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Unformatted text preview: Fixed-b Asymptotics for Spatially Dependent Robust Nonparametric Covariance Matrix Estimators * C. Alan Bester, * Timothy G. Conley, * Christian B. Hansen, † and Timothy J. Vogelsang ‡ August 2008; This Version May 2009 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 non-degenerate limiting random variables that depend on the HAC smoothing parameters and kernel. We show that the limit distributions of commonly used test statistics are pivotal but non-standard, so critical values must be obtained by simulation. We provide a simple and general simulation procedure based on the i.i.d. bootstrap that can be used to obtain critical values. We illustrate the potential gains of the new approximation through simulations and an empirical example that examines the effect of unjust dismissal doctrine on temporary help services employment. Keywords: HAC, panel, robust JEL Codes: C12, C21, C22, C23 * We thank Silvia Gon¸ calves for helpful discussions. We are grateful for support from the Neubauer Family Faculty Fund and from the IBM Corporation Faculty Research Fund at the University of Chicago Graduate School of Business. † Graduate School of Business, University of Chicago ‡ Department of Economics, Michigan State University 1 1. Introduction Many economic analyses rely on dependent data. To conduct inference with time series data, researchers often employ heteroskedasticity and autocorrelation consistent (HAC) inference procedures. The essence of HAC procedures is the use of a nonparametric estimator for the variance of model parameters, which provides consistent standard errors in the presence of intertemporal correlation. 1 The use of standard error estimators that account for temporal dependence has also become common in microeconomic applications involving panel data, where researchers employ clustered covariance estimators with clusters given by the cross- sectional units of observation. 2 An often neglected feature of cross-sectional and panel data is cross-sectional or spatial correlation: Data or residuals from one observation may be statistically related to data or residuals from other neighboring observations. As is the case with temporal correlation, inference procedures that do not account for such spatial correlation will usually be incorrect when it exists in the data. To account for this problem, spatial HAC procedures have been developed....
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- Fall '08
- Normal Distribution, critical values, θn, FCLT, Timothy G. Conley