Economics 245A
Panel Data Models
To understand panel data models it is helpful to begin with the following
i) A sequence of random variables
f
Y
i
g
n
i
=1
is said to be a
crosssection
data set
if the subscript
i
indexes distinct observations made at the same point in time.
ii) A sequence of random variables
f
Y
t
g
T
t
=1
is said to be a
timeseries
data set
if the subscript
t
indexes observations made at distinct points in time.
iii) A sequence of random variables
f
Y
i;t
g
t
=1
;:::;T
i
=1
;:::;n
is said to be a
crosssection
timeseries
data set if the subscript
i;t
indexes distinct observations at each of
T
points of time.
iv) A sequence of random variables
f
Y
i;t
g
t
=1
;:::;T
i
=1
;:::;n
is said to be a
panel
data set
if the subscript
i;t
indexes observations on the
same set
of
n
individuals at each
of
T
points of time.
Example.
If we sample students from the freshmen class at UCSB in each of two years,
UCSB in their freshmen year, and sample the same &ve students in their sopho
more year, then we have a panel data set.
As the example makes clear, a panel data set is a special case of a crosssection
timeseries data set.
What advantages arise from sampling data in this way? The most substantial
advantage is that stronger identi&cation can be obtained from panel data sam
role in the recent literature on testing for unit roots but is not part of the older
literature on panel data models, is empirical ±identi&cation². Empirical identi&
cation is obtained as in the following
Example.
Let
Y
i;t
be the observation for country
i
in period
t
. Initially, we gather data
for only one country (
i
= 1
) and estimate
Y
1
;t
=
&
0
+
1
X
1
;t
+
U
1
;t
;
where
t
= 1
;:::T
. Unfortunately,
T
is not large enough to learn much about
1
,
that is, the variance of the estimator of
1
is quite large. We need to increase the
sample size. Yet we must wait one period for each addition to
T
(and in many
cases a period is a year), so increasing
T
takes too long. If we believe that the
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View Full Documentsame relation holds for another country (
i
= 2
), then we have
2
T
observations to
estimate
1
.
obtained as in the following
Example.
Let
Y
i;t
be the wage for individual
i
in year
t
. Let
X
i;t
be the education of
individual
i
in year
t
. If we believe that the e/ect of education on wage is di/erent
for each individual, then in a given year
Y
i
=
&
0
+
1
;i
X
i
+
U
i
:
Because
1
;i
di/ers over individuals, we cannot identify the marginal e/ect of
education on a worker by studying educational di/erences across workers. Rather,
we must study the same worker at multiple time periods. If we move from a cross
section to a panel data set, we can identify (and estimate)
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 Fall '08
 Staff
 Economics, Linear Regression, Regression Analysis, Panel data, Zi E Zi

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