On Sat, 21 Jan 2017, Kharin Sergei wrote: I'm cc-ing this to the gretl user list since this is something that is likely to be useful to others as well. It sounds as if you're interested in testing for Granger causality in a cointegrated VAR. As far as I know, this is something that can be done in 2 ways. One is "right", but is prone to lots and lots of inferential complications; the other one is "sly", and is much easier to perform, but the test you get out of it is somewhat lacking in terms of power. The "right" way was studied by Toda and Phillips (1993) and implies using tests that have non-standard distributions. I guess you can find critical values by simulation, but that's definitely outside the standard methods you'll find pre-packaged in gretl (or any other software, for that matter). Alternatively, you can use a popular trick, discovered independetly by Toda and Yamamoto (1995) and Dolado and Lütkepohl (1996): suppose your var has p lags; then you run an oversized unrestricted VAR (with p+1 or more lags), and then running the causality tests by using only the first p matrices of coefficients. This can be easily done in gretl by using the ols + restrict combo. A further alternative could be using some form of modified OLS, such as PCB Phillips' fully modified OLS (not provided in gretl natively, but easy to code) or some other trick such as Saikkonen's or Stock-Watson's augmented univariate regressions (with HAC-robust standard errors). Again, you can do this easily in gretl via ols + restrict. You'll have noticed all this is econometric technology from the 1990s, which shows my venerable age, I suppose. If anything else happened in the meantime, I guess some of the younger guys will be kind enough to let me know! ;) ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti -------------------------------------------------------