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Bias Reduction in Instrumental Variable Estimation through First-Stage Shrinkage

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  • Jann Spiess

Abstract

The two-stage least-squares (2SLS) estimator is known to be biased when its first-stage fit is poor. I show that better first-stage prediction can alleviate this bias. In a two-stage linear regression model with Normal noise, I consider shrinkage in the estimation of the first-stage instrumental variable coefficients. For at least four instrumental variables and a single endogenous regressor, I establish that the standard 2SLS estimator is dominated with respect to bias. The dominating IV estimator applies James-Stein type shrinkage in a first-stage high-dimensional Normal-means problem followed by a control-function approach in the second stage. It preserves invariances of the structural instrumental variable equations.

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  • Jann Spiess, 2017. "Bias Reduction in Instrumental Variable Estimation through First-Stage Shrinkage," Papers 1708.06443, arXiv.org, revised Oct 2017.
    • Handle: RePEc:arx:papers:1708.06443
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    References listed on IDEAS

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    1. Gary Chamberlain, 2007. "Decision Theory Applied to an Instrumental Variables Model," Econometrica, Econometric Society, vol. 75(3), pages 609-652, May.
    2. Bruce E. Hansen, 2017. "Stein-like 2SLS estimator," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 840-852, October.
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    Cited by:

    1. Jann Spiess, 2017. "Unbiased Shrinkage Estimation," Papers 1708.06436, arXiv.org, revised Oct 2017.
    2. 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.

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