The Econometric SocietyEdited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262
Econometrica: Sep, 2021, Volume 89, Issue 5
https://doi.org/10.3982/ECTA17764
p. 2439-2458
This paper develops a uniformly valid and asymptotically nonconservative test based on projection for a class of shape restrictions. The key insight we exploit is that these restrictions form convex cones, a simple and yet elegant structure that has been barely harnessed in the literature. Based on a monotonicity property afforded by such a geometric structure, we construct a bootstrap procedure that, unlike many studies in nonstandard settings, dispenses with estimation of local parameter spaces, and the critical values are obtained in a way as simple as computing the test statistic. Moreover, by appealing to strong approximations, our framework accommodates nonparametric regression models as well as distributional/density‐related and structural settings. Since the test entails a tuning parameter (due to the nonstandard nature of the problem), we propose a data‐driven choice and prove its validity. Monte Carlo simulations confirm that our test works well.
This zip file contains the replication material for the manuscript.
This supplement is organized as follows. Appendix B discusses particular shape restrictions with the convex cone property, Appendix C specializes our test to the regular case where rn{ˆθ_n − θ0} converges, Appendix D collects additional proofs and auxiliary results, and Appendix E presents additional simulation studies and an empirical application. Appendix F verifies the main assumptions for our examples, Appendix G provides proofs for Appendix C, while Appendix H contains simulation results omitted from the main text and Appendix E, all of which are relegated to the arXiv version of this paper (https://arxiv.org/abs/1910.07689) due to space limitation.
