1068

# QUARTERLY JOURNAL OF ECONOMICS

(1)

Pr[U(Y_{w}, L_{w}, P_{w}, X)

U(Y_{nw}, L_{nw }

, P_{nw}, X)],

where the randomness in this event comes from the stochastic term .

Income when working is pretax earnings minus taxes, plus AFDC and Food Stamps, plus Medicaid benets. Income when not working is the maximum AFDC/Food Stamp benet and Medicaid benets. In each case we calculate the earnings, taxes, and benets for a given individual incorporating family composi- tion (number and ages of children), and characteristics of state and federal policies at the time. We calculate real income and benets across states using a cost of living index that depends on state housing costs. The decision to work should depend on the real return to work, not the nominal return.^{8 }

A key issue in implementing this approach is the form of the uncertainty about a woman’s wage and hours should she work. In the estimates reported here, we take a woman to have no more knowledge of her potential wage and hours than we do as re- searchers.^{9 }Thus, we take her wage to be a random draw from a distribution (to be specied below) and her hours worked to be a random draw from a distribution (also to be specied below) that is conditional on the wage realization. Then the probability of working is just

(2)

Pr{E[U_{w}]

U_{nw}},

where the expectation here is over the joint wage and hours distribution.

# To estimate equation (2), we take the distribution of

to be

normal and take U to be linear in income and nonmarket time (we have relaxed this latter assumption in other work). In the linear

case (2) has a very simple form:

(3)

Pr{ (E[Y_{w}]

Y_{nw})

(E[L_{w}]

L_{nw})

(E[P_{w}]

P_{nw})

X

nw

_{w}},

where X is other variables that may affect the work decision such

8. Our base specication includes a state cost of living adjustment following the approach of National Research Council [1995]. One can argue that housing costs largely reect local amenities. However, to the extent that these amenities are largely xed benets of an area, one would still want to account for state differences in housing costs when calculating the value of additional income.

9. We have also considered two alternatives: 1) a woman knows her wage and hours before choosing to work, and 2) a woman knows her wage, but not her hours before choosing to work. Our experiments with these alternatives yielded results qualitatively similar to our main results.