Compensating variation and Hicksian choice probabilities in random utility models that are nonlinear in income

In this paper we discuss Hicksian demand and compensating variation in the context of discrete choice. We first derive Hicksian choice probabilities and the distribution of the (random) expenditure function in the general case when the utilities are nonlinear in income. We subsequently derive exact and simple formulae for the expenditure and choice probabilities under price (policy) changes conditional on the initial utility level. This is of particular interest for welfare measurement because it enables the researcher to compute the distribution of compensating variation in a simple way. We also derive formulae for the joint distribution of expenditure, the choice before and after a policy change has been introduced.