This paper combines a term structure model of credit default swaps (CDS) with weak-identification robust methods to jointly estimate the probability of default and the loss given default of the underlying firm. The model is not globally identified because it forgoes parametric time series restrictions that have aided identification in previous studies, but that are also difficult to verify in the data. The empirical results show that informative (small) confidence sets for loss given default are estimated for half of the firm-months in the sample, and most of these are much lower than and do not include the conventional value of 0.60. This also implies that risk-neutral default probabilities, and hence risk premia on default probabilities, are underestimated when loss given default is exogenously fixed at the conventional value instead of estimated from the data.