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

Author

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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.

Suggested Citation

  • Andrea Mercatanti, 2008. "A likelihood-based analysis for relaxing the exclusion restriction in randomized experiments with imperfect compliance," Temi di discussione (Economic working papers) 683, Bank of Italy, Economic Research and International Relations Area.
  • Handle: RePEc:bdi:wptemi:td_683_08
    as

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    References listed on IDEAS

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    1. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, Oxford University Press, vol. 106(4), pages 979-1014.
    2. 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.
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    4. Denny, Kevin & Harmon, Colm, 2000. "Education Policy Reform and the Return to Schooling from Instrumental Variables," CEPR Discussion Papers 2518, C.E.P.R. Discussion Papers.
    5. 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, Oxford University Press, vol. 116(2), pages 705-746.
    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.
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    9. 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 1284-1286, December.
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    13. 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.
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    More about this item

    Keywords

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

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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