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A Stata package for the application of semiparametric estimators of dose–response functions


  • Michela Bia


  • Carlos A. Flores

    () (California Polytechnic State University)

  • Alfonso Flores-Lagunes

    () (State University of New York, Binghamton)

  • Alessandra Mattei

    () (University of Florence)


In many observational studies, the treatment may not be binary or categorical but rather continuous, so the focus is on estimating a continuous dose– response function. In this article, we propose a set of programs that semiparametrically estimate the dose–response function of a continuous treatment under the unconfoundedness assumption. We focus on kernel methods and penalized spline models and use generalized propensity-score methods under continuous treatment regimes for covariate adjustment. Our programs use generalized linear models to estimate the generalized propensity score, allowing users to choose between alternative parametric assumptions. They also allow users to impose a common support condition and evaluate the balance of the covariates using various approaches. We illustrate our routines by estimating the effect of the prize amount on subsequent labor earnings for Massachusetts lottery winners, using data collected by Imbens, Rubin, and Sacerdote (2001, American Economic Review, 778–794). Copyright 2014 by StataCorp LP.

Suggested Citation

  • Michela Bia & Carlos A. Flores & Alfonso Flores-Lagunes & Alessandra Mattei, 2014. "A Stata package for the application of semiparametric estimators of dose–response functions," Stata Journal, StataCorp LP, vol. 14(3), pages 580-604, September.
  • Handle: RePEc:tsj:stataj:v:14:y:2014:i:3:p:580-604
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    References listed on IDEAS

    1. Kluve, Jochen & Schneider, Hilmar & Uhlendorff, Arne & Zhao, Zhong, 2007. "Evaluating Continuous Training Programs Using the Generalized Propensity Score," IZA Discussion Papers 3255, Institute of Labor Economics (IZA).
    2. Michela Bia & Philippe Van Kerm, 2014. "Space-filling location selection," Stata Journal, StataCorp LP, vol. 14(3), pages 605-622, September.
    3. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
    4. Carlos A. Flores & Alfonso Flores-Lagunes & Arturo Gonzalez & Todd C. Neumann, 2012. "Estimating the Effects of Length of Exposure to Instruction in a Training Program: The Case of Job Corps," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 153-171, February.
    5. 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.
    6. Michela Bia & Alessandra Mattei, 2012. "Assessing the effect of the amount of financial aids to Piedmont firms using the generalized propensity score," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(4), pages 485-516, November.
    7. Maarten L. Buis & Nicholas J. Cox & Stephen P. Jenkins, 2003. "BETAFIT: Stata module to fit a two-parameter beta distribution," Statistical Software Components S435303, Boston College Department of Economics, revised 03 Feb 2012.
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    Cited by:

    1. Steckenleiter, Carina & Lechner, Michael & Pawlowski, Tim & Schüttoff, Ute, 2019. "Do local public expenditures on sports facilities affect sports participation in Germany?," Economics Working Paper Series 1905, University of St. Gallen, School of Economics and Political Science.
    2. Mehdi Chowdhury & Dragana Radicic, 2019. "Remittances and Asset Accumulation in Bangladesh: A Study Using Generalised Propensity Score," Journal of International Development, John Wiley & Sons, Ltd., vol. 31(6), pages 475-494, August.
    3. Zoltán Bakucs & Imre Fertő & Zsófia Benedek, 2019. "Success or Waste of Taxpayer Money? Impact Assessment of Rural Development Programs in Hungary," Sustainability, MDPI, Open Access Journal, vol. 11(7), pages 1-23, April.
    4. Manuela Coromaldi & Alessandra Garbero & Marco Letta, 2019. "Recovering the counterfactual as part of ex-ante impact assessments: an application to the PASIDP – II project in Ethiopia," Economics Bulletin, AccessEcon, vol. 39(3), pages 1844-1854.
    5. Chiara Bocci & Marco Mariani, 2015. "L’approccio delle funzioni dose-risposta per la valutazione di trattamenti continui nei sussidi alla r&s," SCIENZE REGIONALI, FrancoAngeli Editore, vol. 2015(3 Suppl.), pages 81-102.
    6. Kyoji Furukawa & Munechika Misumi & John B. Cologne & Harry M. Cullings, 2016. "A Bayesian Semiparametric Model for Radiation Dose‐Response Estimation," Risk Analysis, John Wiley & Sons, vol. 36(6), pages 1211-1223, June.
    7. Alejo, Javier & Galvao, Antonio F. & Montes-Rojas, Gabriel, 2018. "Quantile continuous treatment effects," Econometrics and Statistics, Elsevier, vol. 8(C), pages 13-36.
    8. Martina Lubyová & Miroslav Štefánik & Pavol Baboš & Daniel Gerbery & Veronika Hvozdíková & Katarína Karasová & Ivan Lichner & Tomáš Miklošovic & Marek Radvanský & Eva Rublíková & Ivana Studená, . "Labour Market in Slovakia 2017+," Books, Institute of Economic Research, SAS, edition 1, number 003.
    9. Tamru, Seneshaw & Minten, Bart, 2018. "Investing in wet mills and washed coffee in Ethiopia: Benefits and constraints," ESSP working papers 121, International Food Policy Research Institute (IFPRI).
    10. Ida D'Attoma & Silvia Pacei, 2018. "Evaluating the Effects of Product Innovation on the Performance of European Firms by Using the Generalised Propensity Score," German Economic Review, Verein für Socialpolitik, vol. 19(1), pages 94-112, February.
    11. Issahaku, Gazali & Abdulai, Awudu, 2020. "Household welfare implications of sustainable land management practices among smallholder farmers in Ghana," Land Use Policy, Elsevier, vol. 94(C).
    12. Giannetti, Caterina, 2019. "Debt specialization and performance of European firms," Journal of Empirical Finance, Elsevier, vol. 53(C), pages 257-271.
    13. Roberto ESPOSTI, 2014. "To match, not to match, how to match: Estimating the farm-level impact of the CAP-first pillar reform (or: How to Apply Treatment-Effect Econometrics when the Real World is;a Mess)," Working Papers 403, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    14. Christopher Baum & Giovanni Cerulli, CNR-IRCrES, 2016. "Estimating a dose-response function with heterogeneous response to confounders when treatment is continuous and endogenous," EcoMod2016 9388, EcoMod.
    15. Davide Dottori & Caterina Giannetti, 2017. "The effect of time preferences on altruism," Discussion Papers 2017/226, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.

    More about this item


    drf; dose–response function; generalized propensity score; kernel estimator; penalized spline estimator; weak unconfoundedness;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
    • J70 - Labor and Demographic Economics - - Labor Discrimination - - - General


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