the hours distribution of the group. Although this assumption is obviously an extreme one, the results should provide insight as to the possible impact of selection bias.
V. Identifying Assumptions
To fix ideas, consider the labor supply equation for wives after the data have been grouped:
h w
w Y
υ µ
ε 3
ijrt f
ijrt f
ijrt m
ijrt ijr
f ijt
f rt
f ijrt
f 1
2 3
= +
+ +
+ +
+ +
α α
α α
η h
w w
Y υ
µ ε
4
ijrt f
ijrt f
ijrt m
ijrt ijr
f ijt
f rt
f ijrt
f 10
1 10
2 10
3 10
10 10
10
= +
+ +
+ +
+ +
α α
α α
η
+ +
+ +
+ +
+
Here t indexes time, f refers to wives, m to husbands, i refers to husband type, j refers to wife type, and r refers to region. So, for example, w
ijrt f
is the average log wage at time t of a woman of type j married to a man of type i in region r. Types are defined
by age and by education level. I treat the group indicators
υ
ijr f
as fixed effects. This feature distinguishes the framework from standard cross-sectional approaches in which education andor age
are excluded and used to instrument wages. Instead, I exploit changes in relative wages to estimate labor supply elasticities. The group dummies capture permanent
differences in labor supply behavior between couples of different types. Some of this permanent variation reflects labor supply responses to permanent differences in wages
but some will also reflect permanent differences in unobservables such as motivation that are correlated with both spouse’s wages.
5
I include couple dummies rather than individual dummies because assortative mating is likely to occur on the basis of unob-
servables as well as observables. For example, a college graduate married to a high school dropout is likely to be different from a college graduate married to another col-
lege graduate.
Because there are only two time periods, the estimation is carried out in differences. By differencing, one washes out the group fixed effects.
Taking differences, one arrives at Equation 5. 5
ijr f
ijr f
ijr m
ijr ij
f r
f ijr
f 1
2 3
∆h w
w Y
µ ε
= +
+ +
+ +
+ α
α α
α η
∆ ∆
∆ ∆
∆ ∆
In all specifications, I treat the region-specific error component
r f
η ∆ as a fixed
effect and so there are region indicator variables in all specifications. Thus, I control
5. There is an argument that labor supply equations should not control for schooling because one wants to exploit the fact that highly educated individuals work longer hours in order to maximize the returns on their
human capital investments see Pencavel 1998 for a recent statement of this view. Furthermore, in a cross- sectional context, there is little reason to believe that wage differences that are unrelated to education are any
less correlated with unobservables like motivation. However, changes in the wage structure allow one to allow for differences in motivation across education groups while utilizing changes in the return to educa-
tion to identify the wage elasticities. This method thus contains the strengths of both cross-sectional approaches but not the weaknesses of either: One can exploit differences in wages that arise because of dif-
ferences in education while allowing unobservable characteristics to differ systematically across education groups.
Devereux 703
for region-specific factors such as local business cycles that may influence labor sup- ply. I estimate two specifications to reflect differing assumptions about the error com-
ponent
ij f
µ ∆ .
The first assumption is that
ij f
µ ∆
is a random error component that is uncorrelated with each of the explanatory variables. Formally, E
ij f
µ ∆ , ∆w
ijrt f
= 0, and E
ij f
µ ∆ ,
ijr m
w ∆
= 0. This implies that differences in female labor supply across groups, condi-
tional on observable variables, remain constant over time. The identification comes from differences across groups in the rate of wage growth of husbands and wives
between 1980 and 1990. One might worry that in the estimator we are comparing hours changes in groups
that are quite different for example, men with college degrees to men without high school diplomas and these groups may be subject to rather different unobserved
shocks. If there is regional variation in changes in relative wages of men and women, one can exploit this variation to identify
α
1
and α
2
by comparing the hours changes of couples with exactly the same education and age characteristics but different
levels of wage growth because they live in different regions. There are reasons to believe that the assumption that changes in unobservables
affecting tastes for work are equal for all groups may be violated in the 1980 and 1990 census data. One issue is simply one of measurement: The questions and coding cat-
egories for the education variables in the 1990 census differ from the corresponding ones in the 1980 census. While I try to make these variables consistent across the two
years, there may still be changes in the composition of the groups between 1980 and 1990.
6
A second issue is the problem of identifying cohort, age, and time effects in repeated cross-sectional data. By grouping by age, I compare groups of similar ages
in 1980 and 1990. This implies that the groups come from different cohorts and these cohorts may systematically differ in terms of tastes for work.
More generally, changes in societal norms and government policies on crime, drug use, consumerism, and other factors such as immigration may have had divergent
influences on either the composition or the behavior of different groups. The problems may be especially large for wives since there have been rapid increases in labor mar-
ket experience for women and a commensurate growing attachment to the labor market. These effects are likely to be greater for higher-skilled women and hence vio-
late the assumption that changes in unobservables affecting tastes for work are equal for all groups.
Thus, in the preferred specifications, I allow for a correlation between
ij f
µ ∆
and the explanatory variables by including indicators for husband type and wife type in the
differenced regression. Specifically, I allow changes in labor supply to depend on indicator variables that are formed by the interaction of the education categories col-
lege graduate, high school diploma, high school dropout, and age categories. Assortative mating implies that changes in unobservables are likely to be correlated
6. In 1980, individuals report highest grade attempted HGA and highest grade completed HGC . Cases are classified as high school dropouts if HGA 12 or HGA = 12 and HGC = 0, high school graduates if
12 HGA 17 and HGC = 0 or 11 HGA 16 and HGC = 1, and college graduates if HGA 16 or HGA = 16 and HGC = 1. In 1990, individuals are classified as high school dropouts if they report less than
12th grade or 12th grade with no diploma. They are classified as high school graduates if they report high school graduate or GED, or some college with no degree, or to having an associate degree. They are classi-
fied as college graduates if they report having a bachelors, masters, professional, or doctorate degree.
The Journal of Human Resources 704
for husbands and wives. Therefore, I also include the equivalent controls for the type of the spouse.
7
VI. Implementation of the Estimators
