Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities

This paper proposes a new way to construct con…dence sets for a parameter of interest in models comprised of …nitely many moment inequalities. Building on results from the literature on multivariate one-sided tests, I show how to test the hypothesis that any particular parameter value is logically consistent with the maintained moment inequalities. The associated test statistic has an asymptotic chi-bar-square distribution, and can be inverted to construct an asymptotic con…dence set for the parameter of interest, even if that parameter is only partially identi…ed. The con…dence sets are easily computed, and Monte Carlo simulations demonstrate good …nite sample performance. JEL classi…cation: C3, C12 Keywords: Partial identi…cation, Inference, Moment inequalities This is a revised version of the …rst chapter of my dissertation. I thank Andrew Chesher, Joel Horowitz, Chuck Manski, Rob Porter, and Jörg Stoye for their insightful suggestions. I am especially grateful to Elie Tamer for continued feedback and encouragement. In addition, I have bene…ted from the comments of seminar participants at BU, Cornell, Northwestern, UBC, UCL, UCSD, UMD, U. Michigan, and U. Penn. Financial support from the Robert Eisner Memorial Fellowship and the Center for the Study of Industrial Organization is gratefully acknowledged. Any and all errors are my own. yDepartment of Economics, University College London, Gower Street, London WC1E 6BT, United Kingdom and Institute for Fiscal Studies, 7 Ridgmount Street, London WC1E 7AE, United Kingdom. Comments welcome at [email protected].