Difference-in-Difference

Question 1

How does Diff-in-Diff construct the counterfactual, and why does this account for unobserved differences?

Answer 1

Compare means between treated and controls in period 0 and 1
Maybe initial differences between treated and un-treated, that we do not need to know about as long as this difference stays constant over time
(Used when treatment choice is decided on by higher level of aggregation)

Question 2

Parallel trends assumption

Answer 2

Constant bias assumption: assumption that other outcomes of treated and non-treated would have changed the same way in the absence of treatment

Question 3

Approaches to overcome non-parallel trends

Answer 3

Propensity score matching to better match treated and non-treated on initial conditions: apply DiD on matched sample
Include time-varying factors into the regression
Synthetic controls

Question 4

Advantages and disadvantages of generalized DiD with multiple groups and multiple time periods

Answer 4

Advantages:
Beneficial for checking parallel trends assumption
Better for statistical significance (standard errors)
Complication: you don’t need just parallel trends, also constant treatment effects

Question 5

How does synthetic control group method overcome the limitations of DiD?

Answer 5

Motivated by the limitation of DiD:

1. Selection of comparison units is not formalized
2. No single unit alone may provide a good comparison for the unit affected by the intervention

Synthetic control group method: combination of unaffected units provides more appropriate comparison than any single unaffected unit alone

Question 6

How does the synthetic control group method obtain the treatment effect and test whether it is significant?

Answer 6

Synthetic control is defined as a weighted average of units in the control group (as counterfactual for the treatment group)
Use permutation-based inference on the sample