In this article, we revise the estimation of the dose–response function described in Hirano and Imbens (2004, Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives, 73–84) by proposing a flexible way to estimate the generalized propensity score when the treatment variable is not necessarily normally distributed. We also provide a set of programs that accomplish this task. To do this, in the existing Dose-response program (Bia and Mattei, 2008, Stata Journal 8: 354–373), we substitute the maximum likelihood estimator in the first step of the computation with the more flexible generalized linear model.
BeckerS. O., and IchinoA.2002. Estimation of average treatment effects based on propensity scores. Stata Journal2: 358–377.
2.
BiaM., and MatteiA.2008. A Stata package for the estimation of the dose–response function through adjustment for the generalized propensity score. Stata Journal8: 354–373.
3.
de JongP., and HellerG. Z.2008. Generalized Linear Models for Insurance Data.New York: Cambridge University Press.
4.
FrygesH.2009. The export–growth relationship: Estimating a dose-response function. Applied Economics Letters16: 1855–1859.
5.
FrygesH., and WagnerJ.2008. Exports and productivity growth: First evidence from a continuous treatment approach. Review of World Economics144: 695–722.
6.
HausmanJ. A., and LeonardG. K.1997. Superstars in the national basketball association: Economic value and policy. Journal of Labor Economics15: 586–624.
7.
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. Chichester, UK: Wiley.
8.
ImbensG. W.2000. The role of the propensity score in estimating dose–response functions. Biometrika87: 706–710.
9.
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.
10.
LechnerM.2001. Identification and estimation of causal effects of multiple treatments under the conditional independence assumption. In Econometric Evaluation of Labour Market Policies, ed. LechnerM., and PfeifferF., 43–58. Heidelberg: Physica-Verlag.
11.
LeuvenE., and SianesiB.2003. psmatch2: Stata module to perform full Mahalanobis and propensity score matching, common support graphing, and covariate imbalance testing. Statistical Software Components S432001, Department of Economics, Boston College. http://ideas.repec.org/c/boc/bocode/s432001.html.
12.
LiuJ.-L., LiuJ.-T., HammittJ. K., and ChouS.-Y.1999. The price elasticity of opium in Taiwan, 1914–1942. Journal of Health Economics18: 795–810.
13.
McCullaghP., and NelderJ. A.1989. Generalized Linear Models. 2nd ed. London: Chapman & Hall/CRC.
14.
PapkeL. E., and WooldridgeJ. M.1996. Econometric methods for fractional response variables with an application to 401(K) plan participation rates. Journal of Applied Econometrics11: 619–632.
15.
Rabe-HeskethS., and EverittB.2007. A Handbook of Statistical Analyses Using Stata. 4th ed. Boca Raton, FL: Chapman & Hall/CRC.
16.
RosenbaumP. R., and RubinD. B.1983. The central role of the propensity score in observational studies for causal effects. Biometrika70: 41–55.
17.
RosenbaumP. R., and RubinD. B.1984. Reducing bias in observational studies using subclassification on the propensity score. Journal of the American Statistical Association79: 516–524.
18.
WagnerJ.2001. A note on the firm size—Export relationship. Small Business Economics17: 229–237.
19.
WooldridgeJ. M.2010. Econometric Analysis of Cross Section and Panel Data. 2nd ed. Cambridge, MA: MIT Press.
