Two sectors NK model

[ManuelG1]

Good Afternoon,

I am trying to work on a very simple two sectors NK model. Although the external file always finds the SS, I got two main issues I am not sure how to interpret/fix:

1. If the consumption sectoral shares are not equal to the employment sectoral shares one of the static equations displays a residual;

2. The model diagnostic command indicates some colinear relationships among the Taylor rule and the productivity shocks. (The Jacobian of the static model is singular).

I thank you in advance for your help.

Manuel

Model_T2_SS.m (1.3 KB) Model_T2.mod (4.2 KB)

[jpfeifer]

See

The Jacobian is singular but Dynare still gives me results

Most of the problem comes from your use of log(Phi) = (1-rho_phi)*log(STEADY_STATE(Phi)) + rho_phi*log(Phi(-1)) + Eps_phi; The steady state of Phi cannot be endogenously computed, it seems. If you use log(Phi) = (1-rho_phi)*log(varphi) + rho_phi*log(Phi(-1)) + Eps_phi; i.e. replace the steady state operator by the steady state you set in the steady_state_model-block, one of the warnings disappears. For the other shock processes, the problem seems to be the same.

Fixing this in Model_T2.mod (4.1 KB) results in only one collinear relationship. Maybe that will help. Could it be that you are trying to pin down nominal levels that are not determinate in NK models?

[ManuelG1]

Dear Dr. Pfeifer,

thanks for your help.

I removed the nominal variables by introducing relative prices and the system does not detect colinear relationships any longer.
However, I still get the error about one of the eigenvalues being close to 0, although If I run model diagnostic the system says “MODEL_DIAGNOSTICS: No obvious problems with this mod-file were detected.”

Am I still missing something?

Thanks

Model_T4.mod (4.0 KB) Model_T4_SS.m (1.3 KB)

[jpfeifer]

It seems this is a fundamental problem with your model. Are you sure that what remains determines all variables in the model uniquely?

[ManuelG1]

It seems I am still missing something. The model now works if I remove the labour market equilibrium equation (h = h1+h2) but this sounds wrong to me. In fact, as soon as I change the calibration (e.g. if the consumption sectoral shares are not equal to the employment sectoral shares) the model stops working since the aggregate wage static equation starts to display a residual when imputing the steady state.

Is it maybe that the model can only work if the consumption and employment shares are endogenized?

Thank you

Model_T6_SS.m (1.3 KB) Model_T6.mod (4.1 KB)

[jpfeifer]

I am not familiar with your model, but that may well be the case. After all, wage income should determine your consumption choices.