//the basic NK model as in Cochrane (2015)

var x, pi;
varexo i;
parameters cbeta, k, sigma;

cbeta = 0.97;
k = 0.2;
sigma = 1;

model;
x = EXPECTATION(-1)(x(+1)) - sigma*(i-(EXPECTATION(-1)(pi(+1))));
pi= cbeta*(EXPECTATION(1)(pi(+1))) + k*x;
end;

//model;
//x = (x(+1)) - sigma*(i-(pi(+1)));
//pi= cbeta*pi(+1) + k*x;
//end;

initval;
i=0;
pi = 0;
x = 0;
end;

endval;
i = 1 ;
end;
steady;

check;


simul(periods=15,stack_solve_algo=0);
rplot x;
rplot pi;