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Alternative Asymptotics and the Partially Linear Model with Many Regressors

Listed author(s):
  • Matias D. Cattaneo

    ()

    (University of Michigan)

  • Michael Jansson

    ()

    (UC Berkeley and CREATES)

  • Whitney K. Newey

    ()

    (MIT Department of Economics)

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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File URL: ftp://ftp.econ.au.dk/creates/rp/12/rp12_02.pdf
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Paper provided by Department of Economics and Business Economics, Aarhus University in its series CREATES Research Papers with number 2012-02.

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Length: 37
Date of creation: 20 Jan 2012
Handle: RePEc:aah:create:2012-02
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Morimune, Kimio, 1983. "Approximate Distributions of k-Class Estimators When the Degree of Overidentifiability Is Large Compared with the Sample Size," Econometrica, Econometric Society, vol. 51(3), pages 821-841, May.
  2. Kolesar, Michal & Chetty, Raj & Friedman, John & Glaeser, Edward Ludwig & Imbens, Guido, 2015. "Identification and Inference With Many Invalid Instruments," Scholarly Articles 27769098, Harvard University Department of Economics.
  3. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
  4. Calhoun, Gray, 2011. "Hypothesis testing in linear regression when k/n is large," Journal of Econometrics, Elsevier, vol. 165(2), pages 163-174.
  5. James G. MacKinnon & Halbert White, 1983. "Some Heteroskedasticity Consistent Covariance Matrix Estimators with Improved Finite Sample Properties," Working Papers 537, Queen's University, Department of Economics.
  6. 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 201110, Rutgers University, Department of Economics.
  7. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
  8. Alvarez, J. & Arellano, M., 1998. "The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators," Papers 9808, Centro de Estudios Monetarios Y Financieros-.
  9. Oliver Linton, 1993. "Second Order Approximation in the Partially Linear Regression Model," Cowles Foundation Discussion Papers 1065, Cowles Foundation for Research in Economics, Yale University.
  10. Wooldridge, Jeffrey M. & Imbens, Guido, 2009. "Recent Developments in the Econometrics of Program Evaluation," Scholarly Articles 3043416, Harvard University Department of Economics.
  11. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2010. "Robust Data-Driven Inference for Density-Weighted Average Derivatives," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1070-1083.
  12. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  13. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2012. "n-uniformly consistent density estimation in nonparametric regression models," Journal of Econometrics, Elsevier, vol. 167(2), pages 305-316.
  14. Joshua D. Angrist & Guido W. Imbens & Alan Krueger, 1995. "Jackknife Instrumental Variables Estimation," NBER Technical Working Papers 0172, National Bureau of Economic Research, Inc.
  15. Donald, S. G. & Newey, W. K., 1994. "Series Estimation of Semilinear Models," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 30-40, July.
  16. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, 07.
  17. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2015. "Some new asymptotic theory for least squares series: Pointwise and uniform results," Journal of Econometrics, Elsevier, vol. 186(2), pages 345-366.
  18. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
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