// Tests the analytic_derivation option

var m P c e W R k d n l gy_obs gp_obs y dA;
varexo e_a e_m;

parameters alp bet gam mst rho psi del;

alp = 0.33;
bet = 0.99;
gam = 0.003;
mst = 1.011;
rho = 0.7;
psi = 0.787;
del = 0.02;

model;
dA = exp(gam+e_a);
log(m) = (1-rho)*log(mst) + rho*log(m(-1))+e_m;
-P/(c(+1)*P(+1)*m)+bet*P(+1)*(alp*exp(-alp*(gam+log(e(+1))))*k^(alp-1)*n(+1)^(1-alp)+(1-del)*exp(-(gam+log(e(+1)))))/(c(+2)*P(+2)*m(+1))=0;
W = l/n;
-(psi/(1-psi))*(c*P/(1-n))+l/n = 0;
R = P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(-alp)/W;
1/(c*P)-bet*P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)/(m*l*c(+1)*P(+1)) = 0;
c+k = exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)+(1-del)*exp(-(gam+e_a))*k(-1);
P*c = m;
m-1+d = l;
e = exp(e_a);
y = k(-1)^alp*n^(1-alp)*exp(-alp*(gam+e_a));
gy_obs = dA*y/y(-1);
gp_obs = (P/P(-1))*m(-1)/dA;
end;

steady_state_model;
  dA = exp(gam);
  gst = 1/dA;
  m = mst;
  khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
  xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
  nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
  n  = xist/(nust+xist);
  P  = xist + nust;
  k  = khst*n;

  l  = psi*mst*n/( (1-psi)*(1-n) );
  c  = mst/P;
  d  = l - mst + 1;
  y  = k^alp*n^(1-alp)*gst^alp;
  R  = mst/bet;
  W  = l/n;
  ist  = y-c;
  q  = 1 - d;

  e = 1;
  
  gp_obs = m/dA;
  gy_obs = dA;
end;

shocks;
var e_a; stderr 0.014;
var e_m; stderr 0.005;
end;

stoch_simul(order=1,periods=200, irf=0,nomoments,noprint);
save('my_data.mat','gp_obs','gy_obs');

estimated_params;
alp, 0.356;
rho, 0.129;
psi, 0.65;
stderr e_a, 0.035449, 0, inf;
stderr e_m, 0.008862, 0, inf;
end;

varobs gp_obs gy_obs;

options_.solve_tolf = 1e-12;

estimation(order=1,mode_compute=9,analytic_derivation,kalman_algo=1,datafile=my_data,nobs=192,mh_replic=0,mh_nblocks=2,mh_jscale=0.8,plot_priors=0,prior_trunc=0);
if (isoctave && user_has_octave_forge_package('optim', '1.6')) || (~isoctave && user_has_matlab_license('optimization_toolbox'))
    estimation(order=1,mode_compute=1,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=1,datafile=my_data,nobs=192,mh_replic=0,mh_nblocks=2,mh_jscale=0.8,plot_priors=0
    %,optim = ('DerivativeCheck', 'on','FiniteDifferenceType','central')
    );
    estimation(order=1,mode_compute=3,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=1,datafile=my_data,nobs=192,mh_replic=0,mh_nblocks=2,mh_jscale=0.8,plot_priors=0);
    estimation(order=1,mode_compute=101,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=1,datafile=my_data,nobs=192,mh_replic=0,mh_nblocks=2,mh_jscale=0.8,plot_priors=0);    
end
if ~isoctave % This estimation randomly fails on Octave
estimation(order=1,mode_compute=5,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=2,datafile=my_data,nobs=192,mh_replic=0,mh_nblocks=2,mh_jscale=0.8,plot_priors=0);
end
estimation(order=1,mode_compute=4,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=1,datafile=my_data,nobs=192,mh_replic=0,mh_nblocks=2,mh_jscale=0.8,plot_priors=0);
estimation(order=1,mode_compute=4,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=2,datafile=my_data,nobs=192,mh_replic=0,mh_nblocks=2,mh_jscale=0.8,plot_priors=0);
options_.debug=1;
estimation(order=1,mode_compute=0,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=1,datafile=my_data,nobs=192,mh_replic=0,plot_priors=0);
fval_ML_1=oo_.likelihood_at_initial_parameters;
estimation(order=1,mode_compute=0,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=2,datafile=my_data,nobs=192,mh_replic=0,plot_priors=0);
fval_ML_2=oo_.likelihood_at_initial_parameters;
options_.analytic_derivation=0;
estimation(order=1,mode_compute=0,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',kalman_algo=1,datafile=my_data,nobs=192,mh_replic=0,plot_priors=0);
fval_ML_3=oo_.likelihood_at_initial_parameters;

if abs(fval_ML_1-fval_ML_2)>1e-5 || abs(fval_ML_1-fval_ML_3)>1e-5
    error('Likelihood does not match')
end
options_.debug=0;

estimated_params(overwrite);
alp, beta_pdf, 0.356, 0.02;
rho, beta_pdf, 0.129, 0.100;
psi, beta_pdf, 0.65, 0.05;
stderr e_a, inv_gamma_pdf, 0.035449, inf;
stderr e_m, inv_gamma_pdf, 0.008862, inf;
end;

estimation(order=1,mode_compute=9,analytic_derivation,kalman_algo=1,datafile=my_data,nobs=192,mh_replic=0,mh_nblocks=2,mh_jscale=0.8,plot_priors=0,prior_trunc=0);
if (isoctave && user_has_octave_forge_package('optim', '1.6')) || (~isoctave && user_has_matlab_license('optimization_toolbox'))
    estimation(order=1,mode_compute=1,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=1,datafile=my_data,nobs=192,mh_replic=0,mh_nblocks=2,mh_jscale=0.8,plot_priors=0
    %,optim = ('DerivativeCheck', 'on','FiniteDifferenceType','central')
    );
    estimation(order=1,mode_compute=3,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=1,datafile=my_data,nobs=192,mh_replic=0,mh_nblocks=2,mh_jscale=0.8,plot_priors=0);
    estimation(order=1,mode_compute=101,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=1,datafile=my_data,nobs=192,mh_replic=0,mh_nblocks=2,mh_jscale=0.8,plot_priors=0);    
end
if ~isoctave % This estimation randomly fails on Octave
estimation(order=1,mode_compute=5,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=2,datafile=my_data,nobs=192,mh_replic=0,mh_nblocks=2,mh_jscale=0.8,plot_priors=0);
end
estimation(order=1,mode_compute=4,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=1,datafile=my_data,nobs=192,mh_replic=0,mh_nblocks=2,mh_jscale=0.8,plot_priors=0);
estimation(order=1,mode_compute=4,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=2,datafile=my_data,nobs=192,mh_replic=0,mh_nblocks=2,mh_jscale=0.8,plot_priors=0);
options_.debug=1;
estimation(order=1,mode_compute=0,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=1,datafile=my_data,nobs=192,mh_replic=0,plot_priors=0);
fval_Bayes_1=oo_.likelihood_at_initial_parameters;
estimation(order=1,mode_compute=0,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',analytic_derivation,kalman_algo=2,datafile=my_data,nobs=192,mh_replic=0,plot_priors=0);
fval_Bayes_2=oo_.likelihood_at_initial_parameters;
options_.analytic_derivation=0;
estimation(order=1,mode_compute=0,mode_file='fs2000_analytic_derivation/Output/fs2000_analytic_derivation_mode',kalman_algo=1,datafile=my_data,nobs=192,mh_replic=0,plot_priors=0);
fval_Bayes_3=oo_.likelihood_at_initial_parameters;

if abs(fval_Bayes_1-fval_Bayes_2)>1e-5 || abs(fval_Bayes_1-fval_Bayes_3)>1e-5
    error('Likelihood does not match')
end
