Ramsey policy with occasionally binding constraints


I am using a simple log-linearized New Keynesian model with fiscal policy, and my goal is to analyze the implications of optimal financial repression (i.e. for a given fiscal shock affecting real debt that cannot be balanced with taxes, how does inflation, output gap etc. react under the optimal policy regime). I used the ramsey_policy command to look at this, and it worked well, but I want to look at more interesting cases where there is some effective lower bound on the policy rate. Occbin doesn’t let me use the ramsey_policy command - is there any alternative or do you have any idea how I could look at ELB implications with optimal loss-minimizing policy?

(since my model is completely linear and the first order conditions of the loss-minimization problem are also fully linear - so errors are additive -, I don’t think that perfect foresight and stochasticity change much as long as shocks come as a surprise, as with the command shocks(surprise)).

Thank you!

ELBmodel.mod (2.1 KB)
I tried using perfect_foresight_solver, adding the ELB through the ramsey constraint and using the Levenberg-Marquardt solver, but the path of the variables seems extremely odd. Any idea as to what could cause that?

I am on vacation and it will take some time to look deeper into this. Occbin does indeed not work with ramsey_model. Perfect foresight seems the right way to go. Let me ask you a question: should your model return back to steady state at the end of times? Or does it explode?

Sure, thank you for your time! It should return to steady state - in the stochastic baseline model that’s obviously the case, with perfect foresight it seems like some variables are suddenly forced back to zero in the last period. Inflation and output gap (infl and ygap) also return to zero, but their path looks completely random. I didn’t add the plot to debt at the end of the code, but its path is also odd: it jumps to 100 in the second period from zero, rises steadily to about 120 and then drops suddenly to zero in the last period. I wonder why these might be.

I think there is a problem with your model setup. What assures that debt converges back to steady state?

ELBmodel.mod (1.8 KB)
The point of the model is that the government finances its expenditures with long-term bonds, and having no opportunity to tax a fiscal shock away, it has to reduce the real returns on bonds (rret) to satisfy the transversality condition on real debt. I’m attaching the simple stochastic version of the model, without the effective lower bound, which seems to follow a smooth path back to steady state - I thought that if the Blanchard-Kahn conditions are satisfied, dynare would automatically impose the transversality conditions. What else should I add to the model to ensure its stability? Again, thank you for your help.

I guess the answer is