We have directly measured the band gap renormalization associated with the Moss-Burstein shift in the perovskite transparent conducting oxide (TCO), La-doped BaSnO_{3}, using hard x-ray photoelectron spectroscopy. We determine that the band gap renormalization is almost entirely associated with the evolution of the conduction band. Our experimental results are supported by hybrid density functional theory supercell calculations. We determine that unlike conventional TCOs where interactions with the dopant orbitals are important, the band gap renormalization in La-BaSnO_{3} is driven purely by electrostatic interactions.