I want to include SIR into a DSGE model with Calvo pricing. As I understand, nonlinearity is a crucial point for epidemic modelling but I need to log-linearize some equations due to the Calvo setup. In the stochastic simulation, I put exp() to other non-linear equations. My question is that is it possible to have some log-linearized equation and the rest is nonlinear to capture nonlinearity in the SIR block ? Is there any problem with this kind of setup? Thank you so much.
- Why do you need to linearize for Calvo? Usually, there is a closed form recursive representation. See e.g. DSGE_mod/Derivation_Recursive_Pricing_Equation.pdf at master · JohannesPfeifer/DSGE_mod · GitHub
- See Mix of equations in levels and log linearized form - #3 by jpfeifer
Thank you so much for your reply,
- I work in my base model so it takes effort for me to transfer back to recursive form but I will notice this the next time I touch Calvo-related pricing.
- For the second point, so as long as I link the nonlinear part and linearized part correctly, should it be fine ? For example, SIR block is written as standard and we have labor (N_t), to use N_t in other blocks with Calvo wage setting, then I have to use log(N_t) (due to the fact all the variables should be mostly in log form.
- I am sorry for keep asking because I never use perfect foresight in practice before. In the stochastic simulation, up to order 1, my above setup should work fine. However, I read somewhere that perfect foresight does not use approximation. So, I guess the order command is not relevant here. Does it affect the intention to mix log-linearize and non-linear equations?
Thank you so much.
- Ideally, you call the log-linearized variables something like N_hat and define
That makes sure the mean is correctly taken care of.
- For perfect foresight, mixing linear and nonlinear equations is problematic, because you will care about nonlinearities but only preserve them in some part of the code.
Thank you so much, I will notice this.