Instrumental variable

[oksana]

Hi guys,

When using the GMM or 2SLS, how appropriate is it to specify a variable as an instrument for itself?? For instance, if I have 4 explanatory variables and put the same 4 variables plus intercept in the Instrumentsfield, why does EViews allow doing that? How does the program treat such a list of instruments that are in fact the same as explanatory variables?? That puzzles me because had that been inappropriate, I assume Eviews wouldn't run estimation, right? But instead it does provide sensible results. Please help to understand if you know!!

Cheers,

Oksana

[startz]

If a variable is exogenous, then using it as an instrument for itself is standard.

[oksana]

That's the thing, the variable is endogenous and I need to find an instrument for it. But if I specify it as an instrument for itself, why does EViews allows doing that and how does it treat such a variable in this case?

[EViews Gareth]

As Startz said, by setting a variable as an instrument for itself, mathematically you're really saying that it is exogenous.

[Zeno]

I was having similar problems like Oksana. For instance, how does EViews know that the list of instruments given by the user in the instruments box (say z1 and z2) should be used for some endogenous variable y2 instead as serving as their own instruments?
In particular, I have problems replicating textbook results manually. I have attached a file from Wooldridge, J. (2003), "Introductory Econometrics", 2ed. The problem is to model the return on education using education, experience and experience^2. Education is correlated with the unobserved variable "ability" which is included in the error term. Mothers education and Fathers education serve as an instrument for educ. The results from the manual two stages are near the EViews results (compare the equation objects tsls_manual and tsls_eviews) but not the same.

Any help is greatly appreciated.

Zeno

[startz]

EViews does two-stage least squares. All instruments are used in the first stage for all variables.

[Zeno]

but the second stage in TSLS is again OLS where the possibly endogenous variable is replaced by the instrument (or a linear combination of them as the variable fittedaux1 from the auxiliary equation object aux1). Therefore I would have expected identical results. Maybe EViews uses a different way to estimate the parameters in TSLS? (from what I read methods of moments or FIML are possible candidates).

Thanks

[startz]

No, it's just that you didn't use the complete set of instruments in your auxiliary first-stage regression.

[Zeno]

Dear Startz,

thanks for your fast replies. The exogenous variables experience and experience^2 do not belong into the auxiliary regression since they do not qualify for possible instruments of ability (they already appear in the main equation, only motheduc and fatheduc are excluded from the main equation. Of course, experience and experience^2 are instruments for themselves but that is not what the auxiliary equation is supposed to model). Besides, if I include them (which I should not) the results are still not the same as in the EViews TSLS object.

Thanks

[startz]

But they do qualify as instruments. They're correlated with education and, presumably, uncorrelated with the error term since you treat them as exogenous. In any event, the definition of 2SLS is that all instruments are used in the first stage for all RHS variables.

The reason you're getting a different answer is that you are using a different sample size for the first stage.

[Zeno]

This is the solution to the problem. Thank you.
I must admit that I find it surprising that exper and expersq do enter the first stage. Besides the reasons I mentioned in the previous post TSLS has been shown to be especially prone to multicollinearity. If you include exper and expersq as instruments for educ, generate the fitted values and then add them again in the main equation in addition to the fitted values you might create serious multicollinearity. This will increase your parameter standard errors substantially as se(beta) = sigma^2/(SST*(1-R^2)) with sigma^2 as the residual variance, SST is the total variation in educ R^2 is the R-squared from the regression of educ_hat (i.e. the fitted values from the auxiliary regression) on exper and expersq.

In any case, thanks for the efficient and quick solution.

Zeno

[startz]

Glad to help. Your postings are very clear, a good model for others to follow.

I do disagree about the multicollinearity comment for TSLS. There's a theorem that says that TSLS is the optimal instrumental variable estimator. One way to see this is that the standard errors depend inversely on the first-stage R-square (as you point out) and that adding more instruments in the first stage increases the R-square.

[oksana]

Hu guys,

I had to return to the Instrumental variable discussion again. As I understand and based on the Startz's replies, including an endogenous variable itslef in the list of instrumental variables is appropriate because [1] technically it satisfies the condition of being correlated with the endogenous variables and [2] by including it in the list of instruments we "make" it uncorrelated with en error term. Is this correct?
The problem is that I haven's been able to find any reference to using such method and whether this is entirely appropriate to do or not - neither in EViews manuals, not in the eoconmetrics books. If by chance you have a reference to this, I'll be greatful for sharing it with me.

Thanks a lot

[startz]

Hu guys,

I had to return to the Instrumental variable discussion again. As I understand and based on the Startz's replies, including an endogenous variable itslef in the list of instrumental variables is appropriate because [1] technically it satisfies the condition of being correlated with the endogenous variables and [2] by including it in the list of instruments we "make" it uncorrelated with en error term. Is this correct?
The problem is that I haven's been able to find any reference to using such method and whether this is entirely appropriate to do or not - neither in EViews manuals, not in the eoconmetrics books. If by chance you have a reference to this, I'll be greatful for sharing it with me.

Thanks a lot

No, including an endogenous variable in the instrument list is wrong. That's because argument [2] above is not correct.

[oksana]

Thank you startz. What if I generate random number as error terms series and then create new series by adding the two series - the endogenous variable and the generated random numbers. Would that be completely inappropriate? I'm just trying to understand what is the best way to deal with endogeneity issue in the absense of an appropriate instrument. Thanks again!