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What Linear Estimators Miss: The Effects of Family Income on Child Outcomes

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  • Katrine V. Løken
  • Magne Mogstad
  • Matthew Wiswall

Abstract

We assess the implications of nonlinearity for IV and FE estimation when the estimated model is inappropriately assumed to be linear. Our application is the causal link between family income and child outcomes. Our nonlinear IV and FE estimates show an increasing, concave relationship between family income and children's outcomes. We find that the linear estimators miss the significant effects of family income because they assign little weight to the large marginal effects in the lower part of the income distribution. We also show that the linear IV and FE estimates differ primarily because of different weighting of marginal effects. (JEL C26, D14, J12, J13)

Suggested Citation

  • Katrine V. Løken & Magne Mogstad & Matthew Wiswall, 2012. "What Linear Estimators Miss: The Effects of Family Income on Child Outcomes," American Economic Journal: Applied Economics, American Economic Association, vol. 4(2), pages 1-35, April.
  • Handle: RePEc:aea:aejapp:v:4:y:2012:i:2:p:1-35
    Note: DOI: 10.1257/app.4.2.1
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    References listed on IDEAS

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    1. Lance Lochner & Enrico Moretti, 2011. "Estimating and Testing Non-Linear Models Using Instrumental Variables," University of Western Ontario, Centre for Human Capital and Productivity (CHCP) Working Papers 20112, University of Western Ontario, Centre for Human Capital and Productivity (CHCP).
    2. Gordon B. Dahl & Lance Lochner, 2012. "The Impact of Family Income on Child Achievement: Evidence from the Earned Income Tax Credit," American Economic Review, American Economic Association, vol. 102(5), pages 1927-1956, August.
    3. Daniela Del Boca & Christopher Flinn & Matthew Wiswall, 2014. "Household Choices and Child Development," Review of Economic Studies, Oxford University Press, vol. 81(1), pages 137-185.
    4. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    5. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    6. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    7. Lance Lochner & Enrico Moretti, 2015. "Estimating and Testing Models with Many Treatment Levels and Limited Instruments," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 387-397, May.
    8. Gary S. Becker & Nigel Tomes, 1994. "Human Capital and the Rise and Fall of Families," NBER Chapters,in: Human Capital: A Theoretical and Empirical Analysis with Special Reference to Education (3rd Edition), pages 257-298 National Bureau of Economic Research, Inc.
    9. Løken, Katrine V., 2010. "Family income and children's education: Using the Norwegian oil boom as a natural experiment," Labour Economics, Elsevier, vol. 17(1), pages 118-129, January.
    10. Milligan, Kevin & Stabile, Mark, 2007. "The integration of child tax credits and welfare: Evidence from the Canadian National Child Benefit program," Journal of Public Economics, Elsevier, vol. 91(1-2), pages 305-326, February.
    11. Martin Dooley & Jennifer Stewart, 2004. "Family income and child outcomes in Canada," Canadian Journal of Economics, Canadian Economics Association, vol. 37(4), pages 898-917, November.
    12. Joshua D. Angrist & Kathryn Graddy & Guido W. Imbens, 2000. "The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 499-527.
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    More about this item

    JEL classification:

    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • D14 - Microeconomics - - Household Behavior - - - Household Saving; Personal Finance
    • J12 - Labor and Demographic Economics - - Demographic Economics - - - Marriage; Marital Dissolution; Family Structure
    • J13 - Labor and Demographic Economics - - Demographic Economics - - - Fertility; Family Planning; Child Care; Children; Youth

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