IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/18564.html
   My bibliography  Save this paper

Nonlinear Policy Rules and the Identification and Estimation of Causal Effects in a Generalized Regression Kink Design

Author

Listed:
  • David Card
  • David Lee
  • Zhuan Pei
  • Andrea Weber

Abstract

We consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known, deterministic, but kinked function of an observed assignment variable. This design arises in many institutional settings where a policy variable (such as weekly unemployment benefits) is determined by an observed but potentially endogenous assignment variable (like previous earnings). We provide new results on identification and estimation for these settings, and apply our results to obtain estimates of the elasticity of joblessness with respect to UI benefit rates. We characterize a broad class of models in which a "Regression Kink Design" (RKD, or RK Design) provides valid inferences for the treatment-on-the-treated parameter (Florens et al. (2008)) that would be identified in an ideal randomized experiment. We show that the smooth density condition that is sufficient for identification rules out extreme sorting around the kink, but is compatible with less severe forms of endogeneity. It also places testable restrictions on the distribution of predetermined covariates around the kink point. We introduce a generalization of the RKD - the "fuzzy regression kink design" - that allows for omitted variables in the assignment rule, as well as certain types of measurement errors in the observed values of the assignment variable and the policy variable. We also show how standard local polynomial regression techniques can be adapted to obtain nonparametric estimates for the sharp and fuzzy RKD. We then use a fuzzy RKD approach to study the effect of unemployment insurance benefits on the duration of joblessness in Austria, where the benefit schedule has kinks at the minimum and maximum benefit level. Our estimates suggest that the elasticity of joblessness with respect to the benefit rate is on the order of 1.5.

Suggested Citation

  • David Card & David Lee & Zhuan Pei & Andrea Weber, 2012. "Nonlinear Policy Rules and the Identification and Estimation of Causal Effects in a Generalized Regression Kink Design," NBER Working Papers 18564, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:18564
    Note: LS
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w18564.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Rafael Lalive & Jan Van Ours & Josef Zweimuller, 2006. "How Changes in Financial Incentives Affect the Duration of Unemployment," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 1009-1038.
    2. J. P. Florens & J. J. Heckman & C. Meghir & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects," Econometrica, Econometric Society, vol. 76(5), pages 1191-1206, September.
    3. Camille Landais, 2015. "Assessing the Welfare Effects of Unemployment Benefits Using the Regression Kink Design," American Economic Journal: Economic Policy, American Economic Association, vol. 7(4), pages 243-278, November.
    4. Meyer, Bruce D, 1990. "Unemployment Insurance and Unemployment Spells," Econometrica, Econometric Society, vol. 58(4), pages 757-782, July.
    5. Emilia Del Bono & Andrea Weber, 2008. "Do Wages Compensate for Anticipated Working Time Restrictions? Evidence from Seasonal Employment in Austria," Journal of Labor Economics, University of Chicago Press, vol. 26(1), pages 181-221.
    6. 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.
    7. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    8. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
    9. David Card & Raj Chetty & Andrea Weber, 2007. "Cash-on-Hand and Competing Models of Intertemporal Behavior: New Evidence from the Labor Market," The Quarterly Journal of Economics, Oxford University Press, vol. 122(4), pages 1511-1560.
    10. Emmanuel Saez, 2010. "Do Taxpayers Bunch at Kink Points?," American Economic Journal: Economic Policy, American Economic Association, vol. 2(3), pages 180-212, August.
    11. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, July.
    12. DiNardo, John & Lee, David S., 2011. "Program Evaluation and Research Designs," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 5, pages 463-536, Elsevier.
    13. Katz, Lawrence F. & Meyer, Bruce D., 1990. "The impact of the potential duration of unemployment benefits on the duration of unemployment," Journal of Public Economics, Elsevier, vol. 41(1), pages 45-72, February.
    14. Solon, Gary R, 1985. "Work Incentive Effects of Taxing Unemployment Benefits," Econometrica, Econometric Society, vol. 53(2), pages 295-306, March.
    15. Kroft, Kory, 2008. "Takeup, social multipliers and optimal social insurance," Journal of Public Economics, Elsevier, vol. 92(3-4), pages 722-737, April.
    16. Marianne Simonsen & Lars Skipper & Niels Skipper, 2016. "Price Sensitivity of Demand for Prescription Drugs: Exploiting a Regression Kink Design," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(2), pages 320-337, March.
    17. Baily, Martin Neil, 1978. "Some aspects of optimal unemployment insurance," Journal of Public Economics, Elsevier, vol. 10(3), pages 379-402, December.
    18. 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.
    19. Guido Imbens & Karthik Kalyanaraman, 2012. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 933-959.
    20. 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.
    21. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    22. Josef Zweim�ller & Rudolf Winter-Ebmer & Rafael Lalive & Andreas Kuhn & Jean-Philippe Wuellrich & Oliver Ruf & Simon B�chi, 2009. "Austrian social security database," IEW - Working Papers 410, Institute for Empirical Research in Economics - University of Zurich.
      • Josef Zweimüller & Rudolf Winter-Ebmer & Rafael Lalive & Andreas Kuhn & Jean-Philippe Wuellrich & Oliver Ruf & Simon Büchi, 2009. "Austrian Social Security Database," NRN working papers 2009-03, The Austrian Center for Labor Economics and the Analysis of the Welfare State, Johannes Kepler University Linz, Austria.
    23. Krueger, Alan B. & Meyer, Bruce D., 2002. "Labor supply effects of social insurance," Handbook of Public Economics, in: A. J. Auerbach & M. Feldstein (ed.), Handbook of Public Economics, edition 1, volume 4, chapter 33, pages 2327-2392, Elsevier.
    24. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    25. Moffitt, Robert, 1985. "Unemployment insurance and the distribution of unemployment spells," Journal of Econometrics, Elsevier, vol. 28(1), pages 85-101, April.
    26. McCrary, Justin, 2008. "Manipulation of the running variable in the regression discontinuity design: A density test," Journal of Econometrics, Elsevier, vol. 142(2), pages 698-714, February.
    27. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    28. Jinyong Hahn & Petra Todd & Wilbert Van der Klaauw, 1999. "Evaluating the Effect of an Antidiscrimination Law Using a Regression-Discontinuity Design," NBER Working Papers 7131, National Bureau of Economic Research, Inc.
    29. Arie Kapteyn & Jelmer Y. Ypma, 2007. "Measurement Error and Misclassification: A Comparison of Survey and Administrative Data," Journal of Labor Economics, University of Chicago Press, vol. 25(3), pages 513-551.
    30. Khan, Shakeeb & Tamer, Elie, 2007. "Partial rank estimation of duration models with general forms of censoring," Journal of Econometrics, Elsevier, vol. 136(1), pages 251-280, January.
    31. Jonathan Guryan, 2001. "Does Money Matter? Regression-Discontinuity Estimates from Education Finance Reform in Massachusetts," NBER Working Papers 8269, National Bureau of Economic Research, Inc.
    32. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    33. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-137, January.
    Full references (including those not matched with items on IDEAS)

    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. David Card & David S. Lee & Zhuan Pei & Andrea Weber, 2015. "Inference on Causal Effects in a Generalized Regression Kink Design," Econometrica, Econometric Society, vol. 83, pages 2453-2483, November.
    2. Camille Landais, 2015. "Assessing the Welfare Effects of Unemployment Benefits Using the Regression Kink Design," American Economic Journal: Economic Policy, American Economic Association, vol. 7(4), pages 243-278, November.
    3. Michihito Ando, 2017. "How much should we trust regression-kink-design estimates?," Empirical Economics, Springer, vol. 53(3), pages 1287-1322, November.
    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. Johannes F. Schmieder & Till von Wachter, 2016. "The Effects of Unemployment Insurance Benefits: New Evidence and Interpretation," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 547-581, October.
    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 Group Publishing Limited.
    7. Pauline Leung & Christopher J. O'Leary, 2015. "Should UI Eligibility Be Expanded to Low-Earning Workers? Evidence on Employment, Transfer Receipt, and Income from Administrative Data," Upjohn Working Papers 15-236, W.E. Upjohn Institute for Employment Research.
    8. 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.
    9. Raj Chetty & Amy Finkelstein, 2012. "Social Insurance: Connecting Theory to Data," NBER Working Papers 18433, National Bureau of Economic Research, Inc.
    10. Mauricio Villamizar‐Villegas & Freddy A. Pinzon‐Puerto & Maria Alejandra Ruiz‐Sanchez, 2022. "A comprehensive history of regression discontinuity designs: An empirical survey of the last 60 years," Journal of Economic Surveys, Wiley Blackwell, vol. 36(4), pages 1130-1178, September.
    11. 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..
    12. Huber, Martin, 2019. "An introduction to flexible methods for policy evaluation," FSES Working Papers 504, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    13. David Card & Raj Chetty & Andrea Weber, 2007. "The Spike at Benefit Exhaustion: Leaving the Unemployment System or Starting a New Job?," American Economic Review, American Economic Association, vol. 97(2), pages 113-118, May.
    14. 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..
    15. David S. Lee & Thomas Lemieux, 2009. "Regression Discontinuity Designs In Economics," Working Papers 1118, Princeton University, Department of Economics, Industrial Relations Section..
    16. Brown, Alessio J.G. & Kohlbrecher, Britta & Merkl, Christian & Snower, Dennis J., 2021. "The effects of productivity and benefits on unemployment: Breaking the link," Economic Modelling, Elsevier, vol. 94(C), pages 967-980.
    17. Andrew C. Johnston & Alexandre Mas, 2018. "Potential Unemployment Insurance Duration and Labor Supply: The Individual and Market-Level Response to a Benefit Cut," Journal of Political Economy, University of Chicago Press, vol. 126(6), pages 2480-2522.
    18. Martin Gonzalez-Rozada & Freddy Llerena Pinto, 2011. "The Effects of a Conditional Transfer Program on the Labor Market: The Human Development Bonus in Ecuador," Department of Economics Working Papers 2011-04, Universidad Torcuato Di Tella.
    19. Susan Athey & Guido W. Imbens, 2017. "The State of Applied Econometrics: Causality and Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 3-32, Spring.
    20. Johannes F. Schmieder† & Till von Wachter & Stefan Bender, 2011. "The Effects Of Extended Unemployment Insurance Over The Business Cycle: Evidence From Regression Discontinuity Estimates Over Twenty Years," Boston University - Department of Economics - Working Papers Series WP2011-063, Boston University - Department of Economics.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction 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:nbr:nberwo:18564. 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/nberrus.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.