A homogeneous approach to testing for Granger non-causality in heterogeneous panels
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A homogeneous approach to testing for Granger non-causality in heterogeneous panels Arturas ¯ Juodis1 · Yiannis Karavias2 · Vasilis Sarafidis3,4 Received: 30 September 2020 / Accepted: 22 October 2020 © The Author(s) 2020
Abstract 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 N T 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. Keywords Panel data · Granger causality · VAR · “Nickell bias” · Bias correction · Fixed effects JEL Classification C12 · C13 · C23 · C33
1 Introduction Predictive causality and feedback between variables is one of the main subjects of applied time series analysis. Granger (1969) provided a definition that allows formal statistical testing of the hypothesis that one variable is not temporally related to (or does not “Granger-cause”) another one. Besides time series models, this hypothe-
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Art¯uras Juodis [email protected]
Extended author information available on the last page of the article
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sis is also important in panel data analysis when examining relationships between macroeconomic or microeconomic variables. The seminal paper of Holtz-Eakin et al. (1988) provided one of the early contributions to the panel data literature on Granger non-causality testing. Using Anderson and Hsiao (1982) type moment conditions, the authors put forward a Generalised Method of Moments (GMM) testing framework for short T panels with homogeneous coefficients. Unfortunately, this approach is less appealing when T is sizeable. This is due to the well-known problem of using too many moment conditions, which often renders the usual GMM-based inference highly inaccurate. While there exist alternative fixed T procedures that can be applicable to cases where T is large (e.g. those of Binder et al. 2005; Karavias and Tzavalis 2017; Juodis 2013; Arellano 2016; Juodis 2018), these methods are designed to estimate panels with homogeneous slope parameters only. Thus, when feedback based on past own values is heterogeneous (i.e. the autoregressive parameters vary across individuals), inferences may not be valid
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