card lemieux 2001
TRANSCRIPT
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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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Estimated College-High School Wage
Differentials for Younger and Older Men
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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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Theoretical framework
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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Theoretical framework
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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Theoretical framework
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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Theoretical framework
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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Theoretical framework
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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College-High School Wage Differentials
by Age and Year (cont.)
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College-High School Wage Differentials
by Age and Year (cont.)
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Age Profiles of the College-High School
Wage Gap
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Age Profiles of the College-High School
Wage Gap
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Age Profiles of the College-High School
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