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# QUARTERLY JOURNAL OF ECONOMICS

(1)

Pr[U(Yw, Lw, Pw, X)

U(Ynw, Lnw

, Pnw, 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 benets. Income when not working is the maximum AFDC/Food Stamp benet and Medicaid benets. In each case we calculate the earnings, taxes, and benets 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 benets 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 specied below) and her hours worked to be a random draw from a distribution (also to be specied below) that is conditional on the wage realization. Then the probability of working is just

(2)

Pr{E[Uw]

Unw},

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[Yw]

Ynw)

(E[Lw]

Lnw)

(E[Pw]

Pnw)

X

nw

w},

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

8. Our base specication includes a state cost of living adjustment following the approach of National Research Council [1995]. One can argue that housing costs largely reect local amenities. However, to the extent that these amenities are largely xed benets 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.

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