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

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) het...

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Bibliographic Details
Published in:Journal of econometrics 2013-01, Vol.172 (1), p.168-182
Main Author: Khan, Shakeeb
Format: Article
Language:English
Subjects:
Binary response
Coefficients
Econometric models
Estimating techniques
Estimation
Heteroskedasticity
Monte Carlo simulation
Normal distribution
Parameter estimation
Probability theory
Probit/Logit
Regression analysis
Sieve estimation
Studies
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Summary: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.
ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2012.08.002