Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-29T12:46:55.274Z Has data issue: false hasContentIssue false
  • English
  • Français

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].
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59(3), 817–858.Google Scholar
Arellano, M. (1987) Computing robust standard errors for within-groups estimators. Oxford Bulletin of Economics and Statistics 49(4), 431–434.Google Scholar
Basu, A.K. & Dorea, C.C.Y. (1979) On functional central limit theorem for stationary martingale random fields. Acta Mathematica Academia Scientiarum Hungaricae 33, 307–316.Google Scholar
Bertrand, M., Duflo, E., & Mullainathan, S. (2004) How much should we trust differences-in-differences estimates? Quarterly Journal of Economics 119, 249–275.Google Scholar
Bester, C.A., Conley, T.G., & Hansen, C.B. (2010) Inference for dependent data using cluster covariance estimators. Available at SSRN: http://ssrn.com/abstract=1708263.Google Scholar
Conley, T.G. (1996) Econometric modelling of cross-sectional dependence. Ph.D. dissertation, University of Chicago.Google Scholar
Conley, T.G. (1999) GMM estimation with cross sectional dependence. Journal of Econometrics 92, 1–45.Google Scholar
Dedecker, J. (2001) Exponential inequalities and functional central limit theorems for random fields. ESAIM: Probability and Statistics 5, 77–104.Google Scholar
Deo, C. (1975) A functional central limit theorem for stationary random fields. Annals of Probability 3(4), 708–715.Google Scholar
Dudley, R.M. (1973) Sample functions of the Gaussian process. Annals of Probability 1, 66–103.Google Scholar
Goldie, C.M. & Greenwood, P.E. (1986) Variance of set-indexed sums of mixing random variables and weak convergence of set-indexed processes. Annals of Probability 14(3), 817–839.Google Scholar
Gonçalves, S. & Vogelsang, T.J. (2011) Block bootstrap HAC robust tests: The sophistication of the naive bootstrap. Econometric Theory 27(4), 745–791.Google Scholar
Hansen, C.B. (2007) Asymptotic properties of a robust variance matrix estimator for panel data when T is large. Journal of Econometrics 141, 597–620.Google Scholar
Ibragimov, R. & Müller, U.K. (2010) t-Statistic based correlation and heterogeneity robust inference. Journal of Business and Economic Statistics 28, 453–468.Google Scholar
Jansson, M. (2004) The error in rejection probability of simple autocorrelation robust tests. Econometrica 72(3), 937–946.Google Scholar
Kelegian, H. & Prucha, I. (2007) HAC estimation in a spatial framework. Journal of Econometrics 140, 131–154.Google Scholar
Kelejian, H.H. & Prucha, I. (1999) A generalized moments estimator for the autoregressive parameter in a spatial model. International Economic Review 40, 509–533.Google Scholar
Kelejian, H.H. & Prucha, I. (2001) On the asymptotic distribution of the Moran I test statistic with applications. Journal of Econometrics 104, 219–257.Google Scholar
Kiefer, N.M. & Vogelsang, T.J. (2002) Heteroskedasticity-autocorrelation robust testing using bandwidth equal to sample size. Econometric Theory 18, 1350–1366.Google Scholar
Kiefer, N.M. & Vogelsang, T.J. (2005) A new asymptotic theory for heteroskedasticity-autocorrelation robust tests. Econometric Theory 21, 1130–1164.Google Scholar
Kim, M.S. & Sun, Y. (2011) Spatial heteroskedasticity and autocorrelation consistent estimation of covariance matrix. Journal of Econometrics 160, 349–371.Google Scholar
Lee, L.-F. (2004) Asymptotic distributions of quasi-maximum likelihood estimators for spatial econometric models. Econometrica 72, 1899–1926.Google Scholar
Lee, L.-F. (2007a) GMM and 2SLS estimation of mixed regressive, spatial autoregressive models. Journal of Econometrics 137, 489–514.Google Scholar
Lee, L.-F. (2007b) Identification and estimation of econometric models with group interactions, contextual factors and fixed effects. Journal of Econometrics 140, 333–374.Google Scholar
Liang, K.-Y. & Zeger, S. (1986) Longitudinal data analysis using generalized linear models. Biometrika 73(1), 13–22.Google Scholar
Newey, W.K. & West, K.D. (1987) A simple, positive semi-definite heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55(3), 703–708.Google Scholar
Sun, Y., Phillips, P.C.B., & Jin, S. (2008) Optimal bandwidth selection in heteroskedasticity-autocorrelation robust testing. Econometrica 76(1), 175–194.Google Scholar
Wooldridge, J.M. (2003) Cluster-sample methods in applied econometrics. American Economic Review 93(2), 133–188.Google Scholar