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Use of quadratic terms in Type 2 Tobit models

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  • Thomas W. Zuehlke

Abstract

A Type 2 Tobit model with a common set of regressors in the selection and regression equations is identified by the nonlinearity of the distribution function. The estimates are relatively less precise than in cases where there are at least some distinct regressors in the two equations. In an attempt to overcome this problem, some authors introduce quadratic terms into one or both equations. As this does not add any new statistical information, just a deterministic function of an existing regressor, the sceptic would question how this could improve the reliability of the estimates. This article shows that arbitrary use of quadratics is not without consequence. It increases the chances of getting either multiple roots, no root or a local root where a global does not exist. The nature of this problem is illustrated with Monte Carlo methods as well as several examples from the literature.

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  • Thomas W. Zuehlke, 2017. "Use of quadratic terms in Type 2 Tobit models," Applied Economics, Taylor & Francis Journals, vol. 49(17), pages 1706-1714, April.
    • Handle: RePEc:taf:applec:v:49:y:2017:i:17:p:1706-1714
    DOI: 10.1080/00036846.2016.1223831
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    1. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 3-61.
    2. Nelson, Forrest D., 1984. "Efficiency of the two-step estimator for models with endogenous sample selection," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 181-196.
    3. Marsaglia, George & Tsang, Wai Wan, 2000. "The Ziggurat Method for Generating Random Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 5(i08).
    4. 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 765-799, July.
    5. Zuehlke, Thomas W & Zeman, Allen R, 1991. "A Comparison of Two-Stage Estimators of Censored Regression Models," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 185-188, February.
    6. Nawata, Kazumitsu, 1994. "Estimation of sample selection bias models by the maximum likelihood estimator and Heckman's two-step estimator," Economics Letters, Elsevier, vol. 45(1), pages 33-40, May.
    7. Olsen, Randall J, 1982. "Distributional Tests for Selectivity Bias and a More Robust Likelihood Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(1), pages 223-240, February.
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    Cited by:

    1. Jonathan A. Cook & Saad Siddiqui, 2020. "Random forests and selected samples," Bulletin of Economic Research, Wiley Blackwell, vol. 72(3), pages 272-287, July.

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