Compensating Variation and Hicksian Choice Probabilities in Random Utility Models that are Nonlinear in Income

Abstract

Abstract: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.Keywords: Random expenditure function, Compensated choice probabilities, Compensating variation. Equivalent variation. JEL classification: C25, D61Acknowledgement: We wish to thank Mårten Palme, Thor O. Thoresen and Steinar Strøm for useful discussions and comments that have improved the paper. We are particularly grateful to a referee whose suggestions have improved the exposition of the paper substantially. Thanks to Anne Skoglund for excellent word processing and proof reading.

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