Essays on bootstrap in econometrics

My dissertation consists of three essays on bootstrap inference in both large panel data models and instrumental variable (IV) models with many instruments and possibly, many weak instruments. Since the asymptotic theory is often not a good approximation to the sampling distribution of test statistics and estimators, I consider the bootstrap as an alternative. These essays try to study the asymptotic validity of existing bootstrap procedures and when they are invalid, to propose new valid bootstrap methods.  The first chapter (co-authored with Sílvia Gonçalves) studies the validity of the bootstrap for inference on a stationary linear dynamic panel data model with individual fixed effects. We consider three bootstrap methods: the recursive-design wild bootstrap, the fixed-design wild bootstrap and the pairs bootstrap. These methods are natural generalizations to the panel context of the bootstrap methods considered by \citeasnoun{GK} in pure time series autoregressive models. We show that the recursive-design wild bootstrap fixed effects OLS estimator contains a built-in bias correction term that mimics the incidental parameter bias. This is in contrast with the fixed-design wild bootstrap and the 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.  The second chapter extends our pairwise bootstrap results to dynamic nonlinear panel data models with fixed effects. These models are often estimated with the Maximum Likelihood Estimator (MLE) which also suffers from an incidental parameter bias. Recently, \citeasnoun{DhaeneJochmans} have proposed the split-jackknife estimation method. Although these estimators have asymptotic normal approximations that are centered at the true parameter, important size distortions remain in finite samples. \citeasnoun{DhaeneJochmans} have proposed the pairs bootstrap as an alternative in this context without a theoretical justification. To fill this gap, I show that this method is asymptotically valid when used to estimate the distribution of the half-panel jackknife estimator although it does not consistently estimate the distribution of the MLE. A Monte Carlo experiment shows that bootstrap-based confidence intervals that rely on the half-panel jackknife estimator greatly help to reduce the distortions associated to the normal approximation in finite samples. In addition, I apply this bootstrap method to a canonical model of female-labor participation to construct valid confidence intervals.  In the last chapter (co-authored with Wenjie Wang), we study the asymptotic validity of bootstrap procedures for instrumental variable (IV) models with many weak instruments. We show analytically that a standard residual-based bootstrap and the restricted efficient (RE) bootstrap of Davidson and MacKinnon (2008, 2010, 2014) cannot consistently estimate the limiting distribution of the LIML estimator. The foremost reason is that they fail to adequately mimic the identification strength in the sample. Therefore, we propose a modified bootstrap procedure which consistently estimates this limiting distribution. Our simulations show that the modified bootstrap procedure greatly reduces the distortions associated to asymptotic Wald ($t$) tests in finite samples, especially when the degree of endogeneity is high.

Keyphrases: Bootstrap, Dynamic panel data, Fixed effects, Incidental parameter bias, Half-panel jackknife, Weak instruments, LIML, RE bootstrap, Split-jackknife