Credit risk models should reflect the observation that the relevant value of collateral is generally not the average value of the asset over all possible states of nature. In most cases, the relevant value of collateral for the lender is its secondary market value in bad states of nature, where marginal utilities are high. Although the negative correlation between recovery rates and default probabilities is well documented, the majority of pricing models does not allow for correlation between the two. In this paper, we propose a relatively parsimonious reduced-form continuous time model that estimates expected recovery rates and default probabilities from the term structure of CDS spreads. The parameters of the model and latent factors driving recovery risk and default risk are estimated using a Bayesian MCMC algorithm. We find that the Bayesian deviance information criterion (DIC) favors the model with stochastic recovery over constant recovery. We also observe that for companies with a good rating, implied constant recovery rates do not differ much from stochastic recovery. However, if a company is very risky, then forward stochastic recovery rates are significantly lower at longer maturities.