Compensated discrete choice with particular reference to labor supply

Dagsvik and Karlström (2005) have demonstrated how one can compute Compensating Variation and Compensated Choice Probabilities by means of analytic formulas in the context of discrete choice models. In this paper we offer a new and simplified derivation of the compensated probabilities. Subsequently, we discuss the application of this methodology to compute compensated labor supply responses (elasticities) in a particular discrete choice labor supply model. Whereas the Slutsky equation holds in the case of the standard microeconomic model with deterministic preferences, this is not so in the case of random utility models. When the non-labor income elasticity is negative the Slutsky equation implies that the compensated wage elasticity is higher than the uncompensated one. In contrast, in our random utility model we show empirically that in a majority of cases the uncompensated wage elasticity is in fact the highest one. We also show that when only the deterministic part of the utility function is employed to yield optimal hours and related elasticities, these elasticities are numerically much higher and decline more sharply across deciles than the random utility ones.