Use of quadratic terms in Type 2 Tobit models

Thomas Zuehlke

Applied Economics, 2017, vol. 49, issue 17, 1706-1714

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.

Date: 2017
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DOI: 10.1080/00036846.2016.1223831

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