

1 > E

( 1 1/ )E =

ht

ct

1/( )t ht t ct t

y H C = +


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Marginal product of high-school workers in age group j:

(5)

(6)

(7)

where (8)

yt yt t

jt t jt

H

H H H

=

1 1 1

ht t t j jt t H H H

= 1

ht t t j jt H H

=

1/ 1( )t ht t ct t

H C = +


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Efficient utilization of different skill groups requires that relative wages are

equated to relative marginal products which implies the following equation:

(9)

,where and are the wage rates of college workers and high

school workers respectively.

log( ) log( ) ( ) log( ) log( ) ( 1) log( )

c cjt j jtt t

h h

jt t t j jt

CC

H H

= + + +

c

jt h

jt


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This equation leads to a model of the observed college-high school wage gap ofworkers in age group j in year t:

(10)

(11)

log( )

c

jt

jt h

jt

r

=

1 1 1log( ) log( ) ( ) log( ) ( ) og( )c j jtt t

jth

t j A E t A jt

CCl e

H H

= + + +

log( ) log( )c

jtjt h

t j

r

= +

1 1( ) log( ) [log( ) log( )]

jtt tjt

E t A jt t

CC Ce

H H H +


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Suppose that the log supply ratio for workers who are of age j in year t consists

of a cohort effect for the group, , and an age effect that is common

across cohorts:

(12)

This implies:

(13)

log( / )jt jt t j j

C H

= +

log( ) log( )c

jt

jt h

t j

r

= +

1 1 1 1( ) ( ) log( ) ( )t

j t j jt

A A E t A

Ce

H

+ +

t j j


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Implementation

Problem: Aggregate supplies of two labor inputs depend on the elasticities ofsubstitution across age groups.

Solution: Three step estimation approach

1. Estimate : (14)

2. Compute the relative efficiency parameters and using the estimate

( ) from the first stage:

and (15)

(16)

3. Estimate equation (11) using the estimates from the first and secondstage.

j j

A (1/ ) log( / )jt j t A jt jt jtr b d C H e= + +

1/ A

log( ) 1/ log log( ) loghjt A jt ht t t jH H + = +

log( ) 1/ log log( ) logc

jt A jt ct t t jC C

+ = +


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College-High School Wage Differentials

by Age and Year


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by Age and Year (cont.)


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by Age and Year (cont.)


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Age Profiles of the College-High School

Wage Gap


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Wage Gap


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Wage Gap


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Decompositions of College-High School

Wage Differentials by Age and Year into

Cohort, Age, and Time Effects


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Decompositions of College-High School

Wage Differentials by Age and Year into

Cohort, Age, and Time Effects (cont.)


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Lecture #12 23

Age-Group Specific Relative Supplies of

College-Educated Labor


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Relative Supply of College-Educated

Workers by Cohort


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Estimated Models for the College-High

School Wage Gap, by Cohort and Year


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Models for the College-High School Wage

Gap, by Cohort and Year


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Aggregate Relative Supply Index for Men


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Robustness of the Results to Alternative

Measures of the College-High School Wage

Gap, United States


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Lecture #12 29

Models for the College-High School Wage Gap

Men and Women,

United States,

by Cohort and Year


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Explanations for Changes in College

Enrollment

Changing costs for college

Changing returns to college

Change in interest rates

Changes in college enrollment associated with the Vietnam war

Changes in unemployment rates

Changes in cohort size

card lemieux 2001

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