Asymptotic Efficiency in Factor Models and Dynamic Panel Data Models

This paper studies the asymptotic efficiency in factor models with serially correlated errors and dynamic panel data models with interactive effects. We derive the efficiency bound for the estimation of factors, factor loadings and common parameters that describe the dynamic structure. We use double asymptotics under which both the cross-sectional sample size and the length of the time series tend to infinity. The results show that the efficiency bound for factors is not affected by the presence of unknown factor loadings and common parameters, and analogous results hold for the bounds for factor loadings and common parameters. The efficiency bound is derived by using an infinite-dimensional convolution theorem. Perturbation to the infinite-dimensional parameters, which consists in an important step of the derivation of the efficiency bound, is nontrivial and is discussed in detail