Lesson 14: Regression Discontinuity and IV

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Questions and Answers

Which covariates should we check to test for evidence of a valid comparison on each side of the cutoff?

Covariates that are determined before the treatment (correct)

Variables that are affected by the treatment

How should you examine if there is continuity at the cutoff?

Both A and B (correct)

Make figures with the predetermined variable on the vertical axis

Estimate regressions and check for evidence of statistically significant changes at the cutoff

Looking at the graph of Gender Composition, do we see any statistically significant changes at the cutoff?

False

Looking at the graph of Employment Rates, do we see any statistically significant changes at the cutoff?

True Signup and view all the answers

Looking at the graph of Marital Status, do we see any statistically significant changes at the cutoff?

True Signup and view all the answers

What is the key to a valid comparison when utilizing regression discontinuity designs?

Having groups that are similar on all dimensions other than the treatment of interest. Signup and view all the answers

What are two key assumptions that must be met when using regression discontinuity designs?

The potential outcomes must be continuous in the running variable at the threshold, and the treatment assignment should be as good as random in the vicinity of the threshold. Signup and view all the answers

Why is checking for a change in density at the cutoff an important aspect of an RD design?

If there is a sharp jump or discontinuity in the density of individuals at the cutoff, it could indicate that the treatment assignment was not random. This would weaken the internal validity of the design, as it suggests that unobserved factors may be driving the outcome rather than the treatment itself. Signup and view all the answers

What does the first stage in an RD design tell us?

The first stage regression tells us the effect of the treatment on the running variable (i.e., the variable used to determine treatment assignment). Signup and view all the answers

What does the reduced form in an RD design tell us?

The reduced form regression tells us the overall effect of the running variable on the outcome variable, without controlling for the treatment effect. Signup and view all the answers

What are the four steps involved in implementing a Regression Discontinuity design?

The four steps involved in implementing a regression discontinuity design are to make a good figure for the first stage and each outcome, estimate regressions, present regression results in a clearly laid out table, and document that the choices you made for the regression are not important. Signup and view all the answers

Study Notes

Lesson 14: Regression Discontinuity: Balance and IV

Regression Discontinuity (RD) designs are being discussed.
Upcoming assignments include Assignment 3.
RD validity includes balance graphs, balance tables, adding covariates, and density tests.
RD analysis incorporates instrumental variables (IV) and overview components.
RD validity relies on the continuity of potential outcomes (E[Yo¡|X; = x] and E[Y₁₁|X₁ = x]) at the threshold in x.
Methods to evaluate this assumption will be examined.

RD: Balance Graphs

A valid RD comparison requires comparable groups except for the treatment of interest.
Groups on either side of the threshold could differ if the program is desirable or people deliberately manipulate the running variable (X) to qualify.
Differential non-response rates at the cutoff can also cause this difference.
Unsuitable regression specifications (e.g., low or high polynomial order) can cause groups to appear different.
Sharp changes in potential outcomes at the threshold violate the continuity assumption.
Balance graphs help examine if untreated and treated potential outcomes are similar on both sides of the threshold.
Graphs investigate potential changes at the cutoff.
Covariates determined before treatment (e.g., fixed characteristics) are checked but not treatment-affected variables.
Specific examples using legal drinking age, clubs, and gender are given, highlighting which characteristics are or aren't suitable to include
Figures should use the pre-determined variable on the y-axis.
Statistical significance at the cutoff is checked using regressions.

RD: Balance Tables

Formal checks for statistical significance of changes at the threshold are needed.
Balance tables, similar to RCTs, are used to check if individuals just above and below the cutoff are similar in observable characteristics.
The assumption is that similarity in observable characteristics implies similarity in potential outcomes.
Regressions with consistent bandwidth and polynomial order of X (first stage and reduced form) are used for this analysis.
Example regression equation is given (e.g., male = β0 + β1Z + β2Age + β3Age² + β4AgeZ + β5Age²Z + ui).
Results are tabulated, with each column representing a different characteristic.

RD: Density Test

Density at the cutoff is checked to find potential changes in the number of people.
This could be applied to understanding situations like changes in tax deductions and their effect on college attendance.
An example involving income eligibility for college tuition and fees deductions is provided, comparing households slightly above and below the 130,000 income cutoff.
Analysis checks if those slightly above and below the threshold have similar characteristics regarding their children attending college.

RD: Adding Covariates

Examining first-stage and reduced-form results with a polynomial in the running variable is the first step.
Adding predetermined characteristics (W) to regressions to increase estimate precision.
Covariates not related to the treatment (e.g., age, race, educational attainment) can be included in W.
Variables affected by treatment (outcomes) should not be included.
Specific examples (drinking last month) are available that demonstrate how to handle covariates appropriately in regression analysis.

RD: IV Estimate

Potential treatment effect of drinking on arrest, given the threshold effect of drinking laws, is a main use case.
The first stage analyzes the impact of legal drinking age on alcohol consumption.
The reduced form analyzes the effect of legal drinking age on arrest rates.
A combined approach calculates the change in crime rates per drinker.
Two key assumptions for valid instrumental variables (IV) analysis are that the instrument affecting variable is independent to other factors and the effects of the instrument affects the variable of interest only.
The instrument's ability to affect the output through the variable of interest is investigated.

Regression Discontinuity: Overview

Procedures involve creating suitable figures and tables that demonstrate balance in covariates, initial stages, and reduced form outcomes.
The figures need to clarify the jump in figures at the threshold.
Polynomial and bandwidth choices can affect outcomes and must be documented.
Regression results should be compiled in a table.

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Description

This quiz covers Regression Discontinuity designs, focusing on the importance of balance graphs and tables, as well as the integration of instrumental variables (IV). It explores the validity of RD analysis through various methods and the critical assumption of continuity at the threshold. Additionally, upcoming assignments related to this topic will be discussed.