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LASSO Methods for Gaussian Instrumental Variables Models

Author

Listed:
  • Alexandre Belloni
  • Victor Chernozhukov
  • Christian Hansen
Abstract
In this note, we propose to use sparse methods (e.g. LASSO, Post-LASSO, sqrt-LASSO, and Post-sqrt-LASSO) to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments in the canonical Gaussian case. The methods apply even when the number of instruments is much larger than the sample size. We derive asymptotic distributions for the resulting IV estimators and provide conditions under which these sparsity-based IV estimators are asymptotically oracle-efficient. In simulation experiments, a sparsity-based IV estimator with a data-driven penalty performs well compared to recently advocated many-instrument-robust procedures. We illustrate the procedure in an empirical example using the Angrist and Krueger (1991) schooling data.

Suggested Citation

  • Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2010. "LASSO Methods for Gaussian Instrumental Variables Models," Papers 1012.1297, arXiv.org, revised Feb 2011.
    • Handle: RePEc:arx:papers:1012.1297
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    References listed on IDEAS

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    Cited by:

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    3. Nepp, Alexander & Okhrin, Ostap & Egorova, Julia & Dzhuraeva, Zarnigor & Zykov, Alexander, 2022. "What threatens stock markets more - The coronavirus or the hype around it?," International Review of Economics & Finance, Elsevier, vol. 78(C), pages 519-539.
    4. Adel Javanmard & Jason D. Lee, 2020. "A flexible framework for hypothesis testing in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 685-718, July.
    5. Alena Skolkova, 2023. "Instrumental Variable Estimation with Many Instruments Using Elastic-Net IV," CERGE-EI Working Papers wp759, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    6. Belloni, Alexandre & Hansen, Christian & Newey, Whitney, 2022. "High-dimensional linear models with many endogenous variables," Journal of Econometrics, Elsevier, vol. 228(1), pages 4-26.
    7. Mehmet Caner & Esfandiar Maasoumi & Juan Andrés Riquelme, 2016. "Moment and IV Selection Approaches: A Comparative Simulation Study," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1562-1581, December.
    8. Felipe González & Magdalena Larreboure, 2021. "The Impact of the Women’s March on the U.S. House Election," Documentos de Trabajo 560, Instituto de Economia. Pontificia Universidad Católica de Chile..
    9. Ellora Derenoncourt, 2022. "Can You Move to Opportunity? Evidence from the Great Migration," American Economic Review, American Economic Association, vol. 112(2), pages 369-408, February.

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