I am pleased to share the new module reg_sandwich, developed by Marcelo Tyszler, Beth Tipton, and myself, that computes cluster-robust variance estimators (a.k.a. sandwich estimators) for linear regressions as specified in the reg or areg commands. Unlike the built-in vce(cluster) option, reg_sandwich incorporate several adjustments for improved small-sample performance:
The package is available on SSC and thus can be installed by typing ssc install reg_sandwich. The development version of the package is available on Github (https://github.com/jepusto/clubSandwich-Stata). The methods are also available as an R package (https://cran.r-project.org/web/packages/clubSandwich/), which includes support for a broader range of models, including generalized linear models, hierarchical linear models, and meta-analysis/meta-regression.
Stata users may have heard of the bias-reduced linearization estimator from Imbens and Kolesaar (2016) or from Angrist and Pischke's (2009) book, Mostly Harmless Econometrics. Angrist and Pischke noted that the approach has problems with some common specifications, such as state-by-year panels with fixed effects in both dimensions. Young (2016) noted similar problems in applying the bias-reduced linearization estimator to a large corpus of estimated models. However, Pustejovsky and Tipton (2016) demonstrated that these problems are easily resolved and that tests based on bias-reduced linearization estimators substantially improve on standard cluster-robust variance estimators (including the versions used Stata) in terms of Type-I error control. The reg_sandwich module implements these tweaks to the bias-reduced linearization estimator, as well as novel methods for testing hypotheses involving multi-dimensional constraints.
References
- Variance-covariance estimators are based on a version of the bias-reduced linearization estimator proposed by Bell and McCaffrey (2002) and further developed by Tipton and Pustejovsky (2015) and Pustejovsky and Tipton (2016):
- Tests of single regression coefficients use Satterthwaite corrections.
- Tests of multiple-contrast hypotheses use Wald-type test statistics with an approximation to Hotelling's T-squared distribution, as proposed by Pustejovsky and Tipton (2016).
The package is available on SSC and thus can be installed by typing ssc install reg_sandwich. The development version of the package is available on Github (https://github.com/jepusto/clubSandwich-Stata). The methods are also available as an R package (https://cran.r-project.org/web/packages/clubSandwich/), which includes support for a broader range of models, including generalized linear models, hierarchical linear models, and meta-analysis/meta-regression.
Stata users may have heard of the bias-reduced linearization estimator from Imbens and Kolesaar (2016) or from Angrist and Pischke's (2009) book, Mostly Harmless Econometrics. Angrist and Pischke noted that the approach has problems with some common specifications, such as state-by-year panels with fixed effects in both dimensions. Young (2016) noted similar problems in applying the bias-reduced linearization estimator to a large corpus of estimated models. However, Pustejovsky and Tipton (2016) demonstrated that these problems are easily resolved and that tests based on bias-reduced linearization estimators substantially improve on standard cluster-robust variance estimators (including the versions used Stata) in terms of Type-I error control. The reg_sandwich module implements these tweaks to the bias-reduced linearization estimator, as well as novel methods for testing hypotheses involving multi-dimensional constraints.
References
- Angrist, J. D., & Pischke, J. (2009). Mostly harmless econometrics: An empiricist’s companion. Princeton, NJ: Princeton University Press.
- Bell, R. M., & McCaffrey, D. F. (2002). Bias reduction in standard errors for linear regression with multi-stage samples. Survey Methodology, 28(2), 169-181.
- Imbens, G. W., & Kolesar, M. (2016). Robust standard errors in small samples: Some practical advice. Review of Economics and Statistics, 98(4), 701-712.
- Pustejovsky, J. E. & Tipton, E. (2016). Small sample methods for cluster-robust variance estimation and hypothesis testing in fixed effects models. Journal of Business and Economic Statistics. In Press. arXiv version: 1601.01981 [stat.ME]
- Tipton, E., & Pustejovsky, J. E. (2015). Small-sample adjustments for tests of moderators and model fit using robust variance estimation in meta-regression. Journal of Educational and Behavioral Statistics, 40(6), 604-634. doi: 10.3102/1076998615606099
- Young, A. (2016). Improved, nearly exact, statistical inference with robust and clustered covariance matrices using effective degrees of freedom corrections. URL: http://personal.lse.ac.uk/YoungA/Improved.pdf
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