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How Much Should We Trust Linear Instrumental Variables Estimators? An Application to Family Size and Children's Education

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  • Mogstad, Magne

    (University of Chicago)

  • Wiswall, Matthew

    (University of Wisconsin-Madison)

Abstract

Many empirical studies specify outcomes as a linear function of endogenous regressors when conducting instrumental variable (IV) estimation. We show that tests for treatment effects, selection bias, and treatment effect heterogeneity are biased if the true relationship is non-linear. These results motivate a re-examination of recent evidence suggesting no causal effect of family size on children's education. Following common practice, a linear IV estimator has been used, assuming constant marginal effects of additional children across family sizes. We find that the conclusion of no effect of family size is an artifact of the linear specification, which masks substantial marginal family size effects.

Suggested Citation

  • 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 of Labor Economics (IZA).
  • Handle: RePEc:iza:izadps:dp4562
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    1. Imbens, G. & Angrist, J.D., 1992. "Average Causal Response with Variable Treatment Intensity," Harvard Institute of Economic Research Working Papers 1611, Harvard - Institute of Economic Research.
    2. 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.
    3. 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.
    4. 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.
    5. Joshua D. Angrist & Jörn-Steffen Pischke, 2010. "The Credibility Revolution in Empirical Economics: How Better Research Design Is Taking the Con out of Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 24(2), pages 3-30, Spring.
    6. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    7. 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.
    8. Martin Dooley & Jennifer Stewart, 2004. "Family income and child outcomes in Canada," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 37(4), pages 898-917, November.
    9. 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).
    10. Edward Vytlacil & James J. Heckman, 2001. "Policy-Relevant Treatment Effects," American Economic Review, American Economic Association, vol. 91(2), pages 107-111, May.
    11. 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.
    12. Dan Maurice Levy & Greg Duncan, 2000. "Using Sibling Samples to Assess the Effect of Childhood Family Income on Completed Schooling," JCPR Working Papers 168, Northwestern University/University of Chicago Joint Center for Poverty Research.
    13. Philip Oreopoulos & Marianne Page & Ann Huff Stevens, 2008. "The Intergenerational Effects of Worker Displacement," Journal of Labor Economics, University of Chicago Press, vol. 26(3), pages 455-483, July.
    14. Anne Case & Christina Paxson, 2008. "Stature and Status: Height, Ability, and Labor Market Outcomes," Journal of Political Economy, University of Chicago Press, vol. 116(3), pages 499-532, June.
    15. Shea, John, 2000. "Does parents' money matter?," Journal of Public Economics, Elsevier, vol. 77(2), pages 155-184, August.
    16. Yitzhaki, Shlomo, 1996. "On Using Linear Regressions in Welfare Economics," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 478-486, October.
    17. Almond, Douglas & Currie, Janet, 2011. "Human Capital Development before Age Five," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 15, pages 1315-1486, Elsevier.
    18. Solon, Gary, 1999. "Intergenerational mobility in the labor market," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 29, pages 1761-1800, Elsevier.
    19. Milligan, Kevin & Stabile, Mark, 2007. "The integration of child tax credits and welfare: Evidence from the Canadian National Child Benefit program," Journal of Public Economics, Elsevier, vol. 91(1-2), pages 305-326, February.
    20. Leamer, Edward E, 1983. "Let's Take the Con Out of Econometrics," American Economic Review, American Economic Association, vol. 73(1), pages 31-43, March.
    21. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    22. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    23. Gordon B. Dahl & Lance Lochner, 2005. "The Impact of Family Income on Child Achievement," NBER Working Papers 11279, National Bureau of Economic Research, Inc.
    24. David M. Blau, 1999. "The Effect Of Income On Child Development," The Review of Economics and Statistics, MIT Press, vol. 81(2), pages 261-276, May.
    25. Becker, Gary S & Tomes, Nigel, 1979. "An Equilibrium Theory of the Distribution of Income and Intergenerational Mobility," Journal of Political Economy, University of Chicago Press, vol. 87(6), pages 1153-1189, December.
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    Cited by:

    1. 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 of Labor Economics (IZA).
    2. 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.
    3. Sandra E. Black & Paul J. Devereux & Katrine V. L�ken & Kjell G. Salvanes, 2014. "Care or Cash? The Effect of Child Care Subsidies on Student Performance," The Review of Economics and Statistics, MIT Press, vol. 96(5), pages 824-837, December.
    4. Daniela Del Boca & Christopher Flinn & Matthew Wiswall, 2016. "Transfers to Households with Children and Child Development," Economic Journal, Royal Economic Society, vol. 126(596), pages 136-183, October.
    5. Shoya Ishimaru, 2021. "Empirical Decomposition of the IV-OLS Gap with Heterogeneous and Nonlinear Effects," Papers 2101.04346, arXiv.org.
    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. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Alexander M. Gelber & Matthew C. Weinzierl, 2012. "Equalizing Outcomes and Equalizing Opportunities: Optimal Taxation when Children's Abilities Depend on Parents' Resources," NBER Working Papers 18332, National Bureau of Economic Research, Inc.
    12. Elizabeth M. Caucutt & Lance Lochner, 2020. "Early and Late Human Capital Investments, Borrowing Constraints, and the Family," Journal of Political Economy, University of Chicago Press, vol. 128(3), pages 1065-1147.
    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 & Alexander Monge-Naranjo, 2012. "Credit Constraints in Education," Annual Review of Economics, Annual Reviews, vol. 4(1), pages 225-256, July.
    15. 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.
    16. 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.
    17. Mogstad, M. & Wiswall, M., 2012. "Instrumental variables estimation with partially missing instruments," Economics Letters, Elsevier, vol. 114(2), pages 186-189.
    18. 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.
    19. 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.
    20. 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.
    21. Sara Cools & Rannveig Kaldager Hart, 2015. "The effect of childhood family size on fertility in adulthood. New evidence form IV estimation," Discussion Papers 802, Statistics Norway, Research Department.
    22. 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).
    23. 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.
    24. repec:esx:essedp:726 is not listed on IDEAS

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    More about this item

    Keywords

    instrumental variables; variable treatment intensity; treatment effect heterogeneity; selection bias; quantity-quality; family size; child outcome;
    All these keywords.

    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
    • J13 - Labor and Demographic Economics - - Demographic Economics - - - Fertility; Family Planning; Child Care; Children; Youth

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