Econometrica: Nov 1973, Volume 41, Issue 6
Regression Analysis when the Dependent Variable Is Truncated Normal
Takeshi AmemiyaThe paper considers the estimation of the parameters of the regression model where the dependent variable is normal but truncated to the left of zero. Tobin  first considered the problem and proposed an iterative solution of the maximum likelihood equations. The paper proves the strong consistency and the asymptotic normality of the maximum likelihood estimator, proves the inconsistency of Tobin's initial estimator, proposes a computationally simple estimator that is consistent and asymptotically normal, and proves the asymptotic efficiency of the second-round estimator in the method of Newton. An extension to the case where the observations are not available at the truncation point is briefly indicated in the Conclusions.
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