In this article, we briefly review the role of the propensity score in estimating dose–response functions as described in Hirano and Imbens (2004, Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives, 73–84). Then we present a set of Stata programs that estimate the propensity score in a setting with a continuous treatment, test the balancing property of the generalized propensity score, and estimate the dose–response function. We illustrate these programs by using a dataset collected by Imbens, Rubin, and Sacerdote.
BeckerS. O., and IchinoA.2002. Estimation of average treatment effects based on propensity scores. Stata Journal2: 358–377.
2.
BiaM., and MatteiA.2007. Application of the generalized propensity score. Evaluation of public contributions to Piedmont enterprises. POLIS Working Paper 80, University of Eastern Piedmont.
3.
HiranoK., and ImbensG. W.2004. The propensity score with continuous treatments. In Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives, ed. GelmanA., and MengX.-L., 73–84. West Sussex, England: Wiley InterScience.
4.
HollandP. W.1986. Statistics and causal inference. Journal of the American Statistical Association8: 945–960.
5.
ImbensG. W., RubinD. B., and SacerdoteB. I.2001. Estimating the effect of unearned income on labor earnings, savings, and consumption: Evidence from a survey of lottery players. American Economic Review91: 778–794.
6.
JeffreysH.1961. Theory of Probability. 3rd ed. Oxford: Oxford University Press.
7.
LeuvenE., and SianesiB.2003. psmatch2: Stata module to perform full Mahalanobis and propensity score matching, common support graphing, and covariate imbalance testing.Boston College Department of Economics, Statistical Software Components. Downloadable from http://ideas.repec.org/c/boc/bocode/s432001.html.
8.
RosenbaumP. R., and RubinD. B.1983. The central role of the propensity score in observational studies for causal effects. Biometrika70: 41–55.
9.
RubinD. B.1976. Inference and missing data. Biometrika63: 581–592.
