4.2 — Difference-in-Difference Models — Class Content

Overview

Today, we look at our last model this semester, one of the most commonly used by professional researchers and econometricians: difference-in-differences, also called “diff-in-diff” or “DND.” The setup of this regression is actually quite simple, consisting (primarily) of a series of dummy variables and an interaction effect:

$$Y_{it}={\beta }_0+{\beta }_1{\text{Before}}_t+{\beta }_2{\text{Treated}}_i+{\beta }_3({\text{Before}}_i\times {\text{Treated}}_t)+u_{it}$$ where $${\text{Treated}}_i=\{\begin{array}{c}1\text{if}i\text{is in treatment group}\\ 0\text{if}i\text{is not in treatment group}\end{array}{\text{After}}_t=\{\begin{array}{c}1\text{if}t\text{is after treatment period}\\ 0\text{if}t\text{is before treatment period}\end{array}$$ Thus, $\widehat{{\beta }_3}$ is the causal effect of the treatment we aim to measure. As an interaction effect between two dummies, we can interpret $\widehat{{\beta }_1}$ as measuring the difference across treatment & control group before any treatments happen, $\widehat{{\beta }_2}$ as the difference over time, and $\widehat{{\beta }_3}$ as the difference of the differences:

Readings

• Ch. 8.5 in Bailey, Real Econometrics
• Dynarski, 1999, “Hope for Whom? Financial Aid for the Middle Class and its Impact on College Attendance”
• Card and Kreuger, 1994, “Minimum Wages and Unemployment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania”

Slides

Below, you can find the slides in two formats. Clicking the image will bring you to the html version of the slides in a new tab. Note while in going through the slides, you can type h to see a special list of viewing options, and type o for an outline view of all the slides.

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