Regression Discontinuity

Synonyms: 
RD Design, Regression Discontinuity Design

Regression Discontinuity Design (RDD) is a quasi-experimental evaluation option that measures the impact of an intervention, or treatment, by applying a treatment assignment mechanism based on a continuous eligibility index which is a variable with a continuous distribution. 

For example, test scores of students can take any value between 0-100 and area of land owned can have infinite values.  If treatment is assigned to those either above or below a certain “cut-off” point, RDD can be used to measure the difference in outcomes of individuals, households, or communities clustered around the defined cut-off point. This necessitates the determination of a ‘bandwidth’ around the cut-off point within which individual units are shown to be statistically comparable. If the assumptions of the option hold, the difference in outcomes between those above and below the cut-off can be attributed to the program. 

Example

School Enrollment, Selection and Test Scores

The study (see table below) analyzed the impact of a scholarship program, the Cambodia Education Sector Support Program (CESSP), on school enrollment, selection, and test scores using a sharp regression discontinuity design (RDD). Eligibility for the $45 scholarship depended on an independently calculated dropout risk score created using household characteristics. The data used included the composite dropout risk scores, mathematics and vocabulary test scores, and a household survey. The cut-off score varied by school size, and the estimates were weighted averages. The sample used in the analysis consisted of children within a ten-point bandwidth range around the cut-off score. The evaluation found that school enrollment and attendance increased 20-25% due to the scholarships. Years of schooling increased by 0.21 years, while annual educational expenses paid by the family rose by $9. The actual program impact was likely to be higher since recipients were, on average, poorer than non-recipients. No significant impacts on learning outcomes were found.  However, recipients had better knowledge of HIV/AIDS, and the program had a positive effect on the recipients’ mental health.  (Filmer & Schady, 2009)

Assumptions:

  • Treatment is assigned on the basis of an observable variable or index
  • There is a discontinuity in the probability of being treated at some cut-off value of the assignment index or variable
  • The cut-off value of the index for treatment is arbitrary, and thus units on either side of the cut-off point are identical, on average, except for the presence of the treatment
  • The same cutoff is not used for determining eligibility for multiple treatments (e.g. households below a certain poverty line have access to multiple government interventions)

 

Program effects on school attendance

Two Versions:

1. Sharp

  • Used in instances where treatment is assigned according to a discrete cut-off point with all eligible receiving the treatment and all ineligible not receiving it. A simple comparison of means is needed to calculate the effect of the treatment.   

2. Fuzzy

  • Used in instances where some eligible fail to receive treatment and/or ineligible receive it (e.g. due to self-selection or administrative overrides). The fuzzy version is more often utilized in practice. 
  • To calculate the effect of the treatment: a) Regress observable characteristics on outcomes to obtain the ‘outcome discontinuity', and b) Regress observable characteristics on the treatment indicator to obtain ‘treatment discontinuity.’ Then, Treatment effect = outcome discontinuity / treatment discontinuity

Advice

Advice for CHOOSING this option (tips and traps)

RDD can be used in situations where:

  • A continuous eligibility index (e.g. test scores, age etc.) is used to rank the population and
  • A clearly defined cut-off point that determines eligibility for treatment is part of the program design and
  • The same cut-off score has not been used in determining eligibility for other treatments.
  • Be aware that RD provides limited external validity as results are only generalizable around the cut-off - provision of a service might make more or less difference to people who are further away from the cut-off point.

Advice for USING this option (tips and traps)

  • Test for the existence of a discontinuity in the probability of receiving treatment (Nichols, 2009)
  • Test for the comparability of units within the bandwidth using ‘leave-one-out’ cross validation test (Ludwig and Miller 2007, Imbens and Lemieux 2008) or asymptotic theory (Imbens and Kalyanaraman 2009).
  • Depending on the type of treatment there may be ‘cross-contamination’ between those eligible for the intervention and those who are not.

Resources

Example

Guide

Sources

Buddelmeyer, H., & Skoufias, E. World Bank, (2004). An evaluation of the performance of regression discontinuity design on PROGRESA (World Bank Policy Research Working Paper 3386). Retrieved from website: http://www-wds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2004/09/09/000009486_20040909125120/additional/103503322_20041117144006.pdf

Campbell, D. T. (1971). Reforms as experiments. Urban Affairs Review, 7, 133-171. Retrieved from http://uar.sagepub.com/content/7/2/133.full.pdf html

Filmer, D., & Schady, N. The World Bank, Human Development and Public Services Team. (2009).School enrollment, selection and test scores (Policy Research Working Paper 4998). Retrieved from website: http://www-wds.worldbank.org/external/default/WDSContentServer/WDSP/IB/2009/07/17/000158349_20090717130545/Rendered/PDF/WPS4998.pdf

Hahn, J., Todd, P., & Van der Klaauw, W. (2001). Identification and estimation of treatment effects with a regression-discontinuity design. Econometrica, 69(1), 201-209. Retrieved from http://www.personal.ceu.hu/staff/Gabor_Kezdi/Program-Evaluation/Hahn-Todd-VanderKlaauw-2001-RegressionDiscontinuity.pdf

Imbens, G., & Lemieux, T. (2007). Regression discontinuity designs: A guide to practice. Journal of Econometrics, 142(2), 615-635. Retrieved from http://faculty.arts.ubc.ca/tlemieux/papers/designs.pdf.

Khandker, S. R., Koolwal, G. B., & Samad, H. A. The International Bank for Reconstruction and Development / The World Bank, (2010).Handbook on impact evaluation quantitative options and practices (52099). Retrieved from website: http://www.esf-agentschap.be/uploadedFiles/Voor_ESF_promotoren/Zelfevaluatie_ESF-project/statistiek%20voor%20quasi%20experimenten.pdf

Nichols, A. STATA, (2009). Causal inference with observational data regression discontinuity and related options in STATA. Retrieved from website: http://www.stata.com/meeting/germany09/nichols.pdf

 

 

Updated: 6th August 2014 - 4:32am
A special thanks to this page's contributors
Author
International Initiative for Impact Evaluation.
Arlington.
Author
Reviewer
Research Fellow, RMIT University.
Melbourne.

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