Christoph Breunig, Xiaohong Chen
arXiv 17 Jun 2020 · Econometrics · publishedEconometrica (2024) · 6 citations (OpenAlex)
arXiv:2006.09587 · PDF · DOI · OpenAlex · Extracted main text
We propose a new adaptive hypothesis test for inequality (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test statistic is based on a modified leave-one-out sample analog of a quadratic distance between the restricted and unrestricted sieve two-stage least squares estimators. We provide computationally simple, data-driven choices of sieve tuning parameters and Bonferroni adjusted chi-squared critical values. Our test adapts to the unknown smoothness of alternative functions in the presence of unknown degree of endogeneity and unknown strength of the instruments. It attains the adaptive minimax rate of testing in $L^{2}$. That is, the sum of the supremum of type I error over the composite null and the supremum of type II error over nonparametric alternative models cannot be minimized by any other tests for NPIV models of unknown regularities. Confidence sets in $L^{2}$ are obtained by inverting the adaptive test. Simulations confirm that, across different strength of instruments and sample sizes, our adaptive test controls size and its finite-sample power greatly exceeds existing non-adaptive tests for monotonicity and parametric restrictions in NPIV models. Empirical applications to test for shape restrictions of differentiated products demand and of Engel curves are presented.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chen and Christensen (2018) Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression | 1.000 | 9 | 3 | 100% |
| 2 | Blundell, Chen, and Kristensen (2007) Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves | 1.000 | 6 | 4 | 100% |
| 3 | Fang and Seo (2021) A Projection Framework for Testing Shape Restrictions That Form Convex Cones | 1.000 | 6 | 4 | 100% |
| 4 | Horowitz (2006) Testing a Parametric Model Against a Nonparametric Alternative with Identification Through Instrumental Variables | 1.000 | 6 | 3 | 100% |
| 5 | Chen and Rei (2011) On Rate Optimality for Ill-Posed Inverse Problems in Econometrics | 0.874 | 6 | 2 | 100% |
| 6 | Chetverikov and Wilhelm (2017) Nonparametric instrumental variable estimation under monotonicity | 0.843 | 3 | 3 | 100% |
| 7 | Bierens (1990) A consistent conditional moment test of functional form | 0.811 | 4 | 2 | 100% |
| 8 | Chernozhukov, Newey, and Santos (2015) Constrained conditional moment restriction models | 0.811 | 4 | 2 | 100% |
| 9 | van der Vaart and Wellner (2000) Weak Convergence and Empirical Processes: With Applications to Statistics (Springer Series in Statistics) | 0.737 | 3 | 2 | 100% |
| 10 | Berry and Haile (2014) Identification in differentiated products markets using market level data | 0.737 | 3 | 2 | 100% |
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