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Estimation of Dose-Response Functions and Optimal Doses with a Continuous Treatment

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  • Carlos A. Flores

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    (Department of Economics, University of Miami)

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    Abstract

    This paper considers the continuous-treatment case and develops nonparametric estimators for the average dose-response function, the treatment level at which this function is maximized (location of the maximum), and the maximum value achieved by this function (size of the maximum). These parameters are identified by assuming that selection into different levels of the treatment is based on observed characteristics. The proposed nonparametric estimators of the location and size of the optimal dose are shown to be jointly asymptotically normal and uncorrelated. More generally, these estimators can be used to estimate the location and size of the maximum of a partial mean (Newey, 1994). To illustrate the utility of our approach, the techniques developed in the paper are used to estimate the turning point of the environmental Kuznets curve (EKC) for NOx, that is, the level of per capita income at which the emissions of NOx reach their peak and start decreasing. Finally, a Monte Carlo exercise is performed partly based on the data used in the empirical application. The results show that the nonparametric estimators of the location and size of the optimal dose developed in this paper work well in practice (especially when compared to a parametric model), in some cases even for relatively small sample sizes.

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    File URL: http://moya.bus.miami.edu/~cflores/research_papers/Flores_OD_111007.pdf
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    Bibliographic Info

    Paper provided by University of Miami, Department of Economics in its series Working Papers with number 0707.

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    Length: 37 pages
    Date of creation: Nov 2007
    Date of revision:
    Publication status: Forthcoming: Under Review
    Handle: RePEc:mia:wpaper:0707

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    Related research

    Keywords: Continuous Treatment; Nonparametric Estimation; Partial Means; Location and Size of the Maximum; Environmental Kuznets Curve;

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    References

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    1. 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.
    2. Jean Imbs & Romain Wacziarg, 2003. "Stages of Diversification," American Economic Review, American Economic Association, vol. 93(1), pages 63-86, March.
    3. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    4. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," NBER Technical Working Papers 0251, National Bureau of Economic Research, Inc.
    5. List, John A. & Gallet, Craig A., 1999. "The environmental Kuznets curve: does one size fit all?," Ecological Economics, Elsevier, vol. 31(3), pages 409-423, December.
    6. Flores-Lagunes, Alfonso & Gonzalez, Arturo & Neumann, Todd C., 2007. "Estimating the Effects of Length of Exposure to a Training Program: The Case of Job Corps," IZA Discussion Papers 2846, Institute for the Study of Labor (IZA).
    7. Chen, Hung & Huang, Mong-Na Lo & Huang, Wen-Jang, 1996. "Estimation of the Location of the Maximum of a Regression Function Using Extreme Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 191-214, May.
    8. Sergio Firpo, 2007. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 75(1), pages 259-276, 01.
    9. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
    10. Jochen Kluve & Hilmar Schneider & Arne Uhlendorff & Zhong Zhao, 2007. "Evaluating Continuous Training Programs Using the Generalized Propensity Score," Discussion Papers of DIW Berlin 752, DIW Berlin, German Institute for Economic Research.
    11. Grossman, Gene & Krueger, Alan B, 1992. "Environmental Impacts of a North American Free Trade Agreement," CEPR Discussion Papers 644, C.E.P.R. Discussion Papers.
    12. Fryges, Helmut, 2006. "The Export-Growth Relationship: Estimating a Dose-Response Function," ZEW Discussion Papers 06-28, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    13. Cropper, Maureen & Griffiths, Charles, 1994. "The Interaction of Population Growth and Environmental Quality," American Economic Review, American Economic Association, vol. 84(2), pages 250-54, May.
    14. Daniel L. Millimet & John A. List & Thanasis Stengos, 2003. "The Environmental Kuznets Curve: Real Progress or Misspecified Models?," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1038-1047, November.
    15. Selden Thomas M. & Song Daqing, 1994. "Environmental Quality and Development: Is There a Kuznets Curve for Air Pollution Emissions?," Journal of Environmental Economics and Management, Elsevier, vol. 27(2), pages 147-162, September.
    16. Stern, David I., 2004. "The Rise and Fall of the Environmental Kuznets Curve," World Development, Elsevier, vol. 32(8), pages 1419-1439, August.
    17. Gene M. Grossman & Alan B. Krueger, 1994. "Economic Growth and the Environment," NBER Working Papers 4634, National Bureau of Economic Research, Inc.
    18. Baltagi, Badi H. & Hidalgo, Javier & Li, Qi, 1996. "A nonparametric test for poolability using panel data," Journal of Econometrics, Elsevier, vol. 75(2), pages 345-367, December.
    19. Susmita Dasgupta & Benoit Laplante & Hua Wang & David Wheeler, 2002. "Confronting the Environmental Kuznets Curve," Journal of Economic Perspectives, American Economic Association, vol. 16(1), pages 147-168, Winter.
    20. Stern , David I., 1998. "Progress on the environmental Kuznets curve?," Environment and Development Economics, Cambridge University Press, vol. 3(02), pages 173-196, May.
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    Citations

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    Cited by:
    1. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers 706, University of Oxford, Department of Economics.
    2. Carlos A. Flores & Oscar A. Mitnik, 2009. "Evaluating Nonexperimental Estimators for Multiple Treatments: Evidence from Experimental Data," Working Papers 2010-10, University of Miami, Department of Economics.
    3. Michela Bia & Alessandra Mattei, 2012. "Assessing the effect of the amount of financial aids to Piedmont firms using the generalized propensity score," Statistical Methods and Applications, Springer, vol. 21(4), pages 485-516, November.
    4. Guadalupe Serrano-Domingo & Francisco Requena-Silvente, 2013. "Examining the non-linear relationship between migration and trade," Working Papers 1310, Department of Applied Economics II, Universidad de Valencia.
    5. Serrano-Domingo, Guadalupe & Requena-Silvente, Francisco, 2013. "Re-examining the migration–trade link using province data: An application of the generalized propensity score," Economic Modelling, Elsevier, vol. 32(C), pages 247-261.

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