Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain
AbstractWe 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.
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Bibliographic InfoArticle provided by Econometric Society in its journal Econometrica.
Volume (Year): 80 (2012)
Issue (Month): 6 (November)
Other versions of this item:
- A. Belloni & D. Chen & Victor Chernozhukov & Christian Hansen, 2010. "Sparse models and methods for optimal instruments with an application to eminent domain," CeMMAP working papers CWP31/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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- 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 & 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.
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