Estimating the dose-response function through the GLM approach
How effective are policy programs with continuous treatment exposure? Answering this question essentially amounts to estimating a dose-response function as proposed in Hirano and Imbens (2004). Whenever doses are not randomly assigned but are given under experimental conditions, estimation of a dose-response function is possible using the Generalized Propensity Score (GPS). Since its formulation, the GPS has been repeatedly used in observational studies, and ad hoc programs have been provided for Stata users (doseresponse and gpscore, Bia and Mattei 2008). However, many applied works remark that the treatment variable may not be normally distributed. In this case, the Stata programs are not usable because they do not allow for different distribution assumptions other than the normal density. In this paper, we overcome this problem. Building on Bia and Mattei's (2008) programs, we provide doseresponse2 and gpscore, which allow one to accommodate different distribution functions of the treatment variable. This task is accomplished through by the application of the generalized linear models estimator in the first step instead of the application of maximum likelihood. In such a way, the user can have a very versatile tool capable of handling many practical situations. It is worth highlighting that our programs, among the many alternatives, take into account the possibility to consistently use the GPS estimator when the treatment variable is fractional, the flogit case by Papke and Wooldridge (1998), a case of particular interest for economists.
References listed on IDEAS
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- Papke, Leslie E & Wooldridge, Jeffrey M, 1996.
"Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates,"
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- Helmut Fryges & Joachim Wagner, 2008.
"Exports and Productivity Growth: First Evidence from a Continuous Treatment Approach,"
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Springer, vol. 144(4), pages 695-722, December.
- Fryges, Helmut & Wagner, Joachim, 2007. "Exports and Productivity Growth: First Evidence from a Continuous Treatment Approach," IZA Discussion Papers 2782, Institute for the Study of Labor (IZA).
- Hemlut Fryges & Joachim Wagner, 2007. "Exports and Productivity Growth – First Evidence from a Continuous Treatment Approach," Working Paper Series in Economics 49, University of Lüneburg, Institute of Economics.
- Fryges, Helmut & Wagner, Joachim, 2007. "Exports and Productivity Growth: First Evidence from a Continuous Treatment Approach," ZEW Discussion Papers 07-032, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
- Helmut Fryges & Joachim Wagner, 2007. "Exports and Productivity Growth - First Evidence from a Continuous Treatment Approach," Jena Economic Research Papers 2007-063, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics.
- Liu, Jin-Long & Liu, Jin-Tan & Hammitt, James K. & Chou, Shin-Yi, 1999. "The price elasticity of opium in Taiwan, 1914-1942," Journal of Health Economics, Elsevier, vol. 18(6), pages 795-810, December.
- Kosuke Imai & David A. van Dyk, 2004. "Causal Inference With General Treatment Regimes: Generalizing the Propensity Score," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 854-866, January.
- Sascha O. Becker & Andrea Ichino, 2002. "Estimation of average treatment effects based on propensity scores," Stata Journal, StataCorp LP, vol. 2(4), pages 358-377, November.
- Hausman, Jerry A & Leonard, Gregory K, 1997. "Superstars in the National Basketball Association: Economic Value and Policy," Journal of Labor Economics, University of Chicago Press, vol. 15(4), pages 586-624, October.
- Helmut Fryges, 2009. "The export-growth relationship: estimating a dose-response function," Applied Economics Letters, Taylor & Francis Journals, vol. 16(18), pages 1855-1859.
- Michela Bia & Alessandra Mattei, 2008. "A Stata package for the estimation of the dose–response function through adjustment for the generalized propensity score," Stata Journal, StataCorp LP, vol. 8(3), pages 354-373, September.
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