Wild bootstrap tests for IV regression

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 unknown form. We apply this procedure to t tests, including heteroskedasticity-robust t tests, and to the Anderson-Rubin test. We provide simulation evidence that it works far better than older methods, such as the pairs bootstrap. We also show how to obtain reliable confidence intervals by inverting bootstrap tests. An empirical example illustrates the utility of these procedures.Instrumental variables estimation, two-stage least squares, weak instruments, wild bootstrap, pairs bootstrap, residual bootstrap, confidence intervals, Anderson-Rubin test

How costly is sustained low inflation for the U.S. economy?

We study the welfare cost of inflation in a general equilibrium life cycle model with growth, costly financial intermediation, and taxes on nominal quantities. We find a stationary equilibrium of the model matches a wide variety of facts about the postwar U.S. economy. We then calculate that the inflation policy of the monetary authority has welfare consequences for agents that are an order of magnitude larger than existing estimates in the literature. These effects are large even at very low inflation rates. The bulk of the welfare cost of inflation can be attributed to the fact that inflation increases the effective tax rate on capital income.Economic conditions - United States ; Inflation (Finance)

Improving the reliability of bootstrap tests with the fast double bootstrap

Two procedures are proposed 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 for asymptotic tests. Then a new procedure is proposed for computing bootstrap P values that will often be more accurate than ordinary ones. This “fast double bootstrap” is closely related to the double bootstrap, but it is far less computationally demanding. Simulation results for three different cases suggest that the fast double bootstrap can be very useful in practice.Bootstrap

Bootstrap inference in a linear equation estimated by instrumental variables

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 (LR)—as functions of six random quantities leads to a number of interesting results about the properties of the tests under weakinstrument asymptotics. We then propose several new procedures for bootstrapping the three non-exact test statistics and also a new conditional bootstrap version of the LR test. These use more efficient estimates of the parameters of the reduced-form equation than existing procedures. When the best of these new procedures is used, both the K and conditional bootstrap LR tests have excellent performance under the null. However, power considerations suggest that the latter is probably the method of choice.bootstrap, weak instruments, IV estimation

Moments of IV and JIVE estimators

We develop a 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 estimator has no moments at all. Simulation results illustrate the consequences of its lack of moments.instrumental variables, JIVE, moments of estimators

Terlipressin or norepinephrine in septic shock: do we have the answer?

Comment on Terlipressin versus norepinephrine as infusion in patients with septic shock: a multicentre, randomised, double-blinded trial. [Intensive Care Med. 2018

The Power of Bootstrap and Asymptotic Tests

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 is of the same order of magnitude under the null hypothesis and under non-null processes described by a Pitman drift. However, complications arise in the measurement of power. If the test statistic is not an exact pivot, critical values depend on which data-generating process (DGP) is used to determine the distribution under the null hypothesis. We propose as the proper choice the DGP which minimizes the bootstrap discrepancy. We also show that, under an asymptotic independence condition, the power of both bootstrap and asymptotic tests can be estimated cheaply by simulation. The theory of the paper and the proposed simulation method are illustrated by Monte Carlo experiments using the logit model.bootstrap test, bootstrap discrepancy, Pitman drift, drifting DGP, Monte Carlo, test power, power, asymptotic test

Regression-Based Methods for Using Control and Antithetic Variates in Monte Carlo Experiments

Methods based on linear regression provide a very easy way to use the information in control and antithetic variates to improve the efficiency with which certain features of the distributions of estimators and test statistics are estimated in Monte Carlo experiments. We propose a new technique that allows these methods to be used when the quantities of interest are quantiles. Ways to obtain approximately optimal control variates in many cases of interest are also proposed. These methods seem to work well in practice, and can greatly reduce the number of replications required to obtain a given level of accuracy.

Moments of IV and JIVE Estimators

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 estimator has no moments at all. Simulation results illustrate the consequences of its lack of moments.polar coordinates, simultaneous equations, JIVE, moments, instrumental variables