[Xtabond2] Gmm selection, observation difference and robustness check in xtabond2

[SangWon Choi]

Dear Stata community,

Hello, i am currently studying how to run system gmm with xtabond2.
For that function, i have read 'Roodman, D. (2009). How to do xtabond2: An introduction to difference and system GMM in Stata. The stata journal, 9(1), 86-136' several times.

But, there are some problems which can't be relaxed with that paper.
Here are my questions.

1. Does my model suffering instrument proliferation problem?


As i wanted to run system gmm, i typed codes as below,
(My data contain 10-years panel data of 229 groups)

xtabond2 lcarbon L.lcarbon lseni losq loqu lGRDPp lGRDPpsq lei i.Year, gmm((lcarbon lseni losq loqu lGRDPp lGRDPpsq lei), lag(2 4) equation(diff)) iv(dylcarbon i.Year, equation(level))  twostep robust

The reason why i typed all the variables into gmm is following the advice from the paper i refered to.
(Ordinarily, put every regressor into the instrument matrix Z, in some form, on page 128)
(And i think all my variables are not strictly exogenous also)


Here's my result table.

As you see, Result of hansen test is 0.341. But i am concerned about the number of instrument variable.
Is it okay to report my result and no IV proliferation problem?
(When i used 'collapse' option, i faced sigificant AR(2) result and unsignificant result of Hansen test.)



2. The number of observations on the result is different from the one of original observation. Is it okay?



As you can on my result, the number of observations is 1,832(229*8) and it is different from 2,290 in my original dataset.
I think it is due to the variable 'dylcarbon' which means lagged-difference variable(y_t-1 - y_t-2) and exogenous for the level equation.

Is it okay to report a result containing different observation due to lagged-difference variable?



3. For robustness check, what should i do more?

I am planning to do robustness check of my result.

For it, i've read some research papers, and they show robustness of their result with coefficient of POLS, FE. (if the result of system gmm is within the range of these coeficient, it is appropriate to use system gmm)
And, some of them show results with 'collapsed' option. But in my model, i think it doesn't work due to unsignificant result of Hansen test.
One thing that shows different results is using a robust regression but i cannot understand how to make this table in Stata. Does anybody know how to do it?

(Source: Wang et al. (2019). The population structural transition effect on rising per capita CO2 emissions: evidence from China. Climate policy, 19(10), 1250-1269.)

Do i have to adjust the number of instrument manually? If so, how many?

Kind Regards,
Sangwon

[Sebastian Kripfganz]

188 instruments with 229 groups seems generally too high. I recommend to use the collapse option. If some of the specification tests become unfavorable in this case, then you should see this as a sign for concern. You then might want to directly address the serial-correlation problem, e.g. by adding further lags of the regressors or by using deeper lags as instruments.

[SangWon Choi]

Thank you for your reply Dr.Sebastian,!

Actually,I have been started with reading your proceeding in 2019 and solved the 2nd question I posted by using xtdpdgmm! (I think it was a bug in xtabond2)
Many thanks for your detailed explanation.

With reading your proceeding, i could set up a strategy for the first question
Would you please check whether those are right?


"Presenting my result with many(188) instruments and other(with the collapse option).
And then, explaining why i use that number of instrument with the results of assumptions (violated Hansen-Sargan, Serial-correlation)."


With this logic, i want to make it clear why i use many instruments and it is reasonable to meet the assumptions.(Meeting the assumptions by using further lags of instruments,)

is it right way?

[Sebastian Kripfganz]

Model misspecification indicated by overidentification or serial-correlation tests cannot be used to argue in favor of using many instruments. If those test results are seemingly okay when you have many instruments, this might simply be a consequence of having too many instruments and not actually indicate correct model specification. In other words, with too many instruments, those tests tend to have low power.

[SangWon Choi]

Dear @Sebastian Kripfganz,

With your advice, i could handle the instrument proliferation problem with collapse option.
But there's one question arising after i handle it.

As i shifted my lags from (2 4) to (4 6), the significance of two variables changed.
(from near past set of instruments to relatively far past set of instruments)
(The others are robust)


Variable 1 is significant with lags (2 4) but it isn't with lags (4 6)
And Variable 2 is significant with lags (4 6) but it isn't with lags (2 4)

Does it mean that the situation of variable 2 is due to long-term effect of variable's feature not from short-term effect?(like GDP)
and the situation of variable 1 is vice versa?

[Sebastian Kripfganz]

I am afraid I cannot answer that question.

[SangWon Choi]

Dear Prof. Sebastian Kripfganz

No matter you can answer it, I want to show appreciation of all of your work for xtdpdgmm.
With your explaination(including files you uploaded before), I could undertstand how it works and make my thesis progress.

It would be honor if you can read my paper someday when my paper published.

Again, Thank you very much!