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The identification power of smoothness assumptions in models with counterfactual outcomes

  • Wooyoung Kim

    (Institute for Fiscal Studies)

  • Koohyun Kwon

    (Institute for Fiscal Studies)

  • Soonwoo Kwon

    (Institute for Fiscal Studies)

  • Sokbae (Simon) Lee


    (Institute for Fiscal Studies)

In this paper, we investigate what can be learned about average counterfactual outcomes when it is assumed that treatment response functions are smooth. The smoothness conditions in this paper amount to assuming that the di fferences in average counterfactual outcomes are bounded under different treatments. We obtain a set of new partial identi fication results for the average treatment response by imposing smoothness conditions alone, by combining them with monotonicity assumptions, and by adding instrumental variables assumptions to treatment responses. We give a numerical illustration of our findings by reanalyzing the return to schooling example of Manski and Pepper (2000) and demonstrate how one can conduct sensitivity analysis by varying the degrees of smoothness assumption. In addition, we discuss how to carry out inference based on the existing literature using our identi cation results and illustrate its usefulness by applying one of our identi fication results to the Job Corps Study dataset. Our empirical results show that there is strong evidence of the gender and race gaps among the less educated population.

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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP17/14.

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Date of creation: Mar 2014
Date of revision:
Handle: RePEc:ifs:cemmap:17/14
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  1. Okumura, Tsunao & Usui, Emiko, 2010. "Concave-Monotone Treatment Response and Monotone Treatment Selection: With an Application to the Returns to Schooling," PIE/CIS Discussion Paper 475, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
  2. Brent Kreider & John V. Pepper & Craig Gundersen & Dean Jolliffe, 2012. "Identifying the Effects of SNAP (Food Stamps) on Child Health Outcomes When Participation Is Endogenous and Misreported," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 958-975, September.
  3. John V. Pepper, 2000. "The Intergenerational Transmission Of Welfare Receipt: A Nonparametric Bounds Analysis," The Review of Economics and Statistics, MIT Press, vol. 82(3), pages 472-488, August.
  4. Gundersen, Craig & Kreider, Brent & Pepper, John V., 2011. "The Impact of the National School Lunch Program on Child Health: A Nonparametric Bounds Analysis," Staff General Research Papers 32720, Iowa State University, Department of Economics.
  5. Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-04, Duke University, Department of Economics.
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  7. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
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  10. Gundersen, Craig & Kreider, Brent, 2006. "Food Stamps and Food Insecurity: What Can Be Learned in the Presence of Non-Classical Measurement Error?," Staff General Research Papers 12690, Iowa State University, Department of Economics.
  11. Victor Chernozhukov & Sokbae (Simon) Lee & Adam Rosen, 2012. "Intersection bounds: estimation and inference," CeMMAP working papers CWP33/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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  15. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
  16. Adam Rosen, 2006. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," CeMMAP working papers CWP25/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  17. Lee, Sokbae & Wilke, Ralf A., 2009. "Reform of Unemployment Compensation in Germany: A Nonparametric Bounds Analysis Using Register Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 193-205.
  18. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09.
  19. Hall, Peter & Yatchew, Adonis, 2010. "Nonparametric least squares estimation in derivative families," Journal of Econometrics, Elsevier, vol. 157(2), pages 362-374, August.
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  21. Jay Bhattacharya & Azeem M. Shaikh & Edward Vytlacil, 2008. "Treatment Effect Bounds under Monotonicity Assumptions: An Application to Swan-Ganz Catheterization," American Economic Review, American Economic Association, vol. 98(2), pages 351-56, May.
  22. 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.
  23. Fan, Yanqin & Park, Sang Soo, 2014. "Nonparametric inference for counterfactual means: Bias-correction, confidence sets, and weak IV," Journal of Econometrics, Elsevier, vol. 178(P1), pages 45-56.
  24. 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.
  25. Yanqin Fan & Jisong Wu, 2010. "Partial Identification of the Distribution of Treatment Effects in Switching Regime Models and its Confidence Sets," Review of Economic Studies, Oxford University Press, vol. 77(3), pages 1002-1041.
  26. Jochen Kluve & Hilmar Schneider & Arne Uhlendorff & Zhong Zhao, 2012. "Evaluating continuous training programmes by using the generalized propensity score," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 175(2), pages 587-617, 04.
  27. Monique de Haan, 2011. "The Effect of Parents' Schooling on Child's Schooling: A Nonparametric Bounds Analysis," Journal of Labor Economics, University of Chicago Press, vol. 29(4), pages 859 - 892.
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