hansen test system GMM

[beth cooper]

I'm currently running system GMM on:

xi: xtabond2 confidential code noconstant robust

but when I look at the Hansen test results it says:

Sargan test of overid. restrictions: chi2(72) = 123.85 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(72) = 24.52 Prob > chi2 = 1.000
(Robust, but weakened by many instruments.)

why is my p value as high as 1, is this a bad thing? It seems to be 1 for all of my tests when including different proxies for inequality.
thanks in advance.

[Sebastian Kripfganz]

The p-value of 1 of the Hansen test is an indicator that you have too many instruments. You could use the collapse suboption of the gmm() option to reduce the number of instruments.

More on the GMM estimation of linear dynamic panel data models:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.

[beth cooper]

Sebastian Kripfganz thank you for your reply

I just had one question, would I collapse all of my instrumental variables? For example:

xi: xtabond2 confidential code noconstant robust

this now makes all of my estimates for inequality insignificant which isn't great for my hypothesis. What does the collapse option actually do?

thanks again!!

[Sebastian Kripfganz]

Normally, you would collapse all of them. It is somewhat difficult to justify the arbitrary decision to collapse only a subset of them.

To see what collapsing is doing, compare the uncollapsed instruments on slide 12 of my 2019 London Stata Conference presentation whith the collapsed instruments on slide 19.

[beth cooper]

Sebastian Kripfganz
If I don't collapse the variables, is this a big issue? When I use the collapse function, it makes all of my estimates (not just some of them, all!) insignificant, leaving not much to write about. Or is there any other way you can think of getting around this issue?

[Sebastian Kripfganz]

It appears that if you do not collapse the instruments, then the too-many-instruments problem makes you results entirely unreliable. You could try to collapse all instruments but to allow for longer lags as instruments, e.g. laglimits(1 3) instead of laglimits(1 1). This might help to stabilize your results.

But sometimes it is simply the case that the data does not support our theory.

[beth cooper]

Sebastian Kripfganz one last thing, I've noticed that after using the collapse function, the robust standard deviations for for my inequality variables are very high, which might be a big reason that they are no longer significant. For example here are some results:

L.p9050	0.12743
	(0.13955)
L.p5010	-0.05407
	(0.08477)
L.ginilis	-0.11260
	(0.77922)

could this be down to the use of the collapse option, or is there a different reason for this. I'm hoping there is a way to lower them?

Thanks for all your help!

[Sebastian Kripfganz]

This could be a consequence of weak instruments, but that's not really related to collapsing. Conversely, small standard errors without collapsing can be a consequence of overfitting the model with too many instruments.

[beth cooper]

What does overfitting actually mean in terms of the econometric model? Does it cause endogeneity? I am confused because in a paper by Voitchovsky (2005), she models a similar regression using system gmm but with a smaller data set (smaller N and T), however doesn't mention overfitting or overidentifying restrictions, and doesn't collapse the instruments.

[Sebastian Kripfganz]

I am not familiar with the Voitchovsky (2005) paper. I briefly skimmed over it but could not find any information about the total number of instruments. Some authors use collapsed instruments without mentioning it in their papers, unfortunately. Replicability is often a problem with empirical papers.

Overfitting in this context refers to the "first-stage regression" of the endogenous regressors on the instruments. In the extreme case, if you have as many instruments as observations, you can perfectly explain the endogenous variables with the instruments, but then the IV/GMM estimator just becomes the OLS estimator again, which we know is inconsistent in the presence of endogenous regressors. You can read more about this in Roodman's Note on the Theme of Too Many Instruments.

[beth cooper]

OK, I understand why this is now. I have instead reduced the number of time periods that I am measuring growth over, meaning that the number of instruments no longer over-fits the model. Do you think this is a bad suggestion (as it significantly reduces the sample size) or do you think it is ok?

[Sebastian Kripfganz]

I am not entirely sure I understand what you have done. If anything, you want to increase the sample size, not reduce it. Computing average growth rates over shorter time periods should increase the sample size. Personally, I am not a friend of computing average growth rates anyway.

[beth cooper]

I haven't reduced the number of countries being observed, I have instead reduced the number of time periods being observed across. Since the time periods are added as instrument dummies in the regression, this hugely decreases the number of included in the regression.

[beth cooper]

Sebastian Kripfganz
Is it bad to include the time dummies in the GMM regression as i.yearn as when doing so it drops a year or shall I add them as separate years e.g. ta yearn, generate(yr) and add them in as yr1 yr2 yr3 ect?

[beth cooper]

actually, it drops one either way! Is that bad?