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Linearity in Instrumental Variables Estimation: Problems and Solutions

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  • Mogstad, Magne

    () (University of Chicago)

  • Wiswall, Matthew

    () (Arizona State University)

Abstract

The linear IV estimator, in which the dependent variable is a linear function of a potentially endogenous regressor, is a major workhorse in empirical economics. When this regressor takes on multiple values, the linear specification restricts the marginal effects to be constant across all margins. This paper investigates the problems caused by the linearity restriction in IV estimation, and discusses possible remedies. We first examine the biases due to nonlinearity in the commonly used tests for non-zero treatment effects, selection bias, and instrument validity. Next, we consider three applications where theory suggests a nonlinear relationship, yet previous research has used linear IV estimators. We find that relaxing the linearity restriction in the IV estimation changes the qualitative conclusions about the relevant economic theory and the effectiveness of different policies.

Suggested Citation

  • Mogstad, Magne & Wiswall, Matthew, 2010. "Linearity in Instrumental Variables Estimation: Problems and Solutions," IZA Discussion Papers 5216, Institute for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp5216
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    Cited by:

    1. Lance Lochner & Alexander Monge-Naranjo, 2012. "Credit Constraints in Education," Annual Review of Economics, Annual Reviews, vol. 4(1), pages 225-256, July.
    2. Lundborg, Petter & Nilsson, Anton & Rooth, Dan-Olof, 2012. "Parental Education and Offspring Outcomes: Evidence from the Swedish Compulsory Schooling Reform," IZA Discussion Papers 6570, Institute for the Study of Labor (IZA).
    3. Mathias Kuepie & Michel Tenikue & Samuel Nouetagni & Nicaise Misangumukini, 2014. "Number, Age Composition and School Achievements of Siblings in Two African Capital Cities," Oxford Development Studies, Taylor & Francis Journals, vol. 42(4), pages 534-552, December.
    4. Mogstad, Magne & Wiswall, Matthew, 2009. "How Much Should We Trust Linear Instrumental Variables Estimators? An Application to Family Size and Children's Education," IZA Discussion Papers 4562, Institute for the Study of Labor (IZA).
    5. Gordon B. Dahl & Lance Lochner, 2012. "The Impact of Family Income on Child Achievement: Evidence from the Earned Income Tax Credit," American Economic Review, American Economic Association, vol. 102(5), pages 1927-1956, August.
    6. Román David Zárate, 2013. "Family size and children quality: New evidence and new exogenous shocks in the case of Colombian Households," DOCUMENTOS CEDE 010588, UNIVERSIDAD DE LOS ANDES-CEDE.
    7. Elizabeth M. Caucutt & Lance Lochner, 2012. "Early and Late Human Capital Investments, Borrowing Constraints, and the Family," NBER Working Papers 18493, National Bureau of Economic Research, Inc.
    8. Jessica Meredith & Frank Neri & Joan Rodgers, 2013. "Family Impacts on Cognitive Development of Young Children: Evidence from Australia," Economics Working Papers wp13-05, School of Economics, University of Wollongong, NSW, Australia.
    9. Daniela Del Boca & Christopher Flinn & Matthew Wiswall, 2014. "Household Choices and Child Development," Review of Economic Studies, Oxford University Press, vol. 81(1), pages 137-185.
    10. Marcela Ibanez & Gerhard Riener, 2018. "Sorting through Affirmative Action: Three Field Experiments in Colombia," Journal of Labor Economics, University of Chicago Press, vol. 36(2), pages 437-478.
    11. Aaberge, Rolf & Mogstad, Magne & Peragine, Vito, 2011. "Measuring long-term inequality of opportunity," Journal of Public Economics, Elsevier, vol. 95(3-4), pages 193-204, April.
    12. Drange, Nina & Havnes, Tarjei & Sandsør, Astrid M.J., 2016. "Kindergarten for all: Long run effects of a universal intervention," Economics of Education Review, Elsevier, vol. 53(C), pages 164-181.
    13. Dev, Pritha & Mberu, Blessing & Pongou, Roland, 2013. "Communitarianism, Oppositional Cultures, and Human Capital Contagion: Theory and Evidence from Formal versus Koranic Education," MPRA Paper 46234, University Library of Munich, Germany, revised 15 Apr 2013.
    14. Lance Lochner & Enrico Moretti, 2015. "Estimating and Testing Models with Many Treatment Levels and Limited Instruments," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 387-397, May.
    15. Katrine V. Løken & Magne Mogstad & Matthew Wiswall, 2012. "What Linear Estimators Miss: The Effects of Family Income on Child Outcomes," American Economic Journal: Applied Economics, American Economic Association, vol. 4(2), pages 1-35, April.
    16. Mogstad, M. & Wiswall, M., 2012. "Instrumental variables estimation with partially missing instruments," Economics Letters, Elsevier, vol. 114(2), pages 186-189.
    17. Lance Lochner & Enrico Moretti, 2011. "Estimating and Testing Non-Linear Models Using Instrumental Variables," University of Western Ontario, Centre for Human Capital and Productivity (CHCP) Working Papers 20112, University of Western Ontario, Centre for Human Capital and Productivity (CHCP).
    18. Parfait Eloundou-Enyegue & Sarah Giroux, 2012. "Fertility Transitions and Schooling: From Micro- to Macro-Level Associations," Demography, Springer;Population Association of America (PAA), vol. 49(4), pages 1407-1432, November.
    19. repec:esx:essedp:726 is not listed on IDEAS

    More about this item

    Keywords

    linear model; variable treatment intensity; nonlinearity; instrumental variables;

    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
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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