Hello, I’m trying to implement into a simple closed-economy DSGE model a digital currency. I have decided to assume non-separability in the utility function between this digital currency and cash. The model runs correctly, but I cannot understand why the shock to the interest rate of the digital currency doesn’t have any effect on some variables of the model. I run model_diagnostics(M_,options_,oo_) and no problems were detected. I would be grateful if somebody could explain me why. Thank you very much.

I’m sorry if I wasn’t clear enough Professoe Pfeifer, I’ll try to clarify myself.
I have defined cash as “mm” and the digital currency as “mdc”. Gammam and Gammadc are two equations that I defined during the derivation of the first order conditions in order to synthesize the equations for the demand of cash and of the digital currency. idc is the interest rate on the digital currency that follows a Taylor rule. mu is the shock to the interest rate on the digital currency. In order to maintain the equality Y = C I assumed that mm + mdc = xim*mm(-1)/PI + Rdc(-1)*mdc(-1), so that the terms would cancel out in the budget constraint when defining the resource constraint (xim is a constant cost for holding cash and Rdc is the return on the digital currency). You can find an updated version of the .mod file in here. My problem now is that, when I run the model (for which I have manually set some steady states), I get the message that the Blanchard-Kahn conditions aren’t verified and I don’t understand why. If I try to lag the variables I get weird IRFs and, moreover, depending on the variables that I lag, the shock to the interest rate of the digital currency has an effect only on some variables rather than all of them.Try4.mod (4.2 KB)
I hope I made myself clear now.

I think that my problem lies in the fact that with the constraint mm + mdc = xim*mm(-1)/PI + Rdc(-1)*mdc(-1)/PI I am defining money as predetermined variables and this implies a non-stable equilibrium. However I still don’t understand how to solve this problem.