PANEL Procedure

F Test for No Fixed Effects

When you fit a fixed-effects model, you obtain an F test for no fixed effects as part of the output. The null hypothesis of that test is that all fixed effects are jointly 0; it is obtained by comparing fixed-effects estimates to those from pooled regression. The F statistic is

upper F equals StartFraction left-parenthesis normal upper S normal upper S normal upper E Subscript r Baseline minus normal upper S normal upper S normal upper E Subscript u Baseline right-parenthesis slash d f 1 Over normal upper S normal upper S normal upper E Subscript u Baseline slash d f 2 EndFraction tilde upper F left-parenthesis d f 1 comma d f 2 right-parenthesis

where normal upper S normal upper S normal upper E Subscript r is the error sum of squares from the restricted model (pooled regression) and normal upper S normal upper S normal upper E Subscript u is the error sum of squares from the unrestricted fixed-effects model.

The numerator degrees of freedom, d f 1, equals upper N minus 1 for one-way models and left-parenthesis upper N minus 1 right-parenthesis plus left-parenthesis upper T minus 1 right-parenthesis for two-way models. The denominator degrees of freedom, d f 2, is equal to the error degrees of freedom from the fixed-effects estimation. If you specify the NOINT option, add 1 to d f 1 to account for the added restriction to the pooled regression.

Last updated: June 19, 2025