Hyperbolic Transformation and Average Elasticity in the Framework of the Fixed Effects Logit Model

Abstract

In this paper, a simple transformation is proposed for the fixed effects logit model, which constructs some valid moment conditions including the first-order condition for one of the conditional MLE proposed by Chamberlain (1980) [1]. Some Monte Carlo experiments are carried out for the GMM estimator based on the transformation. In addition, the average elasticity of the logit probability with respect to the exponential function of explanatory variable is proposed in the framework of the fixed effects logit model, which is computable without the fixed effects.

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Y. Kitazawa, "Hyperbolic Transformation and Average Elasticity in the Framework of the Fixed Effects Logit Model," Theoretical Economics Letters, Vol. 2 No. 2, 2012, pp. 192-199. doi: 10.4236/tel.2012.22034.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] G, Chamberlain, “Analysis of Covariance with Qualitative Data,” Review of Economic Studies, Vol. 47, No. 1, 1980, pp. 225-238. doi:10.2307/2297110
[2] J. Neyman and E. L. Scott, “Consistent Estimates Based on Partially Consistent Observations,” Econometrica, Vol. 16, No. 1, 1948, pp. 1-32.
[3] G, Rasch, “Probabilistic Models for Some Intelligence and Attainment Tests,” The Danish Institute for Educational Research, 1960.
[4] G, Rasch, “On General Laws and the Meaning of Measurement in Psychology,” Preceeding of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 4, 1961, pp. 321-333.
[5] B. E. Honoré and E. Kyriazidou, “Panel Data Discrete Choice Models with Lagged Dependent Variables,” Econometrica, Vol. 68, No. 4, 2000, pp. 839-874. doi:10.1111/1468-0262.00139
[6] C. Hsiao, “Analysis of Panel Data,” 2nd Edition, Cam- bridge University Press, Cambridge, 2003.
[7] A. Thomas, “Consistent Estimation of Binary-Choice Panel Data Models with Heterogeneous Linear Trends,” Econometrics Journal, Vol. 9, No. 3, 2006, pp. 177-195. doi:10.1111/j.1368-423X.2006.00181.x
[8] J. Hahn and W. Newey, “Jackknife and Analytical Bias Reduction for Nonlinear Panel Models,” Econometrica, Vol. 72, No. 4, 2004, pp. 1295-1319. doi:10.1111/j.1468-0262.2004.00533.x
[9] D. R. Cox and N. Reid, “Parameter Orthogonality and Approximate Conditional Inference,” Journal of the Royal Statistical Society, Series B, Vol. 49, No. 1, 1987, pp. 1-39.
[10] T. Lancaster, “Orthogonal Parameters and Panel Data,” Review of Economic Studies, Vol. 69, No. 3, 2002, pp. 647-666. doi:10.1111/1467-937X.t01-1-00025
[11] M. Arellano, “Discrete Choices with Panel Data,” Inves- tigaciones Económicas, Vol. 27, No. 3, 2003, pp. 423-458. doi:10.2139/ssrn.261048
[12] M. Arellano and S. Bonhomme, “Robust Priors in Non- linear Panel Data Models,” Econometrica, Vol. 77, No. 2, 2009, pp. 489-536. doi:10.3982/ECTA6895
[13] J, Carro, “Estimating Dynamic Panel Data Discrete Choice Models with Fixed Effects,” Journal of Econo- metrics, Vol. 140, No. 2, 2007, pp. 503-528. doi:10.2139/ssrn.384021
[14] I. Fernández-Val, “Fixed Effects Estimation of Structural Parameters and Marginal Effects in Panel Probit Models,” Journal of Econometrics, Vol. 150, No. 1, 2009, pp. 71- 85. doi:10.1016/j.jeconom.2009.02.007
[15] T. A. Severini, “An Approximation to the Modified Pro- file Likelihood Function,” Biometrika, Vol. 85, No. 2, 1998, 403-411. doi:10.1093/biomet/85.2.403
[16] L. Pace and A. Salvan, “Adjustments of the Profile Like- lihood from a New Perspective,” Journal of Statistical Planning and Inference, Vol. 136, No. 10, 2006, pp. 3554-3564. doi:10.1016/j.jspi.2004.11.016
[17] A. Bester and C. Hansen, “A Penalty Function Approach to Bias Reduction in Nonlinear Panel Models with Fixed Effects,” Journal of Business and Economic Statistics, Vol. 27, No. 2, 2009, pp. 131-148. doi:10.1198/jbes.2009.0012
[18] M. Arellano and J. Hahn, “Understanding Bias in Non- linear Panel Models: Some Recent Developments,” In: R. Blundell, W. Newey and T. Persson, Eds., Advances in Economics and Econometrics, Cambridge University Press, Cambridge, 2007, pp. 381-409.
[19] C. Hsiao, “Longitudinal Data Analysis,” In: S. N. Durlauf and E. B. Blume, Eds., Microeconometrics, Palgrave and Macmillan, Basingstoke, 2010, pp. 89-107.
[20] L. P. Hansen, “Large Sample Properties of Generalized Method of Moments Estimators,” Econometrica, Vol. 50, No. 4, 1982, pp. 1029-1054.
[21] R, Blundell, R. Griffith and F. Windmeijer, “Individual Effects and Dynamics in Count Data Models,” Journal of Econometrics, Vol. 108, No. 1, 2002, pp. 113-131. doi:10.1016/S0304-4076(01)00108-7
[22] A. C. Cameron and P. K. Trivedi, “Microeconometrics: Methods and Applications,” Cambridge University Press, Cambridge, 2005.
[23] F. Hayashi, “Econometrics,” Princeton University Press, Princeton, 2000.
[24] M. J. Lee, “Panel Data Econometrics,” Academic Press, London, 2002.
[25] S. Bonhomme, “Functional Differencing,” Econometrica, 2012, in Press.
[26] J. M. Wooldridge, “Econometric Analysis of Cross-Sec- tion and Panel Data,” MIT Press, Cambridge, 2002.
[27] J. Abrevaya, “The Equivalence of Two Estimators of the Fixed Effects Logit Model,” Economics Letters, Vol. 55, No. 1, 1997, pp. 41-43. doi:10.1016/S0165-1765(97)00044-X
[28] B. H. Hall and C. Cummins, “TSP 5.0 User’s Guide,” TSP International, 2006.
[29] R. Blundell and S. Bond, “Initial Conditions and Moment Restrictions in Dynamic Panel Data Models,” Journal of Econometrics, Vol. 87, No. 1, 1998, pp. 115-143. doi:10.1016/S0304-4076(98)00009-8

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