We are interested in making inference on the AR parameter in an AR(1) panel data model when the time-series dimension is fixed and the cross-section dimension is large. We consider a GMM estimator based on the second order moments of the observed variables. It turns out that when the AR parameter equals unity and certain restrictions apply to the other parameters in the model then local identification fails. We show that the parameters and in particular the AR parameter can still be estimated consistently but at a slower rate than usual. Also we derive the asymptotic distribution of the parameter estimators which turns out to be non-standard. The properties of this estimator of the AR parameter are very different from those of the widely used Arellano-Bond GMM estimator which is obtained by taking first-differences of the variables and then use lagged levels as instruments. It is well-known that this estimator performs poorly when the AR parameter is close to unity. The reason for this difference between the two estimators is that with the Arellano-Bond moment conditions global identification fails for the specific values of the parameters considered here whereas with the non-linear GMM estimator that uses all information from the second order moments only local identification fails. We illustrate the results in a simulation study.