We provide a finite sample inference method for the structural parameters of a semiparametric binary response model under a conditional median restriction originally studied by Manski (1975, 1985). Our inference method is valid for any sample size and irrespective of whether the structural...

We propose a bootstrap-based calibrated projection procedure to build con fidence intervals for single components and for smooth functions of a partially identi fied parameter vector in moment (in)equality models. The method controls asymptotic coverage uniformly over a large class of data...

In this paper, we consider estimation of the identified set when the number of moment inequalities is large relative to sample size, possibly infinite. Many applications in the recent literature on partially identified problems have this feature, including dynamic games, set-identified IV...

This paper is concerned with tests and confidence intervals for parameters that are not necessarily identified and are defined by moment inequalities. In the literature, different test statistics, critical value methods, and implementation methods (i.e., the asymptotic distribution versus the...

This paper develops methods of inference for nonparametric and semiparametric parameters defined by conditional moment inequalities and/or equalities. The parameters need not be identified. Confidence sets and tests are introduced. The correct uniform asymptotic size of these procedures is...

This paper explores the empirical content of the weak axiom of revealed preference (WARP) for repeated cross-sections. In a heterogeneous population, the fraction of consumers who violate WARP is not point identified but can be bounded. These bounds, as well as some nonparametric refinements,...

This chapter reviews the microeconometrics literature on partial identification , focusing on the developments of the last thirty years. The topics presented illustrate that the available data combined with credible maintained assumptions may yield much information about a parameter of interest,...

This chapter sets out the extension of the scope of the classical IV model to cases in which unobserved variables are set-valued functions of observed variables. The resulting Generalized IV (GIV) models can be used when outcomes are discrete while unobserved variables are continuous, when there...