We study $1s$ and $2p$ hard x-ray photoemission spectra (XPS) in a series of
late transition metal oxides: Fe$_2$O$_3$ (3$d^{5}$), FeTiO$_3$ (3$d^{6}$), CoO
(3$d^{7}$) and NiO (3$d^{8}$). The experimental spectra are analyzed with two
theoretical approaches: the MO$_6$ cluster model and the local density
approximation (LDA) + dynamical mean-field theory (DMFT). Owing to the absence
of the core-valence multiplets and spin-orbit coupling, 1$s$ XPS is found to be
a sensitive probe of chemical bonding and nonlocal charge-transfer screening,
providing complementary information to 2$p$ XPS. The 1$s$ XPS spectra are used
to assess the accuracy of the $ab$-initio LDA+DMFT approach, developed recently
to study the material-specific charge-transfer effects in core-level XPS.