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

Author

Listed:
  • Alexandre Belloni

    (Institute for Fiscal Studies)

  • D. Chen

    (Institute for Fiscal Studies)

  • Victor Chernozhukov

    (Institute for Fiscal Studies and MIT)

  • 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.

Suggested Citation

  • Alexandre 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.
    • Handle: RePEc:ifs:cemmap:31/10
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    File URL: http://cemmap.ifs.org.uk/wps/cwp3110.pdf
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    References listed on IDEAS

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