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How Linear Models Can Mask Non-Linear Causal Relationships. An Application to Family Size and Children's Education

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  • Magne Mogstad
  • Matthew Wiswall

    ()
    (Statistics Norway)

Abstract

Many empirical studies specify outcomes as a linear function of endogenous regressors when conducting instrumental variable (IV) estimation. We show that commonly used tests for treatment effects, selection bias, and treatment effect heterogeneity are biased if the true relationship is non-linear. In particular, using linear models can only lead to under-rejection of the null hypothesis of no treatment effects. In light of these results, we re-examine the recent evidence suggesting that family size has no causal effect 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 show that the conclusion of no causal effect of family size is an artifact of the specification of a linear model, which masks significant marginal family size effects. Estimating a model that is non-parametric in family size, we find that family size matters substantially for children's educational attainment, but in a non-monotonic way. Our findings illustrate that IV estimation of models which relax linearity restrictions is an important addition to empirical research, particularly when OLS estimation and theory suggests the possibility of non-linear causal effects.

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Bibliographic Info

Paper provided by Research Department of Statistics Norway in its series Discussion Papers with number 586.

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Date of creation: May 2009
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Handle: RePEc:ssb:dispap:586

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

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Cited by:
  1. Løken, Katrine Vellesen & Mogstad, Magne & Wiswall, Matthew, 2011. "What Linear Estimators Miss: The E ects of Family Income on Child Outcomes," Working Papers in Economics 02/11, University of Bergen, Department of Economics.
  2. Rolf Aaberge & Magne Mogstad & Vito Peragine, 2010. "Measuring long-term inequality of opportunity," Working Papers 158, ECINEQ, Society for the Study of Economic Inequality.
  3. Mogstad, M. & Wiswall, M., 2012. "Instrumental variables estimation with partially missing instruments," Economics Letters, Elsevier, vol. 114(2), pages 186-189.
  4. 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.
  5. Parfait Eloundou-Enyegue & Sarah Giroux, 2012. "Fertility Transitions and Schooling: From Micro- to Macro-Level Associations," Demography, Springer, vol. 49(4), pages 1407-1432, November.

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