I’m troubled with an equation in this paper. In page 12, there is the probability of endogenous separation:

and the overall separation rate:

where F(*) is cumulative distribution function, and variable ‘at’ is preference shock.

My question is how do you show these two equations in equilibrium conditions?
I couldn’t derive log-differences of these equations without knowing specific expression of F(*).
I have alrealdy uploaded the pdf and highlighted the equations.
If anyone could help, I would be very much appreciate.

What exactly is your question? The first equation seems to be an assumption. Whenever the threshold a_t is reached, there will be endogenous separation. The probability of that happening of course depends on the distribution of a_t, which follows the CDF F(). Of course, to work with the model, you need to specify some characteristics of that distribution.
The second equation simply states that at time t, relations are separated for exogenous reasons \rho^x or, if you did not separate for exogenous reasons (probability (1-\rho^x)), you still have probability \rho_t^n to separate for endogenous reasons.

Thank you for your reply.
And yes, I need to work with the model. But I don’t know how. I mean a CDF can not be entered into Dynare, right? Although the paper says ’ The distribution F of the idiosyncratic shock is assumed to be lognormal with mean µa and standard deviation σa’ , it is still not a variable.
Could you please enlighten me a little?

So in the Dynare, my linear model will be rho_n=-(1-rho_n)*normcdf(a_bar,mu,sigma)/rho_n
And I have to decide the value of parameters mu and sigma. Is that right?
Also I want the distribution F to be lognormal, what should I do?
Thank you in advance.