c$, where $t_{1}$ is the first-stage $t$-statistic, and the first-stage sign is given. Although pervasive in empirical practice, pretesting on the first-stage $F$-statistic exacerbates bias and distorts inference. We show, however, that median bias is both minimized and roughly halved by setting $c=0$, that is by screening on the sign of the \textit{estimated} first stage. This bias reduction is a free lunch: conventional confidence interval coverage is unchanged by screening on the estimated first-stage sign. To the extent that IV analysts sign-screen already, these results strengthen the case for a sanguine view of the finite-sample behavior of just-ID IV."> c$, where $t_{1}$ is the first-stage $t$-statistic, and the first-stage sign is given. Although pervasive in empirical practice, pretesting on the first-stage $F$-statistic exacerbates bias and distorts inference. We show, however, that median bias is both minimized and roughly halved by setting $c=0$, that is by screening on the sign of the \textit{estimated} first stage. This bias reduction is a free lunch: conventional confidence interval coverage is unchanged by screening on the estimated first-stage sign. To the extent that IV analysts sign-screen already, these results strengthen the case for a sanguine view of the finite-sample behavior of just-ID IV.">
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One Instrument to Rule Them All: The Bias and Coverage of Just-ID IV

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  • Joshua Angrist
  • Michal Koles'ar
Abstract
We revisit the finite-sample behavior of single-variable just-identified instrumental variables (just-ID IV) estimators, arguing that in most microeconometric applications, the usual inference strategies are likely reliable. Three widely-cited applications are used to explain why this is so. We then consider pretesting strategies of the form $t_{1}>c$, where $t_{1}$ is the first-stage $t$-statistic, and the first-stage sign is given. Although pervasive in empirical practice, pretesting on the first-stage $F$-statistic exacerbates bias and distorts inference. We show, however, that median bias is both minimized and roughly halved by setting $c=0$, that is by screening on the sign of the \textit{estimated} first stage. This bias reduction is a free lunch: conventional confidence interval coverage is unchanged by screening on the estimated first-stage sign. To the extent that IV analysts sign-screen already, these results strengthen the case for a sanguine view of the finite-sample behavior of just-ID IV.

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  • Joshua Angrist & Michal Koles'ar, 2021. "One Instrument to Rule Them All: The Bias and Coverage of Just-ID IV," Papers 2110.10556, arXiv.org, revised Dec 2022.
    • Handle: RePEc:arx:papers:2110.10556
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    1. Isaiah Andrews & Timothy B. Armstrong, 2017. "Unbiased instrumental variables estimation under known first‐stage sign," Quantitative Economics, Econometric Society, vol. 8(2), pages 479-503, July.
    2. David S. Lee & Justin McCrary & Marcelo J. Moreira & Jack Porter, 2022. "Valid t-Ratio Inference for IV," American Economic Review, American Economic Association, vol. 112(10), pages 3260-3290, October.
    3. Alan B. Krueger, 1999. "Experimental Estimates of Education Production Functions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 497-532.
    4. Isaiah Andrews & James H. Stock & Liyang Sun, 2019. "Weak Instruments in Instrumental Variables Regression: Theory and Practice," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 727-753, August.
    5. Young, Alwyn, 2022. "Consistency without inference: instrumental variables in practical application," LSE Research Online Documents on Economics 115011, London School of Economics and Political Science, LSE Library.
    6. Angrist, Joshua D. & Krueger, Alan B., 1999. "Empirical strategies in labor economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 23, pages 1277-1366, Elsevier.
    7. Angrist, Joshua D & Evans, William N, 1998. "Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size," American Economic Review, American Economic Association, vol. 88(3), pages 450-477, June.
    8. Anna Mikusheva & Liyang Sun, 2022. "Inference with Many Weak Instruments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(5), pages 2663-2686.
    9. Hall, Alastair R & Rudebusch, Glenn D & Wilcox, David W, 1996. "Judging Instrument Relevance in Instrumental Variables Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 283-298, May.
    10. Moreira, Marcelo J., 2009. "Tests with correct size when instruments can be arbitrarily weak," Journal of Econometrics, Elsevier, vol. 152(2), pages 131-140, October.
    11. Emmanuel Saez & Gabriel Zucman, 2016. "Editor's Choice Wealth Inequality in the United States since 1913: Evidence from Capitalized Income Tax Data," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(2), pages 519-578.
    12. Michael Keane & Timothy Neal, 2021. "A Practical Guide to Weak Instruments," Discussion Papers 2021-05c, School of Economics, The University of New South Wales.
    13. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records: Errata," American Economic Review, American Economic Association, vol. 80(5), pages 1284-1286, December.
    14. Chernozhukov, Victor & Hansen, Christian, 2008. "The reduced form: A simple approach to inference with weak instruments," Economics Letters, Elsevier, vol. 100(1), pages 68-71, July.
    15. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," American Economic Review, American Economic Association, vol. 80(3), pages 313-336, June.
    16. Lang, Kevin, 1993. "Ability Bias, Discount Rate Bias and the Return to Education," MPRA Paper 24651, University Library of Munich, Germany.
    17. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-787, October.
    18. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    19. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 979-1014.
    20. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    21. Young, Alwyn, 2022. "Consistency without Inference: Instrumental Variables in Practical Application," European Economic Review, Elsevier, vol. 147(C).
    22. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    23. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    24. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-1160, September.
    25. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 555-574.
    26. Michael Keane & Timothy Neal, 2021. "A Practical Guide to Weak Instruments," Discussion Papers 2021-05b, School of Economics, The University of New South Wales.
    27. Hanushek, Eric A, 1986. "The Economics of Schooling: Production and Efficiency in Public Schools," Journal of Economic Literature, American Economic Association, vol. 24(3), pages 1141-1177, September.
    28. Joshua D. Angrist & Victor Lavy, 1999. "Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 533-575.
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    3. Tsiboe, Francis & Turner, Dylan, 2023. "The crop insurance demand response to premium subsidies: Evidence from U.S. Agriculture," Food Policy, Elsevier, vol. 119(C).
    4. Isaiah Andrews & Anna Mikusheva, 2022. "GMM is Inadmissible Under Weak Identification," Papers 2204.12462, arXiv.org, revised May 2023.
    5. Robert A. Moffitt & Matthew V. Zahn, 2019. "The Marginal Labor Supply Disincentives of Welfare: Evidence from Administrative Barriers to Participation," NBER Working Papers 26028, National Bureau of Economic Research, Inc.
    6. Michael Keane & Timothy Neal, 2021. "Robust Inference for the Frisch Labor Supply Elasticity," Discussion Papers 2021-07b, School of Economics, The University of New South Wales.
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    9. Ankel-Peters, Jörg & Vance, Colin & Bensch, Gunther, 2022. "Spotlight on researcher decisions – Infrastructure evaluation, instrumental variables, and first-stage specification screening," OSF Preprints sw6kd, Center for Open Science.
    10. Michael P Keane & Timothy Neal, 2024. "Robust inference for the Frisch labor supply," IFS Working Papers W24/46, Institute for Fiscal Studies.
    11. Wozniak, Abigail & Baker, Michael T. & Carter, Susan P., 2024. "Peer Effects and Marriage Formation," IZA Discussion Papers 17443, Institute of Labor Economics (IZA).
    12. Zachrisson, Henrik Daae & Dearing, Eric & Borgen, Nicolai T. & Sandsør, Astrid Marie Jorde & Karoly, Lynn A., 2021. "Zachrisson et al 2021 ECEC Achievement," EdArXiv zrctw, Center for Open Science.
    13. Keane, Michael & Neal, Timothy, 2023. "Instrument strength in IV estimation and inference: A guide to theory and practice," Journal of Econometrics, Elsevier, vol. 235(2), pages 1625-1653.
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    More about this item

    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
    • 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
    • J08 - Labor and Demographic Economics - - General - - - Labor Economics Policies

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