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
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by HAL in its series Working Papers with number hal-00591732.
Date of creation: 01 Sep 2011
Date of revision:
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00591732/en/
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/
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)
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.:
- Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
- Alastair Hall & Fernanda Peixe, 2003.
"A Consistent Method for the Selection of Relevant Instruments,"
Taylor & Francis Journals, vol. 22(3), pages 269-287.
- 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.
- 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.
- 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.
- 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.
- 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.
- Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
- 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.
- Mehmet Caner, 2006.
"A lasso type gmm estimator,"
210, University of Pittsburgh, Department of Economics, revised Jan 2006.
- Okui, Ryo, 2011. "Instrumental variable estimation in the presence of many moment conditions," Journal of Econometrics, Elsevier, vol. 165(1), pages 70-86.
- 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.
- Fan, Jianqing & Liao, Yuan, 2012. "Endogeneity in ultrahigh dimension," MPRA Paper 38698, University Library of Munich, Germany.
- 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.
- Alexandre Belloni & Victor Chernozhukov & Lie Wang, 2013. "Pivotal estimation via square-root lasso in nonparametric regression," CeMMAP working papers CWP62/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Eric Gautier & Alexandre Tsybakov, 2013.
"Pivotal estimation in high-dimensional regression via linear programming,"
- Eric Gautier & Alexandre Tsybakov, 2013. "Pivotal estimation in high-dimensional regression via linear programming," Papers 1303.7092, arXiv.org, revised Apr 2013.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).
If references are entirely missing, you can add them using this form.