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k-Class Instrumental Variables Quantile Regression

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Abstract

With standard instrumental variables regression, k-class estimators have the potential to reduce bias, which is larger with weak instruments. With instrumental variables quantile regression, weak instrument-robust estimation is even more important because there is less guidance for assessing instrument strength. Motivated by this, we introduce an analogous k-class of estimators for instrumental variables quantile regression. We show the first-order asymptotic distribution under strong instruments is equivalent for all conventional choices of k. We evaluate finite-sample median bias in simulations. Computation is fast, and the "LIML" k reliably reduces median bias compared to the k=1 benchmark across a variety of data-generating processes, especially with greater degrees of overidentification. We also revisit some empirical estimates of consumption Euler equations. All code is provided online.

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  • David M. Kaplan & Xin Liu, 2021. "k-Class Instrumental Variables Quantile Regression," Working Papers 2104, Department of Economics, University of Missouri.
    • Handle: RePEc:umc:wpaper:2104
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    1. Motohiro Yogo, 2004. "Estimating the Elasticity of Intertemporal Substitution When Instruments Are Weak," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 797-810, August.
    2. Nelson, Charles R & Startz, Richard, 1990. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 58(4), pages 967-976, July.
    3. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
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    7. Kaplan, David M. & Sun, Yixiao, 2017. "Smoothed Estimating Equations For Instrumental Variables Quantile Regression," Econometric Theory, Cambridge University Press, vol. 33(1), pages 105-157, February.
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    11. Blomquist, Soren & Dahlberg, Matz, 1999. "Small Sample Properties of LIML and Jackknife IV Estimators: Experiments with Weak Instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 69-88, Jan.-Feb..
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    More about this item

    Keywords

    bias; weak instruments;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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