Occbin ZLB non-convergence and almost singularity

Occbin
1

Hello Friends,

Im trying to replicate Chapter 3.2 of Sims (2023) four equation new-keynesian model.

Here a ZLB binds in expectation 4 periods due to an adverse natural rate shock.

I have so far replicated most findings of the paper, my reference model is thus operational.

I do, however run into issues with my ZLB config. I get the following error of: "Operation terminated by user during occbin.mkdatap_anticipated_dyn (line 100)

In occbin.solve_one_constraint (line 190)
[zdatalinear_, SS_out.T(:,:,shock_period), SS_out.R(:,:,shock_period), SS_out.C(:,shock_period), SS, update_flag]=occbin.mkdatap_anticipated_dyn(nperiods_0,DM,…

In occbin.solver (line 84)
[out, ss, error_flag ] = occbin.solve_one_constraint(M_,dr,options_.occbin.simul,solve_dr);

In OptimalPolicyZLB.driver (line 475)
[oo_.dr, oo_.occbin.simul]= occbin.solver(M_, options_, oo_.dr , oo_.steady_state, oo_.exo_steady_state, oo_.exo_det_steady_state);

In dynare (line 310)
evalin(‘base’,[fname ‘.driver’]);"

I suspect, that I can’t use the linearised model for this or need to account for the nominal gross interest rate sticking to 1. Otherwise, maybe, I need to give ss - values for the model, which I have not since I encoded the model block as linear.

I would rly appreciate any help, thank you !

OptimalPolicyZLB.mod (8.3 KB)

2

Please see

3

Thank you for this note Professor Pfeifer.

I have now included Gross Rates, which I assign SS-Values of unity (hence, the economy starts directly at the ZLB).

This results in convergence, yet I still receive the error message:
“Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 5.393744e-22.”

The resulting graphs look, at first glance, satisfactory. Yet it results in unrealistically large gap and deflation values.

image
image1108×992 57.6 KB

The log deviation from ss of the gap would be negative 2*10^8, which is basically a move back to Stone Age upon impact of a 100 bp natural rate shock.

Is there anything I can do to fix this?
Or should I move to a deterministic simulation? If so, do you have a reference for a stochastic simulation at the ZLB that could translate to my model?

Thank you!

Best,
David
OptimalPolicyZLB.mod (9.0 KB)

4

I now believe, that the unusual large losses are due to my models inability of communicating the (expected) duration of the ZLB. Indeed, the IRF’s of r_s (nominal rate) is never zero (even after 20 periods). Hence, x and pie are almost infinite expected discounted sums. @jpfeifer is there any way of communicating to the model, that the ZLB will be left after a certain time elapsed? For example is there a possibility in OccBin, in addition to the existing unexpected negative shock, to add an expected positive shock to the natural rate?
Thank you !

5

You need to check your setup. I would have expected something like this:
OptimalPolicyZLB.mod (8.7 KB)

6

Thank you for your help professor ! The new constraint makes sense to me. Yet I believe, that I need to use a different implementation strategy of the ZLB for the replication, one where I can communicate expected duration of the ZLB and the adverse Shock more clearly. Ill likely make use of Eggertson et al.'s Toolkit which allows for stochastic ZLB’s. ZLB_Toolkit.pdf - Google Drive