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Robust Inference in High Dimensional Linear Model with Cluster Dependence

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  • Ng Cheuk Fai

Abstract

Cluster standard error (Liang and Zeger, 1986) is widely used by empirical researchers to account for cluster dependence in linear model. It is well known that this standard error is biased. We show that the bias does not vanish under high dimensional asymptotics by revisiting Chesher and Jewitt (1987)'s approach. An alternative leave-cluster-out crossfit (LCOC) estimator that is unbiased, consistent and robust to cluster dependence is provided under high dimensional setting introduced by Cattaneo, Jansson and Newey (2018). Since LCOC estimator nests the leave-one-out crossfit estimator of Kline, Saggio and Solvsten (2019), the two papers are unified. Monte Carlo comparisons are provided to give insights on its finite sample properties. The LCOC estimator is then applied to Angrist and Lavy's (2009) study of the effects of high school achievement award and Donohue III and Levitt's (2001) study of the impact of abortion on crime.

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  • Ng Cheuk Fai, 2022. "Robust Inference in High Dimensional Linear Model with Cluster Dependence," Papers 2212.05554, arXiv.org.
    • Handle: RePEc:arx:papers:2212.05554
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    1. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "High-Dimensional Methods and Inference on Structural and Treatment Effects," Journal of Economic Perspectives, American Economic Association, vol. 28(2), pages 29-50, Spring.
    2. Guido W. Imbens & Michal Kolesár, 2016. "Robust Standard Errors in Small Samples: Some Practical Advice," The Review of Economics and Statistics, MIT Press, vol. 98(4), pages 701-712, October.
    3. John J. Donohue III & Steven D. Levitt, 2001. "The Impact of Legalized Abortion on Crime," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(2), pages 379-420.
    4. Anatolyev, Stanislav, 2018. "Almost unbiased variance estimation in linear regressions with many covariates," Economics Letters, Elsevier, vol. 169(C), pages 20-23.
    5. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2018. "Inference in Linear Regression Models with Many Covariates and Heteroscedasticity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1350-1361, July.
    6. Chesher, Andrew & Austin, Gerard, 1991. "The finite-sample distributions of heteroskedasticity robust Wald statistics," Journal of Econometrics, Elsevier, vol. 47(1), pages 153-173, January.
    7. Joshua Angrist & Victor Lavy, 2009. "The Effects of High Stakes High School Achievement Awards: Evidence from a Randomized Trial," American Economic Review, American Economic Association, vol. 99(4), pages 1384-1414, September.
    8. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-1222, September.
    9. William Rogers, 1994. "Regression standard errors in clustered samples," Stata Technical Bulletin, StataCorp LP, vol. 3(13).
    10. Arellano, M, 1987. "Computing Robust Standard Errors for Within-Groups Estimators," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 49(4), pages 431-434, November.
    11. Patrick Kline & Raffaele Saggio & Mikkel Sølvsten, 2020. "Leave‐Out Estimation of Variance Components," Econometrica, Econometric Society, vol. 88(5), pages 1859-1898, September.
    12. Bester, C. Alan & Conley, Timothy G. & Hansen, Christian B., 2011. "Inference with dependent data using cluster covariance estimators," Journal of Econometrics, Elsevier, vol. 165(2), pages 137-151.
    13. Koen Jochmans, 2022. "Heteroscedasticity-Robust Inference in Linear Regression Models With Many Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 887-896, April.
    14. Valentin Verdier, 2020. "Estimation and Inference for Linear Models with Two-Way Fixed Effects and Sparsely Matched Data," The Review of Economics and Statistics, MIT Press, vol. 102(1), pages 1-16, March.
    15. A. Colin Cameron & Douglas L. Miller, 2015. "A Practitioner’s Guide to Cluster-Robust Inference," Journal of Human Resources, University of Wisconsin Press, vol. 50(2), pages 317-372.
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