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

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

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 $$\Delta_i \Delta_t: \beta_3$$