F10 Difference-in-Difference Flashcards
What are the elements of the most basic DiD design?
Two groups in two time periods - pretreatment and post treatment period (2x2)
What is the mathematical specification of a simple 2x2 design?
delta = (yt-bar^post - yt-bar^pre) - (yc-bar^post - yc-bar^pre)
In other words a difference between two differences. The temporal difference in the control group and the treatment group.
What is the central assumption?
Parallel trends assumption: Up until the intervention groups have the same trajectory on an outcome of interest.
No time-variant group specific unobservables.
No anticipation effects.
What does the parallel trends assumption mean? How is it measured?
The control group is used as a counterfactual development for the treatment group, as we assume they would have had parallel trends in absence of treatment.
Potential outcomes: Comparison of the potential outcome pre- and post treatment had both groups not been treated (unobserved)
What type of effect are we estimating?
ATT: Average treatment effect on the treated (+ selektionbias)
Treatment is not randomization. The Y1 is not assume to be the same.
What is the regression for a simple 2x2 DiD? And what do the different parts express?
Y = α + λT + γD + δTD + ε
α: Control in pretreatment
α + λ: Control in post treatment
α + γ: Treatment in pretreatment
α + λ + γ + δ: Treatment in post treatment
What is a triple DiD?
Three dimensions. Not only between time and unit but also within a unit (e.g. subpopulations, locations, or policies). Can be used for placebo.
8 groups are now relevant e.g. control group pretreatment high income.
How does a regression for a triple DiD look?
Y = α + T + D + Z + TD + TZ + DZ + δTDZ + ε
So all categories for themselves, as interactionterms and then as three-way interaction.
Delta is still the effect estimate (when all dummies are =1)
What kind of estimate is the triple DiD?
ATT: Average treatment effect on the treated for a subgroup of units (we can’t rule out heterogeneous treatment effects).
What is a staggered DiD?
Two-way fixed effects differential timing in treatment.
Treatment occur at diffrent times for different units (multiple time periods).
E.g. US states implementing medicaid at different points in time. Or EU countries implementing WLBD in different tempi.
A weighted ATT based on an average of all possible ATTs
Staggered is NOT a two-way fixed effects estimator (staggered has much stronger assumptions)
What is problematic in a staggered DiD? 3 things
Units treated late might be compared to units that were always treated or treated early.
Bacons decomposition:
1) Treatment group can be used as both control and treatment
2) Assign weights to individual 2x2 DiD depending on time of treatment (in the middle). Shortening/lengthening the panel changes the estimate - theoretical nonsense
3) Assume no timevariant ATT heterogeneity
When is a staggered DiD problematic?
When treatment effect is heterogeneous or dynamic over time.
What is important for coefficients for time periods leading up to the intervention?
They must de insignificant otherwise the effect is triggered by something else than the intervention.
What is serial correlation and why is it a problem?
Also known as autocorrelation. Serial correlation (or autocorrelation) occurs when the residuals (errors) in a regression model are correlated across time.
Often occurs in times series data. With more observations for the same unit, I kind of artificially inflate the number of observations and thereby the power (effective sample size is smaller).
This probably result in much lower p-values than what can be justified (type I errors or false positives)
Does DiD look at changes og levels?
We study changes (within variation)
