Difference-in-Differences (DiD) Method

Parallel Trends Assumption: In the absence of treatment, the average difference in outcomes between the treatment and control groups would have remained constant over time.

Regression Model: \[ Y_{it} = \beta_0 + \beta_1 \text{Treated}_i + \beta_2 \text{Post}_t + \delta \,(\text{Treated}_i \times \text{Post}_t) + \epsilon_{it} \]

• \( Y_{it} \) is the outcome for individual \(i\) at time \(t\).
• \( \text{Treated}_i \) equals 1 if the individual is in the treatment group, 0 otherwise.
• \( \text{Post}_t \) equals 1 for the post-intervention period, 0 for the pre-intervention period.
• The coefficient \( \delta \) is the Differences-in-Differences estimator, capturing the causal effect of the treatment.

Computation of the DiD Estimator: \[ \hat{\delta}_{\text{DiD}} = (\overline{Y}_{\text{Treated, After}} - \overline{Y}_{\text{Treated, Before}}) - (\overline{Y}_{\text{Control, After}} - \overline{Y}_{\text{Control, Before}}) \]