INTRODUCTION

This paper considers nonparametric identification in models with nonadditive unobservables, where choices are either the dependent or the explanatory variables. For models where choices are dependent variables, the paper presents some of the latest developments in nonparametric identification, in the context of two popular models of consumer demand: the classical consumer demand and discrete choice. For models where choices are explanatory variables, it discusses several of the methods that have recently been developed to deal with their endogeneity.

Choice is the selection of an alternative from a set of alternatives. In many economic models, the role of economic agents is to make choices. Workers choose how to allocate their time between leisure and work-time. Consumers choose how to allocate their income between consumption and savings. Firms choose what and how much to produce. Governments choose taxes and subsidies. The usual assumption made in these economic models is that when making a choice, each economic agent has an objective function, and the choice is made so as to maximize that objective function over the set of possible alternatives.

Observable choices, made either by an agent or by different agents, are typically heterogeneous. This heterogeneity may be the result of heterogeneous choice sets, or of heterogenous objective functions. Some of this heterogeneity may be explained by different values of observable variables. Some may be explained by different values of unobservable variables. Understanding the source and shape of heterogeneity in choices is important, among other things, for accurately predicting behavior under new environments, and for evaluating the differential effect of policies over heterogeneous populations.