Making the Most out of Discontinuities

1. Laura Chioda Making the Most out of Discontinuities

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 • (see Florence’s presentation) and now Regression Discontinuity Design.

3. RegressionDiscontinuityDesigns • RRD is closer cousin of randomized experiments than other competitors • Major element in the toolkit for empirical research • Now very fashionable but it goes back to the early sixties • went into hibernation for two decades • experienced a renaissance with the new millennium 

4. RDD Example • Policy: US drinking age – if less than 21, alcohol consumption is illegal • Outcomes: alcohol consumption and mortality rate • Observation: The policy treats people aged 20 and 11 months and 29 days and 21 year olds differently. However, do we think that these individuals are inherently different? • Are 20 years & 11 months and 29 days 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:use this policy rule to assign people to treatment and control groups: • treatmentgroup: those who are 20 years and 11 months old • control group: individuals who just turned 21 – Why is this a sensible assignment rule? It is as if people were assigned to treatment and control at random.

6. RDD Example (3)

7. RDD Example (4)

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 km2 then farmer receives vouchers • If plot bigger than 2 km2 then no voucher • Size of plot not easily manipulable over night, 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 plot 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 km2.

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 2km2) • 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 km2 plot vs farmer who owns 50 km2 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