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

Alexandre Belloni, D. Chen, Victor Chernozhukov and Christian Hansen
Additional contact information
Alexandre Belloni: Institute for Fiscal Studies
D. Chen: Institute for Fiscal Studies
Christian Hansen: Institute for Fiscal Studies and Chicago GSB

No CWP31/10, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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.

Date: 2010-10-22
New Economics Papers: this item is included in nep-ecm
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Related works:
Working Paper: Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain (2015)
Journal Article: Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain (2012)
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