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 all the test statistics--Student's t, Anderson-Rubin, Kleibergen's K, and likelihood ratio (LR)--can be written as functions of six...

We perform an extensive series of Monte Carlo experiments to compare the performance of two variants of the "Jackknife Instrumental Variables Estimator," or JIVE, with that of the more familiar 2SLS and LIML estimators. We find no evidence to suggest that JIVE should ever be used. It is always...

We introduce the concept of the bootstrap discrepancy, which measures the difference in rejection probabilities between a bootstrap test based on a given test statistic and that of a (usually infeasible) test based on the true distribution of the statistic. We show that the bootstrap discrepancy...

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....

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...