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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.)

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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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Paper provided by Bank of Italy, Economic Research Department 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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Related research
Keywords: compliers; exclusion restriction; mixture distributions; return to schooling.;

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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  1. 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. [Downloadable!] (restricted)
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  2. Barbara Roffia & Andrea Zaghini, 2007. "Excess money growth and inflation dynamics," Working Paper Series 749, European Central Bank. [Downloadable!]
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  3. Kevin Denny & Colm Harmon, 2000. "Education policy reform and the return to schooling from instrumental variables," IFS Working Papers W00/06, Institute for Fiscal Studies. [Downloadable!]
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  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.
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  5. Fabio Busetti, 2003. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Temi di discussione (Economic working papers) 476, Bank of Italy, Economic Research Department. [Downloadable!]
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  6. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-23, May. [Downloadable!] (restricted)
  7. Card, David, 1999. "The causal effect of education on earnings," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 30, pages 1801-1863 Elsevier. [Downloadable!] (restricted)
  8. 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 358-64, July.
  9. 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. [Downloadable!]
  10. David Card, 1994. "Earnings, Schooling, and Ability Revisited," NBER Working Papers 4832, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  11. Kiefer, Nicholas M, 1978. "Discrete Parameter Variation: Efficient Estimation of a Switching Regression Model," Econometrica, Econometric Society, vol. 46(2), pages 427-34, March. [Downloadable!] (restricted)
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