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Re: st: RE: lagged variables in FE models
From
Misha Spisok <[email protected]>
To
[email protected]
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
<[email protected]> wrote:
> Dear Mareike,
>
> This is well explained in most standard textbooks. See for instance
>
> http://www.econ.kuleuven.be/gme/
>
> Rodolphe
>
>
>
> -----Original Message-----
> From: [email protected] [mailto:[email protected]] On Behalf Of Mareike
> Sent: 16 June 2010 16:06
> To: [email protected]
> 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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