Fix several identification issues

Consider the following mod-file

var C Y T Dd;
varexo eps_1 eps_2 eps_3;

parameters root1 root2;

//rho1=1.5;
//rho2=-0.6;
root1=0.95; //root1=1.5/2+sqrt((1.5/2)^2+(-0.6))
root2=0.55; //root1=1.5/2-sqrt((1.5/2)^2+(-0.6))

model;
// parameter conversion
# rho1= (root1+root2);
# rho2= - root1*root2;

// model equation
Y = T + C;
C = rho1*C(-1)+rho2*C(-2)+ eps_1;
(T-T(-1))-(T(-1)-T(-2))= Dd(-1) + eps_2-eps_2(-1);
Dd = eps_3;
end;

// 2. Steady-state
steady_state_model;
T = 1;
Y = 1;
Dd=0;
C = 0;
end;

shocks;
var eps_1; stderr 0.1;
var eps_2; stderr 0.1;
var eps_3; stderr 0.1;
end;

stoch_simul(periods=2501, order=1);
save d_obs Y;

//3.2 ML Estimation

estimated_params;
stderr eps_1, 0.01, 0, 1;
stderr eps_2, 0.01, 0, 1;
stderr eps_3, 0.01, 0, 1;
root1, 0.95, -0.9999, 0.9999;
root2, 0.55, -0.9999, 0.9999;
end;

varobs Y;
identification(diffuse_filter);
estimation(datafile=d_obs, presample=4, first_obs=1, mode_compute=4, mode_check, diffuse_filter); // simulated data (MLE)

1. The problem is that after identification_analysis resets the number of autocorrelations, we have the line evalin('caller',['options_ident.ar=',int2str(nlags),';']); that is, only in the original caller, which is dynare_identification.m, is it reset. When the mod-file now reaches simulated_moment_uncertainty.m the variable accessed is options and not options_ident where ar is still at the old value.

   I am not sure what is the best design choice to solve this issue. That is why I would leave it to you.

2. Now use

estimated_params;
//stderr eps_1, 0.01, 0, 1;
stderr eps_2, 0.01, 0, 1;
//stderr eps_3, 0.01, 0, 1;
root1, 0.95, -0.9999, 0.9999;
// root2, 0.55, -0.9999, 0.9999;
end;

instead and there will be a different crash due to nonconformable dimensions in S=[S;zeros(size(JJ,2)-length(indJJ),1)]; in identification_analysis

1. I wonder why the standard deviation of eps_2 is not identifiable in the original mod-file, but the likelihood function shows curvature, although ML is used.