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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 Lee

    ()

    (Institute for Fiscal Studies and 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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File URL: http://www.cemmap.ac.uk/wps/cwp171414.pdf
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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: 26 Mar 2014
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Handle: RePEc:ifs:cemmap:17/14
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  4. Donald W.K. Andrews & Gustavo Soares, 2007. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Cowles Foundation Discussion Papers 1631, Cowles Foundation for Research in Economics, Yale University.
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  7. 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 Archive 32719, Iowa State University, Department of Economics.
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  10. Craig Gundersen & Brent Kreider, 2008. "Food Stamps and Food Insecurity: What Can Be Learned in the Presence of Nonclassical Measurement Error?," Journal of Human Resources, University of Wisconsin Press, vol. 43(2), pages 352-382.
  11. Hall, Peter & Yatchew, Adonis, 2010. "Nonparametric least squares estimation in derivative families," Journal of Econometrics, Elsevier, vol. 157(2), pages 362-374, August.
  12. Donald W.K. Andrews & Panle Jia, 2008. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Cowles Foundation Discussion Papers 1676, Cowles Foundation for Research in Economics, Yale University.
  13. Charles F. Manski & John V. Pepper, 1998. "Monotone Instrumental Variables with an Application to the Returns to Schooling," NBER Technical Working Papers 0224, National Bureau of Economic Research, Inc.
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  15. Kreider, Brent & Hill, Steven C., 2005. "Partially Identifying Treatment Effects with an Application to Covering the Uninsured," Staff General Research Papers Archive 12296, Iowa State University, Department of Economics.
  16. Okumura, Tsunao & Usui, Emiko, 2010. "Concave-Monotone Treatment Response and Monotone Treatment Selection: With an Application to the Returns to Schooling," IZA Discussion Papers 4986, Institute for the Study of Labor (IZA).
  17. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, 09.
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  19. Richard Blundell & Amanda Gosling & Hidehiko Ichimura & Costas Meghir, 2007. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," Econometrica, Econometric Society, vol. 75(2), pages 323-363, 03.
  20. 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.
  21. Sokbae Lee & Ralf A. Wilke, 2005. "Reform of unemployment compensation in Germany: a nonparametric bounds analysis using register data," CeMMAP working papers CWP02/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  22. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, 09.
  23. 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.
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  25. 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.
  26. Kluve, Jochen & Schneider, Hilmar & Uhlendorff, Arne & Zhao, Zhong, 2012. "Evaluating continuous training programmes by using the generalized propensity score," EconStor Open Access Articles, ZBW - German National Library of Economics, pages 587-617.
  27. 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.
  28. 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.
  29. Pedro Carneiro & Sokbae Lee, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," CeMMAP working papers CWP01/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  30. 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.
  31. 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.
  32. Federico A. Bugni, 2010. "Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set," Econometrica, Econometric Society, vol. 78(2), pages 735-753, 03.
  33. Guido Imbens & Charles F. Manski, 2003. "Confidence intervals for partially identified parameters," CeMMAP working papers CWP09/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  34. Galichon, Alfred & Henry, Marc, 2009. "A test of non-identifying restrictions and confidence regions for partially identified parameters," Journal of Econometrics, Elsevier, vol. 152(2), pages 186-196, October.
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