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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

    () (Arizona State University)

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 for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp4562
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    Cited by:

    1. 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.
    2. 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.
    3. Ibañez, Marcela & Rai, Ashok & Riener, Gerhard, 2015. "Sorting through affirmative action: Three field experiments in Colombia," DICE Discussion Papers 183, University of Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    4. 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.
    5. 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.
    6. Mogstad, M. & Wiswall, M., 2012. "Instrumental variables estimation with partially missing instruments," Economics Letters, Elsevier, vol. 114(2), pages 186-189.
    7. 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.

    More about this item

    Keywords

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

    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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