5.2 — Difference-in-Differences — Class Content
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
\[\text{Treated}_i= \begin{cases}1 \text{ if } i \text{ is in treatment group}\\ 0 \text{ if } i \text{ is not in treatment group}\end{cases} \quad \text{After}_t= \begin{cases}1 \text{ if } t \text{ is after treatment period}\\ 0 \text{ if } t \text{ is before treatment period}\end{cases}\]
Thus, \(\hat{\beta_3}\) is the causal effect of the treatment we aim to measure. As an interaction effect between two dummies, we can interpret \(\hat{\beta_1}\) as measuring the difference across treatment & control group before any treatments happen, \(\hat{\beta_2}\) as the difference over time, and \(\hat{\beta_3}\) as the difference of the differences:
Control | Treatment | Group Diff \((\Delta Y_i)\) | |
---|---|---|---|
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 \((\Delta Y_t)\) | \(\beta_2\) | \(\beta_2+\beta_3\) | Diff-in-diff \(\Delta_i \Delta_t: \beta_3\) |
Readings
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)!