Panel Data Course for Pfizer - Nationalekonomiska institutionen 辉瑞- nationalekonomiska institutionen面板数据的过程.doc

Panel Data Course
Spring 2004
REGRESSION (Revision)
Cross section: (NON-ORDERED)
Individuals, firms, countries etc.
Time Series: (ORDERED)
Variables:
yi (yt): DEPENDENT (Endogenous)
xki (xkt): INDEPENDENT (Exogenous),
MODEL
a and b are parameters. e is a stochastic error
NOTE: The model can be written in matrix form
, where , , etc
The simple regression model
is used as an example in this course. We always write "K" as the number of exogenous variables, however
ASSUMPTIONS
Correct Model
Exogeneity
Homoscedasticity , constant
Serial independence
Normality
No incidental parameters
(K does not grow with N)
(1), (2) and (6) are needed for CONSISTENCY (., in large samples OLS parameter estimates will be correct "on the average")
(3) and (4) are needed for EFFICIENCY (., in large samples OLS yields "best" estimates, significance tests are correct, etc.)
(5) is needed for small sample properties
Problem when
FORMULAE for OLS (Ordinary Least Squares)
,
Residual:
Error variance: ,
where , the degrees of freedom
Variance;
Standard error;
t-value;
MATRIX FORMULAE
, etc
PANEL DATA MODELS
THE POOLED MODEL
Here we are NOT using any Panel information.
The data are treated as if there was only a single index.
TRADITIONAL PANEL MODEL
The constant terms, , vary from individual to individual.
This is called INDIVIDUAL (UNOBSERVED) HETEROGENEITY
The slopes are, however, the same for all individuals.
In both the Pooled and Panel Models we assume that the errors are homoscedastic and serially independent both within and between individuals
SUR MODEL
SEEMINGLY UNRELATED REGRESSIONS
The constant terms, , and slopes, , vary from individual to individual.
In SUR models the errors are allowed to be contemporally correlated and heteroscedastic between individuals. We still assume serial independence as well as homoscedasticity within individuals
MON SITUATIONS
There are a LARGE number of independent individuals observed f