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Inference with Many Weak Instruments and Heterogeneity

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  • Luther Yap

Abstract

This paper considers inference in a linear instrumental variable regression model with many potentially weak instruments and heterogeneous treatment effects. I first show that existing test procedures, including those that are robust to only either weak instruments or heterogeneous treatment effects, can be arbitrarily oversized in this setup. Then, I propose a valid inference procedure based on a score statistic and a leave-three-out variance estimator. To establish this procedure's validity, this paper proves that the score statistic is asymptotically normal and the variance estimator is consistent. The power of the score test is also close to a power envelope in an empirical application.

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  • Luther Yap, 2024. "Inference with Many Weak Instruments and Heterogeneity," Papers 2408.11193, arXiv.org, revised Sep 2024.
    • Handle: RePEc:arx:papers:2408.11193
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    References listed on IDEAS

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    1. Graham Elliott & Ulrich K. Müller & Mark W. Watson, 2015. "Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis," Econometrica, Econometric Society, vol. 83, pages 771-811, March.
    2. Crudu, Federico & Mellace, Giovanni & Sándor, Zsolt, 2021. "Inference In Instrumental Variable Models With Heteroskedasticity And Many Instruments," Econometric Theory, Cambridge University Press, vol. 37(2), pages 281-310, April.
    3. Chao, John C. & Swanson, Norman R. & Hausman, Jerry A. & Newey, Whitney K. & Woutersen, Tiemen, 2012. "Asymptotic Distribution Of Jive In A Heteroskedastic Iv Regression With Many Instruments," Econometric Theory, Cambridge University Press, vol. 28(1), pages 42-86, February.
    4. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    5. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    6. Phillips, Garry D A & Hale, C, 1977. "The Bias of Instrumental Variable Estimators of Simultaneous Equation Systems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(1), pages 219-228, February.
    7. Lim, Dennis & Wang, Wenjie & Zhang, Yichong, 2024. "A conditional linear combination test with many weak instruments," Journal of Econometrics, Elsevier, vol. 238(2).
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