29.6 One Difference

The regression formula is as follows (Liaukonytė, Tuchman, and Zhu 2023):

$$y_{ut} = \beta \text{Post}_t + \gamma_u + \gamma_w(t) + \gamma_l + \gamma_g(u)p(t) + \epsilon_{ut}$$

where

• $y_{ut}$: Outcome of interest for unit u in time t.
• $\text{Post}_t$: Dummy variable representing a specific post-event period.
• $\beta$: Coefficient measuring the average change in the outcome after the event relative to the pre-period.
• $\gamma_u$: Fixed effects for each unit.
• $\gamma_w(t)$: Time-specific fixed effects to account for periodic variations.
• $\gamma_l$: Dummy variable for a specific significant period (e.g., a major event change).
• $\gamma_g(u)p(t)$: Group x period fixed effects for flexible trends that may vary across different categories (e.g., geographical regions) and periods.
• $\epsilon_{ut}$: Error term.

This model can be used to analyze the impact of an event on the outcome of interest while controlling for various fixed effects and time-specific variations, but using units themselves pre-treatment as controls.

References

Liaukonytė, Jūra, Anna Tuchman, and Xinrong Zhu. 2023. “Frontiers: Spilling the Beans on Political Consumerism: Do Social Media Boycotts and Buycotts Translate to Real Sales Impact?” Marketing Science 42 (1): 11–25.