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Nonparametric Estimators of Dose-Response Functions

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  • BIA Michela
  • FLORES Carlos A.
  • MATTEI Alessandra

Abstract

We propose two semiparametric estimators of the dose-response function based on spline techniques. Under uncounfoundedness, the generalized propensity score can be used to estimate dose-response functions (DRF) and marginal treatment effect functions. In many observational studies treatment may not be binary or categorical. In such cases, one may be interested in estimating the dose-response function in a setting with a continuous treatment. We evaluate the performance of the proposed estimators using Monte Carlo simulation methods. The simulation results suggested that the estimated DRF is robust to the specific semiparametric estimator used, while the parametric estimates of the DRF were sensitive to model mis-specification. We apply our approach to the problem of evaluating the effect on innovation sales of Research and Development (R&D) financial aids received by Luxembourgish firms in 2004 and 2005.

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Bibliographic Info

Paper provided by CEPS/INSTEAD in its series CEPS/INSTEAD Working Paper Series with number 2011-40.

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Length: 24 pages
Date of creation: Jul 2011
Date of revision:
Handle: RePEc:irs:cepswp:2011-40

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Keywords: Continuous treatment; Dose-response function; Generalized Propensity Score; Non-parametric methods; R&D investment;

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References

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  1. Giovanni Cerulli, 2010. "Modelling and Measuring the Effect of Public Subsidies on Business R&D: A Critical Review of the Econometric Literature," The Economic Record, The Economic Society of Australia, vol. 86(274), pages 421-449, 09.
  2. David, Paul A. & Hall, Bronwyn H. & Toole, Andrew A., 1999. "Is Public R&D a Complement or Substitute for Private R&D? A Review of the Econometric Evidence," Department of Economics, Working Paper Series qt1sz6g8bv, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  3. Ben Jann & Roberto G. Gutierrez, 2008. "PSPLINE: Stata module providing a penalized spline scatterplot smoother based on linear mixed model technology," Statistical Software Components S456972, Boston College Department of Economics, revised 25 Jan 2009.
  4. Lechner, Michael, 1999. "Identification and Estimation of Causal Effects of Multiple Treatments Under the Conditional Independence Assumption," IZA Discussion Papers 91, Institute for the Study of Labor (IZA).
  5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, April.
  6. Czarnitzki, Dirk & Lopes Bento, Cindy, 2010. "Evaluation of public R&D policies: A cross-country comparison," ZEW Discussion Papers 10-073, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  7. 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.
  8. Jochen Kluve & Hilmar Schneider & Arne Uhlendorff & Zhong Zhao, 2007. "Evaluating Continuous Training Programs Using the Generalized Propensity Score," Ruhr Economic Papers 0035, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
  9. 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.
  10. DAUTEL Vincent & WALTHER Olivier, 2011. "The geography of innovation in the Luxembourg metropolitan region: an intra-regional approach," CEPS/INSTEAD Working Paper Series 2011-38, CEPS/INSTEAD.
  11. Nancy T. Gallini, 2002. "The Economics of Patents: Lessons from Recent U.S. Patent Reform," Journal of Economic Perspectives, American Economic Association, vol. 16(2), pages 131-154, Spring.
  12. Almus, Matthias & Czarnitzki, Dirk, 2003. "The Effects of Public R&D Subsidies on Firms' Innovation Activities: The Case of Eastern Germany," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(2), pages 226-36, April.
  13. Lu B. & Zanutto E. & Hornik R. & Rosenbaum P.R., 2001. "Matching With Doses in an Observational Study of a Media Campaign Against Drug Abuse," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1245-1253, December.
  14. 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).
  15. Kluve, Jochen & Schneider, Hilmar & Uhlendorff, Arne & Zhao, Zhong, 2007. "Evaluating continuous training programs using the generalized propensity score1," Technical Reports 2007,39, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  16. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(02), pages 1-21, June.
  17. Martin Falk, 2004. "Employment of High-skilled Labour, Computer Investment and Innovation Expenditures. Speed-up of Technological Change," WIFO Monatsberichte (monthly reports), WIFO, vol. 77(3), pages 213-222, March.
  18. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, April.
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