GMM - counting of instruments

[tvonbrasch]

Hi,

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

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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 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 7922 times

gmm2.png (17.61 KiB) Viewed 7922 times

gmm3.png (17.54 KiB) Viewed 7922 times

[EViews Gareth]

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?

[tvonbrasch]

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

[startz]

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

[tvonbrasch]

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

[startz]

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

[tvonbrasch]

Aha, great, thanks for your feedback!
t