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FIXED-b ASYMPTOTICS FOR SPATIALLY DEPENDENT ROBUST NONPARAMETRIC COVARIANCE MATRIX ESTIMATORS

Published online by Cambridge University Press:  19 November 2014

C. Alan Bester ,
Timothy G. Conley ,
Christian B. Hansen  and
Timothy J. Vogelsang
C. Alan Bester
Affiliation:
University of Western Ontario
Timothy G. Conley
Affiliation:
University of Western Ontario
Christian B. Hansen*
Affiliation:
University of Chicago Booth School of Business
Timothy J. Vogelsang
Affiliation:
Michigan State University
*
*Address correspondence to Christian Hansen, University of Chicago Booth School of Business, 5807 S Woodlawn Ave, Chicago, IL 60637, USA. e-mail: [email protected].
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Abstract

This paper develops a method for performing inference using spatially dependent data. We consider test statistics formed using nonparametric covariance matrix estimators that account for heteroskedasticity and spatial correlation (spatial HAC). We provide distributions of commonly used test statistics under “fixed-b” asymptotics, in which HAC smoothing parameters are proportional to the sample size. Under this sequence, spatial HAC estimators are not consistent but converge to nondegenerate limiting random variables that depend on the HAC smoothing parameters, the HAC kernel, and the shape of the spatial region in which the data are located. We illustrate the performance of the “fixed-b” approximation in the spatial context through a simulation example.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 1 , February 2016 , pp. 154 - 186
Copyright
Copyright © Cambridge University Press 2014 

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