The Effect of and a Test for Misspecification in the Censored-Normal Model

Abstract

It is well-known that ordinary least-squares will produce inconsistent estimates of the regression parameters if the dependent variable is censored or truncated. Maximum likelihood estimation with a normality assumption on Tobit and other limited dependent variable models is being employed with increasing frequency to avoid this inconsistency. It is not so commonly acknowledged, however, that such estimates lack robustness : The assumptions required of these models are quite strong and any violation, such as heteroscedasticity or nonnormality, may result in an asymptotic bias as severe as in the naive OLS formulations. But to recognize the potential inconsistency in the face of misspecification without a test for and solution to such misspecification is of little use. The purpose of this paper is to examine the nature of the inconsistency and to suggest a general test for misspecification.

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