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Generalized Semiparametric Binary Prediction

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  • Jeff Racine

    () (Department of Economics, University of South Florida)

Abstract

This paper proposes a semiparametric approach to the estimation of ¡®generalized¡¯ binary choice models. A ¡®generalized¡¯ binary choice model is one with separate indices for each conditioning variable which constitutes a generalization of the standard single-index approach typically employed in applied work. The choice probability distribution is therefore a joint distribution across these indices as opposed to the typical univariate distribution on a scalar index commonly found in applied work. Interest lies in estimating choice probabilities and the gradient of choice probabilities with respect to the conditioning information, and these are estimated nonparametrically using the method of kernels. A data-driven cross-validatory method for bandwidth selection and index-parameter estimation is proposed for maximization of the nonparametric likelihood function. The functional form of the indices enters this nonparametric likelihood function thereby permitting data-driven determination of the index functions in addition to the shape of the joint cumulative distribution function itself. Applications are considered.

Suggested Citation

  • Jeff Racine, 2002. "Generalized Semiparametric Binary Prediction," Annals of Economics and Finance, Society for AEF, vol. 3(1), pages 117-134, May.
  • Handle: RePEc:cuf:journl:y:2002:v:3:i:1:p:117-134
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    References listed on IDEAS

    as
    1. McFadden, Daniel L., 1984. "Econometric analysis of qualitative response models," Handbook of Econometrics,in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 24, pages 1395-1457 Elsevier.
    2. Lee, Lung-fei, 1995. "Semiparametric maximum likelihood estimation of polychotomous and sequential choice models," Journal of Econometrics, Elsevier, vol. 65(2), pages 381-428, February.
    3. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    4. Picone, Gabriel A. & Butler, J.S., 2000. "Semiparametric Estimation Of Multiple Equation Models," Econometric Theory, Cambridge University Press, vol. 16(04), pages 551-575, August.
    5. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    6. Chen, Heng Z. & Randall, Alan, 1997. "Semi-nonparametric estimation of binary response models with an application to natural resource valuation," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 323-340.
    7. Amemiya, Takeshi, 1981. "Qualitative Response Models: A Survey," Journal of Economic Literature, American Economic Association, vol. 19(4), pages 1483-1536, December.
    8. Ichimura, Hidehiko & Thompson, T. Scott, 1998. "Maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution," Journal of Econometrics, Elsevier, vol. 86(2), pages 269-295, June.
    9. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-782, May.
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    More about this item

    Keywords

    Semiparametric; Nonparametric methods;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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