Estimation of a Dynamic Tobit Model with a Unit Root

TL;DR

This paper develops robust estimation methods for the dynamic Tobit model under local-to-unity asymptotics, demonstrating the consistency and distribution of ML and CLAD estimators, and enabling reliable model selection in practical applications.

Contribution

It extends the theoretical understanding of ML and CLAD estimators in dynamic Tobit models under LUR asymptotics, including their consistency and asymptotic distributions.

Findings

ML and CLAD estimators are consistent under LUR.

Asymptotic distributions of ML and CLAD are Gaussian for short-run parameters.

OLS remains consistent but has non-standard t-statistics under LUR.

Abstract

This paper studies robust estimation in the dynamic Tobit model under local-to-unity (LUR) asymptotics. We show that both Gaussian maximum likelihood (ML) and censored least absolute deviations (CLAD) estimators are consistent, extending results from the stationary case where ordinary least squares (OLS) is inconsistent. The asymptotic distributions of MLE and CLAD are derived; for the short-run parameters they are shown to be Gaussian, yielding standard normal t-statistics. In contrast, although OLS remains consistent under LUR, its t-statistics are not standard normal. These results enable reliable model selection via sequential t-tests based on ML and CLAD, paralleling the linear autoregressive case. Applications to financial and epidemiological time series illustrate their practical relevance.