Difference GMM (Arellano and Bond)

[Max Brauer]

Hello all,

I'm running a difference GMM model for the first time to address a potential reverse causality issue. I have panel data covering every other year from 2009-2019 (six waves), and I have about 10,000 panelists (unbalanced panel).

I have four questions:

(1) I have read Leszczenky and Wolbring (2019). They compare difference GMM with (1) contemporaneous Xs, (2) lagged Xs, and (3) both contemporaneous and lagged Xs. Can anyone explain to me the appropriateness of each with respect to the reverse causality issue. If my IV theoretically would influence my DV at time t, can I use contemporaneous and sleep well about reverse causality? If my IV theoretically could influence my DV at t and t-1, should I run the model with both contemporaneous and lagged Xs?

(2) I use two different dependent variables. For both DVs, my Hansen tests suggest overidentification (DV1, P = 0.073; DV2, P=0.000). The former p value is too close to 0.05 for comfort; the latter is troubling. What is the solution for the Hansen test violation?

(3) Similarly, DV2 model is suffers from AR2 serial correlation (also p value of 0.064). My understanding is the fix for AR(2) is to use 3 lags. Is this correct?

(4) On a practical note, my IV of interest is insignificant in all of my models. However, this is an important finding. It it worth fixing the overidentifying restrictions and the AR(2) issue? That is, will fixing these only make my insignificant results even less significant? Or is there reason to think that the significance would improve?

Thanks!

[Sebastian Kripfganz]

(1) The choice oft the regressors / the regression model should not depend on your instruments. Whether your Xs affect y contemporaneously or not is a question that you should answer before you even think about instruments. Once you decided this, you then ask yourself whether there is any endogeneity problem, i.e. whether you need instruments. Then you search for appropriate instruments, if needed.

(2) If you have more instruments than regressors, then your model is overidentified. The Hansen test checks whether these overidentifying restrictions are valid. In simplified terms, it checks whether the additional instruments are valid once you assume that there are as many valid instruments as regressors. (You can never check the validity of all instruments.) When you are not happy with the Hansen test results, then you would need to question the validity of your instruments (or the correct specification of the regression model). You could possibly look for other instruments, remove questionable instruments, and/or add some more regressors/lags to the regression model to avoid misspecification.

(3) The best way to deal with serial correlation is usually to add more lags of the dependent variable and/or independent variables in order to make the model dynamically complete.

(4) If your model does not pass the specification tests, then the regression results may not be very informative. The coefficients and their significance could go either way when you modify the model/instruments.

[Max Brauer]

Thanks!

Just to clarify, based on previous literature, I have have known reverse causality between Y and X. My regression equation consists of Y, X, a bunch of confounding variables, and time fixed effects. Just to clarify I should be lagging X in addition to all of the confounding variables? This is an example of the code I used:

. xtabond2 ihsdti L.ihsdti L(1/1)happy1 L(1/1)age L(1/1)age2 L(1/1)child L(1/1)race L(1/1)married L(1/1)widow L(1/1)divsep
 L(1/1)employd L(1/1)unemploy L(1/1)edu1 L(1/1)lnrinc15 L(1/1)numfam year13 year15 year17 year19, iv(year13 year15 year17 year19) gmm(L.lndti L.happy1 L.age L.age2 L.child L.race L.married L.widow L.divsep L.employd L.unemploy L.edu1 L.lnrinc15 L.numfam, collapse) noleveleq robust

I have a specific and related question about flunking Hansen tests after collapsing instruments. It seemed to be a little different than this thread, so I posted the new question here:

https://www.statalist.org/forums/for...se-doesn-t-fix

Thanks very much for your help.