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Re: st: Re: Why include leads (in a model with lags)?


From   Misha Spisok <misha.spisok@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Re: Why include leads (in a model with lags)?
Date   Thu, 8 Oct 2009 13:44:41 -0700

Thank you for pointing out that my question is related to Granger
causality.  I assume that a test of Granger causality that includes
leads (rather than only lags) would address my initial question.  I
have questions about implementing this below.

I also appreciated David Greenberg's intuitive response.

The short version of my new question is, "How can I test for Granger
causality with more than two variables in a panel data setting?"  I
may be asking the wrong question, so I give more detail below.  In
short, -var- does not allow panel data or leads and the only
suggestion I found to address this mentioned -levinlin-, the
application of which is not clear to me.

Going back and revising my proposed model, I suppose I should add some
of the complications that I face.

y_i,t = b_0 + b_1*X_i,t + b_2*X_i,t-1 + b_3*X_i,t-2 + P'Z_i,t + u_i,t

To be clear, I have added a subscript 'i' to indicate that this is a
panel and have also included a number of other regressors, Z_i,t, and
their coefficients, P.  Also, let's suppose that the Z_i,t are
"accepted" as being explanatory variables for y_i,t, but testing the
role of X_i,t is the goal.  So the suggestion is to add leads of X_i,t
to the proposed model.

y_i,t = b_0 + b_1*X_i,t + b_2*X_i,t-1 + b_3*X_i,t-2 + b_4*X_i,t+1 +
b_5*X_i,t+2 + P'Z_i,t + e_i,t

If I understand correctly from the wiki, I would begin by estimating
the following,

Delta y_i,t = a_0 + a_1*Delta y_i,t-1 + ... + a_k*Delta y_i,t-k

adding Delta y_i,t-k until the p-value increased (or t-stat decreased)
past some threshold.  The next step would be to add Delta X_i,t-j as
long as the addition of Delta X_i,t-j is statistically significant and
provides explanatory power.

In the context of a model with additional regressors, should those
regressors be included?  If so, should they be included while adding
Delta y_i,t-k?  Or only after determining the appropriate number of
lags to include of Delta y_i,t?

Also, when adding Delta X_i,t-j, does the order of adding leads or lags matter?

Finally, if I had, instead of only one variable of interest (here,
X_i,t), I had an additional variable of interest (say, W_i,t), would
the procedure be the same except that I would add incremental leads
and lags of X and W at the same time?  Or would it be of interest to
carry out the procedure with, say, X, then repeat the procedure with W
and see whether that differs from the results when carrying out the
procedure with W and then X?

The wiki article mentions that a test of more than two variables can
be handled with vector autoregression.  However, Stata's -var- command
does not work on panel data (at least in Stata 10.1); moreover, -var-
does not seem to allow leads (which assumes that this would be an
appropriate way to test for the significance of leads).  Assuming I
haven't bollocksed up everything to this point, can someone suggest a
"manual" way to test for Granger causality among three variables in a
panel data setting?  I noted a thread titled "Granger with fixed
effect - panel data", but I am unsure of (1) how testing for a unit
root using -levinlin- relates to Granger causality and (2) how this
could be extended to two or more variables.

Many thanks for your time and attention.

Misha

On Thu, Oct 1, 2009 at 3:55 AM, Kit Baum <baum@bc.edu> wrote:
> <>
>
> wikipedia granger causality
>
> On Oct 1, 2009, at 2:33 AM, Misha wrote:
>
> My question in brief is, "What does including leads in a model that
> 'should' only have lags tell me?"
>>
>>
>> Is there a command in Stata (or other references, a tutorial, etc.)
>> that can help me understand this (possible) problem better?
>
>
> Kit Baum   |   Boston College Economics & DIW Berlin   |
> http://ideas.repec.org/e/pba1.html
>                              An Introduction to Stata Programming  |
> http://www.stata-press.com/books/isp.html
>   An Introduction to Modern Econometrics Using Stata  |
> http://www.stata-press.com/books/imeus.html
>
> *
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