Compensated discrete choice with particular reference to labor supply

Recently 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 in the case with independent random utility models. Subsequently, we discuss the application of this methodology to compute compensated labor supply responses (elasticisities) in discrete labor supply models. 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. Note that since the non-labor income elasticity is negative the Slutsky equation implies that the compensated wage elasticity is higher than the uncompensated one. With a random utility model we show empirically that in many cases the uncompensated wage elasticity is in fact the highest one.