Monocular depth estimation in endoscopy videos can enable assistive and robotic surgery to obtain better coverage of the organ and detection of various health issues. Despite promising progress on mainstream, natural image depth estimation, techniques perform poorly on endoscopy images due to a lack of strong geometric features and challenging illumination effects. In this paper, we utilize the photometric cues, i.e., the light emitted from an endoscope and reflected by the surface, to improve monocular depth estimation. We first create two novel loss functions with supervised and self-supervised variants that utilize a per-pixel shading representation. We then propose a novel depth refinement network that leverages the same per-pixel shading representation. Finally, we introduce teacher-student transfer learning to produce better depth maps from both synthetic data with supervision and clinical data with self-supervision. We achieve state-of-the-art results on the C3VD dataset while estimating high-quality depth maps from clinical data.