## Wednesday, May 22, 2013

### Regression Discontinuity Designs

Suppose a policy or intervention is implemented or a treatment is applied based on arbitrary values of some observed covariate value or values X0. If there is some positive relationship between ‘X’ and the outcome ‘Y’ then how do we know if a treatment applied to subjects where X > X0 isn’t biased since subjects with higher values of X are more likely to exhibit higher levels of the outcome variable Y anyway?  Is it valid to make comparisons of observed outcomes (Y) between groups with differing values of (X)?  One solution would be to implement matched comparisons between groups with similar values of covariates.  Regression discontinuity designs allow us to compare differences between groups in the neighborhood of the cutoff value X0 giving us unbiased estimates of treatment effects.

• Treatment effects can be characterized by a change in intercept or main effect at the discontinuity.
•  Treatment assignment is equivalent to random assignment within the neighborhood of the cutoff   (Lee & Lemieux,2010).
• More complicated functional forms may be estimated:

Y = f(x) +ρ D + e where f(x) may be a pth order polynomial
• Comparisons of outcomes in the neighborhood of X0 provide estimates of the treatment effect  ρ that does not depend on an exactly correct specification of the functional form of E[Y|X] (Angrist &Pischke, 2009)
•  Even more complicated methods including local linear regression may be implemented

The above illustrates only one potential visualization of RD designs.  As illustrated below, treatment effects  can be visualized as discontinuities  or changes in either the intercept or slope or both at the cutoff X0

Application:

In Shaping Policies Related to Developmental Education: An Evaluation Using the Regression-Discontinuity Design,  the authors use RD design to assess the impact of developmental education on student success in subsequent level English courses :

They find that ‘students’ participation in the program increases English academic achievement to levels similar to those of students not needing developmental coursework.’ Note in this case, the treatment (developmental course work) is applied where X < X0 = 85, vs. where X > X0 in the cases I presented above. The discontinuity/treatment effect in this case is represented by a change in slope/interaction at the cutoff.

References:

Brian G. Moss  and William H. Yeaton
Shaping Policies Related to Developmental Education: An Evaluation Using the Regression-Discontinuity Design. EDUCATIONAL EVALUATION AND POLICY ANALYSIS September 21, 2006 vol. 28 no. 3 215-229

Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.

Regression Discontinuity Designs in Economics
David S. Lee and Thomas Lemieux.
Journal of Economic Literature 48 (June 2010)281-355

REGRESSION DISCONTINUITY
PATRICIA BAUMER

Mostly Harmless Econometrics. Angrist & Pischke. 2009.