An emerging method to cheaply improve a weaker language model is to finetune it on outputs from a stronger model, such as a proprietary system like ChatGPT (e.g., Alpaca, Self-Instruct, and others). In this work, we critically analyze this approach of imitating language models. We first finetune a series of LMs that imitate ChatGPT using varying base model sizes (1.5B--13B), data sources, and imitation data amounts (0.3M--150M tokens). We then evaluate the models using crowd raters and canonical NLP benchmarks. Initially, we were surprised by the output quality of our imitation models---they appear far better at following instructions, and crowd workers rate their outputs as competitive with ChatGPT. However, when conducting more targeted automatic evaluations, we find that imitation models close little to none of the gap from the base LM to ChatGPT on tasks that are not heavily supported in the imitation data. We show that these performance discrepancies may slip past human raters because imitation models are adept at mimicking ChatGPT’s style but not its factuality. Overall, we conclude that while model imitation can be useful for training models to follow instructions and avoid toxic outputs, it falls short its full promise in many ways. In particular, there exists a substantial capabilities gap between open and closed LMs that we find cannot be bridged merely by adding more imitation data. Instead, we find that fine-tuning more capable base LMs has a significantly more substantial effect on closing this gap. In turn, we argue that the higher leverage action for improving open-source models is to tackle the difficult challenge of developing better base LMs, rather than taking the shortcut of imitating proprietary systems.