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 \[\text{Treated}_i= \begin{cases}1 \text{ if } i \text{ is in treatment group}\\ 0 \text{ if } i \text{ is not in treatment group}\end{cases} \quad \text{After}_t= \begin{cases}1 \text{ if } t \text{ is after treatment period}\\ 0 \text{ if } t \text{ is before treatment period}\end{cases}\] 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
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.
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)!
Assignments
Problem Set 5 Due Tues Nov 23
Problem Set 5 is due by the end of the day on Tuesday, November 23. This will be your final graded homework!
Problem Set 6 Ungraded For Practice
Problem Set 6 on Unit IV topics may help you study for the final. It will not be collected or graded.