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A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs

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  • Seojeong Lee

Abstract

Under treatment effect heterogeneity, an instrument identifies the instrument-specific local average treatment effect (LATE). With multiple instruments, two-stage least squares (2SLS) estimand is a weighted average of different LATEs. What is often overlooked in the literature is that the postulated moment condition evaluated at the 2SLS estimand does not hold unless those LATEs are the same. If so, the conventional heteroscedasticity-robust variance estimator would be inconsistent, and 2SLS standard errors based on such estimators would be incorrect. I derive the correct asymptotic distribution, and propose a consistent asymptotic variance estimator by using the result of Hall and Inoue (2003, Journal of Econometrics) on misspecified moment condition models. This can be used to correctly calculate the standard errors regardless of whether there is more than one LATE or not.

Suggested Citation

  • Seojeong Lee, 2018. "A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(3), pages 400-410, July.
    • Handle: RePEc:taf:jnlbes:v:36:y:2018:i:3:p:400-410
    DOI: 10.1080/07350015.2016.1186555
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    Cited by:

    1. Mogstad, Magne & Torgovitsky, Alexander, 2024. "Instrumental variables with unobserved heterogeneity in treatment effects," Handbook of Labor Economics,, Elsevier.
    2. Hwang, Jungbin & Kang, Byunghoon & Lee, Seojeong, 2022. "A doubly corrected robust variance estimator for linear GMM," Journal of Econometrics, Elsevier, vol. 229(2), pages 276-298.
    3. Tom Boot & Didier Nibbering, 2024. "Inference on LATEs with covariates," Papers 2402.12607, arXiv.org, revised Dec 2024.
    4. Bruce E. Hansen & Seojeong Lee, 2021. "Inference for Iterated GMM Under Misspecification," Econometrica, Econometric Society, vol. 89(3), pages 1419-1447, May.
    5. Jung, Dawoon & Lee, Jinkook & Meijer, Erik, 2022. "Revisiting the effect of retirement on Cognition: Heterogeneity and endowment," The Journal of the Economics of Ageing, Elsevier, vol. 21(C).
    6. Basu, Arnab K. & Byambasuren, Tsenguunjav & Chau, Nancy H. & Khanna, Neha, 2024. "Cooking fuel choice and child mortality in India," Journal of Economic Behavior & Organization, Elsevier, vol. 222(C), pages 240-265.
    7. Jan Priebe, 2020. "Quasi-experimental evidence for the causal link between fertility and subjective well-being," Journal of Population Economics, Springer;European Society for Population Economics, vol. 33(3), pages 839-882, July.
    8. Frank Kleibergen & Zhaoguo Zhan, 2025. "Double robust inference for continuous updating GMM," Quantitative Economics, Econometric Society, vol. 16(1), pages 295-327, January.
    9. Bruce E. Hansen & Seojeong Jay Lee, 2018. "Inference for Iterated GMM Under Misspecification and Clustering," Discussion Papers 2018-07, School of Economics, The University of New South Wales.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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