IDEAS home Printed from https://ideas.repec.org/a/wly/quante/v10y2019i4p1537-1577.html
   My bibliography  Save this article

Measuring quality for use in incentive schemes: The case of “shrinkage” estimators

Author

Listed:
  • Nirav Mehta

Abstract

Researchers commonly “shrink” raw quality measures based on statistical criteria. This paper studies when and how this transformation's statistical properties would confer economic benefits to a utility‐maximizing decision‐maker across common asymmetric information environments. I develop the results for an application measuring teacher quality. The presence of a systematic relationship between teacher quality and class size could cause the data transformation to do either worse or better than the untransformed data. I use data from Los Angeles to confirm the presence of such a relationship and show that the simpler raw measure would outperform the one most commonly used in teacher incentive schemes.

Suggested Citation

  • Nirav Mehta, 2019. "Measuring quality for use in incentive schemes: The case of “shrinkage” estimators," Quantitative Economics, Econometric Society, vol. 10(4), pages 1537-1577, November.
  • Handle: RePEc:wly:quante:v:10:y:2019:i:4:p:1537-1577
    DOI: 10.3982/QE950
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/QE950
    Download Restriction: no

    File URL: https://libkey.io/10.3982/QE950?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Rothschild, Michael, 1974. "Searching for the Lowest Price When the Distribution of Prices Is Unknown," Journal of Political Economy, University of Chicago Press, vol. 82(4), pages 689-711, July/Aug..
    2. Daniel Player, 2010. "Nonmonetary Compensation in the Public Teacher Labor Market," Education Finance and Policy, MIT Press, vol. 5(1), pages 82-103, January.
    3. Lazear, Edward P & Rosen, Sherwin, 1981. "Rank-Order Tournaments as Optimum Labor Contracts," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 841-864, October.
    4. Steven G. Rivkin & Eric A. Hanushek & John F. Kain, 2005. "Teachers, Schools, and Academic Achievement," Econometrica, Econometric Society, vol. 73(2), pages 417-458, March.
    5. Thomas Dohmen & Armin Falk, 2010. "You Get What You Pay For: Incentives and Selection in the Education System," Economic Journal, Royal Economic Society, vol. 120(546), pages 256-271, August.
    6. Raj Chetty & Nathaniel Hendren, 2018. "The Impacts of Neighborhoods on Intergenerational Mobility II: County-Level Estimates," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(3), pages 1163-1228.
    7. Patrick Bolton & Mathias Dewatripont, 2005. "Contract Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262025760, December.
    8. Babcock, Bruce A. & Choi, E. Kwan & Feinerman, Eli, 1993. "Risk And Probability Premiums For Cara Utility Functions," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 18(1), pages 1-8, July.
    9. Tahir Andrabi & Jishnu Das & Asim Ijaz Khwaja & Tristan Zajonc, 2011. "Do Value-Added Estimates Add Value? Accounting for Learning Dynamics," American Economic Journal: Applied Economics, American Economic Association, vol. 3(3), pages 29-54, July.
    10. Papay, John P. & Kraft, Matthew A., 2015. "Productivity returns to experience in the teacher labor market: Methodological challenges and new evidence on long-term career improvement," Journal of Public Economics, Elsevier, vol. 130(C), pages 105-119.
    11. Buddin, Richard, 2011. "Measuring teacher and school effectiveness at improving student achievement in Los Angeles elementary schools," MPRA Paper 31963, University Library of Munich, Germany.
    12. 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.
    13. Weili Ding & Steven F. Lehrer, 2010. "Estimating Treatment Effects from Contaminated Multiperiod Education Experiments: The Dynamic Impacts of Class Size Reductions," The Review of Economics and Statistics, MIT Press, vol. 92(1), pages 31-42, February.
    14. Joseph E. Stiglitz, 1991. "Symposium on Organizations and Economics," Journal of Economic Perspectives, American Economic Association, vol. 5(2), pages 15-24, Spring.
    15. Piskorski, Tomasz & Westerfield, Mark M., 2016. "Optimal dynamic contracts with moral hazard and costly monitoring," Journal of Economic Theory, Elsevier, vol. 166(C), pages 242-281.
    16. Jesse Rothstein, 2009. "Student Sorting and Bias in Value-Added Estimation: Selection on Observables and Unobservables," Education Finance and Policy, MIT Press, vol. 4(4), pages 537-571, October.
    17. Raj Chetty & Nathaniel Hendren, 2018. "The Impacts of Neighborhoods on Intergenerational Mobility I: Childhood Exposure Effects," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(3), pages 1107-1162.
    18. Carl Nadler & Matthew Wiswall, 2011. "Risk Aversion and Support for Merit Pay: Theory and Evidence from Minnesota's Q Comp Program," Education Finance and Policy, MIT Press, vol. 6(1), pages 75-104, January.
    19. Barrett, Nathan & Toma, Eugenia F., 2013. "Reward or punishment? Class size and teacher quality," Economics of Education Review, Elsevier, vol. 35(C), pages 41-52.
    20. Daniel F. McCaffrey & Tim R. Sass & J. R. Lockwood & Kata Mihaly, 2009. "The Intertemporal Variability of Teacher Effect Estimates," Education Finance and Policy, MIT Press, vol. 4(4), pages 572-606, October.
    21. Stinebrickner, Todd R, 2001. "A Dynamic Model of Teacher Labor Supply," Journal of Labor Economics, University of Chicago Press, vol. 19(1), pages 196-230, January.
    22. Alma Cohen & Liran Einav, 2007. "Estimating Risk Preferences from Deductible Choice," American Economic Review, American Economic Association, vol. 97(3), pages 745-788, June.
    23. Timothy N. Bond & Kevin Lang, 2013. "The Evolution of the Black-White Test Score Gap in Grades K–3: The Fragility of Results," The Review of Economics and Statistics, MIT Press, vol. 95(5), pages 1468-1479, December.
    24. Petra E. Todd & Kenneth I. Wolpin, 2007. "The Production of Cognitive Achievement in Children: Home, School, and Racial Test Score Gaps," Journal of Human Capital, University of Chicago Press, vol. 1(1), pages 91-136.
    25. Jere R. Behrman & Michela M. Tincani & Petra E. Todd & Kenneth I. Wolpin, 2016. "Teacher Quality in Public and Private Schools under a Voucher System: The Case of Chile," Journal of Labor Economics, University of Chicago Press, vol. 34(2), pages 319-362.
    26. Kevin Lang, 2010. "Measurement Matters: Perspectives on Education Policy from an Economist and School Board Member," Journal of Economic Perspectives, American Economic Association, vol. 24(3), pages 167-182, Summer.
    27. Eric A. Hanushek, 1979. "Conceptual and Empirical Issues in the Estimation of Educational Production Functions," Journal of Human Resources, University of Wisconsin Press, vol. 14(3), pages 351-388.
    28. Cassandra M. Guarino & Mark D. Reckase & Jeffrey M. Woolrdige, 2014. "Can Value-Added Measures of Teacher Performance Be Trusted?," Education Finance and Policy, MIT Press, vol. 10(1), pages 117-156, November.
    29. Christopher Ferrall & Bruce Shearer, 1999. "Incentives and Transactions Costs Within the Firm: Estimating an Agency Model Using Payroll Records," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(2), pages 309-338.
    30. C. Kirabo Jackson, 2014. "Teacher Quality at the High School Level: The Importance of Accounting for Tracks," Journal of Labor Economics, University of Chicago Press, vol. 32(4), pages 645-684.
    31. Gadi Barlevy & Derek Neal, 2012. "Pay for Percentile," American Economic Review, American Economic Association, vol. 102(5), pages 1805-1831, August.
    32. repec:mpr:mprres:7407 is not listed on IDEAS
    33. Kane, Thomas J. & Rockoff, Jonah E. & Staiger, Douglas O., 2008. "What does certification tell us about teacher effectiveness? Evidence from New York City," Economics of Education Review, Elsevier, vol. 27(6), pages 615-631, December.
    34. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    35. Joshua D. Angrist & Peter D. Hull & Parag A. Pathak & Christopher R. Walters, 2017. "Erratum to “Leveraging Lotteries for School Value-Added: Testing and Estimation”," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(4), pages 2061-2062.
    36. Mehta, Nirav, 2018. "The potential output gains from using optimal teacher incentives: An illustrative calibration of a hidden action model," Economics of Education Review, Elsevier, vol. 66(C), pages 67-72.
    37. Peter Z. Schochet & Hanley S. Chiang, "undated". "What Are Error Rates for Classifying Teacher and School Performance Using Value-Added Models?," Mathematica Policy Research Reports 8cc459dd9c574c3d832ed4182, Mathematica Policy Research.
    38. Lippman, Steven A & McCall, John J, 1976. "The Economics of Job Search: A Survey: Part I," Economic Inquiry, Western Economic Association International, vol. 14(2), pages 155-189, June.
    39. Petra E. Todd & Kenneth I. Wolpin, 2003. "On The Specification and Estimation of The Production Function for Cognitive Achievement," Economic Journal, Royal Economic Society, vol. 113(485), pages 3-33, February.
    40. Imberman, Scott A. & Lovenheim, Michael F., 2016. "Does the market value value-added? Evidence from housing prices after a public release of school and teacher value-added," Journal of Urban Economics, Elsevier, vol. 91(C), pages 104-121.
    41. Christopher Jepsen & Steven Rivkin, 2009. "Class Size Reduction and Student Achievement: The Potential Tradeoff between Teacher Quality and Class Size," Journal of Human Resources, University of Wisconsin Press, vol. 44(1).
    42. Andrew Clausen, 2013. "Moral Hazard with Counterfeit Signals," Edinburgh School of Economics Discussion Paper Series 225, Edinburgh School of Economics, University of Edinburgh.
    43. Oakes, J. Michael, 2004. "The (mis)estimation of neighborhood effects: causal inference for a practicable social epidemiology," Social Science & Medicine, Elsevier, vol. 58(10), pages 1929-1952, May.
    44. Donald Boyd & Hamilton Lankford & Susanna Loeb & James Wyckoff, 2013. "Measuring Test Measurement Error," Journal of Educational and Behavioral Statistics, , vol. 38(6), pages 629-663, December.
    45. Jonah E. Rockoff, 2004. "The Impact of Individual Teachers on Student Achievement: Evidence from Panel Data," American Economic Review, American Economic Association, vol. 94(2), pages 247-252, May.
    46. Cassandra M. Guarino & Michelle Maxfield & Mark D. Reckase & Paul N. Thompson & Jeffrey M. Wooldridge, 2015. "An Evaluation of Empirical Bayes’s Estimation of Value-Added Teacher Performance Measures," Journal of Educational and Behavioral Statistics, , vol. 40(2), pages 190-222, April.
    47. 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.
    48. Cory Koedel & Julian Betts, 2010. "Value Added to What? How a Ceiling in the Testing Instrument Influences Value-Added Estimation," Education Finance and Policy, MIT Press, vol. 5(1), pages 54-81, January.
    49. Douglas O. Staiger & Jonah E. Rockoff, 2010. "Searching for Effective Teachers with Imperfect Information," Journal of Economic Perspectives, American Economic Association, vol. 24(3), pages 97-118, Summer.
    50. Jeffrey Penney, 2017. "Test Score Measurement and the Black-White Test Score Gap," The Review of Economics and Statistics, MIT Press, vol. 99(4), pages 652-656, July.
    51. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    52. repec:mpr:mprres:6829 is not listed on IDEAS
    53. Lippman, Steven A & McCall, John J, 1976. "The Economics of Job Search: A Survey," Economic Inquiry, Western Economic Association International, vol. 14(3), pages 347-368, September.
    54. Brian A. Jacob & Lars Lefgren, 2008. "Can Principals Identify Effective Teachers? Evidence on Subjective Performance Evaluation in Education," Journal of Labor Economics, University of Chicago Press, vol. 26(1), pages 101-136.
    55. Karthik Muralidharan & Venkatesh Sundararaman, 2011. "Teacher Performance Pay: Experimental Evidence from India," Journal of Political Economy, University of Chicago Press, vol. 119(1), pages 39-77.
    56. Steven Glazerman & Hanley Chiang & Alison Wellington & Jill Constantine & Dan Player, "undated". "Impacts of Performance Pay Under the Teacher Incentive Fund: Study Design Report," Mathematica Policy Research Reports 0b5ad90028e54c259d54a1bf0, Mathematica Policy Research.
    57. Michael Rothschild, 1974. "Searching for the Lowest Price When the Distribution of Prices Is Unknown: A Summary," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 1, pages 293-294, National Bureau of Economic Research, Inc.
    58. Charles T. Clotfelter & Helen F. Ladd & Jacob L. Vigdor, 2006. "Teacher-Student Matching and the Assessment of Teacher Effectiveness," Journal of Human Resources, University of Wisconsin Press, vol. 41(4).
    59. Wiswall, Matthew, 2013. "The dynamics of teacher quality," Journal of Public Economics, Elsevier, vol. 100(C), pages 61-78.
    60. Hugh Macartney, 2016. "The Dynamic Effects of Educational Accountability," Journal of Labor Economics, University of Chicago Press, vol. 34(1), pages 1-28.
    61. Roland G. Fryer & Steven D. Levitt, 2004. "Understanding the Black-White Test Score Gap in the First Two Years of School," The Review of Economics and Statistics, MIT Press, vol. 86(2), pages 447-464, May.
    62. John Cawley & James Heckman & Edward Vytlacil, 1999. "On Policies To Reward The Value Added By Educators," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 720-727, November.
    63. Michael J. Podgursky & Matthew G. Springer, 2007. "Teacher performance pay: A review," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 26(4), pages 909-950.
    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. Michael Gilraine & Jiaying Gu & Robert McMillan, 2020. "A New Method for Estimating Teacher Value-Added," NBER Working Papers 27094, National Bureau of Economic Research, Inc.
    2. Johannes S. Kunz & Carol Propper & Kevin E. Staub & Rainer Winkelmann, 2023. "Assessing the Quality of Public Services: For-profits, Chains, and Concentration in the Hospital Market," Papers 2023-01, Centre for Health Economics, Monash University.
    3. Propper, Carol & Kunz, Johannes & Staub, Kevin & Winkelmann, Rainer, 2020. "Assessing the Quality of Public Services: Does Hospital Competition Crowd Out the For-Profit Quality Gap?," CEPR Discussion Papers 15045, C.E.P.R. Discussion Papers.

    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. Nirav Mehta, 2014. "Targeting the Wrong Teachers: Estimating Teacher Quality for Use in Accountability Regimes," University of Western Ontario, Centre for Human Capital and Productivity (CHCP) Working Papers 20143, University of Western Ontario, Centre for Human Capital and Productivity (CHCP).
    2. Koedel, Cory & Mihaly, Kata & Rockoff, Jonah E., 2015. "Value-added modeling: A review," Economics of Education Review, Elsevier, vol. 47(C), pages 180-195.
    3. Dan Goldhaber & Michael Hansen, 2013. "Is it Just a Bad Class? Assessing the Long-term Stability of Estimated Teacher Performance," Economica, London School of Economics and Political Science, vol. 80(319), pages 589-612, July.
    4. Koedel Cory & Leatherman Rebecca & Parsons Eric, 2012. "Test Measurement Error and Inference from Value-Added Models," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 12(1), pages 1-37, November.
    5. Figlio, D. & Karbownik, K. & Salvanes, K.G., 2016. "Education Research and Administrative Data," Handbook of the Economics of Education,, Elsevier.
    6. Mehta, Nirav, 2018. "The potential output gains from using optimal teacher incentives: An illustrative calibration of a hidden action model," Economics of Education Review, Elsevier, vol. 66(C), pages 67-72.
    7. Harris, Douglas N. & Sass, Tim R., 2014. "Skills, productivity and the evaluation of teacher performance," Economics of Education Review, Elsevier, vol. 40(C), pages 183-204.
    8. Stacy, Brian & Guarino, Cassandra & Wooldridge, Jeffrey, 2018. "Does the precision and stability of value-added estimates of teacher performance depend on the types of students they serve?," Economics of Education Review, Elsevier, vol. 64(C), pages 50-74.
    9. Audra J. Bowlus & Eda Bozkurt & Lance Lochner, 2017. "Wages and Employment: The Canonical Model Revisited," University of Western Ontario, Centre for Human Capital and Productivity (CHCP) Working Papers 20179, University of Western Ontario, Centre for Human Capital and Productivity (CHCP).
    10. Gershenson, Seth, 2021. "Identifying and Producing Effective Teachers," IZA Discussion Papers 14096, Institute of Labor Economics (IZA).
    11. Stacy, Brian, 2014. "Ranking Teachers when Teacher Value-Added is Heterogeneous Across Students," EconStor Preprints 104743, ZBW - Leibniz Information Centre for Economics.
    12. Papay, John P. & Kraft, Matthew A., 2015. "Productivity returns to experience in the teacher labor market: Methodological challenges and new evidence on long-term career improvement," Journal of Public Economics, Elsevier, vol. 130(C), pages 105-119.
    13. 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.
    14. 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.
    15. Azam, Mehtabul & Kingdon, Geeta Gandhi, 2015. "Assessing teacher quality in India," Journal of Development Economics, Elsevier, vol. 117(C), pages 74-83.
    16. 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.
    17. Hanushek, Eric A., 2011. "The economic value of higher teacher quality," Economics of Education Review, Elsevier, vol. 30(3), pages 466-479, June.
    18. Naven, Matthew, 2019. "Human-Capital Formation During Childhood and Adolescence: Evidence from School Quality and Postsecondary Success in California," MPRA Paper 97716, University Library of Munich, Germany.
    19. Sean Corcoran & Dan Goldhaber, 2013. "Value Added and Its Uses: Where You Stand Depends on Where You Sit," Education Finance and Policy, MIT Press, vol. 8(3), pages 418-434, July.
    20. Eric Parsons & Cory Koedel & Li Tan, 2019. "Accounting for Student Disadvantage in Value-Added Models," Journal of Educational and Behavioral Statistics, , vol. 44(2), pages 144-179, April.

    More about this item

    JEL classification:

    • J01 - Labor and Demographic Economics - - General - - - Labor Economics: General
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
    • I28 - Health, Education, and Welfare - - Education - - - Government Policy
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:wly:quante:v:10:y:2019:i:4:p:1537-1577. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.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.