On Bootstrapping Panel Factor Series - Extended Version

This paper studies the asymptotic validity of sieve bootstrap for nonstationary panel factor series. Two main results are shown. Firstly, a bootstrap Invariance Principle is derived pointwise in i, obtaining an upper bound for the order of truncation of the AR polynomial that depends on n and T. Consistent estimation of the long run variances is also studied for (n,T)→∞. Secondly, joint bootstrap asymptotics is also studied, investigating the conditions under which the bootstrap is valid. The extent of cross sectional dependence which can be allowed for is investigated, showing that, in the presence of strong cross dependence, consistent estimation of the long run variance (and therefore validity of the bootstrap) is no longer possible. The paper also considers extensions to the case of a mixture of stationary and nonstationary common factors