In this article, I present ctreatreg, a command for estimating a dose–response function when i) treatment is continuous, ii) individuals may react het-erogeneously to observable confounders, and iii) the selection into treatment may be endogenous. I implement two estimation procedures: ordinary least squares under conditional mean independence and instrumental variables under selection endogeneity. Finally, I present a Monte Carlo experiment to test the reliability of the proposed command.
AdornoV., BerniniC., and PellegriniG.2007. The impact of capital subsidies: New estimations under continuous treatment. Giornale degli Economisti e Annali di Economia66: 67–92.
2.
AngristJ. D., and PischkeJ.-S.2009. Mostly Harmless Econometrics: An Empiricist's Companion.Princeton, NJ: Princeton University Press.
3.
BiaM., FloresC. A., Flores-LagunesA., and MatteiA.2014. A Stata package for the application of semiparametric estimators of dose–response functions. Stata Journal14: 580–604.
4.
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.
5.
CattaneoM. D.2010. Efficient semiparametric estimation of multi-valued treatment effects under ignorability. Journal of Econometrics155: 138–154.
6.
CattaneoM. D., DrukkerD. M., and HollandA. D.2013. Estimation of multivalued treatment effects under conditional independence. Stata Journal13: 407–450.
7.
CerulliG.2014. ivtreatreg: A command for fitting binary treatment models with heterogeneous response to treatment and unobservable selection. Stata Journal14: 453–480.
8.
GuardabascioB., and VenturaM.2014. Estimating the dose–response function through a generalized linear model approach. Stata Journal14: 141–158.
9.
HeckmanJ. J.1979. Sample selection bias as a specification error. Econometrica47: 153–161.
10.
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.
11.
ImaiK., and van DykD. A.2004. Causal inference with general treatment regimes: Generalizing the propensity score. Journal of the American Statistical Association99: 854–866.
12.
ImbensG. W., and AngristJ. D.1994. Identification and estimation of local average treatment effects. Econometrica62: 467–475.
13.
RobertsonC., BoyleP., HsiehC. C., MacFarlaneG. J., and MaisonneuveP.1994. Some statistical considerations in the analysis of case-control studies when the exposure variables are continuous measurements. Epidemiology5: 164–170.
14.
RoystonP., and SauerbreiW.2008. Multivariable Model-building: A Pragmatic Approach to Regression Analysis Based on Fractional Polynomials for Modelling Continuous Variables.Chichester, UK: Wiley.
15.
RubinD. B.1974. Estimating causal effects of treatments in randomized and nonran-domized studies. Journal of Educational Psychology66: 688–701.
16.
WooldridgeJ. M.1997. On two stage least squares estimation of the average treatment effect in a random coefficient model. Economics Letters56: 129–133.
17.
WooldridgeJ. M.2003. Further results on instrumental variables estimation of average treatment effects in the correlated random coefficient model. Economics Letters79: 185–191.
18.
WooldridgeJ. M.2010. Econometric Analysis of Cross Section and Panel Data. 2nd ed. Cambridge, MA: MIT Press.
