Regression discontinuity

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Regression discontinuity Correlation Coefficient
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What is regression discontinuity?

Regression discontinuity is an evaluation in quasi-experimental design. As we know, quasi-experimental design is different from true experimental with respect to random sample assignment. Quasi experiments need tests to determine which subjects of the population will go to which group – treatment or control group. 

Regression discontinuity is a quasi-experimental evaluation technique that is used in experiments or program that has an eligibility criteria telling who from the population can participate and who cannot. This eligibility is called a cut-off point in an experiment. Regression discontinuity, also known as regression discontinuity design helps the researchers to check people for their eligibility by evaluating them below or above the cut-off point. 

Example: Marks of students can be from 0 to 100. Teacher decides to assign students that have a poor performance to a special course which will enhance their skills. So the group of students who will take the course will be put to a treatment group and those who have decent scores will not go through any treatment, hence they are called control group. 

RDD can be used to measure the outcomes of the students and decide which students are above the decided cut-off and below the cut-off.

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What are the conditions and assumptions for regression discontinuity design?

Conditions for regression discontinuity design:

  • Continuous eligibility index is a continuous measure by used to rank the population.
  • Defined cut-off point – it is a point on the index which is defined as a cut-off point. It is a point below or above of which the population is said to be eligible for the program. 

Assumptions for regression discontinuity design: 

  • Eligibility index should be continuous around the cut-off point without any jumps. 
  • The individuals should not manipulate their eligibility index so that they can included or excluded from a program. 
  • The distribution of unobserved and the observed variables needs to be continuous in nature around the threshold.

Types of regression discontinuity

There is an assignment rule for assigning people to particular programs. If the assignment rule is deterministic, then the regression discontinuity has a sharp design and if the assignment rule is probabilistic, the regression discontinuity has a fuzzy design.

Sharp regression discontinuity design

In sharp design, the probability of having a treatment to people is either 0 or 1. The person is either selected for a program or he is not. Example: school decides to award students who have scored above the threshold of 90%. Hence, the treatment probability is 0 or 1. 

 

Regression discontinuity Correlation Coefficient

Fuzzy regression discontinuity design

This is a case where some of the eligible people do not receive the treatment or some ineligible people receive it. Example: some workers with below cut-off wages did not get the allowance according to the company program and some that were above the threshold wage got it. This fuzziness in the assignment may give imperfect or incorrect justification to the rule or a program that was put in place.

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What is a regression discontinuity estimate?

The estimate is a difference in means “just above” and “just below” c, where c is the cut-off point.

Regression discontinuity Correlation Coefficient
  • Estimates average treatment effect when XX is at cc
  • τRD=E[Y1−Y0|X=c]τRD=E[Y1−Y0|X=c] in potential outcomes notation
  • Till E[Y1|X]E[Y1|X] and E[Y0|X]E[Y0|X] continuous, there are no jumps in anything except treatment at c
  • Interpretation: weighted average treatment effect at cc with weighting proportional to probability Xi=cXi=c
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