Exogenous tradable goods price in a two sector model

[kofiemma]

In a two-sector model in this book, the price of tradable goods is exogenous. That is, p^T_t = rer_t\; p^{T*}_t where p^{T*}_t \sim AR(1). I am currently stuck on implementing this in my two-sector model because:

1. I have to introduce one more variable (p^{T*}_t)
2. But two equations ( p^T_t = rer_t\; p^{T*}_t and p^{T*}_t \sim AR(1))

Thus I will have more equations than variables in dynare. So I guess I should merge two existing equations into one? Maybe two FOCs for the household sector…would that be right?

I dopped y_t = \frac{p^T_t y^T_t + p^N_t p^N_t }{p_t} from the model, so only y_t = c_t + i_t + g_t +tb_t remains in the mod file and the mod file runs in dynare, but this isn’t correct, right? Not sure if the trick is to merge two FOCs or identities into one…or maybe drop some equation.

p^N_t is normalized to 1. Maybe I can relax that assumption and bring that variable back? Like if model variables exceed equations, then normalize one price to one? If the opposite is the case, then do not normalize any price? Some kind of a trick…

Thanks for the help.

The book authors use neural networks to solve the model, so maybe, that’s why it is possible?

EDIT: p^N_t is normalized to 1. Maybe I can relax that assumption and bring that variable back? Like if model variables exceed equations, then normalize one price to one? If the opposite is the case, then do not normalize any price? Some kind of a trick…?

[HelloDynare]

@kofiemma

EDIT: p^N_t is normalized to 1. Maybe I can relax that assumption and bring that variable back? Like if model variables exceed equations, then normalize one price to one? If the opposite is the case, then do not normalize any price? Some kind of a trick…?

My own experience for foreign variables,

1. if they are important, you may want to have a full analysis on them, model them in a two country model, or at least put them in equal-numbered foreign equations.

2. if they are less important, model them as AR(1), in an SOE model

3. if they are less less important, model them as constants (care about the relative prices between them)

4. if they are least important, normalize them to 1.

cross-reference for point 1:

Question on Foreign country modelling

Hello everyone, I’m a novice in Macro and Dynare. Recently, I read a paper:annotated International spillovers and exchange rate dynamics.pdf (413.0 KB) As annotated on page 11, 17, and 22, Corsetti et al. first model the dynamics of Foreign country, and next given them, model the Home country. I expect it will produce more dynamics of Home country than usual SOE literature, i.e. directly setting exogenous Foreign variables be constant. (If my understanding was wrong, please kindly point it out…

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Regarding the interaction between deep learning and DSGE, you can have a look at:

DP14024-3.pdf