Consistent Test for Conditional Moment Restriction Models in Reproducing Kernel Hilbert Spaces

15:30-17:00, Friday, December 9, 2022

Tencent Meeting（Meeting ID：642 398 405）

Dr. Yuhao Li is now an Assistant Professor of Economics at Wuhan University. He earned his Ph.D. in Economics from Universidad Carlos III de Madrid in 2019. His research interests include Econometrics, Health and Labor Economics. 

In this paper, we represent Integrated Conditional Moment (ICM) tests in Reproducing Kernel Hilbert Spaces (RKHS). There are several advantages of doing so. First, reproducing kernels embody dimension and integral measure, and hence, are effective dimension reduction tools. This phenomenon can be explained by the isometrically isomorphic relationship among infinite dimensional Hilbert spaces. Second, the test statistics, expressed in terms of kernels, have analytic closed forms, making them easy to compute in practice. Third, one can generate kernels easily and massively from existing kernels. Each kernel corresponds to an ICM test, thus, for certain models, one may obtain a more sensitive test than by using conventional ones. We further propose projection-based kernels to eliminate estimation effect, leading to a simple multiplier bootstrap procedure to obtain critical values. A minimum distance estimator is developed as a byproduct. Monte Carlo exercises are performed to examine the finite sample performance of the proposed test, and an empirical application is studied.

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