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

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  • Bester, C. Alan
  • Conley, Timothy G.
  • Hansen, Christian B.
  • Vogelsang, Timothy J.

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.

Suggested Citation

  • Bester, C. Alan & Conley, Timothy G. & Hansen, Christian B. & Vogelsang, Timothy J., 2016. "FIXED-b ASYMPTOTICS FOR SPATIALLY DEPENDENT ROBUST NONPARAMETRIC COVARIANCE MATRIX ESTIMATORS," Econometric Theory, Cambridge University Press, vol. 32(1), pages 154-186, February.
    • Handle: RePEc:cup:etheor:v:32:y:2016:i:01:p:154-186_00
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    Cited by:

    1. Timothy G. Conley & Sílvia Gonçalves & Min Seong Kim & Benoit Perron, 2023. "Bootstrap inference under cross‐sectional dependence," Quantitative Economics, Econometric Society, vol. 14(2), pages 511-569, May.
    2. Ulrich K. Müller & Mark W. Watson, 2021. "Spatial Correlation Robust Inference," Working Papers 2021-61, Princeton University. Economics Department..
    3. J. Hidalgo & M. Schafgans, 2020. "Inference without smoothing for large panels with cross-sectional and temporal dependence," Papers 2006.14409, arXiv.org.
    4. Kim, Min Seong & Sun, Yixiao & Yang, Jingjing, 2017. "A fixed-bandwidth view of the pre-asymptotic inference for kernel smoothing with time series data," Journal of Econometrics, Elsevier, vol. 197(2), pages 298-322.
    5. Hwang, Jungbin & Sun, Yixiao, 2017. "Asymptotic F and t tests in an efficient GMM setting," Journal of Econometrics, Elsevier, vol. 198(2), pages 277-295.
    6. Gupta, Abhimanyu, 2018. "Autoregressive spatial spectral estimates," Journal of Econometrics, Elsevier, vol. 203(1), pages 80-95.
    7. Hwang, Jungbin & Sun, Yixiao, 2018. "Should we go one step further? An accurate comparison of one-step and two-step procedures in a generalized method of moments framework," Journal of Econometrics, Elsevier, vol. 207(2), pages 381-405.
    8. David Powell, 2017. "Inference with Correlated Clusters," Working Papers WR-1137-1, RAND Corporation.
    9. Eyal Frank & Anant Sudarshan, 2024. "The Social Costs of Keystone Species Collapse: Evidence from the Decline of Vultures in India," American Economic Review, American Economic Association, vol. 114(10), pages 3007-3040, October.
    10. Abhimanyu Gupta & Javier Hidalgo, 2020. "Nonparametric prediction with spatial data," Papers 2008.04269, arXiv.org, revised Nov 2021.
    11. Xiaoqing Ye & Yixiao Sun, 2018. "Heteroskedasticity- and autocorrelation-robust F and t tests in Stata," Stata Journal, StataCorp LP, vol. 18(4), pages 951-980, December.
    12. Kaicheng Chen & Timothy J. Vogelsang, 2023. "Fixed-b Asymptotics for Panel Models with Two-Way Clustering," Papers 2309.08707, arXiv.org, revised Aug 2024.
    13. Bartalotti Otávio, 2019. "Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-26, January.
    14. Ulrich K. Muller & Mark W. Watson, 2021. "Spatial Correlation Robust Inference," Papers 2102.09353, arXiv.org.
    15. Hanan G. Jacoby, 2016. "Food Prices, Wages, And Welfare In Rural India," Economic Inquiry, Western Economic Association International, vol. 54(1), pages 159-176, January.
    16. Min Seong Kim, 2021. "Robust Inference for Diffusion-Index Forecasts with Cross-Sectionally Dependent Data," Working papers 2021-04, University of Connecticut, Department of Economics.
    17. Carolina Caetano & Gregorio Caetano & Hao Fe & Eric R. Nielsen, 2021. "A Dummy Test of Identification in Models with Bunching," Finance and Economics Discussion Series 2021-068, Board of Governors of the Federal Reserve System (U.S.).
    18. Eduardo A. Souza-Rodrigues, 2016. "Nonparametric Regression with Common Shocks," Econometrics, MDPI, vol. 4(3), pages 1-17, September.

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