GV249 Seminar WT9: Difference-in-Differences

2025-03-18

📋 Outline

Recap of DiD
Example of DiD
Lab for RDD and DiD

🥣 Ingredients

A treatment that some units were exposed to and others were not.
Panel data: Outcomes for the same units over time.
- Minimum 2 periods (before and after), but ideally many more pre-treatment periods

📊 Estimation

📊 Estimation

With a DiD, we are estimating the ATT:

\(ATE = \mu(Y_i^1 - Y_i^0)\)
\(ATT = \mu(Y_i^1[D_i=1] - Y_i^0[D_i=1])\)
Because treatment assignment is not independent of background characteristics, the ATT is potentially meaningfully different from the ATE.

☝️ Key assumptions

Differently from causal research designs we have covered so far, the main assumptions are about the shape of potential outcomes rather than how units were assigned to treatment.

☝️ Key assumptions

Parallel trends: trends in outcomes would have been parallel between treated and untreated units in the absence of treatment.
Can we directly test the parallel trends assumption?
How can we provide evidence the parallel trends assumption holds?
- Look at whether pre-treatment trends are parallel

☝️ Key assumptions

Parallel trends: trends in outcomes would have been parallel between treated and untreated units in the absence of treatment.
Excludability: nothing but the treatment changes at the same time.
Non-interference: units do not affect each other’s potential outcomes.

🇧🇷 Example: Cavgias, et al. (2023)

What is the effect of biased news on voters’ vote choices?

Case:
- Brazil, 1989. First election after democratization in 1988.
- Collor vs Lula.
- During the campaign, a major TV network (Globo) released biased coverage about a candidate debate between the first and second rounds of the election.
- TV Globo’s signal was not available everywhere in the country.
- They compare vote share for left-wing candidates before and after the coverage in a DiD design.

🇧🇷 Example: Cavgias, et al. (2023)

🇧🇷 Example: Cavgias, et al. (2023)

Exposure to Globo’s debate coverage “is associated with a reduction of 1.2-1.8 percentage points in the vote share of the left” (p. 12).
Where Globo was the sole TV channel - the higher intensity treatment group - the reduction in left vote share was 3.6 percentage points.

🇧🇷 Example: Cavgias, et al. (2023)

What design difficulty does this case present? (Hint: the authors are studying the first democratic elections after re-democratization.)

💻 Lab