Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/192568 
Year of Publication: 
2009
Series/Report no.: 
Discussion Papers No. 586
Publisher: 
Statistics Norway, Research Department, Oslo
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.
Subjects: 
Instrumental variables
variable treatment intensity
treatment effect heterogeneity
selection bias
quantity-quality
family size
child outcome
JEL: 
C31
C14
J13
Document Type: 
Working Paper

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