Distribution free estimation of heteroskedastic binary response models using Probit/Logit criterion functions

Shakeeb Khan

Journal of Econometrics, 2013, vol. 172, issue 1, 168-182

Abstract: In this paper estimators for distribution free heteroskedastic binary response models are proposed. The estimation procedures are based on relationships between distribution free models with a conditional median restriction and parametric models (such as Probit/Logit) exhibiting (multiplicative) heteroskedasticity. The first proposed estimator is based on the observational equivalence between the two models, and is a semiparametric sieve estimator (see, e.g. Gallant and Nychka (1987), Ai and Chen (2003) and Chen et al. (2005)) for the regression coefficients, based on maximizing standard Logit/Probit criterion functions, such as NLLS and MLE. This procedure has the advantage that choice probabilities and regression coefficients are estimated simultaneously. The second proposed procedure is based on the equivalence between existing semiparametric estimators for the conditional median model (Manski, 1975, 1985; Horowitz, 1992) and the standard parametric (Probit/Logit) NLLS estimator. This estimator has the advantage of being implementable with standard software packages such as Stata. Distribution theory is developed for both estimators and a Monte Carlo study indicates they both perform well in finite samples.

Keywords: Binary response; Heteroskedasticity; Probit/Logit; Sieve estimation (search for similar items in EconPapers)
JEL-codes: C13 C14 C24 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (20)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:172:y:2013:i:1:p:168-182

DOI: 10.1016/j.jeconom.2012.08.002

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