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Quasi-Experimental Identification and Estimation in the Regression Kink Design


  • David Card

    (UC Berkeley and NBER)

  • David S. Lee

    (Princeton University and NBER)

  • Zhuan Pei

    (Princeton University)


We consider nonparametic identification of the average marginal effect of a continuous endogenous regressor in a generalized nonseparable model when the regressor of interest is a known, deterministic, but kiniked function of an observed continuous assignment variable. This design arises in many institutional settings where a policy variable of interest (such as weekly unemployment benefits) is mechanically related to an observed but potentially endogenous variable (like previous earnings). We characterize a broad class of models in which a "Regression Kink Design" (RKD) provides valid inferences for the underlying marginal effects. Importantly, this class includes cases where the assignment variable is endogenously chose. Under suitable conditions we show that the RKD estimand identifies the "treatment on the treated" parameter (Florens et al., 2009) or the "local average response" (altonji and Matzkin, 2005) that is identified in an ideal randomized experiment. As in a regression discontinuity design, the required indentification assumption implies strong and readilt testable predictions for the pattern of predetermined covariates around the kink point. Standard local linear regression techniques can be easily adapted to obtain "nonparametris" RKD estimates. We illustrate the RKD approach by examining the effect of unemployment insurance benefits on the duration of benefit claims, using rich microdata from the state of Washington.

Suggested Citation

  • David Card & David S. Lee & Zhuan Pei, 2009. "Quasi-Experimental Identification and Estimation in the Regression Kink Design," Working Papers 1206, Princeton University, Department of Economics, Industrial Relations Section..
  • Handle: RePEc:pri:indrel:553

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    References listed on IDEAS

    1. Helena Skyt Nielsen & Torben Sørensen & Christopher Taber, 2010. "Estimating the Effect of Student Aid on College Enrollment: Evidence from a Government Grant Policy Reform," NBER Chapters,in: Income Taxation, Trans-Atlantic Public Economics Seminar (TAPES), pages 185-215 National Bureau of Economic Research, Inc.
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    1. repec:spr:empeco:v:53:y:2017:i:3:d:10.1007_s00181-016-1155-8 is not listed on IDEAS
    2. David Card & Andrew Johnston & Pauline Leung & Alexandre Mas & Zhuan Pei, 2015. "The Effect of Unemployment Benefits on the Duration of Unemployment Insurance Receipt: New Evidence from a Regression Kink Design in Missouri, 2003-2013," American Economic Review, American Economic Association, vol. 105(5), pages 126-130, May.
    3. Michihito Ando, 2017. "How much should we trust regression-kink-design estimates?," Empirical Economics, Springer, vol. 53(3), pages 1287-1322, November.
    4. Raj Chetty & John N. Friedman & Søren Leth-Petersen & Torben Heien Nielsen & Tore Olsen, 2014. "Active vs. Passive Decisions and Crowd-Out in Retirement Savings Accounts: Evidence from Denmark," The Quarterly Journal of Economics, Oxford University Press, vol. 129(3), pages 1141-1219.
    5. Bartalotti, Otávio C. & Brummet, Quentin O., 2016. "Regression Discontinuity Designs with Clustered Data: Variance and Bandwidth Choice," Staff General Research Papers Archive 3393, Iowa State University, Department of Economics.
    6. David Card & David S. Lee & Zhuan Pei & Andrea Weber, 2017. "Regression Kink Design: Theory and Practice," Advances in Econometrics,in: Regression Discontinuity Designs, volume 38, pages 341-382 Emerald Publishing Ltd.
    7. Andrew Hanson, 2012. "The Incidence of the Mortgage Interest Deduction: Evidence from the Market for Home Purchase Loans," Public Finance Review, , vol. 40(3), pages 339-359, May.
    8. David Autor & Mark Duggan & Jonathan Gruber, 2014. "Moral Hazard and Claims Deterrence in Private Disability Insurance," American Economic Journal: Applied Economics, American Economic Association, vol. 6(4), pages 110-141, October.
    9. Bartalotti, Otávio C. & Calhoun, Gray & He, Yang, 2016. "Bootstrap Confidence Intervals for Sharp Regression Discontinuity Designs with the Uniform Kernel," Staff General Research Papers Archive 3394, Iowa State University, Department of Economics.

    More about this item


    Unemployment benefits; Washington State; unemployment insurance; regression kink design;

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity
    • J08 - Labor and Demographic Economics - - General - - - Labor Economics Policies
    • J64 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Unemployment: Models, Duration, Incidence, and Job Search


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