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

 From Michael McCulloch To statalist@hsphsun2.harvard.edu Subject Re: st: instrumental variables, reg3, simultaneous equation model, var Date Wed, 24 Feb 2010 09:26:06 -0800

Hello, it would be helpful if your question were more informative, for example on your question, is the procedure correct and appropriate for what type of data? Perhaps you could consult the Statalist FAQ, particularly sections 3.2 ("Write clear questions") and 4 ("What to do if you do not get an answer"), and then re-submit a more informative question:
```
http://www.stata.com/support/faqs/res/statalist.html#question

Michael

On Feb 24, 2010, at 9:19 AM, Agrar Fagma wrote:

```
```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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```
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```

Best wishes,

Michael McCulloch
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San Anselmo, CA 94960-2674
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```