Imbens/Wooldridge, Lecture Notes 10, Summer ’07
What
’
s New in Econometrics
?
NBER
,
Summer 2007
Lecture 10
,
Tuesday
,
July 31st
,
4
.
30

5
.
30 pm
DifferenceinDifferences Estimation
These notes provide an overview of standard differenceindifferences methods that have
been used to study numerous policy questions. We consider some recent advances in Hansen
(2007a,b) on issues of inference, focusing on what can be learned with various group/time
period dimensions and serial independence in grouplevel shocks. Both the repeated cross
sections and panel data cases are considered. We discuss recent work by Athey and Imbens
(2006) on nonparametric approaches to differenceindifferences, and Abadie, Diamond, and
Hainmueller (2007) on constructing synthetic control groups.
1
.
Review of the Basic Methodology
Since the work by Ashenfelter and Card (1985), the use of differenceindifferences
methods has become very widespread. The simplest set up is one where outcomes are observed
for two groups for two time periods. One of the groups is exposed to a treatment in the second
period but not in the first period. The second group is not exposed to the treatment during
either period. In the case where the same units within a group are observed in each time period,
the average gain in the second (control) group is substracted from the average gain in the first
(treatment) group. This removes biases in second period comparisons between the treatment
and control group that could be the result from permanent differences between those groups, as
well as biases from comparisons over time in the treatment group that could be the result of
trends. We will treat the panel data case in Section 4.
With repeated cross sections, we can write the model for a generic member of any of
groups as
y
0
1
dB
0
d
2
1
d
2
dB
u
(1.1)
where
y
is the outcome of interest,
d
2 is a dummy variable for the second time period. The
dummy variable
dB
captures possible differences between the treatment and control groups
prior to the policy change. The time period dummy,
d
2, captures aggregate factors that would
cause changes in
y
even in the absense of a policy change. The coefficient of interest,
1
,
multiplies the interaction term,
d
2
dB
, which is the same as a dummy variable equal to one
for those observations in the treatment group in the second period. The
differenceindifferences estimate is
̂
1
y
̄
B
,2
−
y
̄
B
,1
−
y
̄
A
,2
−
y
̄
A
,1
.
(1.2)
1