Inference for unit roots in dynamic panels where the time dimension is fixed

This paper derives similar, asymptotic unit root tests for first-order autoregressive panel data models, assuming that the time dimension of the panel is fixed. It is shown that the limiting distributions of the test statistics are normal. The assumption that the time dimension is fixed allows us to derive analytical expressions for the moments of the distributions. Similarity with respect to the initial conditions of the data generating process is achieved by including fixed effect dummy variables in the regression model, while similarity with respect to fixed effects in the data generating process is achieved by including a linear deterministic trend for each individual unit of the panel. When fixed effects or individual trends are included as regressors the least squares estimator of the autoregressive parameter is inconsistent and thus the test statistics must be appropriately adjusted. Monte Carlo evidence suggests that the proposed tests have empirical size that is very close to the nominal five percent level and substantially more power than the corresponding unit root tests for the single time series case.