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Bootstrap Tests for the Effect of a Treatment on the Distribution of an Outcome Variable

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  • Alberto Abadie

Abstract

This paper considers the problem of assessing the distributional consequences of a treatment on some outcome variable of interest when treatment intake is (possibly) non-randomized but there is a binary instrument available for the researcher. Such scenario is common in observational studies and in randomized experiments with imperfect compliance. One possible approach to this problem is to compare the counterfactual cumulative distribution functions of the outcome with and without the treatment. Here, it is shown how to estimate these distributions using instrumental variable methods and a simple bootstrap procedure is proposed to test distributional hypotheses, such as equality of distributions, first-order stochastic dominance and second order stochastic dominance. These tests and estimators are applied to the study of the effects of veteran status on the distribution of civilian earnings. The results show a negative effect of military service in Vietnam that appears to be concentrated on the lower tail of the distribution of earnings. First order stochastic dominance cannot be rejected by the data.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0261.

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Date of creation: Sep 2000
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Publication status: published as Abadie, Alberto. "Bootstrap Tests For Distributional Treatment Effects In Instrumental Variable Models," Journal of the American Statistical Association, 2002, v97(457,Mar), 284-292.
Handle: RePEc:nbr:nberte:0261

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  1. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
  2. Imbens, Guido W & Rubin, Donald B, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," Review of Economic Studies, Wiley Blackwell, vol. 64(4), pages 555-74, October.
  3. Joshua Angrist & Alan Krueger, 1993. "Split Sample Instrumental Variables," Working Papers 699, Princeton University, Department of Economics, Industrial Relations Section..
  4. 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.
  5. Joshua Angrist, 1989. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," Working Papers 631, Princeton University, Department of Economics, Industrial Relations Section..
  6. 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.
  7. Angrist, Joshua D & Krueger, Alan B, 1995. "Split-Sample Instrumental Variables Estimates of the Return to Schooling," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(2), pages 225-35, April.
  8. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-93, September.
  9. Foster, James E & Shorrocks, Anthony F, 1988. "Poverty Orderings," Econometrica, Econometric Society, vol. 56(1), pages 173-77, January.
  10. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
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Cited by:
  1. Alberto Abadie, 2000. "Semiparametric Estimation of Instrumental Variable Models for Causal Effects," NBER Technical Working Papers 0260, National Bureau of Economic Research, Inc.

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