Finally, the last equation defines the model equation for the final regime where the IRR constraint is binding, but the INEG one is not.

However, I think that lines 92-93 are redundant because there can’t be such case where IRRI_t\geq \phi I_{SS} is binding but INEGI_t\geq I_{SS} is not with \phi <1. Am I correct on this? I checked that I get the same results without those lines.

@jpfeifer Can I ask a quick follow-up question? I was just wondering about the underlying matlab functions for occbin_setup and occbin_solver. What would be the equivalent setup using matlab functions to run a simulation, for example, using stoch_simul.m or simult_.m after dynare file_name.mod?

I just want to compare the irfs with different values of parameters in the same figure. I could have different mod files but would like to have a single mod file. If this is too complicated, then that’s fine!

Thanks @jpfeifer! I will think about it along that line.

One difficulty I can think of is that the welfare calculation requires at least 2nd order approximation, but Occbin solves the model to the first order. Does that mean it is not possible to compute welfare with Occbin?

It depends on what you are trying to do. For welfare properties in fully stochastic economies a first order approximation is indeed generally not sufficient to evaluate the welfare effects of fluctuations around trend.
But with Occbin, we are usually not concerned with such fully stochastic properties, but rather with the level effects of a particular given shock. Here, a piecewise linear approximation to the laws of motion may be sufficient.