 # MIU (Sidrauski) model equilibrium specification

Hi. I am trying to reproduce the equilibrium conditions of a basic MIU model using Dynare in MATLAB, but I cannot understand what I am doing wrong. I guess it is something related with the specification of equilibrium conditions.

I reproduce my code next:

``````% Endogenous variables:

var c m b k l r w y I i pi M p;

% Parameters:

parameters g1 g2 alpha beta delta tao;

g1     = 0.2;
g2     = 0.3;
alpha  = 0.35;
beta   = 0.99;
delta  = 0.04;
tao    = 0.2;

% Modelo, condiciones de equilibrio:

model;
(-g2*(1/(1-l)))/(g1*(1/c)) = w;                                 % Leisure - Consuption equilibrium condition
g1*(1/c)) = beta*(g1*(1/c(+1)))*(1+r(+1)-delta);    % Intertemporal consumption equilibrium condition
(1+i)/(1+pi(+1)) = (1+r(+1)-delta);                         % Fisher relationship
((1-g1-g2)*(1/m))/(g1*(1/c)) = i/(1+i);                    % Money - Consuption equilibrium condition
alpha*(k(-1)^(alpha-1))*(l^(1-alpha))  = w;            % Wage
(k(-1)^(alpha))*(1-alpha)*(l^(-alpha)) = r;              % Return on capital
y = (k(-1)^(alpha))*(l^(1-alpha));                           % Production  function
k = (1-delta)*k(-1) + I;                                           % Capital movement law
y = c + I;                                                               % Goods market clearing condition
M = (1+tao)*M(-1);                                                % Nominal money balances
1+pi = (m/m(-1))*(1+tao);                                     % Inflation
m = M/p;                                                               % Real money balances
b = 0;                                                                   % Bonds market clearing condition
end;

initval;
y = 1;
c = 0.9;
I = 0.1;
k = 10;
b = 0;
m = 0.1;
r = 0.3;
w = 0.7;
i = 0.1;
pi = 1;
M=1;
p= 1;
l=10;
end;

check;

stoch_simul;
``````

When I run dynare I get:

``````Configuring Dynare ...
[mex] Generalized QZ.
[mex] Sylvester equation solution.
[mex] Kronecker products.
[mex] Sparse kronecker products.
[mex] Local state space iteration (second order).
[mex] Bytecode evaluation.
[mex] k-order perturbation solver.
[mex] k-order solution simulation.
[mex] Quasi Monte-Carlo sequence (Sobol).
[mex] Markov Switching SBVAR.

Using 64-bit preprocessor
Starting Dynare (version 4.5.4).
Starting preprocessing of the model file ...
Found 13 equation(s).
Evaluating expressions...done
Computing static model derivatives:
- order 1
Computing dynamic model derivatives:
- order 1
- order 2
Processing outputs ...
done
Preprocessing completed.

Residuals of the static equations:

Equation number 1 : -3.0199e-06
Equation number 2 : -3.8334e-07
Equation number 3 : 0
Equation number 4 : 3.3552e-06
Equation number 5 : 4.2762e-06
Equation number 6 : -3.2339e-07
Equation number 7 : 2.7008e-07
Equation number 8 : 0
Equation number 9 : 0
Equation number 10 : 0
Equation number 11 : 0
Equation number 12 : 1152290.4146
Equation number 13 : 0

Error using print_info (line 83)
Impossible to find the steady state. Either the model doesn't have a steady state, there are an
infinity of steady states, or the guess values are too far from the solution

print_info(info,options_.noprint, options_);

Error in a (line 181)

Error in dynare (line 223)
evalin('base',fname) ;
``````

I will be really grateful if you help me.

Bests,

Martin

Not sure, but do you think the equation for nominal money balances is explosive?
M = (1+0.2)M(-1)

Yes, It might be explosive, but even when I set a smaller value for tao, e.g. 0.01, results do not change.

Thanks!

1.01 would still imply explosiveness, right?

Did you try writing down the model in terms of real variables? Get rid of the levels of nominal variables, write in terms of price inflation and not price levels…

Reuben