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Instrumental Variables Estimation with Partially Missing Instruments

Author

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  • Mogstad, Magne

    (University of Chicago)

  • Wiswall, Matthew

    (University of Wisconsin-Madison)

Abstract

We examine instrumental variables estimation in situations where the instrument is only observed for a sub-sample, which is fairly common in empirical research. Typically, researchers simply limit the analysis to the sub-sample where the instrument is non-missing. We show that when the instrument is non-randomly missing, standard IV estimators require strong, auxiliary assumptions to be consistent. In many (quasi)natural experiments, the auxiliary assumptions are unlikely to hold. We therefore introduce alternative IV estimators that are robust to non-randomly missing instruments without auxiliary assumptions. A Monte-Carlo study illustrates our results.

Suggested Citation

  • Mogstad, Magne & Wiswall, Matthew, 2010. "Instrumental Variables Estimation with Partially Missing Instruments," IZA Discussion Papers 4689, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp4689
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    References listed on IDEAS

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    1. Pedro Carneiro & James J. Heckman, 2002. "The Evidence on Credit Constraints in Post--secondary Schooling," Economic Journal, Royal Economic Society, vol. 112(482), pages 705-734, October.
    2. David Card, 1993. "Using Geographic Variation in College Proximity to Estimate the Return to Schooling," Working Papers 696, Princeton University, Department of Economics, Industrial Relations Section..
    3. Magne Mogstad & Matthew Wiswall, 2009. "How Linear Models Can Mask Non-Linear Causal Relationships. An Application to Family Size and Children's Education," Discussion Papers 586, Statistics Norway, Research Department.
    4. Angrist, Joshua D, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 2-16, January.
    5. Julio Cáceres-Delpiano, 2006. "The Impacts of Family Size on Investment in Child Quality," Journal of Human Resources, University of Wisconsin Press, vol. 41(4).
    6. 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.
    7. Rosenzweig, Mark R & Wolpin, Kenneth I, 1980. "Testing the Quantity-Quality Fertility Model: The Use of Twins as a Natural Experiment," Econometrica, Econometric Society, vol. 48(1), pages 227-240, January.
    8. repec:fth:prinin:317 is not listed on IDEAS
    9. Joshua Angrist & Victor Lavy & Analia Schlosser, 2010. "Multiple Experiments for the Causal Link between the Quantity and Quality of Children," Journal of Labor Economics, University of Chicago Press, vol. 28(4), pages 773-824, October.
    10. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    11. David Card, 1993. "Using Geographic Variation in College Proximity to Estimate the Return to Schooling," Working Papers 696, Princeton University, Department of Economics, Industrial Relations Section..
    12. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
    13. 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.
    14. repec:fth:prinin:311 is not listed on IDEAS
    15. Thomas J. Kane & Cecilia E. Rouse, 1993. "Labor Market Returns to Two- and Four-Year Colleges: Is a Credit a Credit and Do Degrees Matter?," NBER Working Papers 4268, National Bureau of Economic Research, Inc.
    16. 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.
    17. Sandra E. Black & Paul J. Devereux & Kjell G. Salvanes, 2005. "The More the Merrier? The Effect of Family Size and Birth Order on Children's Education," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(2), pages 669-700.
    18. Åslund, Olof & Grönqvist, Hans, 2010. "Family size and child outcomes: Is there really no trade-off?," Labour Economics, Elsevier, vol. 17(1), pages 130-139, January.
    19. Angrist, Joshua D, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 27-28, January.
    20. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-1160, September.
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    2. Bhalotra, Sonia & Clarke, Damian, 2022. "Analysis of Twins," The Warwick Economics Research Paper Series (TWERPS) 1428, University of Warwick, Department of Economics.
    3. Chris Muris, 2020. "Efficient GMM Estimation with Incomplete Data," The Review of Economics and Statistics, MIT Press, vol. 102(3), pages 518-530, July.
    4. Melvin Stephens & Takashi Unayama, 2019. "Estimating the Impacts of Program Benefits: Using Instrumental Variables with Underreported and Imputed Data," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 468-475, July.
    5. Jesper Bagger & Javier A Birchenall & Hani Mansour & Sergio Urzúa, 2021. "Education, Birth Order and Family Size [Family size and children’s education in Vietnam]," The Economic Journal, Royal Economic Society, vol. 131(633), pages 33-69.
    6. Wang, Le, 2013. "Estimating returns to education when the IV sample is selective," Labour Economics, Elsevier, vol. 21(C), pages 74-85.
    7. Lipeng Li & Apurbo Sarkar & Xi Zhou & Xiuling Ding & Hua Li, 2022. "Influence and Action Mechanisms of Governmental Relations Embeddedness for Fostering Green Production Demonstration Household: Evidence from Shaanxi, Sichuan, and Anhui Province, China," IJERPH, MDPI, vol. 19(19), pages 1-25, September.
    8. Michele Giannola, 2024. "Parental Investments and Intra-household Inequality in Child Human Capital: Evidence from a Survey Experiment," The Economic Journal, Royal Economic Society, vol. 134(658), pages 671-727.
    9. Peter Grajzl & Valentina Dimitrova-Grajzl & Katarina Zajc, 2016. "Inside post-socialist courts: the determinants of adjudicatory outcomes in Slovenian commercial disputes," European Journal of Law and Economics, Springer, vol. 41(1), pages 85-115, February.
    10. Ryo Kato & Takahiro Hoshino, 2020. "Semiparametric Bayesian Instrumental Variables Estimation for Nonignorable Missing Instruments," Discussion Paper Series DP2020-06, Research Institute for Economics & Business Administration, Kobe University.

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    JEL classification:

    • 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
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models

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