Alternative Asymptotics and the Partially Linear Model with Many Regressors
AbstractNon-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 InfoPaper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-02.
Date of creation: 20 Jan 2012
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partially linear model; many terms; adjusted variance.;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
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- White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
- 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.
- Matias D. Cattaneo & Richard K. Crump & Michael Jansson, 2009. "Robust Data-Driven Inference for Density-Weighted Average Derivatives," CREATES Research Papers 2009-46, School of Economics and Management, University of Aarhus.
- James G. MacKinnon & Halbert White, 1983.
"Some Heteroskedasticity Consistent Covariance Matrix Estimators with Improved Finite Sample Properties,"
537, Queen's University, Department of Economics.
- MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
- 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.
- Joshua D. Angrist & Guido W. Imbens & Alan Krueger, 1995.
"Jackknife Instrumental Variables Estimation,"
NBER Technical Working Papers
0172, National Bureau of Economic Research, Inc.
- repec:cup:cbooks:9780521496032 is not listed on IDEAS
- Calhoun, Gray, 2010. "Hypothesis Testing in Linear Regression when K/N is Large," Staff General Research Papers 32216, Iowa State University, Department of Economics.
- Chao, John C. & Swanson, Norman R. & Hausman, Jerry A. & Newey, Whitney K. & Woutersen, Tiemen, 2012.
"Asymptotic Distribution Of Jive In A Heteroskedastic Iv Regression With Many Instruments,"
Cambridge University Press, vol. 28(01), pages 42-86, February.
- Chao & Swanson & Hausman & Newey & Woutersen, 2010. "Asymptotic Distribution of JIVE in a Heteroskedastic IV Regression with Many Instruments," Economics Working Paper Archive 567, The Johns Hopkins University,Department of Economics.
- 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.
- Calhoun, Gray, 2011. "Hypothesis testing in linear regression when k/n is large," Journal of Econometrics, Elsevier, vol. 165(2), pages 163-174.
- Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
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