  Semiconducting skutterudite CeFe$_4$P$_{12}$ is investigated by synchrotron
x-ray photoemission spectroscopy (PES) and x-ray absorption spectroscopy (XAS).
Ce 3$d$ core-level PES and 3$d-4f$ XAS, in combination with single impurity
Anderson model (SIAM) calculations, confirm features due to $f^0$, $f^1$ and
$f^2$ configurations. The Ce 4$f$ density of states (DOS) indicates absence of
a Kondo resonance at Fermi level, but can still be explained by SIAM with a
small gap in non-$f$ DOS. While Ce 4$f$ partial DOS from band structure
calculations are also consistent with the main Ce 4$f$ DOS, the importance of
SIAM for core and valence spectra indicates Kondo semiconducting mixed valence
for CeFe$_4$P$_{12}$, derived from strong hybridization between non-$f$
conduction and Ce 4$f$ DOS.
