This paper employs a random sample of matched employer - employee data from the UK to test seven possible explanations for the positive relationship between employer size and pay. Individual wage equations show a large employer size wage premium. We then control for a range of establishment-level variables, based on seven hypotheses typically advanced to explain this premium. Each establishment-level factor reduces the wage premium, but a sizeable premium nonetheless remains. In adjudicating on these hypotheses, we find a strong association between the internal labour market and the employer size - wage premium. This finding supports the theory that the employer size - wage effect may be due to the higher costs of turnover or monitoring in larger firms. However, we find contrasting effects for public versus private sector establishments.