This paper develops a new method for testing for Granger non-causality in panel data models with large cross-sectional (N) and time series (T) dimensions. The method is valid in models with homogeneous or heterogeneous coefficients. The novelty of the proposed approach lies in the fact that under the null hypothesis, the Granger-causation parameters are all equal to zero, and thus they are homogeneous. Therefore, we put forward a pooled least-squares (fixed effects type) estimator for these parameters only. Pooling over cross sections guarantees that the estimator has a $$\sqrt{NT}$$ NT convergence rate. In order to account for the well-known “Nickell bias”, the approach makes use of the well-known Split Panel Jackknife method. Subsequently, a Wald test is proposed, which is based on the bias-corrected estimator. Finite-sample evidence shows that the resulting approach performs well in a variety of settings and outperforms existing procedures. Using a panel data set of 350 U.S. banks observed during 56 quarters, we test for Granger non-causality between banks’ profitability and cost efficiency.

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In this article, we consider the properties of the Pesaran CD test for cross-section correlation when applied to residuals obtained from panel data models with many estimated parameters. We show that the presence of period-specific parameters leads the CD test statistic to diverge as the time dimension of the sample grows. This result holds even if cross-section dependence is correctly accounted for and hence constitutes an example of the incidental parameters problem. The relevance of this problem is investigated for both the classical two-way fixed-effects estimator and the Common Correlated Effects estimator of Pesaran. We suggest a weighted CD test statistic which re-establishes standard normal inference under the null hypothesis. Given the widespread use of the CD test statistic to test for remaining cross-section correlation, our results have far reaching implications for empirical researchers.

We analyse the finite sample properties of maximum likelihood estimators for dynamic panel data models. In particular, we consider transformed maximum likelihood (TML) and random effects maximum likelihood (RML) estimation. We show that TML and RML estimators are solutions to a cubic first‐order condition in the autoregressive parameter. Furthermore, in finite samples both likelihood estimators might lead to a negative estimate of the variance of the individual‐specific effects. We consider different approaches taking into account the non‐negativity restriction for the variance. We show that these approaches may lead to a solution different from the unique global unconstrained maximum. In an extensive Monte Carlo study we find that this issue is non‐negligible for small values of T and that different approaches might lead to different finite sample properties. Furthermore, we find that the Likelihood Ratio statistic provides size control in small samples, albeit with low power due to the flatness of the log‐likelihood function. We illustrate these issues modelling US state level unemployment dynamics.