CPANEL Procedure
One-Way Fixed-Effects Model (FIXONE and FIXONETIME Options)
You perform one-way fixed-effects estimation by specifying the FIXONE option in the MODEL statement. The error structure for the one-way fixed-effects model is
where the 
are nonrandom parameters that are restricted to sum to 0, and the 
are iid with zero mean and variance 
.
The fixed-effects model can be estimated by ordinary least squares (OLS), treating the as coefficients on dummy variables that identify the cross sections. However, when N is large, you might want to estimate only 
and not .
Let 
. The matrix 
represents the within transformation, the conversion of the raw data to deviations from a cross section’s mean. Let 
and 
. The within estimator of is
The previous estimation does not involve the intercept term because 
is the same whether or not the intercept 
is included in the model.
Standard errors, t statistics, and fit statistics such as mean square error (MSE) are all equivalent to those obtained from OLS regression of 
on 
. The only exception is the error degrees of freedom, which equals 
to account for the tacit estimation of the N fixed effects.
The estimate of the intercept is
where 
is the overall mean of 
and 
is the overall mean of 
.
Fixed effects are not estimated as part of the regression, but they can be obtained by specifying the PRINTFIXED option in the MODEL statement. Each fixed effect is estimated as
where 
and 
are cross-sectional means.
Variance estimates of 
and 
are obtained by the delta method. If you specify the NOINT option, then the are shifted to absorb .
The FIXONETIME option works similarly, except that the data are grouped by time period instead of by cross section.