Jermann Quadrini (2012) with collateral constraints

Stochastic simulations
1

Hi all,
I am trying to solve the NK version of Jermann Quadrinni’s (2012) paper with collateral constraints. I modify the constraint to be Kyotaki-Moore style instead of earning constraint. I double-checked my code to make sure that variables have proper timing (in particular capital), but still get the same error “Blanchard & Kahn conditions are not satisfied: indeterminacy.” and “The rank condition ISN’T verified!”.

Could someone help me?

simple_model.mod (8.8 KB)
simple_model_steadystate.m (4.4 KB)

2

I thin I resolved the issue. It was a problem with calibration.

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3

Hi all,
I think the main issue in this model is that the nominal prices (price of consumption goods and wages) are moving to a new equilibrium after the monetary shock. And Taylor rule breaks. I have attached the updated code and IRFs. I used the version of the Taylor rule, which only reacts to the output gap.

Does anyone have an intuition about why the price doesn’t return to equilibrium after the shock? Is it a feature of the model, or did I make a mistake somewhere?

simple_model.mod (9.5 KB)
simple_model_steadystate.m (4.7 KB)
main_output_gap.fig (175.8 KB)
qwd_output_gap.fig (64.7 KB)

4

See e.g.

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5

Thank you! I get it now.

Another question:what can be a reason that the original Taylor rule doesn’t work, while a simplified version works?
When I switch to the

rho_R*(r_taylor(-1)-steady_state(r_taylor))+(1-rho_R)*nu_1*(P-P(-1))+((1-rho_R)*nu_2+nu_3)*(Y-steady_state(Y))-nu_3*(Y(-1)-steady_state(Y))-eps_r-(r_taylor-steady_state(r))=0;

I get
Blanchard & Kahn conditions are not satisfied: no stable equilibrium.

6

That’s hard to tell. But the determinacy/stability region can be complicated in larger models.

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7

Also, I notices that although all real variables are going into the write direction, the Price and Wage go in opposite. An increase in real interest rate leads to an increase in inflation. Can it be the results of altered taylor rule, or something is definitely wrong in the model?

8

That indeed sounds a bit strange. But it’s hard to tell whether it’s a feature of the model or a bug. Have you tried moving your model more closely to the original model, e.g. by changing parameters? That may give you new insights.

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