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Treatment Effect Heterogeneity in Theory and Practice

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  • Joshua Angrist

Abstract

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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Bibliographic Info

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
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Handle: RePEc:ecm:nawm04:186

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Keywords: Instrumental variables; causal effects; marital stability; welfare;

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References

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  1. Jeff Grogger & Stephen G. Bronars, 1997. "The Effect of Welfare Payments on the Marriage and Fertility Behavior of Unwed Mothers: Results from a Twins Experiment," NBER Working Papers 6047, National Bureau of Economic Research, Inc.
  2. 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, American Economic Association, vol. 88(3), pages 450-77, June.
  3. James J. Heckman & Edward J. Vytlacil, 2000. "Local Instrumental Variables," NBER Technical Working Papers 0252, National Bureau of Economic Research, Inc.
  4. Frölich, Markus, 2002. "Nonparametric IV Estimation of Local Average Treatment Effects with Covariates," IZA Discussion Papers 588, Institute for the Study of Labor (IZA).
  5. 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, American Economic Association, vol. 84(5), pages 1141-56, December.
  6. Andrew Cherlin, 1977. "The effect of children on marital dissolution," Demography, Springer, Springer, vol. 14(3), pages 265-272, August.
  7. Angrist, J.D. & Imbens, G.W., 1991. "Sources of Identifying Information in Evaluation Models," Harvard Institute of Economic Research Working Papers, Harvard - Institute of Economic Research 1568, Harvard - Institute of Economic Research.
  8. 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, American Statistical Association, vol. 19(1), pages 2-16, January.
  9. Heckman, J J & Tobias, Justin & Vytlacil, Ed, 2001. "Four Parameters of Interest in the Evaluation of Social Programs," Staff General Research Papers 12022, Iowa State University, Department of Economics.
  10. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, American Economic Association, vol. 80(2), pages 319-23, May.
  11. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, Econometric Society, vol. 62(2), pages 467-75, March.
  12. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, Elsevier, vol. 113(2), pages 231-263, April.
  13. V. Joseph Hotz & Guido W. Imbens & Jacob A. Klerman, 2000. "The Long-Term Gains from GAIN: A Re-Analysis of the Impacts of the California GAIN Program," NBER Working Papers 8007, National Bureau of Economic Research, Inc.
  14. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, American Economic Association, vol. 80(2), pages 313-18, May.
  15. Rebecca M. Blank, 2002. "Evaluating Welfare Reform in the United States," NBER Working Papers 8983, National Bureau of Economic Research, Inc.
  16. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, Econometric Society, vol. 46(6), pages 1251-71, November.
  17. Peter C.B. Phillips, 2003. "Vision and Influence in Econometrics: John Denis Sargan," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1393, Cowles Foundation for Research in Economics, Yale University.
  18. Wooldridge, Jeffrey M., 1997. "On two stage least squares estimation of the average treatment effect in a random coefficient model," Economics Letters, Elsevier, Elsevier, vol. 56(2), pages 129-133, October.
  19. Becker, Gary S & Landes, Elisabeth M & Michael, Robert T, 1977. "An Economic Analysis of Marital Instability," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 85(6), pages 1141-87, December.
  20. Arellano, Manuel, 2002. "Sargan's Instrumental Variables Estimation and the Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(4), pages 450-59, October.
  21. Tim Heaton, 1990. "Marital stability throughout the child-rearing years," Demography, Springer, Springer, vol. 27(1), pages 55-63, February.
  22. Wooldridge, Jeffrey M., 2003. "Further results on instrumental variables estimation of average treatment effects in the correlated random coefficient model," Economics Letters, Elsevier, Elsevier, vol. 79(2), pages 185-191, May.
  23. Melissa Schettini Kearney, 2004. "Is There an Effect of Incremental Welfare Benefits on Fertility Behavior?: A Look at the Family Cap," Journal of Human Resources, University of Wisconsin Press, vol. 39(2).
  24. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, Elsevier, vol. 34(3), pages 305-334, March.
  25. Chamberlain, Gary, 1986. "Asymptotic efficiency in semi-parametric models with censoring," Journal of Econometrics, Elsevier, Elsevier, vol. 32(2), pages 189-218, July.
  26. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, Econometric Society, vol. 70(1), pages 91-117, January.
  27. Moffitt, Robert A., 1999. "New developments in econometric methods for labor market analysis," Handbook of Labor Economics, Elsevier, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 24, pages 1367-1397 Elsevier.
  28. 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.
  29. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
  30. 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.
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