TANK with Forward Guidance - collinear equations

Dear all,
I am a beginner of dynare and I am trying to write a TANK model with a forward guidance shock, attached you can find the code.
It finds a steady state but the values are a bit off, especially the bonds, B, which should be zero in net supply.
I ran model_diagnostics, and it says that equations 16 ,17,18,20 are collinear, and I really do not understand what I should do.
Could someone help me?
Thank you very much!
model1.mod (4.1 KB)

I think the first issue you should solve is to get rid off P, which is non-stationary and introduces a unit root in the model. Also, I am not sure that the Phillips Curve is written correctly. Are you replicating a specific model?

Valerio

Hi Valerio!
I am basing my model on Debortoli and Gali(2017), and to that I am adding the forward guidance shock according to McKay et al. So are you suggesting that I write it directly in pi terms instead that P like this
" pi=betapi(+1)+((1-betatheta)(1-theta)(1/(1+epsiloneta))(1/sigma+(1+eta)/phi+eta))*(Y)/Y_ss " ?
Because with this form, dynare cannot find the steady state.
Thank you very much!

Maria Ludovica Ambrosino

The price level in NK models is non-stationary, so you will have a unit root and the steady state cannot be computed endogenously. Expressing everything in terms of inflation rates is the way to go.

I had a look at your code, there are some equations missing, and some other equations that are redundant (one Euler equation implies the other one, one trasfer equation implies the other one). I would suggest you to reduce the number of equations and variables as much as possible. When the code works you can start to add other equations and variables. For instance, I would keep:

  • Euler equation for ricardian (eq 9)
  • Wage schedule (eq 11)
  • Aggregate production (eq 16)
  • Labor demand (eq at the beginning of page 14)
  • Phillips curve (eq 12)
  • Market clearing (eq 15, use the definition of Delta)
  • Taylor rule

These 7 equations are standard in a basic NK model and describe the equilibrium for Cr Y N W mu pi i. In this TANK model you also need:

  • The budget constraint of k houseolds
  • Definition of aggregate consumption
  • Transfers for k households (eq 13)
  • The definition of profits (given at the end of page 15)
  • the stochastic process for nu

These additional 5 equations carry other 5 variables: Ck C Trk D nu. So you should have 12 equations for 12 variables.

I hope this can help.

Got it! Thank you very much!

Dear Valerio,
thank you very much! This has been really helpful. If you do not mind, I encountered another problem. So, I tried what you suggested and I have followed the calibration in Debortoli&Gali (2017), and set the shock in period 20 to the interest rate. But now the model says that rank condition is not verified and my plot is flat. How could I fix this?
Attached you can find the code. I hope not to disturb you and thank you so much in advance!
Ludovica
model3.m (257 Bytes) model3.mod (3.8 KB)

The error is in the Taylor rule, where the ss of i is missing. It should be:

i=i_ss+chi_y*(Y-Y_ss)/Y_ss+chi_pi*(Pi-1)+nu;

In this way, in the steady state you will have:

i=i_ss
Y=Y_ss
Pi=1

Does it work now?