What’s New in Econometrics?
Lecture 8
Cluster and Stratified Sampling
Jeff Wooldridge
NBER Summer Institute, 2007
1. The Linear Model with Cluster Effects
2. Estimation with a Small Number of Groups and
Large Group Sizes
3. What if
G
and
M
g
are Both “Large”?
4. Nonlinear Models
1

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1
.
The Linear Model with Cluster Effects
.
∙
For each group or cluster
g
, let
y
gm
,
x
g
,
z
gm
:
m
1,...,
M
g
be the observable
data, where
M
g
is the number of units in cluster
g
,
y
gm
is a scalar response,
x
g
is a 1
K
vector
containing explanatory variables that vary only at
the group level, and
z
gm
is a 1
L
vector of
covariates that vary within (as well as across)
groups.
∙
The linear model with an additive error is
y
gm
x
g
z
gm
v
gm
(1)
for
m
1,...,
M
g
,
g
1,...,
G
.
∙
Key questions: Are we primarily interested in
or
? Does
v
gm
contain a common group effect, as
in
2