Problem Calvo pricing at steady state

Steady state
1

Hello, the residuals of my static equations are almost all 0 except the one from the Calvo pricing equation. They are equations number 32 and 33 in this code:espoir.mod (6.7 KB)

I have used the equations that Eric Sims provides in his website, that is to say the following ones
z

I set Pi star (the rest price) as 0 in the steady state since I assume 0 inflation at the steady state. But the x_1t and x_2t equations (z_1 and z_2 in my code) don’t have 0 residuals. What should I do please ?

2

Maybe you sent wrong file. First, Z_1=*((1/Xss)-1)/(1-theta*beta_l); appears to be incomplete given that the lhs starts with a *. Second, there is no value for sigma_A in the mod file.

3

Thank you for your answer. Sorry I indeed attached the wrong file, here is a corrected one:inf.mod (6.6 KB)

I did not assume any value for sigma_A as I assume A to be a constant parameter, I just forgot to erase sigma_A, it’s done in the new file I have sent.

4

The net inflation rate is indeed 0, but the \Pi is the gross inflation rate, which is 1 in steady state.

5

Thank you for your answer. I indeed have set the net inflation rate=0 (Pi=0 and Pi_star=0 in my file). And the gross inflation rate and gross reset inflation rates equations are definied as 1+Pi and 1+ Pi_star so I don’t see why you see a problem.
1+
pi

6

For those equations it’s fine, but Z_1 and Z_2 do not have (1+Pi(+1))

7

Thank you very much jpfeifer it solved my problem !

I have two other small questions if you don’t mind.

  1. I still have an non zero residual for my equation (15) (the patient budget constraint) and I don’t know why. Here is the equation on the pic. Since he is a lender then the loans to Government b_lg and the loan to other consumers b_l are negative, this is why I put a minus in front of them in the budget constraint:
    patient1
    patient11182×67 2.9 KB

Here is the budget constraint in my Latex:
patient2

But for unknown reason residuals of equation (15) are non zero

  1. Is there a way to have very small residuals for my equations and still enable dynare to run ? It’s because my equations 21 and 23 have very small residuals and it prevents me from runing dynare, and yet I did not do any mistake in those two equations.

UUUU

8

Unless you are going for an analytical steady state residuals are not a problem if subsequently a steady state is found during numerical steady state finding. That may then also solve point 2.

9

Thank you very much. Indeed Dynare found a steady state. The only problem is that I have 2 steady state close to 0 :
hh
It creates some error:

err
err919×243 7.18 KB

I will try to have alternative formulations for H_1_borrower and H_1_lender to solve the problem.