The bootstrap and hypothesis tests in econometrics

摘要

Much of applied econometric research involves testing hypotheses about the parameters of econometric models. A hypothesis test typically consists of a null hypothesis, H_0, a test statistic, and a critical value. In principle, the critical value should be chosen so that the test rejects a correct H_0 with a probability #alpha# that is specified by the analyst. Such a critical value may be called the #alpha#-level Type I critical value because it sets the probability of a Type I error equal to #alpha# (Horowitz and Savin, 2000). Calculating the Type I critical value in an application may be easy or impossible, depending on H_0 and the data generation process (DGP). The calculation is easy if H_0 is simple. A simple H_0 completely specifies the DGP.Therefore, the finite-sample distribution of a test statistic under a simple H_0 can be calculated or, if it is analytically intractable, estimated with any desired accuracy by Monte Carlo simulation. The Type I critical value can be calculated or estimated by inverting the finitesample distribution function.