Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection

The topic of this paper is inference in models in which parameters are defined by moment inequalities and/or equalities. The parameters may or may not be identified. This paper introduces a new class of confidence sets and tests based on generalized moment selection (GMS). GMS procedures are shown to have correct asymptotic size in a uniform sense and are shown not to be asymptotically conservative. The power of GMS tests is compared to that of subsampling, m out of n bootstrap, and “plug‐in asymptotic” (PA) tests. The latter three procedures are the only general procedures in the literature that have been shown to have correct asymptotic size (in a uniform sense) for the moment inequality/equality model. GMS tests are shown to have asymptotic power that dominates that of subsampling, m out of n bootstrap, and PA tests. Subsampling and m out of n bootstrap tests are shown to have asymptotic power that dominates that of PA tests.     

A Three‐step Method for Choosing the Number of Bootstrap Repetitions

This paper considers the problem of choosing the number of bootstrap repetitions B for bootstrap standard errors, confidence intervals, confidence regions, hypothesis tests, p‐values, and bias correction. For each of these problems, the paper provides a three‐step method for choosing B to achieve a desired level of accuracy. Accuracy is measured by the percentage deviation of the bootstrap standard error estimate, confidence interval length, test's critical value, test's p‐value, or bias‐corrected estimate based on B bootstrap simulations from the corresponding ideal bootstrap quantities for which B=∞. The results apply quite generally to parametric, semiparametric, and nonparametric models with independent and dependent data. The results apply to the standard nonparametric iid bootstrap, moving block bootstraps for time series data, parametric and semiparametric bootstraps, and bootstraps for regression models based on bootstrapping residuals. Monte Carlo simulations show that the proposed methods work very well.