In this work, we provide an extensive part-of-speech analysis of the discourse of social media users with depression. Research in psychology revealed that depressed users tend to be self-focused, more preoccupied with themselves and ruminate more about their lives and emotions. Our work aims to make use of large-scale datasets and computational methods for a quantitative exploration of discourse. We use the publicly available depression dataset from the Early Risk Prediction on the Internet Workshop (eRisk) 2018 and extract part-of-speech features and several indices based on them. Our results reveal statistically significant differences between the depressed and non-depressed individuals confirming findings from the existing psychology literature. Our work provides insights regarding the way in which depressed individuals are expressing themselves on social media platforms, allowing for better-informed computational models to help monitor and prevent mental illnesses.