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

 From agfa1970@gmx.de To statalist@hsphsun2.harvard.edu Subject st: instrumental variables, reg3, simultaneous equation model, var Date Wed, 24 Feb 2010 16:53:15 +0100

```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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