Indicator function in a stochastic context

Dear all,

I am trying to build a model involving an indicator variables and I am having issues with the approximation of the model.

The model involve the computation of a risk premium which depends on whether the banking losses are covered by the government.
V_t is the risk premium, J_t the default probability and b_t is the share of losses covered by the government. Ommitting the non-important terms for thmyis question, the premium could be written as:
V_t = (1-b_t)J_t
such that it should be zero when the losses are fully covered (b=1).
I put my model in level in Dynare without thinking that when b_t is equal to 1, V_t is different from 0 due to the approximation error related to the log-linearization of the model.

Is there any trick (model transformation, Dynare option…) which could help me to obtain impulse responses consistent with the theory ?



Basically, your answer is at [Max( ) fails in the stochastic environment?)