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Is neglected heterogeneity really an issue in binary and fractional regression models? A simulation exercise for logit, probit and loglog models

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  • Esmeralda A. Ramalho

    () (Universidade de Evora, Departamento de Economia, CEFAGE-UE)

  • Joaquim J. S. Ramalho

    () (Universidade de Evora, Departamento de Economia, CEFAGE-UE)

Abstract

In this paper we examine theoretically and by simulation whether or not unobserved heterogeneity independent of the included regressors is really an issue in logit, probit and loglog models with both binary and fractional data. We found that unobserved heterogeneity: (i) produces an attenuation bias in the estimation of regression coefficients; (ii) is innocuous for logit estimation of average sample partial effects, while in the probit and loglog cases there may be important biases in the estimation of those quantities; (iii) has much more destructive effects over the estimation of population partial effects; (iv) only for logit models does not affect substantially the prediction of outcomes; and (v) is innocuous for the size and consistency of Wald tests for the significance of observed regressors but, in small samples, reduces their power substantially.

Suggested Citation

  • Esmeralda A. Ramalho & Joaquim J. S. Ramalho, 2009. "Is neglected heterogeneity really an issue in binary and fractional regression models? A simulation exercise for logit, probit and loglog models," CEFAGE-UE Working Papers 2009_10, University of Evora, CEFAGE-UE (Portugal).
  • Handle: RePEc:cfe:wpcefa:2009_10
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    References listed on IDEAS

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    1. Chesher, Andrew & Peters, Simon, 1994. "Symmetry, Regression Design, and Sampling Distributions," Econometric Theory, Cambridge University Press, vol. 10(01), pages 116-129, March.
    2. Esmeralda A. Ramalho & Joaquim J. S. Ramalho, 2012. "Alternative Versions of the RESET Test for Binary Response Index Models: A Comparative Study," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(1), pages 107-130, February.
    3. Chesher, Andrew, 1995. "A Mirror Image Invariance for M-Estimators," Econometrica, Econometric Society, vol. 63(1), pages 207-211, January.
    4. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
    5. Lee, Lung-Fei, 1982. "Specification error in multinomial logit models : Analysis of the omitted variable bias," Journal of Econometrics, Elsevier, vol. 20(2), pages 197-209, November.
    6. Cramer,J. S., 2011. "Logit Models from Economics and Other Fields," Cambridge Books, Cambridge University Press, number 9780521188036.
    7. J. S. Cramer, 2007. "Robustness of Logit Analysis: Unobserved Heterogeneity and Mis-specified Disturbances," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(4), pages 545-555, August.
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    Cited by:

    1. Rahmouni, Mohieddine & Ayadi, Mohamed & YIldIzoglu, Murat, 2010. "Characteristics of innovating firms in Tunisia: The essential role of external knowledge sources," Structural Change and Economic Dynamics, Elsevier, vol. 21(3), pages 181-196, August.
    2. Esmeralda A. Ramalho & Joaquim J. S. Ramalho, 2017. "Moment-based estimation of nonlinear regression models with boundary outcomes and endogeneity, with applications to nonnegative and fractional responses," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 397-420, April.
    3. Shuang Zhu & R. Pace, 2014. "Modeling Spatially Interdependent Mortgage Decisions," The Journal of Real Estate Finance and Economics, Springer, vol. 49(4), pages 598-620, November.
    4. Achim Hecker & Alois Ganter, 2016. "Organisational And Technological Innovation And The Moderating Effect Of Open Innovation Strategies," International Journal of Innovation Management (ijim), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-31, February.
    5. Geerling, Wayne & Magee, Gary B. & Brooks, Robert, 2015. "Cooperation, defection and resistance in Nazi Germany," Explorations in Economic History, Elsevier, vol. 58(C), pages 125-139.

    More about this item

    Keywords

    Binary models; fractional models; neglected heterogeneity; partial effects; prediction; wald tests.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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