Marginal compensated effects in discrete labor supply models

Abstract This paper develops analytic results for marginal compensated effects in discrete labor supply models, including a Slutsky equation. The Slutsky equation is aggregate in the sense that it establishes the relationship between the marginal compensated effects of the probability of working and the mean hours of work in terms of the corresponding marginal uncompensated effects. The Slutsky equation differs somewhat from the Slutsky equation in the standard continuous labor supply models. Specifically, the marginal compensated effect of an increase in the wage rate differs from the corresponding effect of a decrease in the wage rate. To illustrate some qualitative properties of the compensated marginal effects we have used an empirical labor supply model to compute numerical compensated (Hicksian) and uncompensated marginal (Marshallian) effects resulting from wage rate changes.