Uniform Nonparametric Series Inference for Dependent Data with an Application to the Search and Matching Model

83 Pages Posted: 12 Jul 2018

See all articles by Jia Li

Jia Li

Duke University

Zhipeng Liao

University of California, Los Angeles (UCLA) - Department of Economics

Date Written: June 17, 2018

Abstract

This paper concerns the uniform inference for nonparametric series estimators in time-series applications. We develop a strong approximation theory of sample averages of serially dependent random vectors with dimensions growing with the sample size. The strong approximation is first proved for heterogeneous martingale difference arrays and then extended to general mixingales via martingale approximation, readily accommodating a majority of applications in applied econometrics. We use these results to justify the asymptotic validity of a uniform confidence band for series estimators and show that it can also be used to conduct nonparametric specification test for conditional moment restrictions. The validity of high-dimensional heteroskedasticity and autocorrelation consistent (HAC) estimators is established for making feasible inference. The proposed method is broadly useful for forecast evaluation, empirical microstructure, dynamic stochastic equilibrium models and inference problems based on inter-section bounds. We demonstrate the empirical relevance of the proposed method by studying the Mortensen–Pissarides search and matching model for equilibrium unemployment, and shed new light on the unemployment volatility puzzle from an econometric perspective.

Keywords: martingale difference, mixingale, series estimation, specification test, strong approximation, uniform inference, unemployment

Suggested Citation

Li, Jia and Liao, Zhipeng, Uniform Nonparametric Series Inference for Dependent Data with an Application to the Search and Matching Model (June 17, 2018). Economic Research Initiatives at Duke (ERID) Working Paper No. 268, Available at SSRN: https://ssrn.com/abstract=3198230 or http://dx.doi.org/10.2139/ssrn.3198230

Jia Li (Contact Author)

Duke University ( email )

100 Fuqua Drive
Durham, NC 27708-0204
United States

Zhipeng Liao

University of California, Los Angeles (UCLA) - Department of Economics ( email )

8283 Bunche Hall
Los Angeles, CA 90095-1477
United States

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