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Emerging market interest rate spreads display substantial time-varying volatility. We show that a baseline model with endogenous sovereign default risk can account for such volatility, even in the absence of shocks to the second moments of the exogenous stochastic variables. In particular, the model features a key non-linearity that allows it to replicate the volatility of interest rate spreads and its comovement with other economic variables. Volatility correlates positively with the level of the spreads and the trade balance and negatively with output and consumption.