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

Magne Mogstad and Matthew Wiswall ()

Discussion Papers from Statistics Norway, Research Department

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.

Keywords: Instrumental variables; variable treatment intensity; treatment effect heterogeneity; selection bias; quantity-quality; family size; child outcome (search for similar items in EconPapers)
JEL-codes: C14 C31 J13 (search for similar items in EconPapers)
Date: 2009-05
New Economics Papers: this item is included in nep-ecm and nep-edu
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Citations: View citations in EconPapers (8)

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Related works:
Working Paper: What Linear Estimators Miss: Re-Examining the Effects of Family Income on Child Outcomes (2010)
Working Paper: Linearity in Instrumental Variables Estimation: Problems and Solutions (2010)
Working Paper: How Much Should We Trust Linear Instrumental Variables Estimators? An Application to Family Size and Children's Education (2009)
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