where αi represents the individual regional effect. The fixed effect model is typically estimated
by the least squares dummy variable (LSDV) method (Greene 2003, p. 287).
The FGLS estimation method takes into account heteroskedasticity, and cross-sectional and
serial correlation. The error terms can be written as
|
' σnΩ11 |
σ12Ω12 |
σ1 N ωi N | |
|
E[εε']=Ω= |
σ 21Ω21 : |
σ22Ω22 |
• σ2 N ω2 N : |
|
σN 1Ω N1 |
σN2ΩN2 |
σNN ω NN _ |
where
|
1 |
Pj |
P2j |
T -1 ∙∙ ρ j | |
|
Pi |
1 |
Pj |
T-2 ∙∙ ρj | |
|
Ωij= |
Pp |
Pi |
1 |
T-3 ρ Pj |
|
_ ρT-1 |
T-2 Pi |
PiT-3 |
1 |
An FGLS panel data model is also called the Parks-Kmenta method (Kmenta 1986). This method
consists of the following steps. Estimate equation (1) by regular OLS. Then use the estimation
residuals to estimate assumed error AR(1) serial correlation coefficient ρ . Use this coefficient to
transform the model to eliminate error serial correlation. Substitute Ω for Ω using estimated ρ
and σ2 , then obtain the FGLS estimator of β as
βGLS = ( X ' ΩX )-1X ' Ω-1 y .
Analysis of Estimation Results
Using the relative gasoline price as the dependent variable, we get estimation results for the
pooled OLS regression, a fixed effect panel data model, and a panel FGLS method; these are
shown in Table 1. The corresponding estimation results for 3:2:1 crack spread are shown in
Table 2.
10
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