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Full-Text Articles in Economics
Adaptive, Rate-Optimal Testing In Instrumental Variables Models, Christoph Breunig, Xiaohong Chen
Adaptive, Rate-Optimal Testing In Instrumental Variables Models, Christoph Breunig, Xiaohong Chen
Cowles Foundation Discussion Papers
This paper proposes simple, data-driven, optimal rate-adaptive inferences on a structural function in semi-nonparametric conditional moment restrictions. We consider two types of hypothesis tests based on leave-one-out sieve estimators. A structure- space test (ST) uses a quadratic distance between the structural functions of endogenous variables; while an image-space test (IT) uses a quadratic distance of the conditional moment from zero. For both tests, we analyze their respective classes of nonparametric alternative models that are separated from the null hypothesis by the minimax rate of testing. That is, the sum of the type I and the type II errors of the …
Adaptive, Rate-Optimal Hypothesis Testing In Nonparametric Iv Models, Christoph Breunig, Xiaohong Chen
Adaptive, Rate-Optimal Hypothesis Testing In Nonparametric Iv Models, Christoph Breunig, Xiaohong Chen
Cowles Foundation Discussion Papers
We propose a new adaptive hypothesis test for polyhedral cone (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 NPIV estimators. We provide computationally simple, data-driven choices of sieve tuning parameters and 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 …