time dummies always should be included in iv part in xtabond2?

[Sang Won Han]

I am now trying to implement xtabond2 for my panel data set spanning from 1998 to 2020. The issue that I have regarding xtabond2 routine is whether I need to include all the independent variables (including time dummies) into either "iv" or "gmm" part. To be specific, let's say that I have one dependent variable and four independent (three endogenous and one exogeneous) and time dummies for 5 years. Then, the usual xtabond2 command should be as follows:

xtabond2 y L.y a b c d i.fyear, gmm(L.y a b c) iv(d i.fyear), robust twostep


But then my question is whether I can exclude some of the independent variables from "iv" or "gmm" part like:

xtabond2 y L.y a b c d i.fyear, gmm(L.y b c) iv(d), robust twostep


Thank you in advance and look forward to hearing from you soon.

[Jeff Wooldridge]

Because you are including time dummies in the main ("structural") equation, they need instruments. I can't think of a reason why they aren't there own IVs. So the first command is correct. I'm not even sure what the second command would do, but it's probably instrumenting for the year dummies using lags of the variables in gmm(). You don't want this. The bottom line is, the year dummies need to be their own IVs.

[Manh Hoang Ba]

Dear Jeff Wooldridge ,

If I run the command:

xtabond2 y L.y a b c d i.fyear, gmm(L.y a b c) iv(d) iv(i.fyear)

The difference-in-hansen test results show that i.fyear are invalid instruments. When I remove them and use the declaration below:

xtabond2 y L.y a b c d i.fyear, gmm(L.y a b c) iv(d)

Then all instruments pass Hansen and difference-in-Hansen.
How should I understand this result and should I use it?

Thanks in advance.

[Sebastian Kripfganz]

I agree with Jeff. There is not really a situation in which you wouldn't instrument the time dummies by themselves. If the (difference-in-)Hansen test rejects the specification with time dummies, then you shouldn't question the time dummies first but the rest of the specification. Note that the (difference-in-)Hansen test cannot assess the validity of a subset of the instruments if some of the other instruments are potentially invalid. It effectively compares two models, the one with the respective instruments to the one without them (similar to a Hausman test). If the model without the suspect instruments is misspecified, then you would compare two potentially misspecified models with other. The test would be meaningless. Even if all instruments were invalid, there is a good chance that the Hansen test might not reject the null hypothesis. You always have to maintain the assumption that at least as many instruments are valid as you have regressors (or all the instruments not tested by the difference-in-Hansen test), but this assumption could be wrong, of course.

Also note that with xtabond2 specifying

iv(d) iv(i.fyear)

is not the same as specifying

iv(d, eq(diff)) iv(i.fyear, eq(diff)) iv(d, eq(level)) iv(i.fyear, eq(level))

Unless you know what the first version without explicitly specifying the equations is doing, you probably want to use the second specification. Even then, it is generally (asymptotically) redundant to specify instruments for the time dummies in the differenced equation when you also instrument them in the level equation.

More on dynamic panel data GMM estimation in Stata (with slides 74 and 75 on the use of time dummies):

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