Microeconometrics Methods and Applications

Introduction

Exact finite-sample results are unavailable for most microeconometrics estimators and related test statistics. The statistical inference methods presented in preceding chapters rely on asymptotic theory that usually leads to limit normal and chi-square distributions.

An alternative approximation is provided by the bootstrap, due to Efron (1979, 1982). This approximates the distribution of a statistic by a Monte Carlo simulation, with sampling done from the empirical distribution or the fitted distribution of the observed data. The additional computation required is usually feasible given advances in computing power. Like conventional methods, however, bootstrap methods rely on asymptotic theory and are only exact in infinitely large samples.

The wide range of bootstrap methods can be classified into two broad approaches. First, the simplest bootstrap methods can permit statistical inference when conventional methods such as standard error computation are difficult to implement. Second, more complicated bootstraps can have the additional advantage of providing asymptotic refinements that can lead to a better approximation in-finite samples.

Applied researchers are most often interested in the first aspect of the bootstrap. Theoreticians emphasize the second, especially in settings where the usual asymptotic methods work poorly in finite samples.

The econometrics literature focuses on use of the bootstrap in hypothesis testing, which relies on approximation of probabilities in the tails of the distributions of statistics. Other applications are to confidence intervals, estimation of standard errors, and bias reduction.