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. However, post-sample model testing requires an often-consequential a priori partitioning of the data into an "in-sample" period - purportedly utilized only for model specification/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 ≤ 150 - as is common in both quarterly data sets and/or in monthly data sets where institutional arrangements 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 both eliminates the aforementioned a priori partitioning and which also substantially ameliorates this power versus credibility 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 always 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 andWest [1] study of the causal relationship between macroeconomic fundamentals and the exchange rate; several of their conclusions are changed by our analysis.