Asymptotic Variance Theory for Trimmed Least Squares and Trimmed Least Absolute Deviations in Censored Panel Models with Fixed Effects

TL;DR

This paper revises and corrects the asymptotic variance formulas for trimmed least squares and absolute deviations estimators in censored panel models with fixed effects, ensuring valid inference.

Contribution

It derives the correct Hessian for TLS, establishes asymptotic normality without restrictive conditions, and corrects variance formulas for both TLS and TLAD estimators.

Findings

Corrected Hessian formula for TLS estimator.

Validated asymptotic normality under weaker conditions.

Provided a bootstrap variance estimator for TLAD.

Abstract

We study inference using trimmed least squares (TLS) and trimmed least absolute deviations (TLAD) estimators of \citet{honore_trimmed_1992} in censored two-period panel-data models with fixed effects. We show that the published asymptotic variance formulas rely on additional regularity conditions that are not fully stated in the original analysis. For TLS, the published Hessian formula requires that the regressor-difference index vanish only when the regressor difference itself is zero, a restriction not explicitly stated in the original paper and violated, for instance, with a zero parameter vector. We derive the correct Hessian, establish asymptotic normality without imposing this restriction, and obtain a consistent plug-in variance estimator. We also show that the Hessian estimator proposed in \citet{honore_trimmed_1992} {\em is} actually consistent for the {\em correct} TLS asymptotic variance. For TLAD, we show that the published variance formula omits a conditional-probability term and that asymptotic normality requires additional continuity conditions. Under these conditions, we derive the corrected asymptotic variance and provide a tuning-parameter-free bootstrap variance estimator.