Inference on time series nonparametric conditional moment restrictions using nonlinear sieves

Xiaohong Chen; Yuan Liao; Weichen Wang

doi:10.1016/j.jeconom.2024.105920

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Inference on time series nonparametric conditional moment restrictions using nonlinear sieves

Journal article

Peer reviewed

Inference on time series nonparametric conditional moment restrictions using nonlinear sieves

Xiaohong Chen, Yuan Liao and Weichen Wang

Journal of econometrics, Vol.249, p.105920

05/2025

DOI: 10.1016/j.jeconom.2024.105920

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Abstract

This paper studies estimation of and inference on dynamic nonparametric conditional moment restrictions of high dimensional variables for weakly dependent data, where the unknown functions of endogenous variables can be approximated via nonlinear sieves such as neural networks and Gaussian radial bases. The true unknown functions and their sieve approximations are allowed to be in general weighted function spaces with unbounded supports, which is important for time series data. Under some regularity conditions, the optimally weighted general nonlinear sieve quasi-likelihood ratio (GN-QLR) statistic for the expectation functional of unknown function is asymptotically Chi-square distributed regardless whether the functional could be estimated at a root-n rate or not, and the estimated expectation functional is asymptotically efficient if it is root-n estimable. Our general theories are applied to two important examples: (1) estimating the value function and the off-policy evaluation in reinforcement learning (RL); and (2) estimating the averaged partial mean and averaged partial derivative of dynamic nonparametric quantile instrumental variable (NPQIV) models. We demonstrate the finite sample performance of our optimal inference procedure on averaged partial derivative of a dynamic NPQIV model in simulation studies.

Dynamic nonparametric quantile instrumental variables

Mixed smoothness

Neural networks

Nonlinear sieves

Reinforcement learning

Weighted compact embedding

β mixing data

Details

Title: Subtitle: Inference on time series nonparametric conditional moment restrictions using nonlinear sieves
Creators: Xiaohong Chen - University of New Haven
Yuan Liao - Rutgers, The State University of New Jersey
Weichen Wang - University of Hong Kong
Resource Type: Journal article
Publication Details: Journal of econometrics, Vol.249, p.105920
DOI: 10.1016/j.jeconom.2024.105920
ISSN: 0304-4076
eISSN: 1872-6895
Publisher: Elsevier B.V
Language: English
Date published: 05/2025
Academic Unit: Economics
Record Identifier: 9984936837202771

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