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Re: st: RE: lagged variables in FE models


From   Misha Spisok <misha.spisok@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: lagged variables in FE models
Date   Wed, 16 Jun 2010 09:45:55 -0700

Dear Mareike,

Do you mean a lagged dependent variable?

If so, I think the reason is, essentially, that the lagged dependent
variable is correlated--by construction--with the error term.

y_i,t = b0 + b1*y_i,t-1 + epsilon_i,t
        = b0 + b1*y_i,t-1 + mu_i + nu_i,t

where epsilon_it = mu_i + nu_it.

That is, in the unobserved effects model (which includes the
fixed-effects model), the unobserved effect is mu_i.

Then,

y_i,t-1 = b0 + b1*y_i,t-2 + epsilon_i,t-1
            = b0 + b1*y_i,t-2 + mu_i + nu_i,t-1

So,

y_i,t = b0 + b1*y_i,t-1 + epsilon_i,t
      = b0 + b1*[b0 + b1*y_i,t-2 + epsilon_i,t-1] + epsilon_i,t
      = b0 + b1*[b0 + b1*y_i,t-2 + mu_i + nu_i,t-1] + mu_i + nu_i,t

Or, more clearly (I hope),

Cov(y_i,t-1, epsilon_i,t) = Cov([b0 + b1*y_i,t-2 + mu_i + nu_i,t-1],
[mu_i + nu_i,t])
                                       ~= 0

The correlation is not equal to zero because, at the very least,
Corr(mu_i, mu_i) = 1.

As usual, please correct my errors.

Best,

Misha



On Wed, Jun 16, 2010 at 9:22 AM, Rodolphe Desbordes
<rodolphe.desbordes@strath.ac.uk> wrote:
> Dear Mareike,
>
> This is well explained in most standard textbooks. See for instance
>
> http://www.econ.kuleuven.be/gme/
>
> Rodolphe
>
>
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Mareike
> Sent: 16 June 2010 16:06
> To: statalist@hsphsun2.harvard.edu
> Subject: st: lagged variables in FE models
>
> Dear Statalist,
>
> is it true that lagged variable cannot be included in fixed effects models?
> That is what I have been told by a friend but I don't really see why that
> should be the case. Unfortunately, I couldn't find any information on this
> topic in the literature so maybe one of you knows something about it.
>
> Thanks in advance
>
> Mareike
>
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