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How much should we trust regression-kink-design estimates?

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  • Michihito Ando

    (National Institute of Population and Social Security Research, Japan)

Abstract

In a regression kink (RK) design with a finite sample, a confounding smooth nonlinear relationship between an assignment variable and an outcome variable around a threshold can be spuriously picked up as a kink and results in a biased estimate. In order to investigate how well RK designs handle such confounding nonlinearity, I firstly implement Monte Carlo (MC) simulations and then study the effect of fiscal equalization grants on local expenditure in Japan using an RK design. Results in both the MC simulations and the empirical application suggest that RK estimation without covariates can be easily biased, and this problem can be mitigated by adding observed covariates to the regressors. On the other hand, a smaller bandwidth or a higher-order polynomial, even a quadratic polynomial, tends to result in imprecise estimates although they may be able to reduce estimation bias. In sum, RK estimation with confounding nonlinearity often suffers from bias or imprecision, and estimates are credible only when relevant covariates are controlled for. I also examine how placebo RK estimation can effectively address these issues.

Suggested Citation

  • Michihito Ando, 2017. "How much should we trust regression-kink-design estimates?," Empirical Economics, Springer, vol. 53(3), pages 1287-1322, November.
  • Handle: RePEc:spr:empeco:v:53:y:2017:i:3:d:10.1007_s00181-016-1155-8
    DOI: 10.1007/s00181-016-1155-8
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    2. Sarah H. Bana & Kelly Bedard & Maya Rossin‐Slater, 2020. "The Impacts of Paid Family Leave Benefits: Regression Kink Evidence from California Administrative Data," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 39(4), pages 888-929, September.
    3. Michihito Ando, 2017. "How much should we trust regression-kink-design estimates?," Empirical Economics, Springer, vol. 53(3), pages 1287-1322, November.
    4. Tomi Kyyrä & Hanna Pesola, 2020. "The Effects of UI Benefits on Unemployment and Subsequent Outcomes: Evidence from a Kinked Benefit Rule," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(5), pages 1135-1160, October.
    5. Chen, Yi & Zhao, Yi, 2022. "The timing of first marriage and subsequent life outcomes: Evidence from a natural experiment," Journal of Comparative Economics, Elsevier, vol. 50(3), pages 713-731.
    6. Degrave, Anne & Lopez-Peceno, Alejandro & Rozenas, Arturas, 2024. "Peasants into Citizens: Suffrage Expansion and Mass Politics in France," TSE Working Papers 24-1529, Toulouse School of Economics (TSE).
    7. 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.
    8. Simona Gamba & Niklas Jakobsson & Mikael Svensson, 2022. "The impact of cost-sharing on prescription drug demand: evidence from a double-difference regression kink design," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 23(9), pages 1591-1599, December.
    9. Damon Jones & Alexander M. Gelber & Daniel W. Sacks & Jae Song, 2017. "Using Kinked Budget Sets to Estimate Extensive Margin Responses: Method and Evidence from the Social Security Earnings Test," Working Papers 2017-034, Human Capital and Economic Opportunity Working Group.
    10. 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.
    11. Ayertey, Winfred & Sharifi, Ayyoob & Yoshida, Yuichiro, 2024. "The impact of increase in block pricing on electricity demand responsiveness: Evidence from Ghana," Energy, Elsevier, vol. 288(C).
    12. Alexander M. Gelber & Damon Jones & Daniel W. Sacks & Jae Song, 2017. "Using Non-Linear Budget Sets to Estimate Extensive Margin Responses: Method and Evidence from the Social Security Earnings Test," NBER Working Papers 23362, National Bureau of Economic Research, Inc.
    13. Kyyrä, Tomi & Paukkeri, Tuuli, 2018. "Does experience rating reduce sickness and disability claims? Evidence from policy kinks," Journal of Health Economics, Elsevier, vol. 61(C), pages 178-192.
    14. Alexander Gelber & Timothy J. Moore & Alexander Strand, 2017. "The Effect of Disability Insurance Payments on Beneficiaries' Earnings," American Economic Journal: Economic Policy, American Economic Association, vol. 9(3), pages 229-261, August.
    15. Antti Saastamoinen & Mika Kortelainen, 2020. "When Does Money Stick in Education? Evidence from A Kinked Grant Rule," Education Finance and Policy, MIT Press, vol. 15(4), pages 708-735, Fall.
    16. Ganong, Peter & Jäger, Simon, 2014. "A Permutation Test and Estimation Alternatives for the Regression Kink Design," IZA Discussion Papers 8282, Institute of Labor Economics (IZA).
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    18. Jaeger, Simon C & Ganong, Peter Nathan, 2014. "A Permutation Test and Estimation Alternatives for the Regression Kink Design," Scholarly Articles 34222894, Harvard University Department of Economics.

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    More about this item

    Keywords

    Regression kink design; Endogenous regressors; Confounding nonlinearity; Intergovernmental grants;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • H71 - Public Economics - - State and Local Government; Intergovernmental Relations - - - State and Local Taxation, Subsidies, and Revenue
    • H72 - Public Economics - - State and Local Government; Intergovernmental Relations - - - State and Local Budget and Expenditures
    • H77 - Public Economics - - State and Local Government; Intergovernmental Relations - - - Intergovernmental Relations; Federalism

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