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Accurately Sized Test Statistics with Misspecified Conditional Homoskedasticity

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  • Steigerwald, Douglas G
  • Erb, Jack

Abstract

We study the problem of obtaining accurately sized test statistics in finite samples for linear regression models where the error dependence is of unknown form. With an unknown dependence structure there is traditionally a trade-off between the maximum lag over which the correlation is estimated (the bandwidth) and the decision to introduce conditional heteroskedasticity. In consequence, the correlation at far lags is generally omitted and the resultant inflation of the empirical size of test statistics has long been recognized. To allow for correlation at far lags we study test statistics constructed under the possibly misspecified assumption of conditional homoskedasticity. To improve the accuracy of the test statistics, we employ the second-order asymptotic refinement in Rothenberg (1988) to determine critical values. We find substantial size improvements resulting from the second-order theory across a wide range of specifications, including substantial conditional heteroskedasticity. We also find that the size gains result in only moderate increases in the length of the associated confidence interval, which yields an increase in size-adjusted power. Finally, we note that the proposed test statistics do not require that the researcher specify the bandwidth or the kernel.

Suggested Citation

  • Steigerwald, Douglas G & Erb, Jack, 2007. "Accurately Sized Test Statistics with Misspecified Conditional Homoskedasticity," University of California at Santa Barbara, Economics Working Paper Series qt5rv0z5dz, Department of Economics, UC Santa Barbara.
  • Handle: RePEc:cdl:ucsbec:qt5rv0z5dz
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    References listed on IDEAS

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    1. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
    2. Hanno Lustig & Adrien Verdelhan, 2007. "The Cross Section of Foreign Currency Risk Premia and Consumption Growth Risk," American Economic Review, American Economic Association, vol. 97(1), pages 89-117, March.
    3. Peter C. B. Phillips & Yixiao Sun & Sainan Jin, 2006. "Spectral Density Estimation And Robust Hypothesis Testing Using Steep Origin Kernels Without Truncation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(3), pages 837-894, August.
    4. Rothenberg, Thomas J, 1988. "Approximate Power Functions for Some Robust Tests of Regression Coefficients," Econometrica, Econometric Society, vol. 56(5), pages 997-1019, September.
    5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    6. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    7. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
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