Bootstrap inference for linear dynamic panel data models with individual fixed effects

Abstract

This paper’s main contribution is to propose and theoretically justify the application of bootstrap methods for inference in autoregressive panel data models with fixed effects. Whereas the focus of the existing literature has been on bias correcting the standard fixed effects OLS estimator (due to the well known incidental parameter bias), our focus here is on improving the quality of inference by relying on the bootstrap instead of the standard normal distribution when computing critical values for test statistics. In particular, we show by simulation that confidence intervals based on the normal distribution can be very distorted in finite samples. Instead, a bootstrap that resamples the residuals and generates the bootstrap observations recursively using the estimated autoregressive panel data model greatly reduces these distortions. We show that this recursive-design residual-based bootstrap fixed effects OLS estimator contains a built-in bias correction term that mimics the incidental parameter bias. Thus, this method can be used to approximate the bias (as well as the entire distribution) of the (biased) fixed effects OLS estimator. This is in contrast with two other methods we consider (a fixed-design residual-based bootstrap and a pairs bootstrap) whose distributions are incorrectly centered at zero. As it turns out, both the recursive-design and the pairs bootstrap are asymptotically valid when applied to the bias-corrected estimator, but the fixed-design bootstrap is not. In the simulations, the recursive-design bootstrap is the method that does best overall.