Endogenous default probability

Dynare help (legacy posts)
1

Hi!
I’m working to a model with endogenous (sovereign) default probability in a soe.
The problem I am facing is that I don’t know how to write in Dynare the binary variable that triggers the default. The set-up is as follows:

  • The probability of default depends on the debt level of the government. Let’s call this probability P.
  • The probability is drawn from a known distribution (for instance a beta distribution).
  • The parameters of the distributions depend (of course) on the level of debt.

Up to here everything is ok. Here it comes the tricky part:

  • When the government defaults, it does so on the entire debt.
  • Let’s call DELTA the BINARY variable of the government to decide whether to deafult or not.
  • The government defaults with probability P. It doesn’t deafult with probability (1-P).

The point is, how can I write the variable DELTA in Dynare?
Does it allow for endogenous (or even exogenous) binary variables?

Thank you very much!
Ciao,
RT

2

Hi! Sorry to bother but any idea about this? thanks!

3

Could you try to write down the equation? The problem I see is that Dynare linearizes the model and a binary variable is not differentiable.

4

Hello,
I work on a different subject but have a similar question. My equation is the following K_t+1 = K_t*(1-x_t+1) where x_t+1 is a binary variable and equals 1 with the probability q_t or equals 0 with a probability (1-q_t). Is there a possibilty to include in Dynare the variable x_t+1 ? I suppose from your previous answer that it is not, but I wanted to be sure. Thank you very much in advance.

5

Hi bkmark,
I think no because as it has been correctly pointed out there is a point which is not differentiable (a kink). It happens that’s exactly the point (steady state) around which the model needs to be log-linearized.
hope this helps,
RT