Add unit test for initialization from calibrated model

tests/estimation/fs2000_initialize_from_calib.mod

+//uses a prior mean for bet that does not allow solving the model. Then uses the calibrated value to initialize.
+var m P c e W R k d n l gy_obs gp_obs y dA;
+varexo e_a e_m e_f;
+
+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;
+
+initval;
+k = 6;
+m = mst;
+P = 2.25;
+c = 0.45;
+e = 1;
+W = 4;
+R = 1.02;
+d = 0.85;
+n = 0.19;
+l = 0.86;
+y = 0.6;
+gy_obs = exp(gam);
+gp_obs = exp(-gam);
+dA = exp(gam);
+end;
+
+shocks;
+var e_a; stderr 0.014;
+var e_m; stderr 0.005;
+var e_f; stderr 0.005;
+corr gy_obs, gp_obs = 0.1;
+end;
+
+steady;
+//check;
+
+estimated_params;
+alp, beta_pdf, 0.356, 0.02;
+bet, normal_pdf, 2, 1;
+gam, normal_pdf, 0.0085, 0.003;
+mst, normal_pdf, 1.0002, 0.007;
+rho, normal_pdf, 0.129, 0.223;
+psi, beta_pdf, 0.65, 0.05;
+del, beta_pdf, 0.01, 0.005;
+stderr e_a, inv_gamma_pdf, 0.035449, inf;
+stderr e_m, inv_gamma_pdf, 0.008862, inf;
+corr e_a, e_m, normal_pdf, 0, 0.007;
+corr e_a, e_f, normal_pdf, 0, 0.007;
+stderr gp_obs, inv_gamma_pdf, 0.008862, inf;
+corr gp_obs, gy_obs, normal_pdf, 0, 0.007;
+end;
+
+varobs gp_obs gy_obs;
+
+estimated_params_init;
+//stderr e_a, 0.014000;
+//stderr e_m, 0.005000;
+//stderr gp_obs, 0.1;
+corr e_m, e_a, 0.1;
+//corr gy_obs, gp_obs, 0.000000;
+//alp, 0.330000;
+//bet, 0.990000;
+gam, 0.003000;
+mst, 1.011000;
+//rho, 0.900000;
+psi, 0.787000;
+del, 0.020000;
+end;
+
+options_.use_calibration_initialization=1;
+options_.plot_priors=0;
+estimation(order=1, datafile=fsdat_simul, nobs=192, loglinear, mh_replic=2000, mh_nblocks=1, mh_jscale=0.8,prior_trunc=0);
\ No newline at end of file

tests/estimation/fs2000_initialize_from_calib_steadystate.m

+% computes the steady state of fs2000 analyticaly
+% largely inspired by the program of F. Schorfheide
+
+% Copyright (C) 2004-2010 Dynare Team
+%
+% This file is part of Dynare.
+%
+% Dynare is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+%
+% Dynare is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
+
+function [ys,check] = fs2000_steadystate(ys,exe)
+  global M_
+  
+  alp = M_.params(1); 
+  bet = M_.params(2); 
+  gam = M_.params(3); 
+  mst = M_.params(4); 
+  rho = M_.params(5); 
+  psi = M_.params(6); 
+  del = M_.params(7); 
+
+  check = 0;
+  
+  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;
+  
+  ys =[
+m     
+P     
+c     
+e     
+W     
+R     
+k     
+d     
+n     
+l     
+gy_obs
+gp_obs
+y     
+dA          ];