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

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  • Khan, Shakeeb

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.

Suggested Citation

  • Khan, Shakeeb, 2013. "Distribution free estimation of heteroskedastic binary response models using Probit/Logit criterion functions," Journal of Econometrics, Elsevier, vol. 172(1), pages 168-182.
  • Handle: RePEc:eee:econom:v:172:y:2013:i:1:p:168-182
    DOI: 10.1016/j.jeconom.2012.08.002
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    References listed on IDEAS

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    Cited by:

    1. T. Arduini, 2016. "Distribution Free Estimation of Spatial Autoregressive Binary Choice Panel Data Models," Working Papers wp1052, Dipartimento Scienze Economiche, Universita' di Bologna.
    2. Le-Yu Chen & Sokbae Lee, 2016. "Best Subset Binary Prediction," Papers 1610.02738, arXiv.org, revised Nov 2017.
    3. Chen, Xiaohong & Liao, Zhipeng, 2015. "Sieve semiparametric two-step GMM under weak dependence," Journal of Econometrics, Elsevier, vol. 189(1), pages 163-186.
    4. Chen, Songnian & Khan, Shakeeb & Tang, Xun, 2016. "Informational content of special regressors in heteroskedastic binary response models," Journal of Econometrics, Elsevier, vol. 193(1), pages 162-182.
    5. Edoardo Rainone, 2017. "Pairwise trading in the money market during the European sovereign debt crisis," Temi di discussione (Economic working papers) 1160, Bank of Italy, Economic Research and International Relations Area.
    6. Tiziano Arduini & Eleonora Patacchini & Edoardo Rainone, 2015. "Parametric and Semiparametric IV Estimation of Network Models with Selectivity," EIEF Working Papers Series 1509, Einaudi Institute for Economics and Finance (EIEF), revised Oct 2015.
    7. Chen, Songnian & Zhang, Hanghui, 2015. "Binary quantile regression with local polynomial smoothing," Journal of Econometrics, Elsevier, vol. 189(1), pages 24-40.

    More about this item

    Keywords

    Binary response; Heteroskedasticity; Probit/Logit; Sieve estimation;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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