Binary Choice Models with Discrete Regressors: Identification and Misspecification

Tatiana Komarova

STICERD - Econometrics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE

Abstract: In semiparametric binary response models, support conditions on the regressors are required to guarantee point identification of the parameter of interest. For example,one regressor is usually assumed to have continuous support conditional on the other regressors. In some instances, such conditions have precluded the use of these models; in others, practitioners have failed to consider whether the conditions are satisfied in their data. This paper explores the inferential question in these semiparametric models when the continuous support condition is not satisfied and all regressors have discrete support. I suggest a recursive procedure that finds sharp bounds on the components of the parameter of interest and outline several applications, focusing mainly on the models under the conditional median restriction, as in Manski (1985). After deriving closed-form bounds on the components of the parameter, I show how these formulas can help analyze cases where one regressor's support becomes increasingly dense. Furthermore, I investigate asymptotic properties of estimators of the identification set. I describe a relation between the maximum score estimation and support vector machines and also propose several approaches to address the problem of empty identification sets when a model is misspecified. Finally, I present a Monte Carlo experiment and an empirical illustration to compare several estimation techniques.

Keywords: Binary response models; Discrete regressors; Partial identification; Misspecification; Support vector machines (search for similar items in EconPapers)
JEL-codes: C10 C14 C2 C25 (search for similar items in EconPapers)
Date: 2012-05
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Persistent link: https://EconPapers.repec.org/RePEc:cep:stiecm:559

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