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Regularized LIML for many instruments

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  • Carrasco, Marine
  • Tchuente, Guy

Abstract

The use of many moment conditions improves the asymptotic efficiency of the instrumental variables estimators. However, in finite samples, the inclusion of an excessive number of moments increases the bias. To solve this problem, we propose regularized versions of the limited information maximum likelihood (LIML) based on three different regularizations: Tikhonov, Landweber–Fridman, and principal components. Our estimators are consistent and asymptotically normal under heteroskedastic error. Moreover, they reach the semiparametric efficiency bound assuming homoskedastic error. We show that the regularized LIML estimators possess finite moments when the sample size is large enough. The higher order expansion of the mean square error (MSE) shows the dominance of regularized LIML over regularized two-staged least squares estimators. We devise a data driven selection of the regularization parameter based on the approximate MSE. A Monte Carlo study and two empirical applications illustrate the relevance of our estimators.

Suggested Citation

  • Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
  • Handle: RePEc:eee:econom:v:186:y:2015:i:2:p:427-442
    DOI: 10.1016/j.jeconom.2015.02.018
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    Cited by:

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    2. Kapetanios, George & Khalaf, Lynda & Marcellino, Massimiliano, 2015. "Factor based identification-robust inference in IV regressions," CEPR Discussion Papers 10390, C.E.P.R. Discussion Papers.
    3. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    4. Shi, Zhentao, 2016. "Econometric estimation with high-dimensional moment equalities," Journal of Econometrics, Elsevier, vol. 195(1), pages 104-119.
    5. Marine Carrasco & Guy Tchuente, 2016. "Regularization Based Anderson Rubin Tests for Many Instruments," Studies in Economics 1608, School of Economics, University of Kent.
    6. Pierre Chausse, 2017. "Regularized Empirical Likelihood as a Solution to the No Moment," Working Papers 1708, University of Waterloo, Department of Economics, revised Nov 2017.
    7. Rahul Singh, 2020. "Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments," Papers 2012.10315, arXiv.org, revised May 2021.
    8. N'Golo Kone, 2021. "Regularized Maximum Diversification Investment Strategy," Working Paper 1450, Economics Department, Queen's University.
    9. Rahul Singh & Liyuan Xu & Arthur Gretton, 2020. "Reproducing Kernel Methods for Nonparametric and Semiparametric Treatment Effects," Papers 2010.04855, arXiv.org, revised Apr 2021.
    10. Rahul Singh, 2021. "Debiased Kernel Methods," Papers 2102.11076, arXiv.org, revised Mar 2021.
    11. Guy Tchuente, 2016. "Estimation of social interaction models using regularization," Studies in Economics 1607, School of Economics, University of Kent.
    12. Joshua Angrist & Brigham Frandsen, 2019. "Machine Labor," NBER Working Papers 26584, National Bureau of Economic Research, Inc.
    13. Marine Carrasco & Guy Tchuente, 2016. "Efficient Estimation with Many Weak Instruments Using Regularization Techniques," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1609-1637, December.
    14. N'Golo Kone, 2021. "Efficient mean-variance portfolio selection by double regularization," Working Paper 1453, Economics Department, Queen's University.
    15. Guy Tchuente, 2019. "Weak Identification and Estimation of Social Interaction Models," Papers 1902.06143, arXiv.org.
    16. N’Golo Koné, 2020. "Regularized Maximum Diversification Investment Strategy," Econometrics, MDPI, Open Access Journal, vol. 9(1), pages 1-23, December.

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    More about this item

    Keywords

    Heteroskedasticity; High-dimensional models; LIML; Many instruments; MSE; Regularization methods;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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