Serial correlation testing in error component models with moderately small T

Abstract: When testing for unrestricted serial correlation in the idiosyncratic error component of a linear panel data model, the number of testable moment restrictions under the null hypothesis of no such correlation increases quadratically in the number of time periods T. We document that a recently proposed portmanteau test designed for fixed T (Jochmans, 2020, Journal of Applied Econometrics) quickly loses power in finite samples - and eventually degenerates - even for time horizons that are widely considered as small. As a remedy, we consider dimensionality reduction strategies in the form of linear combinations of the moment restrictions. Motivated by similar approaches to collapse and curtail the internal instruments in the estimation of linear dynamic panel data models, the modified tests can achieve substantial power gains - even for T as small as 3. In particular, we suggest a test statistic based on a combination of short and longer differences. This new test has superior power against a wide range of stationary and nonstationary alternatives; it does not lose power as the process under the alternative approaches a random walk - unlike the Arellano and Bond (1991, Review of Economic Studies) and Yamagata (2008, Journal of Econometrics) tests - and it is robust to large variances of the unit-specific error component - unlike the portmanteau test. All of the considered tests are applicable to models with predetermined or endogenous regressors.

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Autor: Responsible: Thomas Steger