A Consistent LM Type Specification Test for Semiparametric Panel Data Models

TL;DR

This paper introduces a new series-based specification test for semiparametric panel data models with fixed effects, providing a reliable and computationally straightforward method with improved finite sample performance.

Contribution

It develops a consistent LM-type test using series methods for semiparametric panel data models, including a degrees of freedom correction for better accuracy.

Findings

Test statistic follows a standard normal distribution asymptotically.

The degrees of freedom correction improves finite sample performance.

The method facilitates easy computation of critical values.

Abstract

This paper develops a consistent series-based specification test for semiparametric panel data models with fixed effects. The test statistic resembles the Lagrange Multiplier (LM) test statistic in parametric models and is based on a quadratic form in the restricted model residuals. The use of series methods facilitates both estimation of the null model and computation of the test statistic. The asymptotic distribution of the test statistic is standard normal, so that appropriate critical values can easily be computed. The projection property of series estimators allows me to develop a degrees of freedom correction. This correction makes it possible to account for the estimation variance and obtain refined asymptotic results. It also substantially improves the finite sample performance of the test.