Impossible to find steady state in Ireland 2003

Steady state
81

You must be doing something very wrong here. In steady state, almost always q=1.

82

There were indeed few mistakes in the equations, I’m attaching corrected file. I still obtain unusual result for q though, i.e. 0.015.

The only changes I’ve made to the original system of equations is inserting the parameter values. I’m also attaching my attempt of solving the system. Here I’ve plugged in the steady state variable values (e.g. pi0=1.3964) and assumed the variables are in the steady state (e.g. k=k(+1)=k(+2)).

Model.mod (1.6 KB)
Model solution.mod (1.3 KB)

83

I am getting various error messages with your files. Did you upload the correct files?

84

I apologize, I’m sending correct files. These are the original non-linearized equations of the steady state system, with parameter values inserted (also shock variables x,a,e,z,v are treated as parameters and set to 1).

Model.mod (1.6 KB)
Model_steadystate.m (1.1 KB)

85

I still don’t understand what you are doing.

ln(r/r0)=0.38*ln(tau/tau0)+1.3*ln(pi/pi0)+0.125*ln(y/y0)+ln(v);

shows residuals, so clearly the variables do not correspond to the r0, y0 etc. values.

86

I understand, the r0, y0, pi0, tau0 values are taken from my panel of observations (quarterly values for Slovenia, Austria and Italy 1991Q1-2020Q1).

r0 = 8.88 (real interest rate)
y0 = 20449.01 (GDP per capita, adjusted with TFP)
pi0 = 1.3964 (inflation rate)
tau0 = 0.014 (growth rate of aggregate M3, corrected from 0.0046)

Perhaps I shouldn’t insert the real world data at this point? I suppose the y0 and other steady state variables could be computed just like the y and other variables themselves from the steady state system of equations by inputting parameter values?

87

Yes, indeed. There is not a one-to-one mapping from the data to the model variables unless you adjust parameters correspondingly. For the steady state interest rate and inflation rate, you need to adjust the discount factor and inflation target accordingly. For y0, this only works if you adjusted the steady state TFP and steady state hours accordingly.

88

I see, now I have a system of 26 equations with 26 variables. However, as I try to compute the steady state variable values, I again obtain q=0.015 (nominal rental rate for capital, I expected values around 0.09, but as per your suggestions I’m after a result approximately 1).

Model.mod (1.6 KB)
Model_steadystate.m (1.1 KB)

89

So I proceeded with the value for q that I obtain, q=0.035.

Now I have 26 equations, and if I assume steady state (var(+1)=var), then I’m generally left with 25 unknowns. However, there are also parameters rhoa, rhoe etc. and parameters epsilona, epsilone etc. Can I assume certain value for the parameters so I can solve the system (like values from literature for rho values and 0 for the epsilon values)? Thank you for the answer in advance.

Model.mod (1.6 KB)
Model_solving.txt (1.4 KB)

90

Hello, I get output that the system cannot be solved:

“Can not solve for i,k,p,r,n,y,h,l,c,m,d,w,f,t”

I have a system of 14 equations with 14 unknowns, but because one equation includes logs of two different variables, the website reports the system cannot be solved. Is this situation solvable?

To get to the system, I plugged in steady state values for the five steady state variables (y_ss=20449.01, pi_ss=1.3964, r_ss=8.88, e_ss=0, z_ss=0, tau_ss=0.014).

91

Again, apply pencil and paper to your problem. It does not seem as if you are making progress. Also, why are you using the base 10 logarithm?