Diff in diff Flashcards
Example of cross-sectional v ITS?
Cross-sectional: compare # of banks in groups 6 and 8 in 1931
ITS: compare # of banks in group 9 in 1929 and then in 1931
What assumption is critical for diff in diff?
Common trends
How do we get the counterfactual trend?
Use trend (changes over time) in untreated group
True or false: Selection bias related to fixed unobserved differences between T and U groups is ok
True, because we capture at both time points
Outcome levels are not important; _____ are important
changes
Write out model for two-group, two-time diff in diff
Yit=B0+B1Di+B2Post+B3(Di*post)+uit
If the model is Yit=B0+B1Di+B2Post+B3(Di*post)+uit,
what does B0 represent?
The mean of the control group in pre-treatment period
If the model is Yit=B0+B1Di+B2Post+B3(Di*post)+uit, what does B0+B2 represent?
The mean of the control group in post-treatment period
If the model is Yit=B0+B1Di+B2Post+B3(Di*post)+uit, what is pre-treatment mean in treatment group?
B0+B1
If the model is Yit=B0+B1Di+B2Post+B3(Di*post)+uit, what is the treatment effect?
B3
If the model is Yit=B0+B1Di+B2Post+B3(Di*post)+uit, which term represents the selection bias?
B1
How can you try to defend common trends assumption (3 ways)?
graph of pre-treatment trends
falsification test
controlling for time trends
Model for generalized diff in diff, for statexyear panel where the treatment is turned on at different times for different groups
Yst=B0+B1(Treats*postt)+B2state+B3year+ust
In this state by year model, what does B1 tell us? Yst=B0+B1(Treats*postt)+B2state+B3year+ust
How much, on average, outcomes differ in post period from that predicted by state and year fixed effects
Within-state changes over time in the outcome, for treatment and control states
In this model, what does B3 tell us? Yst=B0+B1(Treats*postt)+B2state+B3year+ust
trends in the outcome common to all states
Three approaches to choosing a comparison group?
- use all available non-T cases
- match on pre-T characteristics using propensity score
- geography
True or false: It is a problem if you add controls to your diff in diff model and the estimates change
True–if adding controls changes estimates, you may have bad controls or non-random assignment to T (endogenous controls)
should only help reduce standard errors
Why could you not just estimate a treatment effect by comparing the outcomes of treated units before and after treatment?
We might pick up the effect of other factors that changed around the time of treatment.
Fancy: Unable to distinguish between true effects and secular time trend changes.
What is the common trends assumption?
Whatever happened to the control group over time is what would have happened to the treatment group in the absence of the program
T or F You can test the common trends assumption
False, we can never observe the true counterfactual (how the outcome would have changed over time without treatment)
Scenario: In what direction would the following be biased: Parallel trends assumption is violated because the outcome was already rising faster in the treatment group than in the control group
The D-in-D estimate would over estimate the impact of the treatment.
What is one way to relax the parallel trends assumption?
To allow for group or unit-specific time trends
How does the inclusion of unit-specific time trends change the interpretation of a diff-in-diff model?
Removes unit specific linear time trends from the outcome, treatment, and covariates.
Allows treatment and control states to follow different trends.
B1 now identified off of “deviations” from the group-specific common trend in the outcome of interest.
Model for group-specific diff in diff, for state-specific time trends
Yst = B0 + B1 (TREAT_s * POST_t) + B2STATEks + B3YEARjt + B4(STATEks * t) + ust
t = linear time trend (as opposed to YEAR which allows effect to vary by year)