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Treatment Effect Heterogeneity in Theory and Practice

  • Joshua Angrist

Instrumental Variables (IV) methods identify internally valid causal effects for individuals whose treatment status is manipulable by the instrument at hand. Inference for other populations inevitably requires some sort of homogeneity assumption. I develop a simple theoretical framework that nests all possible homogeneity assumptions for a causal treatment-effects model with a binary instrument. This framework suggests a new specification test for selection bias and simple strategies for using IV to estimate average treatment effects. These ideas are illustrated in an application using sibling-sex composition to estimate the effect of child-bearing on marital status, poverty status, and welfare receipt for the population of mothers with two or more children. The application is motivated by American welfare reform, which penalizes further childbearing by welfare mothers on the grounds that additional childbearing makes continued poverty and welfare receipt more likely. The results generally support this conjecture, though the ability to make sharp distinctions between alternative average effects is limited by the imprecision of IV estimates.

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Paper provided by Econometric Society in its series Econometric Society 2004 North American Winter Meetings with number 186.

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Date of creation: 11 Aug 2004
Date of revision:
Handle: RePEc:ecm:nawm04:186
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  1. Angrist, Joshua D, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 2-16, January.
  2. Phillips, Peter C.B., 2003. "Vision And Influence In Econometrics: John Denis Sargan," Econometric Theory, Cambridge University Press, vol. 19(03), pages 495-511, June.
  3. Melissa Schettini Kearney, 2002. "Is There an Effect of Incremental Welfare Benefits on Fertility Behavior? A Look at the Family Cap," NBER Working Papers 9093, National Bureau of Economic Research, Inc.
  4. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
  5. Tim Heaton, 1990. "Marital stability throughout the child-rearing years," Demography, Springer, vol. 27(1), pages 55-63, February.
  6. Angrist, J.D. & Imbens, G.W., 1991. "Sources of identifying information in evaluation models," Discussion Paper 1991-42, Tilburg University, Center for Economic Research.
  7. James J. Heckman & Edward J. Vytlacil, 2000. "Local Instrumental Variables," NBER Technical Working Papers 0252, National Bureau of Economic Research, Inc.
  8. repec:att:wimass:8909 is not listed on IDEAS
  9. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
  10. Angrist, Joshua D & Evans, William N, 1998. "Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size," American Economic Review, American Economic Association, vol. 88(3), pages 450-77, June.
  11. Markus Froelich, 2002. "Nonparametric IV estimation of local average treatment effects with covariates," University of St. Gallen Department of Economics working paper series 2002 2002-19, Department of Economics, University of St. Gallen.
  12. Andrew Cherlin, 1977. "The effect of children on marital dissolution," Demography, Springer, vol. 14(3), pages 265-272, August.
  13. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-18, May.
  14. James Heckman & Justin L. Tobias & Edward Vytlacil, 2001. "Four Parameters of Interest in the Evaluation of Social Programs," Southern Economic Journal, Southern Economic Association, vol. 68(2), pages 210-223, October.
  15. Wooldridge, Jeffrey M., 2003. "Further results on instrumental variables estimation of average treatment effects in the correlated random coefficient model," Economics Letters, Elsevier, vol. 79(2), pages 185-191, May.
  16. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-75, March.
  17. Alberto Abadie & Joshua Angrist & Guido Imbens, 1999. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Working papers 99-16, Massachusetts Institute of Technology (MIT), Department of Economics.
  18. Rebecca M. Blank, 2002. "Evaluating Welfare Reform in the United States," Journal of Economic Literature, American Economic Association, vol. 40(4), pages 1105-1166, December.
  19. V. Joseph Hotz & Guido W. Imbens & Jacob A. Klerman, 2001. "The Long-Term Gains from GAIN: A Re-Analysis of the Impacts of the California GAIN Program," Working Papers 01-03, RAND Corporation Publications Department.
  20. Arellano, Manuel, 2002. "Sargan's Instrumental Variables Estimation and the Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 450-59, October.
  21. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, vol. 46(6), pages 1251-71, November.
  22. Wooldridge, Jeffrey M., 1997. "On two stage least squares estimation of the average treatment effect in a random coefficient model," Economics Letters, Elsevier, vol. 56(2), pages 129-133, October.
  23. J.D. Angrist & Guido W. Imbens & D.B. Rubin, 1993. "Identification of Causal Effects Using Instrumental Variables," NBER Technical Working Papers 0136, National Bureau of Economic Research, Inc.
  24. Joshua D. Angrist, 1991. "Instrumental Variables Estimation of Average Treatment Effects in Econometrics and Epidemiology," NBER Technical Working Papers 0115, National Bureau of Economic Research, Inc.
  25. Jeff Grogger & Stephen G. Bronars, 2001. "The Effect of Welfare Payments on the Marriage and Fertility Behavior of Unwed Mothers: Results from a Twins Experiment," Journal of Political Economy, University of Chicago Press, vol. 109(3), pages 529-545, June.
  26. Moffitt, Robert A., 1999. "New developments in econometric methods for labor market analysis," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 24, pages 1367-1397 Elsevier.
  27. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
  28. Chamberlain, Gary, 1986. "Asymptotic efficiency in semi-parametric models with censoring," Journal of Econometrics, Elsevier, vol. 32(2), pages 189-218, July.
  29. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-23, May.
  30. Bronars, Stephen G & Grogger, Jeff, 1994. "The Economic Consequences of Unwed Motherhood: Using Twin Births as a Natural Experiment," American Economic Review, American Economic Association, vol. 84(5), pages 1141-56, December.
  31. Becker, Gary S & Landes, Elisabeth M & Michael, Robert T, 1977. "An Economic Analysis of Marital Instability," Journal of Political Economy, University of Chicago Press, vol. 85(6), pages 1141-87, December.
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