There is empirical evidence that recovery rates tend to go down just when the
number of defaults goes up in economic downturns. This has to be taken into
account in estimation of the capital against credit risk required by Basel II
to cover losses during the adverse economic downturns; the so-called "downturn
LGD" requirement. This paper presents estimation of the LGD credit risk model
with default and recovery dependent via the latent systematic risk factor using
Bayesian inference approach and Markov chain Monte Carlo method. This approach
allows joint estimation of all model parameters and latent systematic factor,
and all relevant uncertainties. Results using Moody's annual default and
recovery rates for corporate bonds for the period 1982-2010 show that the
impact of parameter uncertainty on economic capital can be very significant and
should be assessed by practitioners.