Alternative Asymptotics and the Partially Linear Model with Many Regressors
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.
|Date of creation:||20 Jan 2012|
|Date of revision:|
|Contact details of provider:|| Web page: http://www.econ.au.dk/afn/|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Guido M. Imbens & Jeffrey M. Wooldridge, 2008.
"Recent Developments in the Econometrics of Program Evaluation,"
NBER Working Papers
14251, National Bureau of Economic Research, Inc.
- Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
- Wooldridge, Jeffrey M. & Imbens, Guido, 2009. "Recent Developments in the Econometrics of Program Evaluation," Scholarly Articles 3043416, Harvard University Department of Economics.
- Guido Imbens & Jeffrey Wooldridge, 2008. "Recent developments in the econometrics of program evaluation," CeMMAP working papers CWP24/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Imbens, Guido W. & Wooldridge, Jeffrey M., 2008. "Recent Developments in the Econometrics of Program Evaluation," IZA Discussion Papers 3640, Institute for the Study of Labor (IZA).
- Javier Alvarez & Manuel Arellano, 2003.
"The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators,"
Econometric Society, vol. 71(4), pages 1121-1159, 07.
- 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-.
- 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, Department of Economics and Business Economics, Aarhus University.
- 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 821-41, May.
- Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
- Jinyong Hahn & Whitney Newey, 2004.
"Jackknife and Analytical Bias Reduction for Nonlinear Panel Models,"
Econometric Society, vol. 72(4), pages 1295-1319, 07.
- Jinyong Hahn & Whitney Newey, 2003. "Jackknife and analytical bias reduction for nonlinear panel models," CeMMAP working papers CWP17/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
- Joshua D. Angrist & Guido W. Imbens & Alan Krueger, 1995.
"Jackknife Instrumental Variables Estimation,"
NBER Technical Working Papers
0172, National Bureau of Economic Research, Inc.
- 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.
- Linton, Oliver, 1995.
"Second Order Approximation in the Partially Linear Regression Model,"
Econometric Society, vol. 63(5), pages 1079-1112, September.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Calhoun, Gray, 2011.
"Hypothesis testing in linear regression when k/n is large,"
Journal of Econometrics,
Elsevier, vol. 165(2), pages 163-174.
- Calhoun, Gray, 2010. "Hypothesis Testing in Linear Regression when K/N is Large," Staff General Research Papers 32216, Iowa State University, Department of Economics.
- Donald, S. G. & Newey, W. K., 1994. "Series Estimation of Semilinear Models," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 30-40, July.
- Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
- 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.
When requesting a correction, please mention this item's handle: RePEc:aah:create:2012-02. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.