Participation , is an indicator for people who worked for even one hour in the year.
Like Juhn 1992, Welch 1997, and Devereux 2003, I make no distinction between periods of nonemployment that are classified as unemployment and periods spent out
of the labor force.
IV. A Specification for Family Labor Supply
I assume a simple linear model of labor supply behavior of husbands and wives. The wife’s labor supply is given by:
h w
w Y
Z v
1
f f
m f
1 2
3 4
= +
+ +
+ +
α α
α α
α where h
f
is the log of annual hours worked by the wife, w
f
is the log of her hourly wage rate, w
m
is the log of the husband’s hourly wage rate, Y is the nonlabor income of the family, Z is a vector of other controls, and v
f
is a stochastic error. The labor sup- ply function for husbands is as follows:
h w
w Y
Z v
2
m f
m m
1 2
3 4
= +
+ +
+ +
β β
β β
β These labor supply functions are appropriate for the current problem because the
identification strategy is to use changes in relative wages to identify the labor supply parameters. Thus, this parameterization of labor supply as a function of the wages of
husband and wife enables the identifying assumptions to be used in a simple and clear fashion.
The emphasis in this paper is on the effects of changes in relative wages on hours worked and how these feed through into changes in the distribution of family earn-
ings. Given the focus on the distribution of earnings across families, I interpret coef- ficients in terms of the standard unitary model of family labor supply. It is worth
noting that nonunitary models of family labor supply would imply different interpre- tations of the estimated coefficients. For example, in collectivist models of labor sup-
ply, changes in wages influence hours in part through their effect on the bargaining power of individual spouses and hence on the sharing rule. Blundell and MaCurdy
1999 provide a discussion of the characteristics of unitary and collectivist models of family labor supply, Chiappori 1988, 1992 develops the labor supply model from a
collective perspective, and Blundell et al. 2001 show how collectivist models can be identified and estimated when not all individuals participate. These models are par-
ticularly useful for evaluating changes in the intra-household distribution of welfare.
The wage and other income variables in Equations 1 and 2 must be considered to be endogenous because of measurement error and unobserved characteristics that are
correlated with wages, nonlabor income, and hours worked. Thus, I take an instru- mental variables approach to the estimation of these equations. Because I am inter-
ested in exploiting changes in relative wages across groups to identify the parameters, the instruments used are group indicators. This instrumental variables approach can
be shown to be exactly equivalent to grouping the data and regressing the group mean of hours on the group means of the right hand side variables using weighted least
squares Angrist 1991.
In practice, I group the data and all statistical analysis is carried out on group means. I categorize married couples into discrete groups, g, such that the means of the
The Journal of Human Resources 700
variables for each group are observed in 1980 and 1990. These groups are the inter- actions of husband type with wife type and with region. In all analyses, the group
means are weighted by the number of underlying observations in each group. The details about how the groups are defined are below in Section VI.
Nonparticipation
The sample is restricted to married couples in which the man participated at some point in the calendar year but includes both participating and nonparticipating wives.
Of the 1,266,752 wives in 1980, 62 percent participate; 74 percent of the 1,271,815 wives in 1990 participate. In this paper, both hours and participation models are esti-
mated for wives. The usual selection problem arises with hours only being positive for participating women and wages being unobserved for nonparticipators. The problem
is ameliorated somewhat because, as we shall see, the models are estimated in differ- ences so it is only changes in participation rates that cause a selection problem.
However, there are sizeable increases in female participation over this period see Table 1, so selection cannot be ignored.
3
In this section, I discuss the approaches taken to the selection problem when estimating Equation 1; in Section VII, I discuss
wage imputation in the context of estimating participation equations. In terms of the grouping estimation strategy, selection bias arises in the hours equa-
tion due to changes in the composition of working individuals that are not fully accounted for by the group and time effects used as controls. These biases will arise,
for example, if an increase in the wage for a certain group leads to the entry into the labor market of individuals who work hours that are below average for the group. This
would tend to bias the own-wage elasticity toward zero. Also if the fall in wages of low-skill men leads to entry of their wives into the labor market at hours below aver-
age for women like them, this would tend to bias the cross-wage elasticity toward zero.
Theory can provide some guidance about the selection problem. If individuals dif- fer in taste for work, then individuals who are less likely to participate are also less
likely to work long hours if they participate. Thus, we would expect groups who increase participation rates to add individuals to the workforce who have low taste for
work and tend to work short hours. However, in the absence of further assumptions, theory provides no solution to the selection problems.
I take two approaches to the selection issue. The first approach Correction 1 is to make structural assumptions about the error term distributions and do a selection cor-
rection in the spirit of Heckman 1979 and Gronau 1974. I add as an extra regres- sor in the hours equation the inverse mills ratio evaluated at
Φ
-1
L
gt
, where Φ
-1
is the inverse of the normal distribution and L
gt
is the proportion of families in group g in which the wife participates in period t see Blundell, Duncan, and Meghir 1998. This
mills ratio term is added as an extra regressor in Equation 1 and the parameter δ is
estimated.
4
3. The participation rates for married men have not changed very much although there is some evidence of a decline in the participation rates of high school dropouts.
4. Because there is no exclusion restriction, this approach may have little power to detect selection bias. Pencavel 1998 also acknowledges this problem. He includes selection parameters in some specifications
and generally finds that they have little effect on the labor supply estimates.
Devereux 701
The second approach Correction 2 is to use the insight from theory than marginal participators are likely to work lower hours than other observationally equivalent
individuals. Since theory cannot inform about how big the differences should be, I take the extreme approach of assuming that new participators come from the bottom
tail of the hours distribution. The approach I take is to artificially truncate the sample so that the proportion of women in a group who work is maintained constant between
1980 and 1990. If a higher proportion work in 1990, individuals with the lowest hours in 1990 are removed until the proportions working are the same in 1980 and 1990.
Analogously, if a higher proportion works in 1980 than 1990, individuals with the lowest hours in 1980 are removed so that the proportions remain the same. This
approach is valid if the marginal participators in each group are from the left tail of The Journal of Human Resources
702
Table 1 Participation Behavior
Log wage Log wage
Participate Participate
FTFY FTFY
Group 1980
1990 1980
1990 1980 1990
Women 21-30HSDO
1.294 1.191
0.514 0.563
0.149 0.190
31-40HSDO 1.385
1.290 0.546
0.603 0.214
0.263 41-50HSDO
1.439 1.358
0.516 0.579
0.232 0.283
51-60HSDO 1.503
1.404 0.416
0.468 0.196
0.226 21-30HSG
1.456 1.417
0.688 0.782
0.298 0.388
31-40HSG 1.526
1.534 0.638
0.759 0.277
0.391 41-50HSG
1.556 1.563
0.646 0.765
0.317 0.429
51-60HSG 1.621
1.589 0.528
0.632 0.272
0.341 21-30CG
1.794 1.872
0.834 0.893
0.334 0.495
31-40CG 1.945
2.015 0.698
0.800 0.221
0.365 41-50CG
1.940 2.044
0.733 0.840
0.239 0.371
51-60CG 1.992
2.025 0.641
0.762 0.224
0.312 Men
21-30HSDO 1.729
1.539 0.947
0.930 0.570
0.574 31-40HSDO
1.890 1.700
0.929 0.905
0.627 0.595
41-50HSDO 1.996
1.826 0.896
0.863 0.646
0.601 51-60HSDO
2.066 1.917
0.813 0.771
0.598 0.540
21-30HSG 1.911
1.764 0.982
0.981 0.736
0.766 31-40HSG
2.123 1.984
0.976 0.971
0.798 0.791
41-50HSG 2.207
2.123 0.960
0.952 0.810
0.793 51-60HSG
2.252 2.168
0.894 0.877
0.737 0.701
21-30CG 2.032
2.069 0.990
0.991 0.780
0.825 31-40CG
2.369 2.373
0.989 0.990
0.827 0.857
41-50CG 2.561
2.555 0.981
0.981 0.821
0.826 51-60CG
2.598 2.604
0.940 0.933
0.777 0.737
Participate is defined as working at any point in the calendar year. FTFY means work at least 50 weeks in the calendar year and at least 35 hours per week.
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
