Sunspot shock in Farmer-Khramov (2013): linear vs exp(.)

General DSGE Modeling Macroeconomic Model Data Base
1

Hello,

This question is about introducing the sunspot shock in Farmer-Khramrov (2013) when the model is not specified as linear (i.e. already log linearized by hand) and instead the non-linear equations written in exp() form in the .mod file.

Specifically, how should the sunspot shock specification be modified when the model in Tables 2 of the paper is written in the non-linear exp() form https://www.imf.org/external/pubs/ft/wp/2013/wp13200.pdf

Thanks

2

Do you want to solve the model at higher order? Indeterminacy is a global property of linear difference equations and local for nonlinear systems. So the sunspot equation is still a linear one. The question is how to add this shock to the other nonlinear equations. Usually, an additive specification should work, but depending on the type of equation, you may need a multiplicative version.

3

Thanks for this clarification. I’m avoiding linearization by hand and would like to put the 40+ model equations in the exp(.) form and use order=1 (so not necessarily solving at higher order). I will check the additive vs multiplicative specifications.

4
  1. I would not recommend doing the exp()-part if you are only interested in some variables. It is more convenient to introduce auxiliary variables storing the logs.
  2. If you work with a first order approximation, you can stick to an additive specification as the approximation will turn all equations linear and additive. So starting with a linear additive version is best.
5

Thanks! I will follow these suggestions.