Combining Two Consistent Estimators
AbstractThis paper shows how a weighted average of a forward and reverse Jackknife IV estimator (JIVE) yields estimators that are robust against heteroscedasticity and many instruments. These estimators, called HFUL (Heteroscedasticity robust Fuller) and HLIM (Heteroskedasticity robust limited information maximum likelihood (LIML)) were introduced by Hausman et al. (2012), but without derivation. Combining consistent estimators is a theme that is associated with Jerry Hausman and, therefore, we present this derivation in this volume. Additionally, and in order to further understand and interpret HFUL and HLIM in the context of jackknife type variance ratio estimators, we show that a new variant of HLIM, under specific grouped data settings with dummy instruments, simplifies to the Bekker and van der Ploeg (2005) MM (method of moments) estimator.
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Bibliographic InfoPaper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 201310.
Length: 20 pages
Date of creation: 16 Jul 2013
Date of revision:
Publication status: Published in: Essays in Honor of Jerry Hausman: Advances in Econometrics, volume 29, Emerald, New York, 33-53.
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endogeneity; instrumental variables; jackknife estimation; many moments; Hausman (1978) test;
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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- 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, 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," Econometric Theory, 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.
- Daniel A. Ackerberg & Paul J. Devereux, 2009.
"Improved JIVE Estimators for Overidentified Linear Models with and without Heteroskedasticity,"
The Review of Economics and Statistics,
MIT Press, vol. 91(2), pages 351-362, May.
- Daniel A. Ackerberg & Paul J. Devereux, 2008. "Improved Jive Estimators for Overidentified Linear Models with and without Heteroskedasticity," Working Papers 200817, School Of Economics, University College Dublin.
- Ackerberg, Daniel & Devereux, Paul J., 2008. "Improved JIVE Estimators for Overidentified Linear Models with and without Heteroskedasticity," CEPR Discussion Papers 6926, C.E.P.R. Discussion Papers.
- Paul A. Bekker & Jan Ploeg, 2005. "Instrumental variable estimation based on grouped data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(3), pages 239-267.
- Phillips, Garry D A & Hale, C, 1977. "The Bias of Instrumental Variable Estimators of Simultaneous Equation Systems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(1), pages 219-28, February.
- Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, 06.
- Angrist, J D & Imbens, G W & Krueger, A B, 1999.
"Jackknife Instrumental Variables Estimation,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb..
- Blomquist, Soren & Dahlberg, Matz, 1999. "Small Sample Properties of LIML and Jackknife IV Estimators: Experiments with Weak Instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 69-88, Jan.-Feb..
- Donald, Stephen G. & Whitney Newey, 1999.
"Choosing the Number of Instruments,"
99-05, Massachusetts Institute of Technology (MIT), Department of Economics.
- Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
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