There are two literature strands that explain stylized facts in emerging economies: the stochastic productivity trend or stationary financial frictions. We evaluate the marginal data density (MDD) of sovereign default models, full-nonlinear dynamic stochastic general equilibrium (DSGE) with micro-founded financial imperfections, applying particle filters in many combinations of parameters. The main finding is that stationary financial frictions rather than trend shocks seem to account for the stylized facts. However, the combination of trend and stationary shocks cannot fully capture the variability of output. Adding stochastic volatility not only improves the model performance in terms of MDD, but also justifies the econometric assumptions including non-Gaussian measurement errors which is necessary for stabilizing the MDD evaluation.