Question about regime switching model in dynare

General DSGE Modeling
1

Dear all, I’m replicating Dong and Xu(2020) 《Cycles of credit expansion and misallocation: The Good, the Bad and the Ugly》 paper nowadays, the dynamic system is below

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The equation (B.3) and (B.5) are piece wise, and the system is regime switching. How to solve model like this in dynare? Thanks!

2

I am not sure how exactly they solve this model. You may have to check their replication files. Which variable it the endogenous state that introduces dynamics?

3

Thanks professor,they do not provide replication files.The endogenous state variable is capital.Kt is aggregate capital, Kht is capital in H sector, Klt is capital in L sector.

4
  1. You could ask the authors.
  2. In the screenshot you provided, everything is dated time t, i.e., there is no obvious intertemporal linkage.
5

Thanks Professor, I miss this equation
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6

Given that the authors consider a permanent one-time shock, this may be solvable as a perfect foresight problem. But I don’t understand the model well enough to definitely say that.

7

Yes,professor,if it can be solved at a perfect foresight problem,how to write equations (B.3) and (B.5) in Dynare?

8

What determines the regime transition? But it looks like MCP tags may work. Alternatively, you can try Boolean indicators.

9

Thanks professor, as the author asy

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(i) and (ii) are regime 1, (iii) is regime 2.
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So K* is the variable that determines regime transition.

10

Are you interested in a nonlinear solution or would a piecewise linear one suffice?

11

I’m not sure which kind of solution can produce this kind of transition dynamics in different regime?

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12

Do I see it correctly that the model is purely backward-looking, i.e. there is no expectation about future model variables involved?

13

Yes professor, the author set the household is hand to mouth, and provide one unit of labor inelastically. And there is no sticky price ,no inflation. There is only one state variable,capital. The policy function is Kt+1=g(Kt).

14

I see. Have you tried coding up the equations yet? That would enable to test the setup in Dynare. That being said, that type of model should be straightforward to code in Matlab. It’s just iterating forward in time from a starting point with a case distinction.

15

Thanks professor, I will try to code up the equation. By the way, if I extend the model to include jump variable and more than one state variable, how to use numerical solution to solve the transition dynamics? Could you provide me some material to learn about it. Thanks in advance.

16

That depends on the exact model. More states would no be an issue, but dealing with expectations would be hard and most likely require (global) solution approaches tailored to the particular problem.