On the asymptotic distribution of the quadratic GMM estimator of a dynamic panel data model under a unit root

This paper considers the GMM estimator, αˆ, of the autoregressive parameter in linear dynamic panel data models with fixed effects when the data-generating process has a unit root. Previous literature has established that the limit distribution of n^1∕4(αˆ−1) is degenerate and nondegenerate each with probability 1/2. We sharpen this result by showing that the limit distribution of n^1∕2(αˆ−1) is nondegenerate when n^1∕4(αˆ−1) converges in probability to 0, and we characterize the limit distribution which is nonstandard.