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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

    (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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    References 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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