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

Author

Listed:
  • 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
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    File URL: http://www.bancaditalia.it/pubblicazioni/temi-discussione/2008/2008-0683/en_tema_683.pdf
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    References listed on IDEAS

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    6. 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 313-336, June.
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    14. Kling, Jeffrey R, 2001. "Interpreting Instrumental Variables Estimates of the Returns to Schooling," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 358-364, July.
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    Cited by:

    1. Bia, Michela & Flores-Lagunes, Alfonso & Mercatanti, Andrea, 2018. "Evaluation of Language Training Programs in Luxembourg Using Principal Stratification," IZA Discussion Papers 11973, Institute of Labor Economics (IZA).
    2. Francesco Fallucchi & Andrea Mercatanti & Jan Niederreiter, 2021. "Identifying types in contest experiments," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 39-61, March.

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    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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