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

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.

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Paper provided by Statistics Norway, Research Department in its series Discussion Papers with number 703.

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Date of creation: Sep 2012
Date of revision:
Handle: RePEc:ssb:dispap:703
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  1. Heckman, James J. & Urzua, Sergio & Vytlacil, Edward, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," IZA Discussion Papers 2320, Institute for the Study of Labor (IZA).
  2. 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).
  3. 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 356-98, June.
  4. 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.
  5. Heckman, James J. & Schmierer, Daniel & Urzua, Sergio, 2009. "Testing the Correlated Random Coefficient Model," IZA Discussion Papers 4525, Institute for the Study of Labor (IZA).
  6. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
  7. Pedro Carneiro & Sokbae (Simon) Lee, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," CeMMAP working papers CWP01/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. Heckman, James J. & Urzua, Sergio, 2009. "Comparing IV with Structural Models: What Simple IV Can and Cannot Identify," IZA Discussion Papers 3980, Institute for the Study of Labor (IZA).
  9. 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 S279-88, Part II, .
  10. 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.
  11. 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 227-40, January.
  12. 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.
  13. 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.
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