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

2026-05-16

AI Summary

This study addresses the incomplete derivation of asymptotic variances for truncated least squares (TLS) and truncated least absolute deviations (TLAD) estimators in two-period censored panel models with fixed effects, as originally presented by Honoré (1992). By identifying implicit and unreasonable restrictions in the original variance formulas, correcting the Hessian expression, incorporating a missing conditional probability term in TLAD, and relaxing unstated regularity conditions, the paper establishes asymptotic normality without requiring additional assumptions. Furthermore, it proposes a tuning-parameter-free bootstrap variance estimator and proves its consistency. The work not only restores the consistency of the original Hessian-based estimator under correct specification but also constructs a valid inference framework for TLAD that satisfies continuity conditions, thereby substantially broadening the applicability of these estimation methods.

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.

Problem

• asymptotic variance
• trimmed least squares
• trimmed least absolute deviations
• censored panel models
• fixed effects

Innovation

• trimmed least squares
• trimmed least absolute deviations
• censored panel models
• asymptotic variance
• fixed effects