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Betit: A Family that Nests Probit and Logit

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  • Wim P.M. Vijverberg

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Abstract

This paper proposes a dichotomous choice model that is based on a transformed beta (or zâ€) distribution. This model, called betit, nests both logit and probit and allows for various skewed and peaked disturbance densities. Because the shape of this density affects the estimated relation between the dichotomous choice variable and its determinants, the greater flexibility of the transformed beta distribution is useful in generating more accurate representations of this relationship. The paper considers asymptotic biases of the logit and probit models under conditions where betit should have been used. It also investigates small sample power and provides two examples of applications that illustrative of the capability of the betit model. [IZA Discussion Paper No. 222]

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Bibliographic Info

Paper provided by eSocialSciences in its series Working Papers with number id:2768.

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Date of creation: Aug 2010
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Handle: RePEc:ess:wpaper:id:2768

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Keywords: Dichotomous choice model; beta distribution; logit; probit;

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  1. Vijverberg, Wim P. M. & Zeager, Lester A., 1994. "Comparing earnings profiles in urban areas of an LDC: Rural-to-urban migrants vs. native workers," Journal of Development Economics, Elsevier, vol. 45(2), pages 177-199, December.
  2. Arabmazar, Abbas & Schmidt, Peter, 1982. "An Investigation of the Robustness of the Tobit Estimator to Non-Normality," Econometrica, Econometric Society, vol. 50(4), pages 1055-63, July.
  3. Mroz, Thomas A, 1987. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," Econometrica, Econometric Society, vol. 55(4), pages 765-99, July.
  4. Bera, Anil K & Jarque, Carlos M & Lee, Lung-Fei, 1984. "Testing the Normality Assumption in Limited Dependent Variable Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(3), pages 563-78, October.
  5. Klein, R.W. & Spady, R.H., 1991. "An Efficient Semiparametric Estimator for Binary Response Models," Papers 70, Bell Communications - Economic Research Group.
  6. Vijverberg, Wim P M, 1987. "Non-normality as Distributional Misspecification in Single-Equation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 49(4), pages 417-30, November.
  7. Amemiya, Takeshi, 1981. "Qualitative Response Models: A Survey," Journal of Economic Literature, American Economic Association, vol. 19(4), pages 1483-1536, December.
  8. Yatchew, Adonis & Griliches, Zvi, 1985. "Specification Error in Probit Models," The Review of Economics and Statistics, MIT Press, vol. 67(1), pages 134-39, February.
  9. Arabmazar, Abbas & Schmidt, Peter, 1981. "Further evidence on the robustness of the Tobit estimator to heteroskedasticity," Journal of Econometrics, Elsevier, vol. 17(2), pages 253-258, November.
  10. Vijverberg, Wim P. M., 1997. "Monte Carlo evaluation of multivariate normal probabilities," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 281-307.
  11. Hurd, Michael, 1979. "Estimation in truncated samples when there is heteroscedasticity," Journal of Econometrics, Elsevier, vol. 11(2-3), pages 247-258.
  12. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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