- 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 X

_{0}.__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

SOUTHERN METHODIST UNIVERS ITY. http://faculty.smu.edu/kyler/courses/7312/presentations/baumer/Baumer_RD.pdf

Mostly Harmless Econometrics. Angrist & Pischke.
2009.

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