wage change from the average log wage change in the region. One very clear effect is that educated groups had much larger wage increases than less educated groups the
numbers tend to become more positive as one moves down a column. The changes in relative wages are not uniform across region. For example, in the Pacific Division,
male high school dropouts aged between 31 and 50 experienced relative wage cuts of about 15 percent, in the South Atlantic group the relative wage cut for this group was
only 5 percent. The groups explain about 87 percent of the total variance in Table A1 for men, and 88 percent for women. The estimator exploits all the variation in Table
A1 to estimate wage elasticities. However, the specifications that control for group indicators in the differenced regressions make use of the approximately 12 percent of
the variation that is not explained by group effects.
A. Hours Elasticities for Wives
The estimates from the log hours equations of wives are in Table 2. In the first panel of Table 2, there is no correction for selection. Columns 1–3 contain the estimates
without controls for husband and wife type, Columns 4–6 add controls for husband type and wife type in the differenced regression. I report results for all three estima-
tors: These are weighted least squares WLS, grouped two stage least squares G2SLS, and the unbiased errors in variables estimator UEVE.
First, consider how the elasticities differ across estimators. The WLS estimates of both the own-wage and cross-wage elasticities are smaller in absolute terms than the
elasticities produced by the other estimators. A plausible explanation for this pattern is that measurement error in the sample means biases the estimated coefficients
toward zero. It is worth noting that the WLS estimates are biased despite there being an average of 843 observations per group. Thus, in this application, both having the
large sample sizes afforded by the Census and using estimators that correct for small sample bias are necessary in order to accurately estimate the behavioral responses. I
will concentrate on the G2SLS estimates in the subsequent exposition. These gener- ally lie between the WLS and UEVE estimates both in terms of coefficient values and
standard errors.
Next, consider the own-wage and cross-wage elasticities. In the specification in Column 2, the own-wage elasticity for women is 1.2. This elasticity is at the high end
of estimates in the literature and suggests a very strong response of female labor sup- ply to increasing female wages.
11
As discussed elsewhere, it is likely that there have been shifts in female labor supply over time that make these estimates invalid. The
estimates in Column 5 are robust to labor supply shifts that differ across wife types provided that they do not also differ across region. The own-wage elasticity from this
specification is much smaller in magnitude and is approximately 0.2 the implied compensated wage elasticity is approximately 0.75.
12
This smaller own-wage elas- ticity is similar to many of the recent estimates for women.
The Journal of Human Resources 706
11. Hyslop 2001 and Pencavel 1998 find a compensated own wage elasticity for married women of about 0.4, both Ransom 1987 and Hausman and Ruud 1984 find elasticities of about 0.75. The compensated
wage elasticity implied by my estimates of the uncompensated own wage elasticity and cross-wage elastic- ity is 1.75.
12. In a collectivist labor supply model, the estimated coefficients on own wage and spouse’s wage cannot be simply interpreted in terms of income and substitution effects because changes in wages change the
The cross-wage elasticity for women is very similar across specifications and is about
−0.4. This suggests that a 10 percent fall in husband’s wage leads to a 4 percent increase in wife’s hours.
13
As such, this represents a sizable behavioral response by women to changes in their husband’s wage. The robustness of this estimate across the
specifications in Columns 2 and 5 is reassuring and provides confidence in the simu- lations that are included later in the paper.
14
Devereux 707
Table 2 Estimates from Differenced Labor Supply Functions Women
WLS G2SLS
UEVE WLS
G2SLS UEVE
1 2
3 4
5 6
Dependent Variable: LogAnnual Hours Logwife’s wage
0.713 1.193
1.242 0.002
0.174 0.381
0.060 0.073
0.110 0.055
0.111 0.292
Loghusband’s −0.128
− 0.415 −0.447
− 0.232 −0.385
−0.473 wage
0.049 0.058
0.088 0.045
0.071 0.129
Nonlabor income −0.115
−0.081 −0.118
− 0.109 −0.127
−0.421 10,000
0.086 0.115
0.139 0.081
0.168 0.477
Husband and wife No
No No
Yes Yes
Yes indicators
Dependent Variable: LogAnnual Hours: Corrections for Nonparticipation Correction 1
Correction 2 Logwife’s wage
0.001 0.133
0.347 0.002
0.172 0.256
0.055 0.108
0.285 0.055
0.111 0.204
Loghusband’s −0.218
−0.342 −0.439
−0.236 −0.384
−0.456 wage
0.045 0.070
0.130 0.045
0.071 0.108
Nonlabor income −0.087
0.002 −0.331
−0.106 −0.120
−0.409 10,000
0.082 0.165
0.467 0.082
0.168 0.397
Husband and wife Yes
Yes Yes
Yes Yes
Yes indicators
Standard errors are calculated using Huber-White covariance matrix. All specifications estimated in dif- ferences. Region indicators are included in all regressions. See text for details about corrections for
nonparticipation.
bargaining position inside the household. Thus, hours respond both to the changes in the budget constraint resulting from the wage changes and also to the resultant changes in the weights placed on each individuals
utility function within the household. 13. This effect is similar in size to that found by Hyslop 2001, Pencavel 1998 and Ransom 1987 but is
much smaller in absolute terms that the cross-wage elasticity of −2.4 found by Hausman and Ruud 1984.
14. I have also estimated quadratic versions of equation 1. I find backward bending labor supply behavior for women with the labor supply curve being upward sloping for the vast majority of women in the sample.
The higher the husband’s wage, the more responsive the wife’s hours are to her wage. Also, the higher the
In the specifications with controls for husband and wife indicators, the own and cross-wage elasticities are generally similar in magnitude. This suggests that it may
be the difference in the log wages that matters rather than the absolute level of the wages. However, tests for the linear restriction that w
f
and w
h
can be replaced by w
f
− w
h
generally reject the restriction. For example, for the estimates in Table 2, Column 5, the hypothesis is rejected using a conventional test for linear restrictions
with a chi-square value of 21. The second panel in Table 2 contains results where the two methods to deal with
selection discussed in Section IV are implemented. Results are reported only for the specification with controls for husband and wife indicators. Reassuringly, the results
with the Heckman-type correction, and the truncation correction are very similar to each other and to the uncorrected results. This suggests that the estimated elasticities
are not suffering from severe selection biases.
15
Nonlabor income is generally found to have a negative but rarely statistically sig- nificant effect on hours.
16
Given the possible endogeneity of nonlabor income, it would be unwise to interpret this correlation as a causal effect. Excluding nonlabor
income from the specification has little impact on the estimated wage elasticities.
17
In unreported results, I have carried out the estimation using data grouped at the national level. At this level, there are 144 groups representing 12 husband types and
12 wife types. I find an own-wage elasticity for women of 1.25 0.10 and a cross- wage elasticity of
−0.44 0.08. These are unsurprisingly similar to the results in Table 2 without the controls for husband and wife types. The similarity suggests that migra-
tion across regions does not appreciably bias the estimates. Also, the estimates in Table 2 are robust to excluding nonnatives from the sample.
B. Hours Elasticities for Husbands
