We first propose two procedures for estimating the rejection probabilities of bootstrap tests in Monte Carlo experiments without actually computing a bootstrap test for each replication. These procedures are only about twice as expensive (per replication) as estimating rejection probabilities...

We develop a new method, based on the use of polar coordinates, to investigate the existence of moments for instrumental variables and related estimators in the linear regression model. For generalized IV estimators, we obtain familiar results. For JIVE, we obtain the new result that this...

We propose a wild bootstrap procedure for linear regression models estimated by instrumental variables. Like other bootstrap procedures that we have proposed elsewhere, it uses efficient estimates of the reduced-form equation(s). Unlike them, it takes account of possible heteroskedasticity of...

We study several tests for the coefficient of the single right-hand-side endogenous variable in a linear equation estimated by instrumental variables. We show that writing all the test statistics -- Student's t, Anderson-Rubin, the LM statistic of Kleibergen and Moreira (K), and likelihood ratio...

Various versions of the wild bootstrap are studied as applied to regression models with heteroskedastic errors. It is shown that some versions can be qualified as 'tamed', in the sense that the statistic bootstrapped is asymptotically independent of the distribution of the wild bootstrap DGP....

Asymptotic and bootstrap tests are studied for testing whether there is a relation of stochastic dominance between two distributions. These tests have a null hypothesis of nondominance, with the advantage that, if this null is rejected, then all that is left is dominance. This also leads us to...

The aim of this paper is to illustrate more than one instance of poor bootstrap performance, and to see how available diagnostic techniques can indicate reliably when and how this poor performance can arise. Two particular features that seem to be important to explain bootstrap discrepancy are...

In an attempt to free bootstrap theory from the shackles of asymptotic considerations, this paper studies the possibility of justifying, or validating, the bootstrap, not by letting the sample size tend to infinity, but by considering the sequence of bootstrap P values obtained by iterating the...

We study the finite-sample properties of tests for overidentifying restrictions in linear regression models with a single endogenous regressor and weak instruments. Under the assumption of Gaussian disturbances, we derive expressions for a variety of test statistics as functions of eight...

Economists are often interested in the coefficient of a single endogenous explanatory variable in a linear simultaneous equations model. One way to obtain a confidence set for this coefficient is to invert the Anderson-Rubin test. The AR confidence sets that result have correct coverage under...