Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain
Date: First version: June 2009, this version October 28, 2010. Preliminary results of this paper were FIRST presented at Chernozhukov's invited Cowles Foundation lecture at the Northern American meetings of the Econometric society in June of 2009. We thank seminar participants at Brown, Columbi...
| Main Authors: | , , , |
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| Format: | Working Paper |
| Language: | en_US |
| Published: |
Cambridge, MA: Department of Economics, Massachusetts Institute of Technology
2011
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| Online Access: | http://hdl.handle.net/1721.1/65157 |
| _version_ | 1826214392807555072 |
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| author | Belloni, Alexandre Chen, Daniel Chernozhukov, Victor Hansen, Christian |
| author_facet | Belloni, Alexandre Chen, Daniel Chernozhukov, Victor Hansen, Christian |
| author_sort | Belloni, Alexandre |
| collection | MIT |
| description | Date: First version: June 2009, this version October 28, 2010. Preliminary results of this paper were FIRST presented at Chernozhukov's invited Cowles Foundation lecture at the Northern American meetings of the Econometric society in June of 2009. We thank seminar participants at Brown, Columbia, Harvard-MIT, the Dutch Econometric Study Group, Fuqua School of Business, and NYU for helpful comments. We also thank Denis Chetverikov, JB Doyle, and Joonhwan Lee for thorough reading of this paper and helpful feedback. |
| first_indexed | 2024-09-23T16:04:42Z |
| format | Working Paper |
| id | mit-1721.1/65157 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:04:42Z |
| publishDate | 2011 |
| publisher | Cambridge, MA: Department of Economics, Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/651572019-04-12T20:57:13Z Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain Belloni, Alexandre Chen, Daniel Chernozhukov, Victor Hansen, Christian Instrumental Variables Optimal Instruments LASSO Post-LASSO Sparsity Eminent Domain Data-Driven Penalty Heteroscedasticity non-Gaussian errors moderate deviations for self-normalized sums Date: First version: June 2009, this version October 28, 2010. Preliminary results of this paper were FIRST presented at Chernozhukov's invited Cowles Foundation lecture at the Northern American meetings of the Econometric society in June of 2009. We thank seminar participants at Brown, Columbia, Harvard-MIT, the Dutch Econometric Study Group, Fuqua School of Business, and NYU for helpful comments. We also thank Denis Chetverikov, JB Doyle, and Joonhwan Lee for thorough reading of this paper and helpful feedback. 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(n1=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. 2011-08-15T20:46:55Z 2011-08-15T20:46:55Z 2011-07-12 Working Paper http://hdl.handle.net/1721.1/65157 en_US Working paper (Massachusetts Institute of Technology, Department of Economics);11-19 An error occurred on the license name. An error occurred getting the license - uri. application/pdf Cambridge, MA: Department of Economics, Massachusetts Institute of Technology |
| spellingShingle | Instrumental Variables Optimal Instruments LASSO Post-LASSO Sparsity Eminent Domain Data-Driven Penalty Heteroscedasticity non-Gaussian errors moderate deviations for self-normalized sums Belloni, Alexandre Chen, Daniel Chernozhukov, Victor Hansen, Christian Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain |
| title | Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain |
| title_full | Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain |
| title_fullStr | Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain |
| title_full_unstemmed | Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain |
| title_short | Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain |
| title_sort | sparse models and methods for optimal instruments with an application to eminent domain |
| topic | Instrumental Variables Optimal Instruments LASSO Post-LASSO Sparsity Eminent Domain Data-Driven Penalty Heteroscedasticity non-Gaussian errors moderate deviations for self-normalized sums |
| url | http://hdl.handle.net/1721.1/65157 |
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