Estimating the Family Labor Supply Functions Derived from the Stone-Geary Utility Function

The Stone-Geary utility function defined over an index of goods, the leisure of the husband, and the leisure of the wife is used to derive the earnings functions of the husband and the wife. The parameters of the utility function are estimated from the parameters of the earnings functions in a way that accounts for a number of theoretical and statistical problems. The effect of family composition on utility is estimated by specifying and estimating adult equivalents in consumption and leisure of various categories of children. On the statistical side the following difficulties are all considered: nonlinear constraints across equations, endogenous marginal income tax rates, variations in tastes in the population, heteroscedasticity, and truncation of the left-hand variable. The data come from the 1967 Survey of Economic Opportunity. The results are generally good and support the view that the effects of family composition on utility can be estimated from behavioral relationships. Alternative results that ignore the complicated statistical problems are presented; they imply that the statistical problems are empirically important and should not be ignored.