Binary Choice Models with Discrete Regressors: Identification and Misspecification
AbstractIn 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.
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Date of creation: May 2012
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Binary response models; Discrete regressors; Partial identification; Misspecification; Support vector machines;
Find related papers by JEL classification:
- C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-05-24 (All new papers)
- NEP-DCM-2013-05-24 (Discrete Choice Models)
- NEP-ECM-2013-05-24 (Econometrics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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