Endogenous default probability

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!

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

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.

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.

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,