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

Author

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  • Carlos A. Flores

    () (Department of Economics, University of Miami)

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.

Suggested Citation

  • Carlos A. Flores, 2007. "Estimation of Dose-Response Functions and Optimal Doses with a Continuous Treatment," Working Papers 0707, University of Miami, Department of Economics.
  • Handle: RePEc:mia:wpaper:0707
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    File URL: http://moya.bus.miami.edu/~cflores/research_papers/Flores_OD_111007.pdf
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    References listed on IDEAS

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    4. Stern, David I., 2004. "The Rise and Fall of the Environmental Kuznets Curve," World Development, Elsevier, vol. 32(8), pages 1419-1439, August.
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    Citations

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    Cited by:

    1. Flores, Carlos A. & Mitnik, Oscar A., 2009. "Evaluating Nonexperimental Estimators for Multiple Treatments: Evidence from Experimental Data," IZA Discussion Papers 4451, Institute for the Study of Labor (IZA).
    2. Apergis, Nicholas & Christou, Christina & Gupta, Rangan, 2017. "Are there Environmental Kuznets Curves for US state-level CO2 emissions?," Renewable and Sustainable Energy Reviews, Elsevier, vol. 69(C), pages 551-558.
    3. repec:sav:ebooks:003 is not listed on IDEAS
    4. 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.
    5. 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.
    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. 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.

    More about this item

    Keywords

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

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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