Sieve bootstrap for nonstationary panel factor models

This paper considers bootstrapping nonstationary panel factor models when possible time dependence is present in the factors dynamics. The analysis does not assume any specific DPG, and a sieve bootstrap algorithm is proposed to approximate the autocorrelation structure of the processes involved in the model. The conditions under which sieve bootstrap yields consistent estimators and test statistics are explored, and a selection rule for order of the approximation of the AR dynamics is derived. Two main results are shown. First, an invariance principle for the partial sums of the bootstrap samples of the first differences of the estimated factors is shown to hold for large T and finite or large n. Secondly, it is proved that bootstrap estimates and test statistics are consistent only for (n, T)-> infinite, whilst the finite n case results in inconsistent bootstrap. Sieve bootstrap is shown to be consistent for the fixed n case only in presence of no serial correlation.