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Re: st: instrumental variables, reg3, simultaneous equation model, var

 From "Agrar Fagma" To statalist@hsphsun2.harvard.edu Subject Re: st: instrumental variables, reg3, simultaneous equation model, var Date Wed, 24 Feb 2010 18:19:44 +0100

```Dear all:

I didn't get an answer yet but a possible solution by myself:

reg3  (F R lagged_F lagger_r) (R F lagged_F lagger_r),inst(lagged_F lagger_r z1 z2 z3 z4)

works. But my question remains: Is this procedure correct and appropriate?

Regards

A.Dedder

-------- Original-Nachricht --------
> Datum: Wed, 24 Feb 2010 16:53:15 +0100
> Von: agfa1970@gmx.de
> An: statalist@hsphsun2.harvard.edu
> Betreff: st: instrumental variables, reg3, simultaneous equation model, var

> Dear all:
>
> The following text my appear long, but it is very precise (and probably
> easy stuff).
>
> I estimated the following VAR(2):
>
> F_{t} =          F_{t-1} + F_{t-2} +...+R_{t-1} + R_{t-2} +...+u_{t}
> R_{t} =          F_{t-1} + F_{t-2} +...+R_{t-1} + R_{t-2} +...+u_{t}
>
> Now I would like to insert contemporaneous values on the right - hand -
> side of the VAR which would become a structural VAR. For identification and
> because of endogeneity, I would need 1 restriction, ie. I could either
> estimate
>
> F_{t} =  R_{t} + F_{t-1} + F_{t-2} +...+R_{t-1} + R_{t-2} +...+u_{t}
> R_{t} =          F_{t-1} + F_{t-2} +...+R_{t-1} + R_{t-2} +...+u_{t}
>
> or
>
> F_{t} =          F_{t-1} + F_{t-2} +...+R_{t-1} + R_{t-2} +...+u_{t}
> R_{t} =  F_{t} + F_{t-1} + F_{t-2} +...+R_{t-1} + R_{t-2} +...+u_{t}
>
> with a normal Choleski-Decomposition.
>
> As I have a bigger VAR as in this example, I cannot enter that many
> restrictions (long-run restrictions are neither possible because I have no
> theory!).
>
> Now comes my point and problem:
>
> I wonder whether I could estimate
>
> F_{t} =  R_{t} + F_{t-1} + F_{t-2} +...+R_{t-1} + R_{t-2} +...+u_{t}
> R_{t} =  F_{t} + F_{t-1} + F_{t-2} +...+R_{t-1} + R_{t-2} +...+u_{t}
>
> and fight the obvious endogeneity by 3SLS or the STATA command reg3 ??
>
> I have 4 instruments (which I do not want to appear on the right hand side
> of the equations if possible as I would not have the original VAR any
> more) with which I would like to "replace" the contemporaneous right hand side
> variables R_{t} and F_{t}. Would this work? I really searched a long time
> but could not find any information regarding 3SLS (or GMM) and estimation of
> a structural VAR.
>
> If I have to include my instruments on the right hand side of the VAR
> (which would become a simultanous equation model), could I still use the 3SLS
> command..? Would GMM be better? Or is there any error in my model/ do I not
> understand the methodology of instrumental variables right?
>
> I tried it without lagged variables and it worked fine (the z's are my
> instruments):
>
> reg3 (F R) (R F), inst(z1 z2 z3 z4)
>
> But:
>
> reg3 (F R = L.F L.R) (R F = L.F L.R), inst(z1 z2 z3 z4)
>
> does not work!
>
> STATA says: "Covariance matrix of errors is singular"
> Where is my mistake?? Is this due to poor instruments? Or is the model not
> testable at all??
>
> Of course, I read the STATA11 manual beforehand but there's nothing about
> a simultaneous equation model with lags..
>
>
>
> Kind regards
>
> Agther F. Dedder
> --
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```