IDEAS home Printed from https://ideas.repec.org/p/iza/izadps/dp4562.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://docs.iza.org/dp4562.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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).
    3. Edward Vytlacil & James J. Heckman, 2001. "Policy-Relevant Treatment Effects," American Economic Review, American Economic Association, vol. 91(2), pages 107-111, May.
    4. 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.
    5. Angrist, J.D. & Imbens, G.W., 1992. "Average causal response with variable treatment intensity," Discussion Paper 1992-34, Tilburg University, Center for Economic Research.
    6. Guido W. Imbens, 2010. "Better LATE Than Nothing: Some Comments on Deaton (2009) and Heckman and Urzua (2009)," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 399-423, June.
    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. Shea, John, 2000. "Does parents' money matter?," Journal of Public Economics, Elsevier, vol. 77(2), pages 155-184, August.
    9. 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.
    10. 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.
    11. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    12. Martin Dooley & Jennifer Stewart, 2004. "Family income and child outcomes in Canada," Canadian Journal of Economics, Canadian Economics Association, vol. 37(4), pages 898-917, November.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Løken, Katrine V., 2010. "Family income and children's education: Using the Norwegian oil boom as a natural experiment," Labour Economics, Elsevier, vol. 17(1), pages 118-129, January.
    18. Daniela Del Boca & Christopher Flinn & Matthew Wiswall, 2014. "Household Choices and Child Development," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(1), pages 137-185.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    25. Gordon B. Dahl & Lance Lochner, 2005. "The Impact of Family Income on Child Achievement," NBER Working Papers 11279, National Bureau of Economic Research, Inc.
    26. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Daniela Del Boca & Christopher Flinn & Matthew Wiswall, 2014. "Household Choices and Child Development," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(1), pages 137-185.
    4. Elizabeth M. Caucutt & Lance Lochner & Youngmin Park, 2017. "Correlation, Consumption, Confusion, or Constraints: Why Do Poor Children Perform so Poorly?," Scandinavian Journal of Economics, Wiley Blackwell, vol. 119(1), pages 102-147, January.
    5. 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.
    6. Naoi, Michio & Akabayashi, Hideo & Nakamura, Ryosuke & Nozaki, Kayo & Sano, Shinpei & Senoh, Wataru & Shikishima, Chizuru, 2021. "Causal effects of family income on educational investment and child outcomes: Evidence from a policy reform in Japan," Journal of the Japanese and International Economies, Elsevier, vol. 60(C).
    7. Kevin Milligan & Mark Stabile, 2011. "Do Child Tax Benefits Affect the Well-Being of Children? Evidence from Canadian Child Benefit Expansions," American Economic Journal: Economic Policy, American Economic Association, vol. 3(3), pages 175-205, August.
    8. 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.
    9. 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.
    10. Randall Akee & William Copeland & E. Jane Costello & Emilia Simeonova, 2018. "How Does Household Income Affect Child Personality Traits and Behaviors?," American Economic Review, American Economic Association, vol. 108(3), pages 775-827, March.
    11. Sergi Sánchez-Coll, 2023. "Born this way: the effect of an unexpected child benefit at birth on longer-term educational outcomes," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 14(1), pages 105-141, March.
    12. Lauber, Verena & Thomas, Lampert, 2014. "The Effect of Early Universal Daycare on Child Weight Problems," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100399, Verein für Socialpolitik / German Economic Association.
    13. George Bulman & Robert Fairlie & Sarena Goodman & Adam Isen, 2021. "Parental Resources and College Attendance: Evidence from Lottery Wins," American Economic Review, American Economic Association, vol. 111(4), pages 1201-1240, April.
    14. Schaubert, Marianna, 2022. "Do courts know how to incentivize? Behavioral response of non-resident parents to child support obligations," Children and Youth Services Review, Elsevier, vol. 137(C).
    15. repec:esx:essedp:726 is not listed on IDEAS
    16. Cécile Bonneau & Sébastien Grobon, 2022. "Unequal access to higher education based on parental income: evidence from France ," World Inequality Lab Working Papers halshs-03693195, HAL.
    17. Melissa S. Kearney & Phillip B. Levine, 2017. "The Economics of Nonmarital Childbearing and the Marriage Premium for Children," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 327-352, September.
    18. Coelli, Michael B., 2011. "Parental job loss and the education enrollment of youth," Labour Economics, Elsevier, vol. 18(1), pages 25-35, January.
    19. Douglas Almond & Janet Currie & Valentina Duque, 2018. "Childhood Circumstances and Adult Outcomes: Act II," Journal of Economic Literature, American Economic Association, vol. 56(4), pages 1360-1446, December.
    20. Francesco Agostinelli & Giuseppe Sorrenti, 2018. "Money vs. Time: Family Income, Maternal Labor Supply, and Child Development," Working Papers 2018-017, Human Capital and Economic Opportunity Working Group.
    21. Sebastian Galiani & Juan Pantano, 2021. "Structural Models: Inception and Frontier," NBER Working Papers 28698, National Bureau of Economic Research, Inc.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:iza:izadps:dp4562. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Holger Hinte (email available below). General contact details of provider: https://edirc.repec.org/data/izaaade.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.