How Much Should We Trust Linear Instrumental Variables Estimators? An Application to Family Size and Children's Education
AbstractMany 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.
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Bibliographic InfoPaper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 4562.
Length: 56 pages
Date of creation: Nov 2009
Date of revision:
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Other versions of this item:
- Magne Mogstad & Matthew Wiswall, 2009. "How Linear Models Can Mask Non-Linear Causal Relationships. An Application to Family Size and Children's Education," Discussion Papers 586, Research Department of Statistics Norway.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-11-27 (All new papers)
- NEP-ECM-2009-11-27 (Econometrics)
- NEP-EDU-2009-11-27 (Education)
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- Loken, Katrine Vellesen & Mogstad, Magne & Wiswall, Matthew, 2010.
"What Linear Estimators Miss: Re-Examining the Effects of Family Income on Child Outcomes,"
IZA Discussion Papers
4971, Institute for the Study of Labor (IZA).
- 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.
- Rolf Aaberge & Magne Mogstad & Vito Peragine, 2010.
"Measuring long-term inequality of opportunity,"
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- 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.
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