Approximating around the stochastic steady state matters: rethinking uncertainty shocks in small open economies

This paper shows that, when solving DSGE models with strong volatility by perturbation, the approximation point matters. In particular, the standard solution can deliver misleading results if the deterministic steady state is far from where the model’s stochastic dynamics occur. This problem can be corrected by approximating around the stochastic steady state instead, a strategy that is now easy to implement with standard software thanks to two-parameter perturbation. Using the small open economy model by Fernández-Villaverde et al. (2011, AER) as a laboratory, I find that approximating their model around the stochastic steady state yields much more accurate dynamics, in which the real effect of uncertainty shocks loses quantitative relevance. The reason is that the debt level is much smaller at this point compared to the deterministic steady state, which greatly diminishes the precautionary incentive to reduce outstanding debt in response to riskier interest rates. The results are robust to the choice of emerging economy, the device used to close the model, slight recalibrations that significantly improve the model’s ability to match data, and alternative solution methods. Overall, the findings suggest that, from a theoretical perspective, uncertainty shocks play a significantly smaller role in driving aggregate fluctuations in small open economies than previously thought.