Chapter 15
Panel Data Analysis
What is in this Chapter?
• This chapter discusses analysis of panel
data.
• This is a situation where there are
observations on individual cross-section
units over a period of time.
• The chapter discusses several models for
the analysis of panel data.
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•
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1. Fixed effects models.
2. Random effects models.
3. Seemingly unrelated regression model.
4. Random coefficient model.
Introduction
• One of the early uses of panel data in
economics was in the context of
estimation of production functions.
• The model used is now referred to as the
"fixed effects" model and is given by
Introduction
• his model is also referred to as the "least
squares with dummy variables" (LSDV)
model.
• The αi are estimated as coefficients of
dummy variables.
The LSDV or Fixed Effects Model
The LSDV or Fixed Effects Model
The LSDV or Fixed Effects Model
The LSDV or Fixed Effects Model
• In the case of several explanatory
variables, Wxx is a matrix and β and Wxy
are vectors.
The LSDV or Fixed Effects Model
The Random Effects Model
• In the random effects model, the αi are treated
as random variables rather than fixed constants.
• The αi are assumed to be independent of the
errors uu and also mutually independent.
• This model is also known as the variance
components model.
• It became popular in econometrics following the
paper by Balestra and Nerlove on the demand
for natural gas.
The Random Effects Model
The Random Effects Model
• For the sake of simplicity we shall use only
one explanatory variable.
• The model is the same as equation (15.1)
except that αi are random variables.
• Since αi are random, the errors now are vit
= αi + uit
The Random Effects Model
The Random Effects Model
• Since the errors are correlated, we have to
use generalized least squares (GLS) to
get efficient estimates.
• However, after algebraic simplification the
GLS estimator can be written in the simple
form
The Random Effects Model
The Random Effects Model
• W refers to within-group
• B refers to between-group
• T refers to total
The Random Effects Model
Thus the OLS and LSDV estimators
are special cases of the GLS estimator with
θ = 1 and θ =0, respectively.
The SUR Model
• Zeilner suggested an alternative method to
analyze panel data, the seemingly
unrelatedregression (SUR) estimation
• In this model a GLS method is applied to exploit
the correlations in the errors across crosssection units
• The random effects model results in a particular
type of correlation among the errors. It is an
equicorrelated model.
• In the SUR model the errors are independent
over time but correlated across cross-section
units:
The SUR Model
The SUR Model
The SUR Model
• If we have large N and small T this method is not
feasible.
• Also, the method is appropriate only if the errors
are generated by a true multivariate distribution.
• When the correlations are due to common
omitted variables it is not clear whether the GLS
method is superior to OLS.
• The argument is similar to the one mentioned in
Section 6.9. See "autocorrelation caused by
omitted variables."
The Random Coefficient Model
The Random Coefficient Model
The Random Coefficient Model
The Random Coefficient Model
• If δ2 is large compared with υi, then the
weights in equation (15.8) are almost
equal and the weighted average would be
close to simple average of the βi.
The Random Coefficient Model