Efficient inference on fractionally integrated panel data models with fixed effects

A dynamic panel data model is considered that contains possibly stochastic individual components and a common stochastic time trend that allows for stationary and nonstationary long memory and general parametric short memory. We propose four different ways of coping with the individual effects so as to estimate the parameters. Like models with autoregressive dynamics, ours nests I(1)I(1) behaviour, but unlike the nonstandard asymptotics in the autoregressive case, estimates of the fractional parameter can be asymptotically normal. For three of the estimates, establishing this property is made difficult due to bias caused by the individual effects, or by the consequences of eliminating them, which appears in the central limit theorem except under stringent conditions on the growth of the cross-sectional size NN relative to the time series length TT, though in case of two estimates these can be relaxed by bias correction, where the biases depend only on the parameters describing autocorrelation. For the fourth estimate, there is no bias problem, and no restrictions on NN. Implications for hypothesis testing and interval estimation are discussed, with central limit theorems for feasibly bias-corrected estimates included. A Monte Carlo study of finite-sample performance is included.