# Monetary rule optimization

Hi,
The purpose of my work is to optimize a monetary rule (obtain the parameter alpha and beta and the theoritical moments). I have estimated coeifficients of my model first and I have inscrived in my script the joint program.
var y, pi, br, tcn;
varexo ey, epi, ebr, etcn;
parameters a1, a2, a3, b1, b2, c1, c2, d1, d2, e, f, g, alpha, beta;
a1=1.0;
a2=0.25;
a3=0.3;
b1=0.48;
b2=0.49;
c1=0.23;
c2=0.31;
d1=-0.004;
d2=0.009;
e=-0.1;
f=0.31;
g=0.8;
model;
y=a1y(-3)+a2y(+1)+a3pi(-2)+b1br(-1)+b2br(-2)+ey;
pi=c1
pi(-1)+c2pi(+1)+d1y(-1)+d2y(-2)+etcn(-3)+epi;
br=gbr(-1)+alphay+betapi+ebr;
tcn=f
tcn(-1)+etcn;
end;
optim_weights;
y 1;
pi 1;
end;
osr_params alpha beta;
alpha=-0.5;
beta=-0.5;
osr;

The results obtained were as follow:

**OPTIMAL VALUE OF THE PARAMETERS:
alpha -0.5

beta -0.5

Objective function : 0

MODEL SUMMARY

Number of variables: 10
Number of stochastic shocks: 4
Number of state variables: 10
Number of jumpers: 2
Number of static variables: 0

MATRIX OF COVARIANCE OF EXOGENOUS SHOCKS

Variables ey epi ebr etcn
ey 0.000000 0.000000 0.000000 0.000000
epi 0.000000 0.000000 0.000000 0.000000
ebr 0.000000 0.000000 0.000000 0.000000
etcn 0.000000 0.000000 0.000000 0.000000

POLICY AND TRANSITION FUNCTIONS
y pi br tcn
br(-1) 0.681096 -0.000364 0.459634 0
tcn(-1) 0.002059 -0.013658 0.005799 0.310000
y(-2) 0.216699 0.009585 -0.113142 0
y(-3) 0.932430 -0.000297 -0.466067 0
pi(-2) 0.279729 -0.000089 -0.139820 0
br(-2) 0.456891 -0.000146 -0.228373 0
tcn(-2) 0.004203 -0.036415 0.016106 0
tcn(-3) 0.007385 -0.108382 0.050498 0
y(-1) 0.050590 -0.001131 -0.024730 0
pi(-1) 0.048223 0.249228 -0.148725 0
ey 0.932430 -0.000297 -0.466067 0
epi -0.073853 1.083819 -0.504982 0
ebr 0.158777 -0.000173 0.920698 0
etcn 0.000793 -0.004589 0.001898 1.000000

THEORETICAL MOMENTS

VARIABLE MEAN STD. DEV. VARIANCE
y 0.0000 0.0000 0.0000
pi 0.0000 0.0000 0.0000
br 0.0000 0.0000 0.0000
tcn 0.0000 0.0000 0.0000

VARIANCE DECOMPOSITION (in percent)

ey epi ebr etcn
y 83.80 4.76 11.34 0.10
pi 0.14 97.84 0.02 2.00
br 42.96 15.66 40.93 0.45
tcn 0.00 0.00 0.00 100.00
All endogenous are constant or non stationary, not displaying correlations and auto-correlations**

I guess that there is a problem somewhere.
Any help?
Thanks

Your model has no unique steady-state (use “check; steady;” to see this); residuals of equation 3 are NAN (use “model_diagnostics(M_,options_,oo_)” to see this).
Regards
Donihue

Thank you donihue,
by applying the first suggestion (check; steady;), I get this result:
**EIGENVALUES:
Modulus Real Imaginary

``````           0               -0                0
0               -0                0
3.372e-017      -3.372e-017                0
1.253e-016      -1.253e-016                0
0.2405           0.2405                0
0.31             0.31                0
0.7696           0.7278           0.2503
0.7696           0.7278          -0.2503
0.8288          -0.3337           0.7586
0.8288          -0.3337          -0.7586
2.977            2.977                0
3.98            -3.98                0
``````

There are 2 eigenvalue(s) larger than 1 in modulus
for 2 forward-looking variable(s)

The rank condition is verified.

y 0.0616721
pi 0.00174291
br 0.0914624
tcn 0
**
So, I think there is steady state.
Any suggestion?

You have not defined any shocks, so all your error terms are set = 0; hence no variation. Add something like
shocks;
var ey; stderr 0.01;
var epi; stderr 0.01;
var ebr; stderr 0.01;
var etcn; stderr 0.01;
end;
and you will obtain IRFs

Regards
Donihue