Credit rating agencies (CRAs) are accused of bearing a strong responsibility for contributing to the subprime crisis by having been deliberately too lax in the ratings of some structured products. In response to this accusation, CRAs argue that such an attitude would be too dangerous for them, since their reputation is at stake. The objective of this article is to examine the validity of this argument within a formal model: Are reputation concerns sufficient to discipline rating agencies? We show that the reputation argument only works when a sufficiency large fraction of the CRA income comes from other sources than rating complex products. By contrast when rating complex products becomes a major source of income for the CRA, we show that it is always too lax with a positive probability and inflates ratings with probability one when its reputation is good enough. We provide some empirical support for this prediction, by showing that ceteris paribus, the proportion of subprime residential mortgage-backed securities (RMBS) that were rated AAA by the three main CRAs indeed increased over the last eight years. We analyze the policy implications of our findings and advocate for a new business model of CRAs that we call the platform-pays model.