EViews.com

Posted: **Wed May 19, 2021 10:07 pm**

Hi,

I am estimating an equation using GMM in a panel workfile:

equation eq.gmm y=exp(c(1))*x1+c(2)*x2+exp(c(3))*x3+(((2*exp(c(1))*(exp(c(3))-1))/( (c(2)^2+4*exp(c(1)))^0.5+c(2)) ) -c(2))*x4 @ x1 x2 x3 x4 ID

where ID is the cross-section identifier. If I alternatively create a dummy variable for each cross-section identifier and estimate the equation

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equation eq.gmm y=exp(c(1))*x1+c(2)*x2+exp(c(3))*x3+(((2*exp(c(1))*(exp(c(3))-1))/( (c(2)^2+4*exp(c(1)))^0.5+c(2)) ) -c(2))*x4 @ x1 x2 x3 x4 dummy1 dummy2 ... dummyN

I get identical results (see pictures below). The advantage of using the first specification is that it is about 15 times faster than the second specification (maybe because of sparse matrix functionality ...).

However, if I remove X1, X2, X3 and X4 as instruments, I can only estimate the second equation. The reason is that EViews states that when using the command

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equation eq.gmm y=exp(c(1))*x1+c(2)*x2+exp(c(3))*x3+(((2*exp(c(1))*(exp(c(3))-1))/( (c(2)^2+4*exp(c(1)))^0.5+c(2)) ) -c(2))*x4 @ ID

the order condition is violated as there are too few instruments. But is this not because EViews counts the ID variable as being one instrument (and not equal to the number of cross-sections?).

Question 1: are the first two gmm equation specifications above equivalent?

Question 2: if yes, why does not EViews count the ID variable as multiple instruments, equal to the number of cross-sections?

t

: gmm1.png (35.19 KiB) Viewed 7928 times

: gmm2.png (17.61 KiB) Viewed 7928 times

: gmm3.png (17.54 KiB) Viewed 7928 times

Posted: **Thu May 20, 2021 7:12 am**

Its weird that they give identical results. You've essentially done this:

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create a 1990 2000 5
series y=nrnd
series x=nrnd
series z1=nrnd
equation eq1.gmm y c x @ c z1 @expand(@crossid)
equation eq2.gmm y c x @ c z1 @crossid

I think?

Posted: **Fri May 21, 2021 11:21 pm**

yes, you are correct. i do not understand why I get identical results ...
t

Posted: **Sat May 22, 2021 7:12 am**

I may have read too quickly, but are all your independent variables also instruments in the first two?

Posted: **Sat May 29, 2021 10:25 pm**

Hi,

Thanks for looking into this. Yes, that is what I did, but it was not what I actually wanted to do. My mistake .... I just wanted to use the indicators as instruments, based on the estimator proposed in Feenstra (1994), i.e. where the instruments are dummy variables across the cross-sections. I thought that the estimation results being equal in my particular case was due to how I constructed Y, X1 etc. But are you indicating it is because I (wrongfully) used all independent variables also as instruments?

t

Feenstra, R. C. (1994). New product varieties and the measurement of international prices. American Economic Review, 84(1), 157–177

Posted: **Sun May 30, 2021 6:33 am**

If you use all the independent variables as instruments, at least in a linear model, you basically get the least squares estimates.

Posted: **Sun May 30, 2021 11:50 am**

Aha, great, thanks for your feedback!
t

EViews.com

GMM - counting of instruments

GMM - counting of instruments

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Re: GMM - counting of instruments

Re: GMM - counting of instruments

Re: GMM - counting of instruments