Instrumental Variables and Regression Discontinuity Design

This session reviews the basics of IV and RDD and then dives into some specific aspects.

Objective

This session aims to strengthen your intuition, technical and practical understanding on IV and RDD, as well as some of the challenges typically associated with such designs.

Summary

Instrumental variables work in negative to other identification strategies: instead of removing endogenous variation in the treatment, it directly extract the exogenous variation. Their implementation might be complex may come with some noteworthy aspects: they estimate an effect that is local to compliers, under certain conditions, weak instruments may hinder the credibility of the results. We also discuss some widely used IV strategies such as shift-share. Regression Discontinuity Designs directly relate to IV: a fuzzy-RD is essentially a local IV. An RDD is also local in the sense that it estimate an ATE at the cutoff. Graphs are central to RDD: they allow to check and support some of the identifying assumptions.

Session Outline

  • IV
    • Introductory example
    • Fundamental principles
    • Locality
    • Estimation
    • Weak instruments
    • Shift-share Instruments
  • RDD
    • Introductory example
    • Fundamental principles
    • Fuzzy-RD
    • Challenges
  • Summaries

Materials

Open slides in html

Open slides in pdf

Exercise

Before class next week, please submit the assignment presented in this document.

Specific resources for this lecture

If you should read only one thing of IVs and one on RDD

Chapter 7 and chapter 6 of Cunningham (2021)

Courses

Specific points

  • Shift-share: Borusyak, Hull, and Jaravel (2025) and Goldsmith-Pinkham, Sorkin, and Swift (2020) present the logic behind shift-share instruments as well as examples
  • Weak instruments: Keane and Neal (2023)
  • Optimal bandwidth: Imbens and Kalyanaraman (2012)
  • Data viz and RDD: Korting et al. (2023) on RDD graphs and Cattaneo et al. (2024) on binscatter

Example papers discussed in class

  • Deryugina et al. (2019) instruments air pollution with wind direction to study its impacts on air pollution
  • Card (1993) instruments education level with proximity to college to estimate the return to schooling
  • Aguilar-Gomez (2025) uses an RDD to estimate the impact of air quality alerts on pollution level and health in Mexico

R Pacakges

There is a breadth of packages to implement IV analyses (ivreg or fixest for instance).

I have used the 3 mentioned above in various projects and recommend using fixest for its versatility. It allows to implement analysis with FE, IVs, limited outcomes and so on. Paired with modelsummary to compute standard errors, you should be able to run a lot of your analyses.

References

Aguilar-Gomez, Sandra. 2025. “Adaptation and Mitigation of Pollution: Evidence from Air Quality Warnings.” Journal of Environmental Economics and Management 134 (November): 103215. https://doi.org/10.1016/j.jeem.2025.103215.
Angrist, Joshua D., and Jörn-Steffen Pischke. 2009. Mostly Harmless Econometrics: An Empiricist’s Companion. 1 edition. Princeton: Princeton University Press.
Borusyak, Kirill, Peter Hull, and Xavier Jaravel. 2025. “A Practical Guide to Shift-Share Instruments.” Journal of Economic Perspectives 39 (1): 181–204. https://doi.org/10.1257/jep.20231370.
Card, David. 1993. “Using Geographic Variation in College Proximity to Estimate the Return to Schooling.” Working {{Paper}} 4483. Working Paper Series. National Bureau of Economic Research. https://doi.org/10.3386/w4483.
Cattaneo, Matias D., Richard K. Crump, Max H. Farrell, and Yingjie Feng. 2024. “On Binscatter.” American Economic Review, May. https://doi.org/10.1257/aer.20221576.
Cunningham, Scott. 2021. Causal Inference: The Mixtape. Yale University Press. https://doi.org/10.2307/j.ctv1c29t27.
Deryugina, Tatyana, Garth Heutel, Nolan H. Miller, David Molitor, and Julian Reif. 2019. “The Mortality and Medical Costs of Air Pollution: Evidence from Changes in Wind Direction.” American Economic Review 109 (12): 4178–4219. https://doi.org/10.1257/aer.20180279.
Goldsmith-Pinkham, Paul, Isaac Sorkin, and Henry Swift. 2020. “Bartik Instruments: What, When, Why, and How.” American Economic Review 110 (8): 2586–2624. https://doi.org/10.1257/aer.20181047.
Huntington-Klein, Nick. 2022. The Effect: An Introduction to Research Design and Causality. 1st edition. Chapman and Hall/CRC.
Imbens, Guido, and Karthik Kalyanaraman. 2012. “Optimal Bandwidth Choice for the Regression Discontinuity Estimator.” The Review of Economic Studies 79 (3): 933–59. https://www.jstor.org/stable/23261375.
Keane, Michael, and Timothy Neal. 2023. “Instrument Strength in IV Estimation and Inference: A Guide to Theory and Practice.” Journal of Econometrics 235 (2): 1625–53. https://doi.org/10.1016/j.jeconom.2022.12.009.
Korting, Christina, Carl Lieberman, Jordan Matsudaira, Zhuan Pei, and Yi Shen. 2023. “Visual Inference and Graphical Representation in Regression Discontinuity Designs.” The Quarterly Journal of Economics 138 (3): 1977–2019. https://doi.org/10.1093/qje/qjad011.