In this article we make two contributions toward a better understanding of the causes and consequences of discrimination in credit markets. First, we develop an explicit theoretical model of loan underwriting in which lenders use a simple Bayesian updating process to evaluate applicant creditworthiness. Using a signal correlated with an applicant's true creditworthiness and their prior beliefs about the distribution of credit risk in the applicant pool, lenders are able to evaluate an applicant's expected or "inferred" creditworthiness to determine which loans to approve and which to deny. Second, we explicitly model the self-selection behavior of individuals. Because these decisions shape lenders' prior beliefs about the distribution of credit risk, they also affect the Bayesian posterior from which lenders compute an applicant's inferred creditworthiness, implying that statistical discrimination can arise endogenously. As an example, we show that in a market in which only some lenders have Beckerian tastes for discrimination, there are conditions under which lenders without racial animus will also discriminate. Our model's flexibility makes it ideal for analyzing a wide variety of empirical and policy questions.