Financial innovations are a common explanation for the rise in credit card debt and bankruptcies. To evaluate this story, we develop a simple model that incorporates two key frictions: asymmetric information about borrowers' risk of default and a fixed cost of developing each contract lenders offer. Innovations that ameliorate asymmetric information or reduce this fixed cost have large extensive margin effects via the entry of new lending contracts targeted at riskier borrowers. This results in more defaults and borrowing, and increased dispersion of interest rates. Using the Survey of Consumer Finances and Federal Reserve Board interest rate data, we find evidence supporting these predictions. Specifically, the dispersion of credit card interest rates nearly tripled while the "new" cardholders of the late 1980s and 1990s had riskier observable characteristics than existing cardholders. Our calculation suggest these new cardholders accounted for over 25% of the rise in bank credit card debt and delinquencies between 1989 and 1998.