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### QUARTERLY JOURNAL OF ECONOMICS

and hours distribution, and we make the same assumption for single childless women. We estimated some specications that used a wage/hours distribution that varied with demographics, although these results are not reported here (see Meyer and Rosenbaum [1999]). Thus, expected earnings if working only vary with the controls and are absorbed by X, which includes variables for the presence and number of children, age, education, state, year, and other variables described fully below. Similarly, non- market time when working and not working, E[L_{w }] and L_{nw }, respectively, are taken to be constant or to vary with X, and thus are absorbed by X. P_{n }_{w }, which identically equals 1, is absorbed into the constant. We then obtain the employment probability:

(5)

{

_{1}E[taxes]

_{2}E[AFDC and Food Stamp benefits if work]

_{3}E[Medicaid coverage if work valued at cost]

_{4}maximum AFDC/Food Stamp benefit _{5}Medicaid coverage if do not work valued at cost

E[P_{w}]

X

}.

We allow the tax and welfare variables in (5) to vary with year, state, and the number and ages of children. To implement this approach, we discretize the wage and hours distribution and perform the numerical integration required in (5), allowing the hours distribution to vary with the wage level because of the pronounced dependence between the two distributions. To calcu- late the wage and hours distribution, we pool 1984 –1996 March CPS data and estimate one distribution that we use for all years. We do this separately for single mothers and single childless women. We approximate these distributions using cells dened by 50 intervals of the joint wage and hours distribution (see Appendix 1 for details). Our approach is both tractable and yet able to capture the fairly complex and highly nonlinear budget constraints of low income single mothers. These complexities are described in detail in Section IV.

III. DATA

The data used in this paper come from the Current Popula- tion Survey (CPS), a nationally representative monthly survey of approximately 60,000 households. We use two types of the CPS data, the March CPS Files and the merged Outgoing Rotation