Difference in Differences (DD) Analysis

Practice vocabulary flashcards covering the key concepts, assumptions, and formulas of Difference in Differences (DD) and Two-Way Fixed Effects (TWFE) models.

Standard DD analysis

A method that compares the difference in average outcomes for the treated observations before and after treatment with the difference in mean outcomes for the control observations before and after treatment.

Average Treatment Effect on the Treated ($ATT$)

The target estimand of a Difference in Differences analysis.

$$E(y_0|g=1, t=1)$$

The unobserved or counterfactual outcome for the treated group in the post-treatment period ($t=1$) representing what would have happened in the absence of treatment.

Parallel trends assumption

The key identifying assumption in a DD analysis stating that the treated and untreated outcomes would follow parallel trends in the absence of the treatment.

Simple before vs. after comparison

An analysis approach for treated observations that misses trends in the outcome not associated with the treatment.

Simple treated vs. control comparison

An analysis approach after treatment that misses factors causing non-random selection into treatment.

$$\gamma$$

The parameter reflecting the average difference between treated and untreated outcomes before treatment ($t=0$).

$$\eta$$

The parameter reflecting the average difference in outcomes before and after treatment for the untreated group, which also reflects the counterfactual average difference between periods 0 and 1 for the treated group.

$$\delta$$

The parameter in a DD regression that represents the DD estimand.

$2 \times 2$ DD Regression

A standard regression analysis of the outcome on a group dummy, a period dummy, and their interaction.

Standard DD Regression Expression

The formal expression given by $y = \mu + \gamma \text{treat} + \eta \text{after} + \delta \text{treat} \cdot \text{after} + u$.

TWFE model

A Two-Way Fixed Effects regression model designed for data containing both a group and a time dimension.

Homogeneous treatment effect

The condition under which estimating a TWFE model with multiple groups and variation in treatment timing can identify the $ATT$.

Clustering at the group level

A requirement for computing correct standard errors for TWFE estimates to account for heteroscedasticity and serial correlation.