Large language models (LLM) have become state of the art in many benchmarks and conversational LLM applications like ChatGPT are now widely used by the public. Those LLMs can be used to generate large amounts of content which is posted on the internet to various platforms. As LLMs are trained on datasets usually collected from the internet, this LLM-generated content might be used to train the next generation of LLMs. Therefore, a self-consuming training loop emerges in which new LLM generations are trained on the output from the previous generations. We empirically study this self-consuming training loop using a novel dataset to analytically and accurately measure quality and diversity of generated outputs. We find that this self-consuming training loop initially improves both quality and diversity. However, after a few generations the output inevitably degenerates in diversity. We find that the rate of degeneration depends on the proportion of real and generated data.