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A likelihood-based analysis for relaxing the exclusion restriction in randomized experiments with imperfect compliance

  • Andrea Mercatanti

    ()

    (Bank of Italy, Economic and Financial Statistics Department.)

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    This paper examines the problem of relaxing the exclusion restriction for the evaluation of causal effects in randomized experiments with imperfect compliance. Exclusion restriction is a relevant assumption for identifying causal effects by the nonparametric instrumental variables technique, in which the template of a randomized experiment with imperfect compliance represents a natural parametric extension. However, the full relaxation of the exclusion restriction yields likelihood functions characterized by the presence of mixtures of distributions. This complicates a likelihood-based analysis because it implies partially identified models and more than one maximum likelihood point. We consider the model identifiability when the outcome distributions of various compliance states are in the same parametric class. A two-step estimation procedure based on detecting the root closest to the method of moments estimate of the parameter vector is proposed and analyzed in detail under normally distributed outcomes. An economic example with real data on return to schooling concludes the paper.

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    File URL: http://www.bancaditalia.it/pubblicazioni/temi-discussione/2008/2008-0683/en_tema_683.pdf
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    Paper provided by Bank of Italy, Economic Research and International Relations Area in its series Temi di discussione (Economic working papers) with number 683.

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    Date of creation: Aug 2008
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    Handle: RePEc:bdi:wptemi:td_683_08
    Contact details of provider: Postal: Via Nazionale, 91 - 00184 Roma
    Web page: http://www.bancaditalia.it

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    1. Kevin J. Denny & Colm P. Harmon, 2000. "Education Policy Reform and the Return to Schooling from Instrumental Variabes," Econometric Society World Congress 2000 Contributed Papers 1422, Econometric Society.
    2. Joshua Angrist & Alan Krueger, 1990. "Does Compulsory School Attendance Affect Schooling and Earnings?," Working Papers 653, Princeton University, Department of Economics, Industrial Relations Section..
    3. David Card & Thomas Lemieux, 2001. "Can Falling Supply Explain The Rising Return To College For Younger Men? A Cohort-Based Analysis," The Quarterly Journal of Economics, MIT Press, vol. 116(2), pages 705-746, May.
    4. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," American Economic Review, American Economic Association, vol. 80(3), pages 313-36, June.
    5. Ichino, Andrea & Winter-Ebmer, Rudolf, 1999. "Lower and upper bounds of returns to schooling: An exercise in IV estimation with different instruments," European Economic Review, Elsevier, vol. 43(4-6), pages 889-901, April.
    6. Henry S. Farber & Jeffrey R. Kling & Alan Krueger, 1999. "Interpreting Instrumental Variables Estimates of the Returns to Schooling," Working Papers 794, Princeton University, Department of Economics, Industrial Relations Section..
    7. Deschenes, Olivier, 2002. "Estimating the Effects of Family Background on the Return to Schooling," University of California at Santa Barbara, Economics Working Paper Series qt2qm3867s, Department of Economics, UC Santa Barbara.
    8. repec:att:wimass:8909 is not listed on IDEAS
    9. Kiefer, Nicholas M, 1978. "Discrete Parameter Variation: Efficient Estimation of a Switching Regression Model," Econometrica, Econometric Society, vol. 46(2), pages 427-34, March.
    10. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-23, May.
    11. J.D. Angrist & Guido W. Imbens & D.B. Rubin, 1993. "Identification of Causal Effects Using Instrumental Variables," NBER Technical Working Papers 0136, National Bureau of Economic Research, Inc.
    12. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records: Errata," American Economic Review, American Economic Association, vol. 80(5), pages 1284-86, December.
    13. Andrea Ichino & Rudolf Winter-Ebmer, 2004. "The Long-Run Educational Cost of World War II," Journal of Labor Economics, University of Chicago Press, vol. 22(1), pages 57-86, January.
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