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Lecture 6 Regression with panel data
What is Panel Data?
Panel data are data collected by following the same group of survey subjects over
time. A
panel dataset
contains observations on the same group of survey subjects
repeatedly over time. Panel data is also called
longitudinal data
Examples
:
•
Data on 1000 students, observed every year in 6 year, for 6,000
observations total.
•
Data on 50 U.S. states, each state is observed in 3 years, for a total of
150 observations.
•
Data on 5000 firms, in ten years, for 50,000 observations total.
Notation for panel data
A double subscript distinguishes subjects and time periods.
i
= subjects,
n
= number of subjects,
so
i
= 1,…,
n
t
= time period (year, month, quarter etc),
T
= number of time periods
so
t
=1,…,
T
Data: Suppose we have 1 regressor. The data are:
(
X
it
,
Y
it
),
i
= 1,…,
n
,
t
= 1,…,
T
n
= number of subjects
T
= number of time periods
In total, we have n
T
observations.
Why are panel data useful?
With panel data, one observes the survey units multiple times, so can control for
fixed effects (or fixed factors, or characteristics) of survey units even when they are
unobserved or unmeasured, i.e., fixed factors are that:
•
Vary across survey units but for the same unit, they stay constant over time
•
For example, innate ability, risk aversion, or state/firm unobserved
characteristics that can be considered fixed over time.
•
Could cause omitted variable bias if they are omitted
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The key idea:
If an omitted variable does not change over time, then any
changes
in
Y
over
time cannot be caused by the omitted variable, so one can look at changes in
Y
to get away from the omitted variable bias.
Examples of a panel data set:
1.
Drunk driving and alcohol taxes
Observational unit: a U.S. state in a year
•
48 U.S. states, so
n
= of entities = 48
•
7 years (1982,…, 1988), so
T
= # of time periods = 7
•
So total # observations = 7
×
48 = 336
Variables:
•
Drunk driving rate (# drunk driving caught in that state in that year, per
10,000 state residents)
•
Alcohol tax
•
Other (legal driving age, average age, percentage of single males etc.)
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 Spring '14
 WI, Panel data, Yit

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