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Identification and Estimation Using a Density Discontinuity Approach

In: Regression Discontinuity Designs

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  • Hugo Jales
  • Zhengfei Yu

Abstract

This chapter reviews recent developments in the density discontinuity approach. It is well known that agents having perfect control of the forcing variable will invalidate the popular regression discontinuity designs (RDDs). To detect the manipulation of the forcing variable,McCrary (2008)developed a test based on the discontinuity in the density around the threshold. Recent papers have noted that the sorting patterns around the threshold are often either the researcher’s object of interest or may relate to structural parameters such as tax elasticities through known functions. This, in turn, implies that the behavior of the distribution around the threshold is not only informative of the validity of a standard RDD; it can also be used to recover policy-relevant parameters and perform counterfactual exercises.

Suggested Citation

  • Hugo Jales & Zhengfei Yu, 2017. "Identification and Estimation Using a Density Discontinuity Approach," Advances in Econometrics, in: Regression Discontinuity Designs, volume 38, pages 29-72, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-905320170000038003
    DOI: 10.1108/S0731-905320170000038003
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    Citations

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    Cited by:

    1. Francisco J.M Costa & João S. De Faria & Felipe S. Iachan & Bárbara Caballero, 2018. "Homicides and the Age of Criminal Responsibility: A Density Discontinuity Approach," Economía Journal, The Latin American and Caribbean Economic Association - LACEA, vol. 0(Fall 2018), pages 59-92, November.
    2. Jales, Hugo & Jiang, Boqian & Rosenthal, Stuart S., 2023. "JUE Insight: Using the mode to test for selection in city size wage premia," Journal of Urban Economics, Elsevier, vol. 133(C).
    3. Bertanha, Marinho & McCallum, Andrew H. & Seegert, Nathan, 2023. "Better bunching, nicer notching," Journal of Econometrics, Elsevier, vol. 237(2).
    4. Zhuan Pei & Yi Shen, 2017. "The Devil is in the Tails: Regression Discontinuity Design with Measurement Error in the Assignment Variable," Advances in Econometrics, in: Regression Discontinuity Designs, volume 38, pages 455-502, Emerald Group Publishing Limited.
    5. Jales, Hugo & Ma, Jun & Yu, Zhengfei, 2017. "Optimal bandwidth selection for local linear estimation of discontinuity in density," Economics Letters, Elsevier, vol. 153(C), pages 23-27.
    6. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    7. Rodrigo Carril & Andres Gonzalez-Lira & Michael S. Walker, 2022. "Competition under incomplete contracts and the design of procurement policies," Economics Working Papers 1824, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Marinho Bertanha & Andrew H. McCallum & Alexis Payne & Nathan Seegert, 2022. "Bunching estimation of elasticities using Stata," Stata Journal, StataCorp LP, vol. 22(3), pages 597-624, September.
    9. Johansson, Naimi & de New, Sonja C. & Kunz, Johannes S. & Petrie, Dennis & Svensson, Mikael, 2023. "Reductions in out-of-pocket prices and forward-looking moral hazard in health care demand," Journal of Health Economics, Elsevier, vol. 87(C).
    10. Emmanuel Guerre & Yao Luo, 2019. "Nonparametric Identification of First-Price Auction with Unobserved Competition: A Density Discontinuity Framework," Papers 1908.05476, arXiv.org, revised Jan 2022.
    11. Jun Ma & Zhengfei Yu, 2020. "Empirical Likelihood Covariate Adjustment for Regression Discontinuity Designs," Papers 2008.09263, arXiv.org, revised May 2024.

    More about this item

    Keywords

    Density function; discontinuity; density jump; sorting; effect structure; C14; C21;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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