Instrumental variables in system GMM

[Joe Moore]

Hi all,

I am trying to estimate the relationship between whether a loan contract has monthly or weekly repayments, and the effect on default rates. Due to potential endogeneity, I am using an instrumental variable as the independent variable.

As the panel has a 'large n and small t', I want to perform a system GMM analysis for which I will use the xtabond2 command. I have read Roodman (2009) but I do not understand how to include an instrumental variable into the regression, in the way you include it in ivregress.

Any help would be appreciated.

[Sebastian Kripfganz]

You specify the instrumental variables with the iv() or gmm() option.

More on 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.
• XTDPDGMM: new Stata command for GMM estimation of linear (dynamic) panel data models

[Hu Weiping]

You specify the instrumental variables with the iv() or gmm() option.

More on 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.
• [URL="https://www.statalist.org/forums/forum/general-stata-discussion/general/1395858-xtdpdgmm-new-stata-command-for-efficient-gmm-estimation-of-linear-dynamic-panel-models-with-nonlinear-moment-conditions"]XTDPDGMM: new Stata command for GMM estimation of linear (dynamic) panel data models[/URL

Hey,Sebastian.
shouid I specify instruments with independent variable in sysGMM when I use xtabond2
this is my code:
xi:xtabond2 INTinve l.INTinve l.INTinvesquare MB SalesGwth CashflowINT l.CashflowINT StkIssue ///
l.StkIssue DebtIssue l.DebtIssue DCash l.DCash yr1980-yr1993 iv(yr1980-yr1993,eq(level)) ///
gmm(CashflowINT StkIssue DebtIssue DCash,lag(2 3) eq(level)) ///
gmm(CashflowINT StkIssue DebtIssue DCash,lag(3 4) eq(diff)) ///
As u can see, i only treat (CashflowINT StkIssue DebtIssue DCash) as potentially endogenous,and did not include independent variable(INTinve) in it. All tests seem fine.

as I know, the feature of sysGMM is shown in the figure below

so is there any problem if I do not include independent variable in Gmmstyle() option? should i change my code like below?
gmm(INTinve CashflowINT StkIssue DebtIssue DCash,lag(2 3) eq(level)) ///
gmm(INTinve CashflowINT StkIssue DebtIssue DCash,lag(3 4) eq(diff)) ///
Looking forward to your help！

[Hu Weiping]

Sorry for my mistake, the above should be the dependent variable

[Hu Weiping]

You specify the instrumental variables with the iv() or gmm() option.

More on 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.
• XTDPDGMM: new Stata command for GMM estimation of linear (dynamic) panel data models

if I remove dependent variable from Gmmstyle() option, Do I still need to consider Arellano-Bond test?

[Sebastian Kripfganz]

In principle, you do not necessarily need to include lags of the dependent variable as instruments. But this requires that the remaining instruments are sufficiently correlated with the lagged dependent variable to avoid a weak instruments problem. The AR(2) test provides some general information whether the model is misspecified. As long as there is residual serial correlation, the model is dynamically incomplete which could still invalidate your remaining instruments (although the argument is less straightforward than with the lagged dependent variable). Yet, it is indeed possible that your instruments are valid even if the AR(2) test rejects the null hypothesis.

[Hu Weiping]

In principle, you do not necessarily need to include lags of the dependent variable as instruments. But this requires that the remaining instruments are sufficiently correlated with the lagged dependent variable to avoid a weak instruments problem. The AR(2) test provides some general information whether the model is misspecified. As long as there is residual serial correlation, the model is dynamically incomplete which could still invalidate your remaining instruments (although the argument is less straightforward than with the lagged dependent variable). Yet, it is indeed possible that your instruments are valid even if the AR(2) test rejects the null hypothesis.

Thank you for your reply.
Are you saying that if we don’t use the lags of the dependent variable as instruments, we still have to consider AR(2) test even if it is not as clear as before？

There's one more thing. As I know, sys GMM results tend to be really unsteady.

there are three different sample periods: 1980–1993, 1994–2002 and 2003-2017

usually，I use the third and fourth lagged level of endogenous variables as instruments for the equation in differences (gmm(CashflowINT StkIssue DebtIssue DCash,lag(3 4) eq(diff))

but I prefer to use the second and the third lagged level when Hansen-J test and Diff-Hansen test seem good(gmm(CashflowINT StkIssue DebtIssue DCash,lag(2 3) eq(diff)). Because they are typically stronger instruments that just the 3rd and 4th lag.

In my thesis, I use the third and the fourth lagged level of endogenous variables in the first two periods but the second and the third lagged level in the final period.

Is there anything wrong？

[Sebastian Kripfganz]

The AR(2) test can help to detect some sort of model misspecification. Whether a rejection of the AR(2) test affects the reliability of your results is a priori unclear. If the Hansen test does not reject the validity of your instruments and you are sufficiently confident in these results, you may not have to put much emphasis on the AR(2) test.

Regarding the choice of your instruments, it would be your responsibility to convince the reader of your results that it was a reasonable thing not to use the 2nd lag in the first two periods. To me, this sounds a bit like fishing for the best (most significant?) results. There may be good reasons for choosing the lags in that particular way, but you would have to justify it. (I would probably expect a theoretical justification, not just an argument on the basis of the Hansen test or the significance of the results.)

[Mohammad Al-Tamimi]

Great