Stata

Panel Data Analysis
Fixed & Random Effects
(ver. 3.0)
Oscar Torres-Reyna
Data Consultant
otorres@princeton.edu

http://dss.princeton.edu/training/
PU/DSS/OTR

Intro

Panel data (also known as
longitudinal or crosssectional time-series data)
is a dataset in which the
behavior of entities are
observed across time.

One example of panel data

year

Y

X1

X2

X3

12000

6.0

7.8

5.8

1.3

1

2001

4.6

0.6

7.9

7.8

1

2002

9.4

2.1

5.4

1.1

2

2000

9.1

1.3

6.7

4.1

2

2001

8.3

0.9

6.6

5.0

2

2002

0.6

9.8

0.4

7.2

3

These entities could be
states, companies,
individuals, countries, etc.

country

2000

9.1

0.2

2.6

6.4

3

2001

4.8

5.9

3.26.4

3

2002

9.1

5.2

6.9

2.1

2
PU/DSS/OTR

Intro

Panel data allows you to control for variables you cannot
observe or measure like cultural factors (when comparing
countries or states within a country –i.e. Utah vs. New
York) or difference in business practices across
companies.
Panel data also help to control for unobservable variables
that change over time butnot across entities (i.e. national
policies, federal regulations, international agreements, etc.)
With panel data you can include variables at different levels
of analysis (i.e. students, schools, districts, states) suitable
for multilevel or hierarchical modeling.

Note: For a comprehensive list of advantages and disadvantages of panel data see Baltagi, Econometric3
Analysis of PanelData.
PU/DSS/OTR

-1.000e+100 1.000e+10 -1.000e+100 1.000e+10 -5.000e+09
-5.000e+09
5.000e+09
-5.000e+09
5.000e+09 -1.000e+100 1.000e+10
5.000e+09

y

use http://dss.princeton.edu/training/Panel101.dta
xtset country year
xtline y
A

B

C

D

E

Intro

F

1990

1995

20001990

1995

2000

G

1990

1995

2000

year
Graphs by country

4
PU/DSS/OTRIntro

-1.000e+10
-5.000e+09

y
0

5.000e+09
1.000e+1

xtline y, overlay

1990

1992

1994

1998

1996

2000

year
A
C
E
G

B
D
F
5
PU/DSS/OTR

Intro

In this document we focus on two techniques
use to analyze panel data:
– Fixed effects
– Random effects

6
PU/DSS/OTR

Fixed effects
Fixed-effects (FE) explore the relationship between predictor andoutcome
variables within an entity (country, person, company, etc.).
Each entity has its own individual characteristics that may or may not influence
the predictor variables (for example being a male or female could influence the
opinion toward certain issue or the political system of a particular country could
have some effect on trade or GDP or the business practices of a company mayinfluence its stock price).
When using FE we assume that something within the individual may impact or
bias the predictor or outcome variables and we need to control for this. This is
the rationale behind the assumption of the correlation between entity’s error
term and predictor variables. FE remove the effect of those time-invariant
characteristics from the predictor variables so we can assessthe predictors’ net
effect.
Another important assumption of the FE model is that those time-invariant
characteristics are unique to the individual and should not be correlated with
other individual characteristics. Each entity is different therefore the entity’s
error term and the constant (which captures individual characteristics) should
not be correlated with the others. If the error termsare correlated then FE is no
suitable since inferences may not be correct and you need to model that
relationship (probably using random-effects), this is the main rationale for the
Hausman test (presented later on in this document).
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PU/DSS/OTR

Fixed effects
The equation for the fixed effects model becomes:
Yit = β1Xit + αi + uit

[eq.1]

Where
– αi (i=1….n) is the unknown...