Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Robust Inference in Panel Data Models: Some Effects of Heteroskedasticity and Leveraged Data in Small Samples (2312.17676v1)

Published 29 Dec 2023 in econ.EM and stat.CO

Abstract: With the violation of the assumption of homoskedasticity, least squares estimators of the variance become inefficient and statistical inference conducted with invalid standard errors leads to misleading rejection rates. Despite a vast cross-sectional literature on the downward bias of robust standard errors, the problem is not extensively covered in the panel data framework. We investigate the consequences of the simultaneous presence of small sample size, heteroskedasticity and data points that exhibit extreme values in the covariates ('good leverage points') on the statistical inference. Focusing on one-way linear panel data models, we examine asymptotic and finite sample properties of a battery of heteroskedasticity-consistent estimators using Monte Carlo simulations. We also propose a hybrid estimator of the variance-covariance matrix. Results show that conventional standard errors are always dominated by more conservative estimators of the variance, especially in small samples. In addition, all types of HC standard errors have excellent performances in terms of size and power tests under homoskedasticity.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (37)
  1. Arellano, M. (1987). Practitioners’ corner: Computing robust standard errors for within-groups estimators. Oxford bulletin of Economics and Statistics, 49(4):431–434.
  2. Influence diagnostics for linear longitudinal models. Journal of the American Statistical Association, 92(439):999–1005.
  3. Fast leave-one-out methods for inference, model selection, and diagnostic checking. The Stata Journal, 20(4):785–804.
  4. How much should we trust differences-in-differences estimates? The Quarterly journal of economics, 119(1):249–275.
  5. Robust estimators for the fixed effects panel data model. The econometrics journal, 10(3):521–540.
  6. Robust inference with multiway clustering. Journal of Business & Economic Statistics, 29(2):238–249.
  7. Microeconometrics: methods and applications. Cambridge university press.
  8. Two-step estimation and inference with possibly many included covariates. The Review of Economic Studies, 86(3):1095–1122.
  9. Inference in linear regression models with many covariates and heteroscedasticity. Journal of the American Statistical Association, 113(523):1350–1361.
  10. The bias of a heteroskedasticity consistent covariance matrix estimator. Econometrica: Journal of the Econometric Society, pages 1217–1222.
  11. Cribari-Neto, F. (2004). Asymptotic inference under heteroskedasticity of unknown form. Computational Statistics & Data Analysis, 45(2):215–233.
  12. A new heteroskedasticity-consistent covariance matrix estimator for the linear regression model. AStA Advances in Statistical Analysis, 95(2):129–146.
  13. Inference under heteroskedasticity and leveraged data. Communications in Statistics - Theory and Methods, 36(10):1877–1888.
  14. Estimation and inference in econometrics. OUP Catalogue.
  15. Efron, B. (1982). The jackknife, the bootstrap, and other resampling plans, volume 38. Siam.
  16. Eicker, F. (1967). Limit theorems for regressions with unequal and dependent errors. In Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, volume 1, pages 59–82.
  17. Bootstrapping an econometric model: Some empirical results. Journal of Business & Economic Statistics, 2(2):150–158.
  18. Godfrey, L. (2006). Tests for regression models with heteroskedasticity of unknown form. Computational Statistics & Data Analysis, 50(10):2715–2733.
  19. Hansen, B. E. (2019). Econometrics. Unpublished manuscript. Latest version: February 2019.
  20. Hansen, C. B. (2007). Asymptotic properties of a robust variance matrix estimator for panel data when t is large. Journal of Econometrics, 141(2):597–620.
  21. Using heteroskedasticity-consistent standard error estimators in ols regression: An introduction and software implementation. Behavior research methods, 39(4):709–722.
  22. Hendry, D. F. (1984). Monte carlo experimentation in econometrics. Handbook of econometrics, 2:937–976.
  23. Hinkley, D. V. (1977). Jackknifing in unbalanced situations. Technometrics, 19(3):285–292.
  24. Estimating heteroscedastic variances in linear models. Journal of the American Statistical Association, 70(350):380–385.
  25. Huber, P. J. et al. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. In Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, volume 1, pages 221–233. University of California Press.
  26. Kezdi, G. (2003). Robust standard error estimation in fixed-effects panel models. Available at SSRN 596988.
  27. Kiviet, J. F. et al. (2012). Monte Carlo simulation for econometricians. now publishers.
  28. Using heteroscedasticity consistent standard errors in the linear regression model. The American Statistician, 54(3):217–224.
  29. MacKinnon, J. G. (2013). Thirty years of heteroskedasticity-robust inference. In Recent advances and future directions in causality, prediction, and specification analysis, pages 437–461. Springer.
  30. Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties. Journal of econometrics, 29(3):305–325.
  31. Silva, J. S. (2001). Influence diagnostics and estimation algorithms for powell’s scls. Journal of Business & Economic Statistics, 19(1):55–62.
  32. Heteroskedasticity-consistent covariance matrix estimators in small samples with high leverage points. Theoretical Economics Letters, 6(04):658.
  33. Heteroskedasticity-robust standard errors for fixed effects panel data regression. Econometrica, 76(1):155–174.
  34. Robust regression in stata. The Stata Journal, 9(3):439–453.
  35. Verbeek, M. (2008). A guide to modern econometrics. John Wiley & Sons.
  36. White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica: Journal of the Econometric Society, pages 817–838.
  37. White, H. (1984). Asymptotic theory for Econometricians. Academic press.

Summary

We haven't generated a summary for this paper yet.

X Twitter Logo Streamline Icon: https://streamlinehq.com