Lecture 7 : Regression Discontinuity Design
Rigissa Megalokonomou University of Queensland
1/50
FirstOnlineQuiz
This quiz, covering topics introduced in Lectures 1-6, may
take you 60-75 minutes to complete, depending on your proficiency in knowledge. The due date for this quiz is September 25th (16:00) (next Friday).
This quiz consists of in total 20 multiple choice questions (MCQ).
There is only one attempt for this quiz, and once started, this test must be completed in one sitting.
2/50
FirstOnlineQuiz
Do not leave the test before clicking Save and Submit.
This quiz is marked out of 100 points but contributes 10%
towards your final.
All MCQ have one and only one correct answer.
You will not need a calculator, as there will be no questions
that require computations.
To pass the course, students must obtain a mark of at least
50% in the two quizzes combined (i.e., 20 out of 40 points).
Next week: Presentation of an Academic Paper and Discussion about the Article Review
3/50
Reading for Lecture 7
Chapters6inMostlyHarmlessEconometrics-An Empiricist’s Companion by Angrist and Psischke (2009)
Chapter25.6inMicroeconometrics:Methodsand Applications by Cameron and Trivedi (2005)
4/50
Introduction
Wheneverrulesorlawscreatesharpthresholdsinthe implementation of policies and programs there is a potential to exploit these cutoffs for identification.
Regressiondiscontinuitydesigns(RDD)exploitnatural experiments generated by arbitrary rules.
Regressiondiscontinuity(RD)designsexploitthefactthat some rules are quite arbitrary and therefore provide good quasi-experiments when you compare people (or cities, firms, countries,…) who are just affected by the rule with people who are just not affected by the rule.
Byquasi-experimentswemeanthatthedesignslackthe element of random assignment of the sample to treatment or control.
5/50
Introduction
Theworldaboundswithsuchrules
Students receive a scholarship if their GPA is above 3.0.
Children are allowed to start school if they turn 6 by 31st of
December of that year.
Individuals are eligible for a micro-finance loan if they own
less than 0.5 acres of land.
Legislators are elected if they receive over 50% of the vote.
Inaworldwithlotsofrules,someofthesewillbearbitrary. Arbitraryrulesprovidewonderfulnaturalexperiments!
6/50
Introduction
ThisideagoesasfarbackasThistlethwaiteandCampbell (1960) who analyzed the impact of winning a merit scholarship on subsequent educational outcomes, using the fact that the allocation of these awards was based on the comparison of the observed test score with a threshold score.
Merit scholarships were awarded (D) to students if their test score x was above a certain threshold c.
x is called running/forcing/assignment variable.
D is variable of our interest.
The main idea behind the research design was that individuals with scores just below the cutoff (who did not receive the award) were good comparisons to those just above the cutoff (who did receive the award).
This allows us to compare individuals (or cities, firms, countries,…) who were just affected by the rule with those who are just not affected by the rule and consider them to be valid counterfactuals.
7/50
Ittookalongtimebeforepeoplerealizedthestrengthof RD designs.
Somewell-receivedRDpapersaretheonesbyAngrist and Lavy (1999), van der Klaauw (2002), or Black (1999).
UnliketheidentificationassumptionsforIVand difference-in-difference, the assumptions for the RD design are testable to a considerable extent.
Intherightcontext,RDdesigncanprovideahighly credible and transparent way of estimating causal effects of programs/interventions.
8/50
Example of a linear RD Setup
9/50
Basic setup
ThistlethwaiteandCampbell(1960)introducedtheRD design by analyzing the impact of winning a merit scholarship on subsequent educational outcomes.
Merit scholarship (i.e. treatment) was awarded if a student’s test score x (i.e. assignment variable) was above a certain threshold c.
Denote future outcomes by y.
LetDdenotethetreatmentstatusD∈{1,0}.
D = 1 if x ≥ c and D = 0 if x < c
Thusthereisadiscontinuousjumpintreatmentatthetest score threshold c.
Howeverthereappearstobenoreasonotherthanthe merit award for y to be a discontinuous function of x.
This is the underlying motivation of the RD design.
10/50
Basic setup
Assuming that the relationship between y and x is otherwise linear, a simple way of estimating the treatment effect τ is by fitting the linear regression:
y =α+Dτ+xβ+u
Disthetreatmentdummyandxistheassignmentvariable.
Comparingindividualsclosetothediscontinuityisthusanatural estimate of the treatment effect.
Inpractice,wecannotonlylookatindividualsclosetothecutoff since the closer we look, the less data points will be available.
Onehasnochoicebuttousedataawayfromthecutoff,toget reasonable estimates for the treated and untreated values of y at x = c.
Iftheunderlyingfunctionislinear,thenτ,thecoefficientonD from OLS estimator, expresses the causal effect of interest.
11/50
12/50
Sharp RD and Fuzzy RD
SharpRD:thetreatment(Di)isadeterministicfunctionof Xi.
Example: if you score above 65% you get into the PhD program.
FuzzyRD:exploitsdiscontinuitiesintheprobabilityof treatment conditional on Xi.
Example: If you score above 65% and you get an IELTS score above 6.5, then you increase your probability of being accepted to the PhD program.
13/50
Sharp RD
InSharpRDdesignsyouexploitthefactthatthetreatment status is a deterministic and discontinuous function of an assignment variable x.
D=1ifx≥c
D=0ifx