Pierre André Chiappori (Columbia) "Family Economics" - Cemmap

5. Empirical issues for the collective model 233
• The distribution factors have a significant impact on both labor supplies.
The signs are as predicted by the theory; that is, a higher sex
ratio (denoting a smaller percentage of women on the marriage market),
as well as divorce laws more favorable to women, reduce the
wife’s labor supply and increase the husband’s, suggesting a transfer
of resources to the wife. Interestingly, these effects are not present for
singles; divorce laws do not impact singles’ labor supplies in a significant
way, whereas the sex ratio has no effect on the labor supply of
single males and increases the labor supply of single women. Finally,
the authors do not reject the prediction from the collective model
that the impacts of the two factors on the two labor supplies should
proportional.
• The corresponding transfers can be evaluated, since the sharing rule is
identified up to an additive constant. A one percentage point increase
in the sex ratio (representing roughly one standard deviation from
the mean) is found to result in an annual transfer to the wife of more
than $2,000, or about 5% of the average household income. Likewise,
a one point increase in the Divorce Laws Index (which varies from 1
to 4, with a mean at 2.8) induces husbands to transfer and additional
$4,300 to their wives. Both estimates are statistically significant at
conventional levels.
• In addition, one can recover the impact of wages and non labor incomes
on the sharing rule. For instance, a one dollar increase in the
wife’s wage rate (which is equivalent to an annual increase of about
$1,750 in her labor income, at the mean of hours worked by women)
translates into more income being transferred to her husband. At
sample mean, the transfer amounts to more than $1,500, although
this effect is not precisely estimated. Also, a one dollar increase in
the husband’s wage rate (equivalent to an annual increase of $2,240
in his labor income) translates into $600 being transferred to his wife,
although again this effect is imprecisely estimated. Finally, a one dollar
increase in household nonlabor income will increase the wife’s
nonlabor income by 70 cents; that non labor income goes mostly to
the wife on average is actually a common finding of most empirical
studies based on the collective framework.
• Finally, wage elasticities can be computed in two ways. A direct estimation
gives a positive, significant elasticity for women, close to
0.2, while men’s wage elasticities are very small and not statistically
significant. The structural model also allows us to estimate the
‘true’ own-wage elasticities of individual labor supplies, taking into
account the impact of wages on the sharing of nonlabor income. Both
women’s and men’s elasticities are significant but smaller than those
reported previously - reflecting the fact that a marginal increase in