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Complete subset averaging with many instruments

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  • Seojeong Lee
  • Youngki Shin

Abstract

SummaryWe propose a two-stage least squares (2SLS) estimator whose first stage is the equal-weighted average over a complete subset with k instruments among K available, which we call the complete subset averaging (CSA) 2SLS. The approximate mean squared error (MSE) is derived as a function of the subset size k by the Nagar (1959) expansion. The subset size is chosen by minimising the sample counterpart of the approximate MSE. We show that this method achieves asymptotic optimality among the class of estimators with different subset sizes. To deal with averaging over a growing set of irrelevant instruments, we generalise the approximate MSE to find that the optimal k is larger than otherwise. An extensive simulation experiment shows that the CSA-2SLS estimator outperforms the alternative estimators when instruments are correlated. As an empirical illustration, we estimate the logistic demand function in Berry et al. (1995) and find that the CSA-2SLS estimate is better supported by economic theory than are the alternative estimates.

Suggested Citation

  • Seojeong Lee & Youngki Shin, 2021. "Complete subset averaging with many instruments," The Econometrics Journal, Royal Economic Society, vol. 24(2), pages 290-314.
    • Handle: RePEc:oup:emjrnl:v:24:y:2021:i:2:p:290-314.
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    File URL: http://hdl.handle.net/10.1093/ectj/utaa033
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    Cited by:

    1. Zhihao Zhao & Xinyu Zhang & Guohua Zou & Alan T. K. Wan & Geoffrey K. F. Tso, 2024. "Model averaging for estimating treatment effects," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(1), pages 73-92, February.
    2. Seojeong Lee & Siha Lee & Julius Owusu & Youngki Shin, 2023. "csa2sls: A complete subset approach for many instruments using Stata," Stata Journal, StataCorp LLC, vol. 23(4), pages 932-941, December.
    3. Lee, Ji Hyung & Shin, Youngki, 2023. "Complete Subset Averaging For Quantile Regressions," Econometric Theory, Cambridge University Press, vol. 39(1), pages 146-188, February.
    4. Chen, Xingyi & Li, Haiqi & Zhang, Jing, 2023. "Complete subset averaging approach for high-dimensional generalized linear models," Economics Letters, Elsevier, vol. 226(C).
    5. Islam, M.S. & Das, Barun K. & Das, Pronob & Rahaman, Md Habibur, 2021. "Techno-economic optimization of a zero emission energy system for a coastal community in Newfoundland, Canada," Energy, Elsevier, vol. 220(C).

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