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This paper studies how non-Gaussian shocks affect risk premia in DSGE models approximated to second and third order. Based on an extension of the work by Schmitt-Grohe and Uribe to third order, we derive propositions for how rare disasters, stochastic volatility, and GARCH affect any risk premia in a wide class of DSGE models. To quantify these effects, we then set up a standard New Keynesian DSGE model where total factor productivity includes rare disasters, stochastic volatility, and GARCH. We find that rare disasters increase the mean level of the ten-year nominal term premium, whereas a key effect of stochastic volatility and GARCH is an increase in the variability of this premium.

How Non-Gaussian Shocks Affect Risk Premia in Non-Linear DSGE Models