xtabond and time-invariant variables

[James Paul]

Hi everyone,

I am running a system GMM model like the following

xtset firm year
xtabond2 L(0/1).y x1 x2 x3 i.year, gmm(L.y x1 x2 x3, lag(1 1) collapse) ivstyle(i.year, equation(level)) robust

x1, x2, x3 are firm's financial variables. I don't think I can assume they are strictly exogenous, so I think the model looks okay.

As far as I know, the estimation is basically consistent with fixed effects model as it uses difference equation where individual time-invariant effects are purged.
Here, while I was doing some experiments, I unintentionally included a time-invariant variable as a regressor and found the coefficient was estimated.
It seems odd to me as I thought xtabond is like a fixed effects model.

Is it a bug or am I mistaken about xtabond2?

[David Roodman]

By default, xtabond2 performs "System GMM", which also includes the undifferenced equation. In that mode, it can estimate coefficients on time-invariant regressors.

[Sebastian Kripfganz]

David is right. However, even though the command spills out an estimate for the coefficient of a time-invariant regressor, it is likely spurious (i.e., not identified in the econometric sense) unless you choose the instruments wisely. If interested, see the following paper:

• Kripfganz, S., and C. Schwarz (2019). Estimation of linear dynamic panel data models with time-invariant regressors. Journal of Applied Econometrics 34 (4), 526-546.