Abstract
In this article, we propose a general method for testing inequality restrictions on nonparametric functions. Our framework includes many nonparametric testing problems in a unified framework, with a number of possible applications in auction models, game theoretic models, wage inequality, and revealed preferences. Our test involves a one-sided version ofLpfunctionals of kernel-type estimators (1 ≤p < ∞) and is easy to implement in general, mainly due to its recourse to the bootstrap method. The bootstrap procedure is based on the nonparametric bootstrap applied to kernel-based test statistics, with an option of estimating “contact sets.” We provide regularity conditions under which the bootstrap test is asymptotically valid uniformly over a large class of distributions, including cases where the limiting distribution of the test statistic is degenerate. Our bootstrap test is shown to exhibit good power properties in Monte Carlo experiments, and we provide a general form of the local power function. As an illustration, we consider testing implications from auction theory, provide primitive conditions for our test, and demonstrate its usefulness by applying our test to real data. We supplement this example with the second empirical illustration in the context of wage inequality.
Highlights
We propose a general method for testing inequality restrictions on nonparametric functions
We find through our local power analysis that this class of tests exhibits dual convergence rates depending on Pitman directi√ons, and in many cases, the faster of the two rates achieves a parametric rate of n, despite the use of kernel-type test statistics
We have proposed a general method for testing inequality restrictions on nonparametric functions and have illustrated its usefulness by looking at two particular empirical applications
Summary
We propose a general method for testing inequality restrictions on nonparametric functions. We establish the asymptotic validity of the proposed test uniformly over a large class of distributions, without imposing restrictions on the covariance structure among nonparametric estimates of vτ, j (·), thereby allowing for degenerate cases. Such a uniformity result is crucial for ensuring good finite sample properties for tests whose (pointwise) limiting distribution under the null hypothesis exhibits various forms of discontinuity. This article’s approach naturally covers a wide class of inequality restrictions among nonparametric functions that the moment inequality framework does not (or at least is cumbersome to) apply Such examples include testing multiple inequalities that are defined by differences in conditional quantile functions uniformly over covariates and quantiles. Online Appendices provide all the proofs of theorems with a roadmap of the proofs to help readers
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
