Download Presentation
Regression Discontinuity

Loading in 2 Seconds...

1 / 19

# Regression Discontinuity - PowerPoint PPT Presentation

Regression Discontinuity. Basic Idea. Sometimes whether something happens to you or not depends on your ‘score’ on a particular variable e.g You get a scholarship if you get above a certain mark in an exam, you get given remedial education if you get below a certain level,

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

## PowerPoint Slideshow about 'Regression Discontinuity' - more

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Regression Discontinuity

Basic Idea
• Sometimes whether something happens to you or not depends on your ‘score’ on a particular variable e.g
• You get a scholarship if you get above a certain mark in an exam,
• you get given remedial education if you get below a certain level,
• a policy is implemented if it gets more than 50% of the vote in a ballot,
• your sentence for a criminal offence is higher if you are above a certain age (an ‘adult’)
• All these are potential applications of the ‘regression discontinuity’ design
More formally..
• assignment to treatment depends in a discontinuous way on some observable variable W
• simplest form has assignment to treatment being based on W being above some critical value w0- the discontinuity
• method of assignment to treatment is the very opposite to that in random assignment – it is a deterministic function of some observable variable.
• But, assignment to treatment is as ‘good as random’ in the neighbourhood of the discontinuity – this is hard to grasp but I hope to explain it
Basics of RDD Estimator
• Suppose average outcome in absence of treatment conditional on W is:
• Suppose average outcome with treatment conditional on W is:
• This is ‘full outcomes’ approach.
• Treatment effect conditional on W is g1(W)-g0(W):
How can we estimate this?
• Basic idea is to compare outcomes just to the left and right of discontinuity i.e. to compare:
• As δ→0 this comes to:
• i.e. treatment effect at W=w0
Comments
• the RDD estimator compares the outcome of people who are just on both sides of the discontinuity - difference in means between these two groups is an estimate of the treatment effect at the discontinuity
• says nothing about the treatment effect away from the discontinuity - this is a limitation of the RDD effect.
• An important assumption is that underlying effect on W on outcomes is continuous so only reason for discontinuity is treatment effect
The procedure in practice
• If take process described above literally should choose a value of δ that is very small
• This will result in a small number of observations
• Estimate may be consistent but precision will be low
• desire to increase the sample size leads one to choose a larger value of δ
Dangers
• If δ is not very small then may not estimate just treatment effect – look at picture
• As one increases δ the measure of the treatment effect will get larger. This is spurious so what should one do about it?
• The basic idea is that one should control for the underlying outcome functions.
If underlying relationship linear
• If the linear relationship is the correct specification then one could estimate the ATE simply by estimating the regression:
• But no good reason to assume relationship is linear and this may cause problems
one would want to control for a different relationship between y and W for the treatment and control groups
• Another problem is that the outcome functions might not be linear in W – it could be quadratic or something else.
• The researcher then typically faces a trade-off:
• a large value of δ to get more precision from a larger sample size but run the risk of a misspecification of the underlying outcome function.
• Choose a flexible underlying functional form at the cost of some precision (intuitively a flexible functional form can get closer to approximating a discontinuity in the outcomes).
In practice
• it is usual for the researcher to summarize all the data in the graph of the outcome against W to get some idea of the appropriate functional forms and how wide a window should be chosen.
• But its always a good idea to investigate the sensitivity of estimates to alternative specifications.
An example
• Lemieux and Milligan “Incentive Effects of Social Assistance: A regression discontinuity approach”, Journal of Econometrics, 2008
• In Quebec before 1989 childless benefit recipients received higher benefits when they reached their 30th birthday
Note
• Note that the more flexible is the underlying relationship between employment rate and age, the less precise is the estimate