Credible Granger-Causality Inference with Modest Sample Lengths: A Cross-Sample Validation Approach

Credible Granger-causality analysis appears to require post-sample inference, as it is well-known that in-sample fit can be a poor guide to actual forecasting effectiveness. But post-sample model testing requires an often-consequential a priori partitioning of the data into an 'in-sample' period - purportedly utilized only for model specifi- cation/estimation - and a 'post-sample' period, purportedly utilized (only at the end of the analysis) for model validation/testing purposes. This partitioning is usually infeasible, however, with samples of modest length – e.g., T less than 100 - as is common in both quarterly data sets and/or in monthly data sets where institutional arrange- ments vary over time, simply because there is in such cases insufficient data available to credibly accomplish both purposes separately. A cross-sample validation (CSV) testing procedure is proposed below which substantially ameliorates this predicament - preserving most of the power of in-sample testing (by utilizing all of the sample data in the test), while also retaining most of the credibility of post-sample testing (by al- ways basing model forecasts on data not utilized in estimating that particular model's coefficients). Simulations show that the price paid, in terms of power relative to the in-sample Granger-causality F test, is manageable. An illustrative application is given, to a re-analysis of the Engel and West (2005) study of the causal relationship between macroeconomic fundamentals and the exchange rate.