Econometric Analysis of Panel Data
Professor William Greene
Phone: 212.998.0876
Office: KMC
778
Home page:www.stern.nyu.edu/~wgreene
Office Hours:
TR, 3:00  5:00
Email: [email protected]
URL for course web page:
www.stern.nyu.edu/~wgreene/Econometrics/PanelDataEconometrics.htm
Assignment 4
Parameter Heterogeneity in Linear
Models: RPM and HLM
The estimation parts of this assignment will be based on the Baltagi and Griffin gasoline
market and the Cornwell and Rupert labor market data sets that are posted on the course
website.
We will begin with the gasoline market.The basic linear regression model in use will be
y
it
=
β
1
+
β
2
x
it
,1
+
β
3
x
it
,2
+
β
4
x
it
,3
+
w
it
where
and
i
= 1,…,18 OECD countries
t
= 1,…,19 years (1960 to 1978).
y
it
=
lgaspcar
= log of per capita gasoline use
x
it
,1
=
lincomep
= log of per capita income
x
it
,2
=
lrpmg
= log of gasoline price index
x
it
,3
=
lcarpcap
= log of cars per capita
w
it
= a disturbance that may have have both permanent (time invariant)
components and time varying components, and may, under some
circumstances, be correlated with
x
it
.
Denote
x
it
=
(1,
x
it
,1
,
x
it
,2
,
x
it
,3
)
and
X
i
=
the 19
×
4 matrix containing all the data on
x
it
for country
i
.
Department of Economics
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View Full DocumentPart I.
Parameter Variation in the Gasoline Market
A.
Homogeneous parameters
:
To begin, we
assume
that all parameters, including the
constant term, are homogeneous across countries and through time and that
w
it
=
ε
it
, a
classical zero mean, homoscedastic disturbances.
1.
Under these assumptions, what are the properties of the pooled OLS estimator?
2.
Estimate the parameters of the model using OLS and report your results.
3.
As a first cut at assessing whether the assumptions are correct, compute the
robust, cluster (country) corrected standard errors for the least squares estimator.
Do they appear to be the same, or close to the same, as the uncorrected OLS
standard errors?
What do you conclude about the disturbances in the equation?
B.
Heterogeneous Constant Terms
:
Now, consider fixed and random effects
formulations of the model.
We write the model as
y
it
=
β
1
i
+
β
2
x
it
,1
+
β
3
x
it
,2
+
β
4
x
it
,3
+
ε
it
where
β
1
i
=
β
1
+
u
i
and E[
u
i
]
=
0.
Thus, this is a model with a random constant term.
By substituting the second equation
into the first, you can see that it is the “effects” model we have discussed in class.
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 Fall '11
 WillamGreene
 Normal Distribution, Regression Analysis, Maximum likelihood, Estimation theory, Likelihood function, Yit

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