Short T$$ T $$ dynamic panel data models with individual, time and interactive effects

This paper proposes a transformed quasi-maximum likelihood (TQML) estimator for short T$$ T $$ dynamic fixed effects panel data models allowing for interactive effects through a multifactor error structure. The proposed estimator is robust to the heterogeneity of the initial values and common unobserved effects, while at the same time allowing for standard fixed and time effects. It is applicable to both stationary and unit root cases. The order condition for identification of the number of interactive effects is established, and conditions are derived under which the parameters are locally identified. It is shown that global identification in the presence of the lagged dependent variable cannot be guaranteed. The TQML estimator is proven to be consistent and asymptotically normally distributed. A sequential multiple testing likelihood ratio procedure is also proposed for estimation of the number of factors which is shown to be consistent. Finite sample results obtained from Monte Carlo simulations show that the proposed procedure for determining the number of factors performs very well, and the TQML estimator has small bias and root mean square error (RMSE) and correct empirical size in most settings. The practical use of the TQML approach is demonstrated by means of two empirical illustrations from the literature on cross county crime rates and cross country growth regressions.