xtabond2 with p-value of AR(1) test > 0.1

[River Huang]

Dear All, In a typical application (xtabond2 to a dynamic panel data model), one often needs to check whether there is no AR(2), along with Hansen over-identifying test. The question is that if there is no AR(1) either, i.e., the p-value of AR(1) test is, say, > 0.1? What would be the problem in this situation?

[Jeff Wooldridge]

I really wish that the xtabond2 command would report the estimate of the AR(1) correlation parameter so we can see how close it is to -0.5, which is the theoretical value when the original errors are serially uncorrelated. This is specification testing gone mad. I can reject for values very far from -0.5. In principle, one should be able to get the FD residuals after Arellano-Bond estimation and compute the first-order correlation. Having a valid confidence interval would be nice to go with it, though.

Depending on how large N is, it's possible that the AR(1) coefficient is close to -0.5 but the standard error is so large that the null of zero is not rejected.

[River Huang]

Dear Jeff, Thank you for this helpful explanation.

[River Huang]

Dear Jeff, Does it mean that the AR(1) test (in xtabond2) is "uninformative"?

[Sebastian Kripfganz]

If there is no evidence for first-order serial correlation in the first-differenced residuals, this could indicate that your level errors are highly serially correlated (near to a unit-root process). That is not necessarily a problem if you estimate the model in first differences but it would be a substantial problem for system GMM estimators that also use instruments for the level equation. Not least, highly serially correlated level errors usually indicate that the model is poorly specified. It is certainly not dynamically complete.

Jeff is right that it might be interesting to know the point estimate of the correlation parameter, or even better its confidence interval. I will give it a thought if that might be a useful addition for some future update of my xtdpdgmm command.

[River Huang]

Dear Sebastian, Thanks for this further clarification, and looking forward to the addition of the estimate of the correlation parameter, along with its confidence interval in your xtdpdgmm command.