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

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  • Andrea Mercatanti

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

Abstract

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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Bibliographic Info

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

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Keywords: compliers; exclusion restriction; mixture distributions; return to schooling.;

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  1. Joshua D. Angrist & Alan B. Krueger, 1990. "Does Compulsory School Attendance Affect Schooling and Earnings?," NBER Working Papers 3572, National Bureau of Economic Research, Inc.
  2. Jeffrey R. Kling, 2000. "Interpreting Instrumental Variables Estimates of the Returns to Schooling," NBER Working Papers 7989, National Bureau of Economic Research, Inc.
  3. 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.
  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. Kevin J Denny & Colm P Harmon, 2000. "Education Policy Reform and the Return to Schooling from Instrumental Variables," Working Papers 200012, School Of Economics, University College Dublin.
  6. 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.
  7. Deschenes, Olivier, 2007. "Estimating the Effects of Family Background on the Return to Schooling," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 265-277, July.
  8. 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.
  9. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-23, May.
  10. Kiefer, Nicholas M, 1978. "Discrete Parameter Variation: Efficient Estimation of a Switching Regression Model," Econometrica, Econometric Society, vol. 46(2), pages 427-34, March.
  11. 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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