Libor is an estimate of interbank borrowing costs computed daily from rates reported by a fixed panel of banks. Evidence suggests that banks have manipulated Libor in recent years by misreporting their borrowing costs. I estimate a strategic reporting model that identifies banks’ borrowing costs as well as their motives for misreporting. The estimation places a lower bound on the value that Libor would have had if banks had truthfully reported their borrowing costs. The model is identified even when unobserved heterogeneity exists in the form of a common cost component that is known by all banks but unobservable to the econometrician and is allowed to follow a nonstationary process. The only data used for identification are banks’ Libor quotes. Overall, I find that the estimated lower bound for the unmanipulated Libor is always above the published Libor, with an average deviation of 25 basis points at the worst of the financial crisis of 2007 – 2008. The estimated bound displays a pattern similar to two other measures of interbank borrowing costs that have been used previously to assess the extent of manipulation. The model is also used to determine the extent to which misreporting was motivated by signaling or banks’ net exposure to Libor. The estimation results indicate that sending creditworthiness signals was the main driver of systematic misreporting from 2007 to 2010.