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Beyond LATE with a discrete instrument. Heterogeneity in the quantity-quality interaction of children

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Abstract

The interpretation of instrumental variables (IV) estimates as local average treatment effects (LATE) of instrument-induced shifts in treatment raises concerns about their external validity and policy relevance. We examine how to move beyond LATE in situations where the instrument is discrete, as it often is in applied research. Discrete instruments do not give sufficient support to identify the full range of marginal treatment effects (MTE) in the usual local instrumental variable approach. We show how an alternative estimation approach allows identification of richer specifications of the MTE when the instrument is discrete. One result is that the alternative approach identifies a linear MTE model even with a single binary instrument. Although restrictive, the linear MTE model nests the standard IV estimator: The model gives the exact same estimate of LATE while at the same time providing a simple test for its external validity and a linear extrapolation. Another result is that the alternative approach allows identification of a general MTE model under the auxiliary assumption of additive separability between observed and unobserved heterogeneity in treatment effects. We apply these identification results to empirically assess the interaction between the quantity and quality of children. Motivated by the seminal quantity-quality model of fertility, a large and growing body of empirical research has used binary instruments to estimate LATEs of family size on child outcomes. We show that the effects of family size are both more varied and more extensive than what the LATEs suggest. Our MTE estimates reveal that the family size effects vary in magnitude and even sign, and that families act as if they possess some knowledge of the idiosyncratic effects in the fertility decision.

Suggested Citation

  • Christian N. Brinch & Magne Mogstad & Matthew Wiswall, 2012. "Beyond LATE with a discrete instrument. Heterogeneity in the quantity-quality interaction of children," Discussion Papers 703, Statistics Norway, Research Department.
  • Handle: RePEc:ssb:dispap:703
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    1. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
    2. Heckman, James J. & Schmierer, Daniel & Urzua, Sergio, 2010. "Testing the correlated random coefficient model," Journal of Econometrics, Elsevier, vol. 158(2), pages 177-203, October.
    3. Heckman, James J. & Urzúa, Sergio, 2010. "Comparing IV with structural models: What simple IV can and cannot identify," Journal of Econometrics, Elsevier, vol. 156(1), pages 27-37, May.
    4. James J. Heckman, 2010. "Building Bridges between Structural and Program Evaluation Approaches to Evaluating Policy," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 356-398, June.
    5. Becker, Gary S & Lewis, H Gregg, 1973. "On the Interaction between the Quantity and Quality of Children," Journal of Political Economy, University of Chicago Press, vol. 81(2), pages 279-288, Part II, .
    6. Joshua Angrist & Victor Lavy & Analia Schlosser, 2010. "Multiple Experiments for the Causal Link between the Quantity and Quality of Children," Journal of Labor Economics, University of Chicago Press, vol. 28(4), pages 773-824, October.
    7. Julio Cáceres-Delpiano, 2006. "The Impacts of Family Size on Investment in Child Quality," Journal of Human Resources, University of Wisconsin Press, vol. 41(4).
    8. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
    9. Rosenzweig, Mark R & Wolpin, Kenneth I, 1980. "Testing the Quantity-Quality Fertility Model: The Use of Twins as a Natural Experiment," Econometrica, Econometric Society, vol. 48(1), pages 227-240, January.
    10. Joshua Angrist & Ivan Fernandez-Val, 2010. "ExtrapoLATE-ing: External Validity and Overidentification in the LATE Framework," NBER Working Papers 16566, National Bureau of Economic Research, Inc.
    11. Bjorklund, Anders & Moffitt, Robert, 1987. "The Estimation of Wage Gains and Welfare Gains in Self-selection," The Review of Economics and Statistics, MIT Press, vol. 69(1), pages 42-49, February.
    12. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    13. Hanushek, Eric A, 1992. "The Trade-Off between Child Quantity and Quality," Journal of Political Economy, University of Chicago Press, vol. 100(1), pages 84-117, February.
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    Cited by:

    1. Patrick Kline & Christopher R. Walters, 2016. "Evaluating Public Programs with Close Substitutes: The Case of HeadStart," The Quarterly Journal of Economics, Oxford University Press, vol. 131(4), pages 1795-1848.
    2. Halla, Martin & Zweimüller, Martina, 2014. "Parental Response to Early Human Capital Shocks: Evidence from the Chernobyl Accident," IZA Discussion Papers 7968, Institute for the Study of Labor (IZA).
    3. Sylvia Frühwirth-Schnatter & Martin Halla & Alexandra Posekany & Gerald J. Pruckner & Thomas Schober, 2014. "The Quantity and Quality of Children: A Semi-Parametric Bayesian IV Approach," Economics working papers 2014-03, Department of Economics, Johannes Kepler University Linz, Austria.
    4. Daniel A. Kamhöfer & Hendrik Schmitz & Matthias Westphal, 2015. "Heterogeneity in Marginal Nonmonetary Returns to Higher Education," CINCH Working Paper Series 1512, Universitaet Duisburg-Essen, Competent in Competition and Health, revised Oct 2015.
    5. Huber, Martin & Wüthrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    6. Felfe, Christina & Lalive, Rafael, 2014. "Does Early Child Care Help or Hurt Children's Development?," IZA Discussion Papers 8484, Institute for the Study of Labor (IZA).

    More about this item

    Keywords

    Local average treatment effects; marginal treatment effects; discrete instrument; quantity-quality; fertility;

    JEL classification:

    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • J13 - Labor and Demographic Economics - - Demographic Economics - - - Fertility; Family Planning; Child Care; Children; Youth

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