GMM Continuously Updating Estimator - convergence not achieved

[Alessandro Franconi]

Dear Statalists,

I am using an IV framework for a collection of "h" regressions (Local projection) using ivreg2, where I have detected serial correlation using the Cumby and Huizinga test (from 1 to 4 lags, depending on "h") but I did not tested for the presence of heteroskedastic yet (for the regressions I employ a Newey-West correction). I am using 2SLS, and given that the Olea and Pflueger (2013) test highlight a problem of weak instruments at some horizons "h", I wanted to check the consistency of the results using additional estimators. First of all, LIML seems to be more centered around the true value of the parameters, however, the assumption of iid errors does not hold in my case. Nevertheless, the results are in line with 2SLS, but with larger standard errors for the horizons where the test for weak instruments has detected that problem. Then, I tried GMM and a Continuously Updating GMM estimator (cue option for ivreg2). When running the, very computationally intense, model Stata tells me: convergence not achieved. Note that the results are very similar to the 2SLS case. How should I interpret that?

Thanks all,
Alessandro

[Joro Kolev]

As you are doing this just for robustness, you should probably disregard the message, and not waste your time on figuring out how to achieve convergence.

In general when we see this message, we might obtain completely meaningless estimates, or completely reasonable estimates. If your estimates without convergence are close to your 2SLS, just carry on with what you are doing using 2SLS. (Btw, it might be that your estimates are close to 2SLS because the continuously updated estimator starts from the 2SLS estimates, and cannot get much further, and this is why they are close by.)

[Alessandro Franconi]

Thanks for the quick reply. It is indeed a robustness check, but it would be nice to count also on additional estimators and comment on their difference with respect to 2SLS, as the GMM cue as is more robust towards weak instruments (even though is not really a big problem in my model, but I want to show very high degree of robustness of my results - for publication).