adding new tests

(cherry picked from commit ca865514aa0dcc101082395891cc7c05c6ce02b3)

tests/Makefile.am

@@ -100,7 +100,10 @@ MODFILES = \
 	kalman_filter_smoother/fs2000.mod \
 	kalman_filter_smoother/fs2000_1.mod \
 	kalman_filter_smoother/fs2000_2.mod \
-	kalman_filter_smoother/fs2000a.mod
+	kalman_filter_smoother/fs2000a.mod \
+	second_order/burnside_1.mod \
+	second_order/ds1.mod \
+	second_order/ds2.mod
 
 EXTRA_DIST = \
 	$(MODFILES) \

tests/second_order/burnside_1.mod

+var y x;
+varexo e;
+
+parameters beta theta rho xbar;
+xbar = 0.0179;
+rho = -0.139;
+theta = -1.5;
+theta = -10;
+beta = 0.95;
+
+model;
+y = beta*exp(theta*x(+1))*(1+y(+1));
+x = (1-rho)*xbar + rho*x(-1)+e;
+end;
+
+shocks;
+var e; stderr 0.0348;
+end;
+
+initval;
+x = xbar;
+y = beta*exp(theta*xbar)/(1-beta*exp(theta*xbar));
+end;
+
+resid(1);
+
+steady;
+
+stoch_simul(order=2,irf=0);
+
+sigma2=M_.Sigma_e;
+i = linspace(1,800,800);
+a = theta*xbar*i+(theta^2*sigma2)/(2*(1-rho)^2)*(i-2*rho*(1-rho.^i)/(1-rho)+rho^2*(1-rho.^(2*i))/(1-rho^2));
+a1 = theta^2*sigma2/(2*(1-rho)^2)*(i-2*rho*(1-rho.^i)/(1-rho)+rho^2*(1-rho.^(2*i))/(1-rho^2));
+b = theta*rho*(1-rho.^i)/(1-rho);
+
+dr = oo_.dr;
+x1 = [dr.ghx(2); dr.ghu(2); dr.ghxx(2); dr.ghuu(2); dr.ghxu(2); dr.ghs2(2)];
+x2 = [
+ sum(beta.^i.*exp(theta*xbar*i).*b*rho)
+ sum(beta.^i.*exp(theta*xbar*i).*b)
+ sum(beta.^i.*exp(theta*xbar*i).*(b*rho).^2)
+ sum(beta.^i.*exp(theta*xbar*i).*b.^2)
+ sum(beta.^i.*exp(theta*xbar*i).*b.^2*rho)
+ sum(beta.^i.*exp(theta*xbar*i).*a1*2)
+];
+if any(abs(x1-x2) > 1e-14);
+   error('burnside_1 doesn''t reproduce the analytical solution');
+end;
\ No newline at end of file

tests/second_order/ds1.mod

+@#define countries = 1:2
+@#define assets = 1:2
+var
+@#for c in countries
+  yk_@{c} yl_@{c} c_@{c}
+@#endfor
+a ze_1 r_1
+;
+
+varexo
+@#for c in countries
+  ek_@{c} el_@{c}
+@#endfor
+;
+
+parameters rho eta omega sig_k sig_l ykbar ylbar;
+
+rho = 1;
+psi = 0.7;
+eta = 0.9;
+g = 0.25;
+ykbar = 1;
+ylbar = 1;
+cbar = ykbar+ylbar;
+nu = 0.5;
+omega = 0.75;
+sig_k = 0.02;
+sig_l = 0.01;
+sig_m = 0;
+betabar = omega*cbar^(-eta);
+
+
+model;
+@#for c in countries
+  yk_@{c} = log(ykbar) + sig_k*ek_@{c};
+  yl_@{c} = log(ylbar) + sig_l*el_@{c};
+  exp(c_@{c})^(eta-rho) = omega*exp(c_@{c}(+1))^(-rho)*r_1(+1);
+@#endfor
+
+a = a(-1)*r_1 + exp(yk_1) + exp(yl_1) - exp(c_1);
+-a = -a(-1)*r_1 + exp(yk_2) + exp(yl_2) - exp(c_2);
+//  r_1+ze_1  = ze_1+exp(yk_1-ze_1(-1));
+  r_1  = exp(yk_1-ze_1(-1));
+
+
+end;
+
+shocks;
+@#for c in countries
+  var ek_@{c} = 1;
+  var el_@{c} = 1;
+@#endfor
+end;
+
+initval;
+@#for c in countries
+  yk_@{c} = log(ykbar);
+  yl_@{c} = log(ylbar);
+  c_@{c} = log(ykbar+ylbar);
+@#endfor
+  r_1 = 1/betabar;
+  ze_1 = log(betabar)+yk_1;
+end;
+
+resid(1);
+steady;
+model_diagnostics(M_,options_,oo_);
+check;
+stoch_simul(order=2,irf=0);

tests/second_order/ds2.mod

+@#define countries = 1:2
+@#define assets = 1:2
+var
+@#for c in countries
+  yk_@{c} yl_@{c} c_@{c}
+@#endfor
+a ze_1 r_1
+;
+
+varexo
+@#for c in countries
+  ek_@{c} el_@{c}
+@#endfor
+;
+
+parameters rho eta omega sig_k sig_l ykbar ylbar;
+
+rho = 1;
+psi = 0.7;
+eta = 0.9;
+g = 0.25;
+ykbar = 1;
+ylbar = 1;
+cbar = ykbar+ylbar;
+nu = 0.5;
+omega = 0.75;
+sig_k = 0.02;
+sig_l = 0.01;
+sig_m = 0;
+betabar = omega*cbar^(-eta);
+
+
+model;
+@#for c in countries
+  yk_@{c} = log(ykbar) + sig_k*ek_@{c};
+  yl_@{c} = log(ylbar) + sig_l*el_@{c};
+  exp(c_@{c})^(eta-rho) = omega*exp(c_@{c}(+1))^(-rho)*r_1(+1);
+@#endfor
+
+a = a(-1)*r_1 + exp(yk_1) + exp(yl_1) - exp(c_1);
+-a = -a(-1)*r_1 + exp(yk_2) + exp(yl_2) - exp(c_2);
+//  r_1+ze_1  = ze_1+exp(yk_1-ze_1(-1));
+  r_1  = exp(yk_1-ze_1(-1))+ze_1-ze_1;
+
+
+end;
+
+shocks;
+@#for c in countries
+  var ek_@{c} = 1;
+  var el_@{c} = 1;
+@#endfor
+end;
+
+initval;
+@#for c in countries
+  yk_@{c} = log(ykbar);
+  yl_@{c} = log(ylbar);
+  c_@{c} = log(ykbar+ylbar);
+@#endfor
+  r_1 = 1/betabar;
+  ze_1 = log(betabar)+yk_1;
+end;
+
+resid(1);
+steady;
+model_diagnostics(M_,options_,oo_);
+check;
+stoch_simul(order=2,irf=0);
+
+o1 = load('ds1_results','oo_');
+oo1 = o1.oo_.dr;
+oo2 = oo_.dr;
+if any(abs(oo1.ghxx-oo2.ghxx) > 1e-14);error('ds1 with missing variable doesn''t reproduce ds2');end;
+if any(abs(oo1.ghuu-oo2.ghuu) > 1e-14);error('ds1 with missing variable doesn''t reproduce ds2');end;
+if any(abs(oo1.ghxu-oo2.ghxu) > 1e-14);error('ds1 with missing variable doesn''t reproduce ds2');end;
+if any(abs(oo1.ghs2-oo2.ghs2) > 1e-14);error('ds1 with missing variable doesn''t reproduce ds2');end;
\ No newline at end of file