Difference in Difference Flashcards
How would you work out a single difference?
Yt,a - Yc,a
T = treatment
C= control
A= after intervention
B= before intervention
What does a single difference give us?
gives us the causal effect if the treatment and control groups were similar before the treatment occurred
Why is single difference insufficeint?
There is a very strong assumption that T and C were exactly the same before the intervention whereas in most cases they are not
How would you work out a double difference?
(Yt,a - Yc,a) - (Yt,b - Yc,b )
A= after treatment
B= before treament
T= treament group
C= control group
average outcome single difference after intervention - average outcome single difference before intervention
How does double difference account for selection bias?
if we observe differences before the intervention then this has nothing to do with the treatment and may be to do with pre-existing differences or selection bias
by subtracting the differences we are reducing the effect of the initial condition and leaving the impact of the intervention or programme
What are the assumptions around difference in difference?
Common trends assumption
- absent of any treatment, the trend in the treatment group is what we should have expected to see in the control group
with more data this assumption can be tested to some extent but not fully tested
the levels don’t have to be the same but the pattern or trends need to be similar before treatment
essentially using the control group as the counterfactual
What is the equation for a difference in difference regression?
Ydt = α + βTreatd + γPostT + δ DD (treatd * Post T) +εdt
where δ DD = the casual effect of the treatment after time and pre-existing conditions have been controlled for
β= selection bias - pre-existing difference between the treatment group and control group
γ= time trend - changes in outcome over time regardless of the treatment
Is the DD assumption valid?
Defend the common trends assumption using
- a compelling graph
- if not compelling, control for group-specific time trends
all about the common trends assumption
might be other policies or interventions that occur at the same time and are relevant for outcomes eg. legal drinking age and beer taxes thus need to control for these effects
Validity?
DD is v context specific
What is key behind the common trends assumption?
trends of the treatment and control group should look parallel before the treatment
treatment effects should be a level shift after the treatment
