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对PCSE不太了解,不过看到的PCSE都是用于固定效应。FGLS一般是随机效应回归用。
A fixed group effect model examines group differences in intercepts, assuming the same slopes
and constant variance across entities or subjects. Since a group (individual specific) effect is
time invariant and considered a part of the intercept, i u is allowed to be correlated to other
regressors. Fixed effect models use least squares dummy variable (LSDV) and within effect
estimation methods. Ordinary least squares (OLS) regressions with dummies, in fact, are fixed
effect models.
A random effect model, by contrast, estimates variance components for groups (or times) and
error, assuming the same intercept and slopes. i u is a part of the errors and thus should not be
correlated to any regressor; otherwise, a core OLS assumption is violated. The difference
among groups (or time periods) lies in their variance of the error term, not in their intercepts. A
random effect model is estimated by generalized least squares (GLS) when the matrix, a
variance structure among groups, is known. The feasible generalized least squares (FGLS)
method is used to estimate the variance structure when is not known. A typical example is
the groupwise heteroscedastic regression model (Greene 2003). There are various estimation
methods for FGLS including the maximum likelihood method and simulation (Baltagi and
Cheng 1994).
详见Hun Myoung Park. Linear Regression Models for Panel Data Using SAS, Stata,
LIMDEP, and SPSS
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