Short-run and long-run causality in time series: Inference. Technical report, Centre de recherche et développement en économique, Université de Montréal, and Institut d’Economie Industrielle, Université des Sciences Sociales de

We propose methods for testing hypothesis of non-causality at various horizons, as defined in Dufour and Renault (1998, Econometrica). We study in detail the case of VAR models and we propose linear methods based on running vector autoregressions at different horizons. While the hypotheses considered are nonlinear, the proposed methods only require linear regression techniques as well as standard Gaussian asymptotic distributional theory. Bootstrap procedures are also considered. For the case of integrated processes, we propose extended regression meth-ods that avoid nonstandard asymptotics. The methods are applied to a VAR model of the U.S. economy. Key words: Granger causality; indirect causality; vector autoregression; bootstrap; macroeco-nomics