Robust testing for serial correlation in linear panel-data models

Serial correlation tests are essential parts of standard model specification toolkits. For static panel models with strictly exogenous regressors, a variety of tests are readily available. However, their underlying assumptions can be very restrictive. For models with predetermined or endogenous regressors, including dynamic panel models, the Arellano–Bond (1991, Review of Economic Studies) test is predominantly used, but it has low power against certain alternatives. While more powerful alternatives exist, they are underused in empirical practice. The recently developed Jochmans (2020, Journal of Applied Econometrics) portmanteau test yields substantial power gains when the time horizon is very short, but it can quickly lose its advantage even for time dimensions that are still widely considered as small. I propose a new test based on a combination of short and longer differences, which overcomes this shortcoming and can be shown to have 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–Bond test—and it is robust to large variances of the unit-specific error component—unlike the Jochmans portmanteau test. I present a new Stata command that flexibly implements these (and more) tests for serial correlation in linear error component panel-data models. The command can be run as a postestimation command after a variety of estimators, including generalized method of moments, maximum likelihood, and bias-corrected estimation.