Dear all,

I was hoping to construct and solve a model with rare disasters. The rare disaster is usually represented by a binary variable that points 1 with some small probability, causing a big negative impact to the economy (capital deterioration, TFP reversals, debt-default, etc…). Due to this discontinuity, usual perturbation methods can’t handle these models.

Indeed, as illustrated by Gourio (2012) and Marlène Isoréa and Urszula Szczerbowicz (2017), one should depend on *stationarizing the equilibrium system such that it only features the (small) probability of a disaster, instead of the (large) original event itself. Thereby, (small) innovations to the (small) probability of disaster can be accurately simulated with conventional high-order perturbation methods, regardless of the disaster regime.* This step usually requires some smart technical tricks that remove the binary disaster variable as a state variable.

**HOWEVER**, Jesús Fernández-Villaverde and Oren Levintal (2018) builds a model with rare disasters and solves it with perturbation method, **with the binary disaster variable as a state variable**. Therefore, **they can simulate a disaster using perturbation methods, differently from Urszula Szczerbowicz (2017)**. I am confident that they’ve used some technical trick in their implementation to smooth this discontinuity but I can’t quite figure it out. It seems that they just provided the equilibrium conditions and took the usual derivatives for perturbation, without further consideration about the binary structure of the disaster variable. I am pretty confident that it could be implemented with dynare.

If anyone would know what technical adjustment were necessary to adapt disaster models for perturbation techniques, I would appreciate any help.

Thanks in advance.

**PS**: I include the Technical Appendix of Jesús Fernández-Villaverde and Oren Levintal (2018) below where they give a detailed explanation of their implementation (see README.pdf and Online_Appendix.pdf).

**Gourio, F. 2012. Disaster Risk and Business Cycles. American Economic Review, 102(6), 2734-2766.**

**Isoré, M. and Szczerbowicz, U. 2017. Disaster Risk and Preference Shifts in a New Keynesian model. Journal of Economic Dynamics & Control, 79, 97-125.**

**Fernández-Villaverde, J. and Levintal, O. 2018. Solution Methods for Models with Rare Disasters. Quantitative Economics, 9, 903-944.**

Matlab_Codes_Rare_Disasters.rar (1.5 MB)