Bootstrap Methods in Econometrics

The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one's data or a model estimated from the data. Under conditions that hold in a wide variety of econometric applications, the bootstrap provides approximations to distributions of statistics, coverage probabilities of confidence intervals, and rejection probabilities of hypothesis tests that are more accurate than the approximations of first-order asymptotic distribution theory. The reductions in the differences between true and nominal coverage or rejection probabilities can be very large. In addition, the bootstrap provides a way to carry out inference in certain settings where obtaining analytic distributional approximations is difficult or impossible. This article explains the usefulness and limitations of the bootstrap in contexts of interest in econometrics. The presentation is informal and expository. It provides an intuitive understanding of how the bootstrap works. Mathematical details are available in the references that are cited.

On the accuracy of bootstrapping sample quantiles of strongly mixing sequences

In this paper, we examine the rate of convergence of moving block bootstrap (MBB) approximations to the distributions of normalized sample quantiles based on strongly mixing observations. Under suitable smoothness and regularity conditions on the one-dimensional marginal distribution function, the rate of convergence of the MBB approximations to distributions of centered and scaled sample quantiles is of order O(n−1¼ log logn).