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Using Lagged Outcomes to Evaluate Bias in Value-Added Models

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  • Raj Chetty
  • John N. Friedman
  • Jonah Rockoff

Abstract

Value-added (VA) models measure the productivity of agents such as teachers or doctors based on the outcomes they produce. The utility of VA models for performance evaluation depends on the extent to which VA estimates are biased by selection, for instance by differences in the abilities of students assigned to teachers. One widely used approach for evaluating bias in VA is to test for balance in lagged values of the outcome, based on the intuition that today’s inputs cannot influence yesterday’s outcomes. We use Monte Carlo simulations to show that, unlike in conventional treatment effect analyses, tests for balance using lagged outcomes do not provide robust information about the degree of bias in value-added models for two reasons. First, the treatment itself (value-added) is estimated, rather than exogenously observed. As a result, correlated shocks to outcomes can induce correlations between current VA estimates and lagged outcomes that are sensitive to model specification. Second, in most VA applications, estimation error does not vanish asymptotically because sample sizes per teacher (or principal, manager, etc.) remain small, making balance tests sensitive to the specification of the error structure even in large datasets. We conclude that bias in VA models is better evaluated using techniques that are less sensitive to model specification, such as randomized experiments, rather than using lagged outcomes.

Suggested Citation

  • Raj Chetty & John N. Friedman & Jonah Rockoff, 2016. "Using Lagged Outcomes to Evaluate Bias in Value-Added Models," NBER Working Papers 21961, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:21961
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    References listed on IDEAS

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    1. Thomas J. Kane & Douglas O. Staiger, 2008. "Estimating Teacher Impacts on Student Achievement: An Experimental Evaluation," NBER Working Papers 14607, National Bureau of Economic Research, Inc.
    2. Raj Chetty & John N. Friedman & Jonah E. Rockoff, 2014. "Measuring the Impacts of Teachers I: Evaluating Bias in Teacher Value-Added Estimates," American Economic Review, American Economic Association, vol. 104(9), pages 2593-2632, September.
    3. Jesse Rothstein, 2010. "Teacher Quality in Educational Production: Tracking, Decay, and Student Achievement," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(1), pages 175-214.
    4. David J. Deming, 2014. "Using School Choice Lotteries to Test Measures of School Effectiveness," American Economic Review, American Economic Association, vol. 104(5), pages 406-411, May.
    5. Joshua D. Angrist & Peter D. Hull & Parag A. Pathak & Christopher R. Walters, 2017. "Leveraging Lotteries for School Value-Added: Testing and Estimation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(2), pages 871-919.
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    Citations

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    Cited by:

    1. Hanushek, Eric A. & Rivkin, Steven G. & Schiman, Jeffrey C., 2016. "Dynamic effects of teacher turnover on the quality of instruction," Economics of Education Review, Elsevier, vol. 55(C), pages 132-148.
    2. Raj Chetty & John N. Friedman & Jonah E. Rockoff, 2017. "Measuring the Impacts of Teachers: Reply," American Economic Review, American Economic Association, vol. 107(6), pages 1685-1717, June.
    3. Canales, Andrea & Maldonado, Luis, 2018. "Teacher quality and student achievement in Chile: Linking teachers' contribution and observable characteristics," International Journal of Educational Development, Elsevier, vol. 60(C), pages 33-50.
    4. Dan Goldhaber, 2018. "Impact and Your Death Bed: Playing the Long Game," Education Finance and Policy, MIT Press, vol. 13(1), pages 1-18, Winter.
    5. Xiaopeng Wu & Tianshu Xu & Jincheng Zhou, 2022. "Sustainability of Evaluation: The Origin and Development of Value-Added Evaluation from the Global Perspective," Sustainability, MDPI, vol. 14(23), pages 1-13, November.
    6. Brian Gill & Christine Ross & Erin Dillon & Ann Li & Patricia Troppe & Eric Isenberg & Anthony Milanowski & Roberta Garrison-Mogren & Louis Rizzo, "undated". "The Transition to ESSA: State and District Approaches to Implementing Title I and Title II-A in 2017–18," Mathematica Policy Research Reports b081b481f0ae4dcca46c338f9, Mathematica Policy Research.
    7. Sam Jones, 2020. "Testing the Technology of Human Capital Production: A General‐to‐Restricted Framework," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1429-1455, December.
    8. Goldhaber, Dan & Krieg, John & Theobald, Roddy, 2020. "Effective like me? Does having a more productive mentor improve the productivity of mentees?," Labour Economics, Elsevier, vol. 63(C).
    9. Cook, Jason B. & Mansfield, Richard K., 2016. "Task-specific experience and task-specific talent: Decomposing the productivity of high school teachers," Journal of Public Economics, Elsevier, vol. 140(C), pages 51-72.
    10. Marco Ovidi, 2021. "Parents know better: primary school choice and student achievement in London," Working Papers 919, Queen Mary University of London, School of Economics and Finance.
    11. Marco Ovidi, 2022. "Parents Know Better: Sorting on Match Effects in Primary School," DISCE - Working Papers del Dipartimento di Economia e Finanza def121, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).

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    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • H75 - Public Economics - - State and Local Government; Intergovernmental Relations - - - State and Local Government: Health, Education, and Welfare
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
    • J01 - Labor and Demographic Economics - - General - - - Labor Economics: General
    • J08 - Labor and Demographic Economics - - General - - - Labor Economics Policies
    • J45 - Labor and Demographic Economics - - Particular Labor Markets - - - Public Sector Labor Markets
    • M50 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics - - - General
    • M54 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics - - - Labor Management

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