On the Asymptotic Normality of the Conditional Maximum Likelihood Estimators for the Truncated Regression Model and the Tobit Model

TL;DR

This paper proves the asymptotic normality of conditional maximum likelihood estimators for truncated regression and Tobit models under general conditions, confirming conjectures by Hayashi (2000).

Contribution

It establishes the asymptotic normality of these estimators under broad conditions, validating previous conjectures.

Findings

Asymptotic normality holds when the matrix x_t x'_t is nonsingular.

Confirms Hayashi's conjectures on the estimators' properties.

Provides theoretical validation for the estimators' asymptotic behavior.

Abstract

In this paper, we study the asymptotic normality of the conditional maximum likelihood (ML) estimators for the truncated regression model and the Tobit model. We show that under the general setting assumed in his book, the conjectures made by Hayashi (2000) \footnote{see page 516, and page 520 of Hayashi (2000).} about the asymptotic normality of the conditional ML estimators for both models are true, namely, a sufficient condition is the nonsingularity of $\mathbf{x_tx'_t}$.