High-dimensional instrumental variables regression and confidence sets
AbstractWe propose an instrumental variables method for estimation in linear models with endogenous regressors in the high-dimensional setting where the sample size n can be smaller than the number of possible regressors K, and L>=K instruments. We allow for heteroscedasticity and we do not need a prior knowledge of variances of the errors. We suggest a new procedure called the STIV (Self Tuning Instrumental Variables) estimator, which is realized as a solution of a conic optimization program. The main results of the paper are upper bounds on the estimation error of the vector of coefficients in l_p-norms for 1
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Date of creation: 01 Sep 2011
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Instrumental variables ; Sparsity ; STIV estimator ; Endogeneity ; High-dimensional regression ; Conic programming ; Optimal instruments ; Hereroscedasticity ; Confidence intervals ; Non-Gaussian errors ; Variable selection ; Unknown variance ; Sign consistency;
Other versions of this item:
- Eric Gautier & Alexandre Tsybakov, 2011. "High-Dimensional Instrumental Variables Regression and Confidence Sets," Working Papers 2011-13, Centre de Recherche en Economie et Statistique.
- NEP-ALL-2011-05-24 (All new papers)
- NEP-ECM-2011-05-24 (Econometrics)
- NEP-ORE-2011-05-24 (Operations Research)
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- Carrasco, Marine & Florens, Jean-Pierre, 2000.
"Generalisation of GMM to a Continuum of Moment Conditions,"
Open Access publications from University of Toulouse 1 Capitole
http://neeo.univ-tlse1.fr, University of Toulouse 1 Capitole.
- Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December.
- Okui, Ryo, 2011. "Instrumental variable estimation in the presence of many moment conditions," Journal of Econometrics, Elsevier, vol. 165(1), pages 70-86.
- Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
- Mehmet Caner, 2006.
"A lasso type gmm estimator,"
210, University of Pittsburgh, Department of Economics, revised Jan 2006.
- Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
- Norman R. Swanson & John C. Chao & Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen, 2011.
"Instrumental Variable Estimation with Heteroskedasticity and Many Instruments,"
Departmental Working Papers
201111, Rutgers University, Department of Economics.
- Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen & John C. Chao & Norman R. Swanson, 2012. "Instrumental variable estimation with heteroskedasticity and many instruments," Quantitative Economics, Econometric Society, vol. 3(2), pages 211-255, 07.
- Jerry Hausman & Whitney Newey & Tiemen Woutersen & John Chao & Norman Swanson, 2007. "Instrumental variable estimation with heteroskedasticity and many instruments," CeMMAP working papers CWP22/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Hausman & Newey & Woutersen & Chao & Swanson, 2009. "Instrumental Variable Estimation with Heteroskedasticity and Many Instruments," Economics Working Paper Archive 566, The Johns Hopkins University,Department of Economics.
- Alastair Hall & Fernanda P. M. Peixe, 2000.
"A Consistent Method for the Selection of Relevant Instruments,"
Econometric Society World Congress 2000 Contributed Papers
0790, Econometric Society.
- Alastair Hall & Fernanda Peixe, 2003. "A Consistent Method for the Selection of Relevant Instruments," Econometric Reviews, Taylor and Francis Journals, vol. 22(3), pages 269-287.
- 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.
- Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Central limit theorems and multiplier bootstrap when p is much larger than," CeMMAP working papers CWP45/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Xu Cheng & Zhipeng Liao, 2012. "Select the Valid and Relevant Moments: A One-Step Procedure for GMM with Many Moments," PIER Working Paper Archive 12-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference for high-dimensional sparse econometric models," CeMMAP working papers CWP41/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Zhu, Ying, 2013. "Sparse Linear Models and Two-Stage Estimation in High-Dimensional Settings with Possibly Many Endogenous Regressors," MPRA Paper 49846, University Library of Munich, Germany.
- Aman Ullah & Huansha Wang, 2013. "Parametric and Nonparametric Frequentist Model Selection and Model Averaging," Econometrics, MDPI, Open Access Journal, vol. 1(2), pages 157-179, September.
- Fan, Jianqing & Liao, Yuan, 2012. "Endogeneity in ultrahigh dimension," MPRA Paper 38698, University Library of Munich, Germany.
- Eric Gautier & Alexandre Tsybakov, 2013.
"Pivotal estimation in high-dimensional regression via linear programming,"
1303.7092, arXiv.org, revised Apr 2013.
- Eric Gautier & Alexandre Tsybakov, 2013. "Pivotal estimation in high-dimensional regression via linear programming," Working Papers hal-00805556, HAL.
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