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Alternative Asymptotics and the Partially Linear Model with Many Regressors

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  • Matias D. Cattaneo

    ()
    (University of Michigan)

  • Michael Jansson

    ()
    (UC Berkeley and CREATES)

  • Whitney K. Newey

    ()
    (MIT Department of Economics)

Abstract

Non-standard distributional approximations have received considerable attention in recent years. They often provide more accurate approximations in small samples, and theoretical improvements in some cases. This paper shows that the seemingly unrelated "?many instruments asymptotics" ?and "?small bandwidth asymptotics" ?share a common structure, where the object determining the limiting distribution is a V-statistic with a remainder that is an asymptotically normal degenerate U-statistic. This general structure can be used to derive new results. We employ it to obtain a new asymptotic distribution of a series estimator of the partially linear model when the number of terms in the series approximation possibly grows as fast as the sample size. This alternative asymptotic experiment implies a larger asymptotic variance than usual. When the disturbance is homoskedastic, this larger variance is consistently estimated by any of the usual homoskedastic-consistent estimators provided a "?degrees-of-freedom correction?" is used. Under heteroskedasticity of unknown form, however, none of the commonly used heteroskedasticity-robust standard-error estimators are consistent under the "?many regressors asymptotics"?. We characterize the source of this failure, and we also propose a new standard-error estimator that is consistent under both heteroskedasticity and ?"many regressors asymptotics"?. A small simulation study shows that these new confidence intervals have reasonably good empirical size in finite samples.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-02.

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Length: 37
Date of creation: 20 Jan 2012
Date of revision:
Handle: RePEc:aah:create:2012-02

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Web page: http://www.econ.au.dk/afn/

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Keywords: partially linear model; many terms; adjusted variance.;

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References

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  1. Calhoun, Gray, 2010. "Hypothesis Testing in Linear Regression when K/N is Large," Staff General Research Papers, Iowa State University, Department of Economics 32216, Iowa State University, Department of Economics.
  2. Joshua D. Angrist & Guido W. Imbens & Alan Krueger, 1995. "Jackknife Instrumental Variables Estimation," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0172, National Bureau of Economic Research, Inc.
  3. Matias D. Cattaneo & Richard K. Crump & Michael Jansson, 2009. "Robust Data-Driven Inference for Density-Weighted Average Derivatives," CREATES Research Papers, School of Economics and Management, University of Aarhus 2009-46, School of Economics and Management, University of Aarhus.
  4. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  5. Norman R. Swanson & John C. Chao & Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen, 2011. "Asymptotic Distribution of JIVE in a Heteroskedastic IV Regression with Many Instruments," Departmental Working Papers, Rutgers University, Department of Economics 201110, Rutgers University, Department of Economics.
  6. Michal Kolesár & Raj Chetty & John N. Friedman & Edward L. Glaeser & Guido W. Imbens, 2011. "Identification and Inference with Many Invalid Instruments," NBER Working Papers 17519, National Bureau of Economic Research, Inc.
  7. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, Econometric Society, vol. 48(4), pages 817-38, May.
  8. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, Elsevier, vol. 79(1), pages 147-168, July.
  9. James G. MacKinnon & Halbert White, 1983. "Some Heteroskedasticity Consistent Covariance Matrix Estimators with Improved Finite Sample Properties," Working Papers, Queen's University, Department of Economics 537, Queen's University, Department of Economics.
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