Advanced Search
MyIDEAS: Login to save this paper or follow this series

Sparse models and methods for optimal instruments with an application to eminent domain

Contents:

Author Info

  • A. Belloni
  • D. Chen
  • Victor Chernozhukov

    ()
    (Institute for Fiscal Studies and Massachusetts Institute of Technology)

  • Christian Hansen

    (Institute for Fiscal Studies and Chicago GSB)

Abstract

We develop results for the use of LASSO and Post-LASSO methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p, that apply even when p is much larger than the sample size, n. We rigorously develop asymptotic distribution and inference theory for the resulting IV estimators and provide conditions under which these estimators are asymptotically oracle-efficient. In simulation experiments, the LASSO-based IV estimator with a data-driven penalty performs well compared to recently advocated many-instrument-robust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the LASSO-based IV estimator substantially reduces estimated standard errors allowing one to draw much more precise conclusions about the economic effects of these decisions. Optimal instruments are conditional expectations; and in developing the IV results, we also establish a series of new results for LASSO and Post-LASSO estimators of non-parametric conditional expectation functions which are of independent theoretical and practical interest. Specifically, we develop the asymptotic theory for these estimators that allows for non-Gaussian, heteroscedastic disturbances, which is important for econometric applications. By innovatively using moderate deviation theory for self-normalized sums, we provide convergence rates for these estimators that are as sharp as in the homoscedastic Gaussian case under the weak condition that log p = o(n 1/3 ). Moreover, as a practical innovation, we provide a fully data-driven method for choosing the user-specified penalty that must be provided in obtaining LASSO and Post-LASSO estimates and establish its asymptotic validity under non-Gaussian, heteroscedastic disturbances.

Download Info

If 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.
File URL: http://cemmap.ifs.org.uk/wps/cwp3110.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP31/10.

as in new window
Length:
Date of creation: Oct 2010
Date of revision:
Handle: RePEc:ifs:cemmap:31/10

Contact details of provider:
Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
Phone: (+44) 020 7291 4800
Fax: (+44) 020 7323 4780
Email:
Web page: http://cemmap.ifs.org.uk
More information through EDIRC

Order Information:
Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
Email:

Related research

Keywords:

Other versions of this item:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
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.:
as in new window
  1. Frank Kleibergen, 2001. "Testing Parameters in GMM without Assuming that they are identified," Tinbergen Institute Discussion Papers 01-067/4, Tinbergen Institute.
  2. 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.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. 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.
  2. 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.
  3. Eric Gautier & Alexandre B, Tsybakov, 2013. "Pivotal Estimation in High-Dimensional Regression via Linear Programming," Working Papers 2013-40, Centre de Recherche en Economie et Statistique.
  4. Mehmet Caner & Anders Bredahl Kock, 2013. "Oracle Inequalities for Convex Loss Functions with Non-Linear Targets," CREATES Research Papers 2013-51, School of Economics and Management, University of Aarhus.
  5. Alexandre Belloni & Victor Chernozhukov & Iván Fernández-Val & Christian Hansen, 2013. "Program evaluation with high-dimensional data," CeMMAP working papers CWP57/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2012. "Inference on treatment effects after selection amongst high-dimensional controls," CeMMAP working papers CWP10/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Alexandre Belloni & Victor Chernozhukov & Ying Wei, 2013. "Honest confidence regions for a regression parameter in logistic regression with a large number of controls," CeMMAP working papers CWP67/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2013. "Uniform post selection inference for LAD regression models," CeMMAP working papers CWP24/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  9. Guy Tchuente & Marine Carrasco, 2013. "Regularized LIML for many instruments," CIRANO Working Papers 2013s-20, CIRANO.
  10. Guy Tchuente & Marine Carrasco, 2013. "Efficient estimation with many weak instruments using regularization techniques," CIRANO Working Papers 2013s-21, CIRANO.
  11. 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.
  12. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2013. "Uniform post selection inference for LAD regression and other z-estimation problems," CeMMAP working papers CWP74/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  13. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2013. "Robust inference in high-dimensional approximately sparse quantile regression models," CeMMAP working papers CWP70/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:ifs:cemmap:31/10. 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: (Stephanie Seavers).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.