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

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This paper considers the GMM estimator, α ˆ , 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 ( α ˆ − 1 ) is degenerate and nondegenerate each with probability 1/2. We sharpen this result by showing that the limit distribution of n 1 ∕ 2 ( α ˆ − 1 ) is nondegenerate when n 1 ∕ 4 ( α ˆ − 1 ) converges in probability to 0, and we characterize the limit distribution which is nonstandard. • We consider a panel dynamic model with fixed effects under standard assumptions. • The GMM estimator exhibits a slow fourth-root convergence in the unit root case. • The limit distribution has a half mass at zero. • The zero part of the limit distribution involves a faster root-n convergence rate. • The asymptotic distribution is non-Gaussian, as verified in simulations.