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Heteroscedasticity and Autocorrelation Robust F and t Tests in Stata

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  • Ye, Xiaoqing
  • Sun, Yixiao

Abstract

In this article, we consider time series OLS and IV regressions and introduce a new pair of commands, har and hart, which implement a more accu- rate class of heteroscedasticity and autocorrelation robust (HAR) F and t tests. These tests represent part of the recent progress on HAR inference. The F and t tests are based on the convenient F and t approximations and are more accurate than the conventional chi-squared and normal approximations. The underlying smoothing parameters are selected to target the type I and type II errors, the two fundamental objects in every hypothesis testing problem. The estimation com- mand har and the post-estimation test command hart allow for both kernel HAR variance estimators and orthonormal series HAR variance estimators. In addition, we introduce another pair of new commands, gmmhar and gmmhart which imple- ment the recently developed F and t tests in a two-step GMM framework. For this command we opt for the orthonormal series HAR variance estimator based on the Fourier bases, as it allows us to develop convenient F and t approxima- tions as in the first-step GMM framework. Finally, we present several examples to demonstrate the use of these commands.

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  • Ye, Xiaoqing & Sun, Yixiao, 2018. "Heteroscedasticity and Autocorrelation Robust F and t Tests in Stata," University of California at San Diego, Economics Working Paper Series qt0bb8d0s9, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt0bb8d0s9
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    References listed on IDEAS

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    1. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(1), pages 116-142, February.
    2. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2008. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Econometrica, Econometric Society, vol. 76(1), pages 175-194, January.
    3. Yixiao Sun, 2013. "A heteroskedasticity and autocorrelation robust F test using an orthonormal series variance estimator," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 1-26, February.
    4. Kim, Min Seong & Sun, Yixiao, 2013. "Heteroskedasticity and spatiotemporal dependence robust inference for linear panel models with fixed effects," Journal of Econometrics, Elsevier, vol. 177(1), pages 85-108.
    5. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    6. Sun, Yixiao, 2011. "Robust trend inference with series variance estimator and testing-optimal smoothing parameter," Journal of Econometrics, Elsevier, vol. 164(2), pages 345-366, October.
    7. 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.
    8. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2002. "Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal To Sample Size," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1350-1366, December.
    9. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    10. Yixiao Sun & Min Seong Kim, 2015. "Asymptotic F-Test in a GMM Framework with Cross-Sectional Dependence," The Review of Economics and Statistics, MIT Press, vol. 97(1), pages 210-233, March.
    11. Michael Jansson, 2004. "The Error in Rejection Probability of Simple Autocorrelation Robust Tests," Econometrica, Econometric Society, vol. 72(3), pages 937-946, May.
    12. 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.
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    14. Sun, Yixiao & Kim, Min Seong, 2012. "Simple and powerful GMM over-identification tests with accurate size," Journal of Econometrics, Elsevier, vol. 166(2), pages 267-281.
    15. Sun, Yixiao, 2014. "Let’s fix it: Fixed-b asymptotics versus small-b asymptotics in heteroskedasticity and autocorrelation robust inference," Journal of Econometrics, Elsevier, vol. 178(P3), pages 659-677.
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    1. Artur Doshchyn, 2023. "Sinking Ships: Illiquidity and the Predictability of Returns on Real Assets in Recessions," Economics Series Working Papers 1028, University of Oxford, Department of Economics.
    2. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.

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