Re: [Gretl-users] Wald test in Gretl
by Riccardo (Jack) Lucchetti

On Sat, 21 Jan 2017, Kharin Sergei wrote:
> Hello,
>
> I am writing to find out about Wald test in Gretl. How can I run it in
> order to study short-term causality in VECM model for coefficients ? I have
> 3 variables (time series), I(1), cointegrated, I need to find out if one
> variable causes another with wale test in VECM.
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! ;)
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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
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