IDEAS home Printed from
   My bibliography  Save this article

Identification of treatment effects under imperfect matching with an application to Chinese elite schools


  • Zhang, Hongliang


This paper extends the treatment effect framework for causal inference to contexts in which the instrument appears in a data set that can only be linked imperfectly to the treatment and outcome variables contained in another data set. To overcome this problem, I form all pairwise links between information on the instrument and information on the treatment and outcome matched by the commonly recorded personal characteristics in both data sets. I show how these imperfect conditional matches can be used to identify both the average and distributional treatment effects for compliers of the common units of the two data sets. This multiple data source approach is then applied to analyze the effect of attending an elite middle school in a Chinese city where schools' admissions lottery records can only be linked imperfectly to the administrative student records.

Suggested Citation

  • Zhang, Hongliang, 2016. "Identification of treatment effects under imperfect matching with an application to Chinese elite schools," Journal of Public Economics, Elsevier, vol. 142(C), pages 56-82.
  • Handle: RePEc:eee:pubeco:v:142:y:2016:i:c:p:56-82 DOI: 10.1016/j.jpubeco.2016.03.004

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Brian A. Jacob, 2007. "Test-Based Accountability and Student Achievement: An Investigation of Differential Performance on NAEP and State Assessments," NBER Working Papers 12817, National Bureau of Economic Research, Inc.
    2. Weili Ding & Steven F. Lehrer, 2007. "Do Peers Affect Student Achievement in China's Secondary Schools?," The Review of Economics and Statistics, MIT Press, vol. 89(2), pages 300-312, May.
    3. Sa A. Bui & Steven G. Craig & Scott A. Imberman, 2014. "Is Gifted Education a Bright Idea? Assessing the Impact of Gifted and Talented Programs on Students," American Economic Journal: Economic Policy, American Economic Association, vol. 6(3), pages 30-62, August.
    4. David S. Lee & Thomas Lemieux, 2010. "Regression Discontinuity Designs in Economics," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 281-355, June.
    5. Thomas J. Kane & Douglas O. Staiger, 2002. "The Promise and Pitfalls of Using Imprecise School Accountability Measures," Journal of Economic Perspectives, American Economic Association, vol. 16(4), pages 91-114, Fall.
    6. Victor Lavy, 2010. "Effects of Free Choice Among Public Schools," Review of Economic Studies, Oxford University Press, vol. 77(3), pages 1164-1191.
    7. Esther Duflo & Pascaline Dupas & Michael Kremer, 2011. "Peer Effects, Teacher Incentives, and the Impact of Tracking: Evidence from a Randomized Evaluation in Kenya," American Economic Review, American Economic Association, vol. 101(5), pages 1739-1774, August.
    8. Clark Damon, 2010. "Selective Schools and Academic Achievement," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 10(1), pages 1-40, February.
    9. David J. Deming, 2011. "Better Schools, Less Crime?," The Quarterly Journal of Economics, Oxford University Press, vol. 126(4), pages 2063-2115.
    10. Ridder, Geert & Moffitt, Robert, 2007. "The Econometrics of Data Combination," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 75 Elsevier.
    11. Dee, Thomas & Lan, Xiaohuan, 2015. "The achievement and course-taking effects of magnet schools: Regression-discontinuity evidence from urban China," Economics of Education Review, Elsevier, vol. 47(C), pages 128-142.
    12. Downes, Thomas A. & Zabel, Jeffrey E., 2002. "The impact of school characteristics on house prices: Chicago 1987-1991," Journal of Urban Economics, Elsevier, vol. 52(1), pages 1-25, July.
    13. Joshua Angrist & Eric Bettinger & Erik Bloom & Elizabeth King & Michael Kremer, 2002. "Vouchers for Private Schooling in Colombia: Evidence from a Randomized Natural Experiment," American Economic Review, American Economic Association, vol. 92(5), pages 1535-1558, December.
    14. David N. Figlio & Maurice E. Lucas, 2004. "What's in a Grade? School Report Cards and the Housing Market," American Economic Review, American Economic Association, vol. 94(3), pages 591-604, June.
    15. Julie Berry Cullen & Brian A Jacob & Steven Levitt, 2006. "The Effect of School Choice on Participants: Evidence from Randomized Lotteries," Econometrica, Econometric Society, vol. 74(5), pages 1191-1230, September.
    16. Brian A. Jacob & Lars Lefgren, 2007. "What Do Parents Value in Education? An Empirical Investigation of Parents' Revealed Preferences for Teachers," The Quarterly Journal of Economics, Oxford University Press, vol. 122(4), pages 1603-1637.
    17. Stephanie Riegg Cellini & Fernando Ferreira & Jesse Rothstein, 2010. "The Value of School Facility Investments: Evidence from a Dynamic Regression Discontinuity Design," The Quarterly Journal of Economics, Oxford University Press, vol. 125(1), pages 215-261.
    18. Cristian Pop-Eleches & Miguel Urquiola, 2013. "Going to a Better School: Effects and Behavioral Responses," American Economic Review, American Economic Association, vol. 103(4), pages 1289-1324, June.
    19. Fang Lai & Elisabeth Sadoulet & Alain de Janvry, 2011. "The Contributions of School Quality and Teacher Qualifications to Student Performance: Evidence from a Natural Experiment in Beijing Middle Schools," Journal of Human Resources, University of Wisconsin Press, vol. 46(1), pages 123-153.
    20. W. Bentley MacLeod & Miguel Urquiola, 2015. "Reputation and School Competition," American Economic Review, American Economic Association, vol. 105(11), pages 3471-3488, November.
    21. Joshua D. Angrist & Kathryn Graddy & Guido W. Imbens, 2000. "The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 499-527.
    22. Will Dobbie & Roland G. Fryer Jr., 2014. "The Impact of Attending a School with High-Achieving Peers: Evidence from the New York City Exam Schools," American Economic Journal: Applied Economics, American Economic Association, vol. 6(3), pages 58-75, July.
    23. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    24. Hsieh, Chang-Tai & Urquiola, Miguel, 2006. "The effects of generalized school choice on achievement and stratification: Evidence from Chile's voucher program," Journal of Public Economics, Elsevier, vol. 90(8-9), pages 1477-1503, September.
    25. Manuel Arellano & Costas Meghir, 1992. "Female Labour Supply and On-the-Job Search: An Empirical Model Estimated Using Complementary Data Sets," Review of Economic Studies, Oxford University Press, vol. 59(3), pages 537-559.
    26. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    27. Justine S. Hastings & Jeffrey M. Weinstein, 2008. "Information, School Choice, and Academic Achievement: Evidence from Two Experiments," The Quarterly Journal of Economics, Oxford University Press, vol. 123(4), pages 1373-1414.
    28. Victor Lavy & Olmo Silva & Felix Weinhardt, 2012. "The Good, the Bad, and the Average: Evidence on Ability Peer Effects in Schools," Journal of Labor Economics, University of Chicago Press, vol. 30(2), pages 367-414.
    29. Atila Abdulkadiro─člu & Joshua Angrist & Parag Pathak, 2014. "The Elite Illusion: Achievement Effects at Boston and New York Exam Schools," Econometrica, Econometric Society, vol. 82(1), pages 137-196, January.
    30. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    31. Joshua Angrist & Eric Bettinger & Michael Kremer, 2006. "Long-Term Educational Consequences of Secondary School Vouchers: Evidence from Administrative Records in Colombia," American Economic Review, American Economic Association, vol. 96(3), pages 847-862, June.
    32. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 555-574.
    33. David J. Deming & Justine S. Hastings & Thomas J. Kane & Douglas O. Staiger, 2014. "School Choice, School Quality, and Postsecondary Attainment," American Economic Review, American Economic Association, vol. 104(3), pages 991-1013, March.
    34. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
    35. David S. Lee, 2009. "Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects," Review of Economic Studies, Oxford University Press, vol. 76(3), pages 1071-1102.
    36. C. Kirabo Jackson, 2010. "Do Students Benefit from Attending Better Schools? Evidence from Rule-based Student Assignments in Trinidad and Tobago," Economic Journal, Royal Economic Society, vol. 120(549), pages 1399-1429, December.
    37. Mizala, Alejandra & Urquiola, Miguel, 2013. "School markets: The impact of information approximating schools' effectiveness," Journal of Development Economics, Elsevier, vol. 103(C), pages 313-335.
    38. Lee, David S., 2008. "Randomized experiments from non-random selection in U.S. House elections," Journal of Econometrics, Elsevier, vol. 142(2), pages 675-697, February.
    39. Eric Bettinger & Michael Kremer & Juan E. Saavedra, 2010. "Are Educational Vouchers Only Redistributive?," Economic Journal, Royal Economic Society, vol. 120(546), pages 204-228, August.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Local average treatment effect; Distributional treatment effects; Imperfect matching; Elite schools; Student achievement;

    JEL classification:

    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
    • I28 - Health, Education, and Welfare - - Education - - - Government Policy


    Access and download statistics


    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:eee:pubeco:v:142:y:2016:i:c:p:56-82. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.