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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 de Jesus Ratinho Lopes Arranhado Ramalho

    (Department of Economics and CEFAGE-UÉ, Universidade de Évora)

  • Joaquim José dos Santos Ramalho

    (CEFAGE)

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 de Jesus Ratinho Lopes Arranhado Ramalho & Joaquim José dos Santos 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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    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Guggisberg Michael, 2019. "Misspecified Discrete Choice Models and Huber-White Standard Errors," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-17, January.

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    Keywords

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    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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