5.2 — Difference-in-Differences — Class Content

Meeting Dates

Monday, November 28, 2022

Upcoming Assignment

Problem Set 5 is due on Monday November 28.

Overview

Today, we look at 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

$${\text{Treated}}_i=\{\begin{array}{l}1\text{ if }i\text{ is in treatment group}\\ 0\text{ if }i\text{ is not in treatment group}\end{array}{\text{After}}_t=\{\begin{array}{l}1\text{ if }t\text{ is after treatment period}\\ 0\text{ if }t\text{ is before treatment period}\end{array}$$

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:

	Control	Treatment	Group Diff $(\mathrm{\Delta }{Y}_i)$
Before	${\beta }_0$	${\beta }_0+{\beta }_1$	${\beta }_1$
After	${\beta }_0+{\beta }_2$	${\beta }_0+{\beta }_1+{\beta }_2+{\beta }_3$	${\beta }_1+{\beta }_3$
Time Diff $(\mathrm{\Delta }{Y}_t)$	${\beta }_2$	${\beta }_2+{\beta }_3$	Diff-in-diff ${\mathrm{\Delta }}_i{\mathrm{\Delta }}_t:{\beta }_3$

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”

Assignments

Problem Set 5 Due Mon Nov 28

Problem Set 5 is due by the end of the day on Wednesday, November 28.

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. The lower button will allow you to download a PDF version of the slides.

I suggest printing the slides beforehand and using them to take additional notes in class (not everything is in the slides)!

Download as PDF