var x pi i ez;
 varexo epsz;
 parameters betta sigma omega eta phipi phix rhoz pi_target;

 betta  =0.98; %Discount factor
 omega =0.75;  %Calvo parameter price stickiness
 phipi =1.5;   %Taylor rule: feedback on expected inflation
 phix  =0.125;   %Taylor rule: feedback on output gap
 eta = 1;      %Labor supply parameter
 sigma = 2;    %CRRA parameter in consumption
 rhoz = 0.9;  %persistence of technology shock
pi_target=1.05;
 
 model(linear);
 x = x(+1)-(1/sigma)*(i-pi(+1))-ez;
 pi = betta*pi(+1)+((sigma+eta)*(1-betta*omega)*(1-omega)/omega)*x;
 i = max(-(1/betta-1),pi_target+phipi*(pi-pi_target)+phix*x);
 ez = rhoz*ez(-1)+epsz;
 end;


 steady;

 shocks;
 var epsz;
periods 1;
values 0.01;
end;

 check;
 simul(periods=100);
rplot x;
rplot pi;
rplot i;
rplot ez;