1. Making the Most out of Discontinuities
Nandini Krishnan
Making the Most out of Discontinuities
This presentation is based on work done by Erich Battistin, Jean-Louis Arcand, Nandini Krishnan and Florence Kondylis.

2. Introduction
Setting: we would like to evaluate policy interventions in an observational setting, i.e. when the analyst cannot manipulate the selection process.
In general: Individuals, households, villages, or other entities, are either exposed or not exposed to a “treatment” or “policy regime” and the two groups are not comparable because of selection.
When randomization is not feasible, how can we exploit implementation features of the program to “measure” its impact?
Answer: Quasi-experiments
Florence’s presentation and now Regression Discontinuity Design.

3. Regression Discontinuity Designs
RRD is closer cousin of randomized experiments than other competitors
Major element in the toolkit for empirical research
It is a “design”, not a “method”, and thus relies on knowledge of the selection process
Logic: Assignment to “treatment” depends- completely or partly – on a “score”, a quantifiable selection criteria

4. RDD Example
Policy: US minimum legal drinking age (MLDA) – if less than 21, alcohol consumption is illegal
Observation: The policy treats people aged 20 years, 11 months and 29 days and 21 year olds differently. However, do we think that these individuals are inherently different?
Are 20 year-, 11 month- and 29 day- olds less wise, less likely to go to parties than 21 year olds? Less obedient?
People born “few days apart” are treated differently, because of the arbitrary age cut off established by the law. However, we hardly think that few days or a month apart could really make a difference in terms of behaviors and attitudes towards alcohol

5. RDD Example (2)
Idea: This policy rule assigns people to treatment and control groups:
Treatment group: those who are 20 years and 11 months old
Control group (Can legally drink alcohol): individuals who just turned 21 –
It is as if people were assigned to treatment and control at random- similar in terms of observable and unobservable characteristics that affect outcomes (mortality rates).
Can isolate the causal impact of alcohol consumption on mortality rates among young adults.

6. RDD Example (3)
MLDA (Treatment) causes lower alcohol consumption

7. RDD Example (4)
Increased alcohol consumption causes higher mortality rates around the age of 21
All deaths
All deaths associated with injuries, alcohol or drug use
All other deaths

8. RDD Logic
General idea: assignment to the treatment depends, either completely or partly, on a continuous “score”, ranking (age in the previous case):
potential beneficiaries are ordered by looking at the score
there is a cut-off point for “eligibility” – clearly defined criterion determined ex-ante
cut-off determines the assignment to the treatment or no-treatment groups
These de facto assignments often arise from administrative decisions, where the incentives to participate are partly limited because of resource constraints, and transparent rules rather than discretion are used for the allocation of incentives

9. Example (2): vouchers
Government offers vouchers for fertilizer for small farmers.
Eligibility rule based on plot size:
If plot less than 2 acres then farmer receives vouchers
If plot bigger than 2 acres then no voucher
Size of plot not easily manipulable overnight, easy to measure and enforce (with admin data on size of plots)
Everyone below the eligibility cut-off receives vouchers.

10. Example: fuzzy design
Now suppose that, for unknown reasons, not all the eligibles farmers receive the voucher. Why?
limited knowledge of the program (didn’t know the program was happening)
Voluntary participation (farmers who take up are different from those who don’t along several dimensions)
The percentage of participants changes discontinuously at cut-off, from zero to less than 100%

11. Probability of Participation under Alternative Designs
100%
75% 0% 0%

12. Sharp and Fuzzy Discontinuities
Ideal setting: Sharp discontinuity
the discontinuity precisely determines treatment status
e.g. ONLY people 21 and older drink alcohol!
Only small plots receive vouchers
Fuzzy discontinuity
the percentage of participants changes discontinuously at cut-off, but not from zero to 100%
e.g. rules determine eligibility but amongst the small farmers there is only partial compliance / take-up
Some people younger than 21 end up consuming alcohol and some older than 21 don’t consume at all

13. Internal Validity
General idea: as a result of the arbitrary cut off associated to a given policy, individuals to the immediate left and right of the cut-off are similar.
Therefore, differences in alcohol consumption and mortality can be thought of as determined by the policy.
Assumption (nothing else is happening): in the absence of the policy, we would not observe a discontinuity in the outcomes around the cut off.
We are assuming that there is nothing else going on around the same cut off that impacts our outcome of interest:
21 year olds can start drinking however the moment they turn 21 they have to enroll in a “drinking responsibly” type seminar
Vouchers: there is another policy that gives equipment to farmers with plots larger than 2 acres.

14. Outcome Profile Before and After the Intervention

15. Outcome Profile Before and After the Intervention
different shape

16. External Validity How general are the results?
Counterfactual: individuals “marginally excluded from benefits” (less than 21, plots less than 2 acres)
Causal conclusions are limited to individuals, households, villages, at the cut-off
The effect estimated is for individuals “marginally eligible for benefits”
extrapolation beyond this point needs additional, often unwarranted, assumptions (or multiple cut-offs)
Fuzzy designs exacerbate the problem

17. The “nuts and bolts” of implementing RDDs
A major advantage of the RDD over competitors lies in its transparency, as it can be illustrated using graphical methods
Requires many observations around cut-off (alternatively, one could down-weight observations away from the cut-off)
Why? Because only near the cut-off can we assume that people find themselves by chance to the left and to the right of the cut-off.
Think about farmer who owns 1 acre plot vs farmer who owns 50 acre plot
or compare a 16 vs a 25 years old.

18. Graphical Analysis

19. Moving the goalpost
Natural-experiments are “naturally” occurring instances which approximate the properties of an experiment
RDDs share the same properties as an experiment locally at the cut-off
Thus “real-world” discontinuities are a gold mine for those fishing for natural experiments 

20. Wrap Up
Modern econometrics views RDDs as a powerful tool to identify causal effects 
Pros: as good as experiments (around the cut off)
Cons: the estimated program effects are representative only of households/villages near the cut off, which may not reflect entire population of interest.

21. Wrap Up
Can be used to design a prospective evaluation when randomization is not feasible
The design applies to all means tested programs
Multiple cut-offs to enhance external validity
Can be used to evaluate ex-post interventions using discontinuities as “natural experiments”.

22. Thank You