IDEAS home Printed from https://ideas.repec.org/p/bdi/wptemi/td_683_08.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://www.bancaditalia.it/pubblicazioni/temi-discussione/2008/2008-0683/en_tema_683.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    2. 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, President and Fellows of Harvard College, vol. 116(2), pages 705-746.
    3. 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.
    4. 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.
    5. repec:fth:prinin:311 is not listed on IDEAS
    6. 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.
    7. David Card, 1994. "Earnings, Schooling, and Ability Revisited," Working Papers 710, Princeton University, Department of Economics, Industrial Relations Section..
    8. Kiefer, Nicholas M, 1978. "Discrete Parameter Variation: Efficient Estimation of a Switching Regression Model," Econometrica, Econometric Society, vol. 46(2), pages 427-434, March.
    9. Thomas J. Kane & Cecilia E. Rouse, 1993. "Labor Market Returns to Two- and Four-Year Colleges: Is a Credit a Credit and Do Degrees Matter?," NBER Working Papers 4268, National Bureau of Economic Research, Inc.
    10. 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.
    11. 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.
    12. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 979-1014.
    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.
    14. 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.
    15. 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.
    16. Joshua 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Bia, Michela & Flores-Lagunes, Alfonso & Mercatanti, Andrea, 2018. "Evaluation of Language Training Programs in Luxembourg using Principal Stratification," GLO Discussion Paper Series 289, Global Labor Organization (GLO).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    2. Angel de la Fuente & Antonio Ciccone, 2003. "Human capital in a global and knowledge-based economy," UFAE and IAE Working Papers 562.03, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    3. Eric Maurin & Theodora Xenogiani, 2007. "Demand for Education and Labor Market Outcomes: Lessons from the Abolition of Compulsory Conscription in France," Journal of Human Resources, University of Wisconsin Press, vol. 42(4).
    4. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-1160, September.
    5. Aakvik, Arild & Salvanes, Kjell G. & Vaage, Kjell, 2003. "Measuring Heterogeneity in the Returns to Education in Norway Using Educational Reforms," IZA Discussion Papers 815, Institute of Labor Economics (IZA).
    6. Daniel A. Kamhöfer & Hendrik Schmitz, 2013. "Analyzing Zero Returns to Education in Germany – Heterogeneous Eff ects and Skill Formation," Ruhr Economic Papers 0446, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    7. Markus Frölich, 2004. "Programme Evaluation with Multiple Treatments," Journal of Economic Surveys, Wiley Blackwell, vol. 18(2), pages 181-224, April.
    8. Guido W. Imbens, 2022. "Causality in Econometrics: Choice vs Chance," Econometrica, Econometric Society, vol. 90(6), pages 2541-2566, November.
    9. Bauer, Thomas K. & Bender, Stefan & Paloyo, Alfredo R. & Schmidt, Christoph M., 2012. "Evaluating the labor-market effects of compulsory military service," European Economic Review, Elsevier, vol. 56(4), pages 814-829.
    10. Daniel A. Kamhöfer & Hendrik Schmitz, 2013. "Analyzing Zero Returns to Education in Germany: Heterogeneous Effects and Skill Formation," SOEPpapers on Multidisciplinary Panel Data Research 598, DIW Berlin, The German Socio-Economic Panel (SOEP).
    11. Josef Fersterer & Jörn‐Steffen Pischke & Rudolf Winter‐Ebmer, 2008. "Returns to Apprenticeship Training in Austria: Evidence from Failed Firms," Scandinavian Journal of Economics, Wiley Blackwell, vol. 110(4), pages 733-753, December.
    12. Rösner, Anja & Haucap, Justus & Heimeshoff, Ulrich, 2020. "The impact of consumer protection in the digital age: Evidence from the European Union," International Journal of Industrial Organization, Elsevier, vol. 73(C).
    13. Peter Hull & Michal Kolesár & Christopher Walters, 2022. "Labor by design: contributions of David Card, Joshua Angrist, and Guido Imbens," Scandinavian Journal of Economics, Wiley Blackwell, vol. 124(3), pages 603-645, July.
    14. John Giles & Albert Park & Meiyan Wang, 2019. "The Great Proletarian Cultural Revolution, Disruptions to Education, and the Returns to Schooling in Urban China," Economic Development and Cultural Change, University of Chicago Press, vol. 68(1), pages 131-164.
    15. Joshua D. Angrist & Alan B. Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 69-85, Fall.
    16. Per-Anders Edin & Peter Fredriksson & Olof Åslund, 2003. "Ethnic Enclaves and the Economic Success of Immigrants—Evidence from a Natural Experiment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(1), pages 329-357.
    17. Xin Meng & Robert G Gregory, "undated". "Impact of Interupted Education on Earnings: The Educational Cost of the Chinese Cultural revolution," Canadian International Labour Network Working Papers 40, McMaster University.
    18. Jörn-Steffen Pischke & Till von Wachter, 2008. "Zero Returns to Compulsory Schooling in Germany: Evidence and Interpretation," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 592-598, August.
    19. Krenz, Astrid, 2010. "La distinction reloaded: Returns to education, family background, cultural and social capital in Germany," University of Göttingen Working Papers in Economics 108, University of Goettingen, Department of Economics.
    20. Christopher Blattman & Jeannie Annan, 2010. "The Consequences of Child Soldiering," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 882-898, November.

    More about this item

    Keywords

    compliers; exclusion restriction; mixture distributions; return to schooling.;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bdi:wptemi:td_683_08. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/bdigvit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.