# Regression discontinuity design

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Regression discontinuity design

In statistics, econometrics, epidemiology and related disciplines, a regression discontinuity design (RDD) is a design that elicits the causal effects of interventions by exploiting a given exogenous threshold determining assignment to treatment. By comparing observations lying closely on either side of the threshold, it is possible to estimate the local treatment effect in environments in which randomization was unfeasible. First applied by Donald Thistlewaite and Donald Campbell to the evaluation of scholarship programs[1], the RDD has become increasingly popular in recent years[2].

## Example

The intuition behind the RDD is well illustrated using the evaluation of merit-based scholarships. The main problem with estimating the causal effect of such an intervention is the endogeneity of assignment to treatment (e.g. scholarship award): Since high performing students are more likely to be awarded the merit scholarship and continue performing well at the same time, comparing the outcomes of awardees and non-recipients would lead to an upward bias of the estimates. Even if the scholarship did not improve marks at all, awardees would have performed better than non-recipients, simply because scholarships were given to students who were performing well ex ante.

Despite the absence of an experimental design, a RDD can exploit exogenous characteristics of the intervention to elicit causal effects. If all students above a given mark - for example 50% - are given the scholarship, it is possible to elicit the local treatment effect by comparing students around the 50% cut-off: The intuition here is that a student scoring 49% is likely to be very similar to a student scoring 51% - given the pre-defined threshold of 50%, however, one student will receive the scholarship while the other will not. Comparing the outcome of the awardee (treatment group) to the counterfactual outcome of the non-recipient (control group) will hence deliver the local treatment effect.

### Other examples

• Developmental education in higher education, when remediation is determined by a placement test [3]
• Policies in which treatment is determined by an age eligibility criterion (e.g. pensions)[4].
• Elections in which one politician wins by a marginal majority[5].

• When properly implemented and analyzed, the RDD yields an unbiased estimate of the local treatment effect[6].
• RDD, as a quasi-experiment, does not require ex ante randomization and circumvents ethical issues of random assignment.

• The statistical power is considerably lower than a randomized experiment of the same sample size, increasing the risk of erroneously dismissing significant effects of the treatment (Type II error)[7]
• The estimated effects are only unbiased if the functional form of the relationship between the treatment and outcome is correctly modelled. The most popular caveats are non-linear relationships that are mistaken as a discontinuity.

## Extensions

The identification of causal effects hinges on the crucial assumption that there is indeed a sharp cut-off, around which there is a discontinuity in the probability of assignment from 0 to 1. In reality, however, cut-offs are often not strictly implemented (e.g. exercised discretion for students who just fell short of passing the threshold) and the estimates will hence be biased.

In contrast to the sharp regression discontinuity design, a fuzzy regression discontinuity design (FRDD) does not require a sharp discontinuity in the probability of assignment but is applicable as long as the probability of assignment is different. The intuition behind a is related to the instrumental variable strategy and intention to treat.

## References

1. ^ Thistlewaite and Campbell: Regression-Discontinuity Analysis: An alternative to the ex post facto experiment, 1960, Journal of Educational Psychology 51: 309-317.
2. ^ Imbens, Guido and Lemieux, Thomas: Regression Discontinuity Designs: A Guide to Practice, 2010, Journal of Economic Literature 48, 281-355
3. ^ Moss BG, Yeaton WH (2006). "Shaping Policies Related to Developmental Education: An Evaluation Using the Regression-Discontinuity Design.". Educational Evaluation and Policy Analysis 28 (3): 215–229. doi:10.3102/01623737028003215.
4. ^ Duflo: Grandmothers and Granddaughters: Old-age Pensions and Intrahousehold Allocation in South Africa, 2003, World Bank Economic Review 17 (1): 1-25.
5. ^ Lee: The electoral advantage to incumbency and voters' valuation of politicians' experience: A regression discontinuity analysis of elections to the US House. NBER Working Papers, No. 8441
6. ^ Rubin: Assignment to Treatment on the Basis of a Covariate, Journal of Educational and Behavioural Statistics, March 1977, vol. 2 no. 1 1-26
7. ^ Angrist and Pischke: Mostly harmless econometrics: An empiricist's companion, 2008, Chapter III, 6. Princeton University Press.

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