Testing for Serial Correlation in Fixed-Effects Panel Data Models

Abstract

In this article, we propose various tests for serial correlation in fixed-effects panel data regression models with a small number of time periods. First, a simplified version of the test suggested by Wooldridge (2002) and Drukker (2003) is considered. The second test is based on the Lagrange Multiplier (LM) statistic suggested by Baltagi and Li (1995), and the third test is a modification of the classical Durbin–Watson statistic. Under the null hypothesis of no serial correlation, all tests possess a standard normal limiting distribution as N tends to infinity and T is fixed. Analyzing the local power of the tests, we find that the LM statistic has superior power properties. Furthermore, a generalization to test for autocorrelation up to some given lag order and a test statistic that is robust against time dependent heteroskedasticity are proposed.

Keywords:

• Fixed-effects panel data
• Hypothesis testing
• Serial correlation

JEL Classification:

• C12
• C23

Notes

¹As pointed out by Baltagi and Wu (1999), the case of gaps within the sequence of observations is more complicated.

²Since this test employs the least-squares estimator in first differences, this test assumes E(Δx_itΔu_it) = 0 or E(x_itu_is) = 0 for all t and s ∈ {t − 1, t, t + 1}.

³This approach is also known as “robust cluster” or “panel corrected” standard errors.

⁴The cross-sectional dimension is held constant at N = 500, results for smaller N are qualitatively similar. Values of c = 0, c = 0.5, and c = 1 therefore imply ρ = 0, ρ = 0.0244, and ρ = 0.0447, respectively.

⁵As suggested by a referee, we also consider non-Gaussian error distributions. The results were very similar and can be obtained on request.

⁶We also considered a wide range of other combinations of α₁ and α₂. In all cases, the turns out to be more powerful than the IS statistics.

⁷Note that for non-symmetric A_T the expression can be rewritten in a symmetric format as .