Imbens/Wooldridge, Lecture Notes 2, Summer ’07
What
’
s New in Econometrics
?
NBER
,
Summer 2007
Lecture 2
,
Monday
,
July 30th
,
11
.
00

12
.
30 am
Linear Panel Data Models
These notes cover some recent topics in linear panel data models. They begin with a
“modern” treatment of the basic linear model, and then consider some embellishments, such as
random slopes and timevarying factor loads. In addition, fully robust tests for correlated
random effects, lack of strict exogeneity, and contemporaneous endogeneity are presented.
Section 4 considers estimation of models without strictly exogenous regressors, and Section 5
presents a unified framework for analyzing pseudo panels (constructed from repeated cross
sections).
1
.
Quick Overview of the Basic Model
Most of these notes are concerned with an unobserved effects model defined for a large
population. Therefore, we assume random sampling in the cross section dimension. Unless
stated otherwise, the asymptotic results are for a fixed number of time periods,
T
, with the
number of cross section observations,
N
, getting large.
For some of what we do, it is critical to distinguish the underlying population model of
interest and the sampling scheme that generates data that we can use to estimate the population
parameters. The standard model can be written, for a generic
i
in the population, as
y
it
t
x
it
c
i
u
it
,
t
1,.
..,
T
,
(1.1)
where
t
is a separate time period intercept (almost always a good idea),
x
it
is a 1
K
vector of
explanatory variables,
c
i
is the timeconstant unobserved effect, and the
u
it
:
t
T
are
idiosyncratic errors. Thanks to Mundlak (1978) and Chamberlain (1982), we view the
c
i
as
random draws along with the observed variables. Then, one of the key issues is whether
c
i
is
correlated with elements of
x
it
.
It probably makes more sense to drop the
i
subscript in (1.1), which would emphasize that
the equation holds for an entire population. But (1.1) is useful to emphasizing which factors
change only across
t
, which change only change across
i
, and which change across
i
and
t
.It is
sometimes convenient to subsume the time dummies in
x
it
.
Ruling out correlation (for now) between
u
it
and
x
it
, a sensible assumption is
contemporaneous exogeneity conditional on c
i
:
E
u
it

x
it
,
c
i
0,
t
T
.
(1.2)
This equation really defines
in the sense that under (1.1) and (1.2),
1