Iterated-bootstrap inference for panel-data models

Fixed-effect estimators for panel data models suffer from bias. In an n × m panel the bias is usually of order 1/m, implying that it is non-negligible unless n/m → 0. Moreover, the limit distribution features a bias term when n and m grow at the same rate. A recent literature has shown that bootstrap inference can correctly account for this asymptotic bias. This implies that inference based on the fixed-effect estimator, when performed by means of the bootstrap, behaves on par with inference based on a bias-corrected estimator. Both procedures are correct provided that n/m3 → 0. This rate arises because the bootstrap, like bias correction, introduces additional bias of order 1/m2. In this paper we argue that, by iterating the bootstrap, one accounts for this higher-order bias, thereby yielding valid inference as long as n/m5 → 0. The double bootstrap based directly on the (uncorrected) fixed-effect estimator therefore delivers gains equivalent to working with a second-order bias-corrected estimator. To illustrate we provide primitive conditions for iterating a residual bootstrap in the autoregressive model and show by means of a simulation exercise that the gains of iterating the bootstrap are substantial.