Preprocessor: fix derivation order for “identification” without “stoch_simul”

Also add a regression test.

Closes: preprocessor#40

preprocessor @ b0c819cb

-Subproject commit 1c44baea0575e30416fcf85830f7e3b2156bc874
+Subproject commit b0c819cb03a37716adbbf73aa485993e9b44188b

tests/Makefile.am

@@ -191,6 +191,7 @@ MODFILES = \
 	identification/as2007/as2007_QT.mod \
 	identification/as2007/as2007_QT_equal_autocorr.mod \
 	identification/as2007/as2007_order_1_2_3.mod \
+	identification/as2007/as2007_order3_no_stoch_simul.mod \
 	identification/BrockMirman/BrockMirman.mod \
 	identification/cgg/cgg_criteria_differ.mod \
 	identification/ident_unit_root/ident_unit_root.mod \

tests/identification/as2007/as2007_order3_no_stoch_simul.mod

+% This is a regression test for issue preprocessor#40
+% (“identification” without “stoch_simul”)
+
+%this is the mod file used in replication files of An and Schorfheide (2007)
+% modified to include some obvious and artificial identification failures
+% and to check whether all kronflags are working
+% created by Willi Mutschler (willi@mutschler.eu)
+
+var y R g z c dy p YGR INFL INT;
+varobs y R g z c dy p YGR INFL INT;
+varexo e_r e_g e_z;
+parameters sigr sigg sigz tau phi psi1 psi2 rhor rhog rhoz rrst pist gamst nu cyst dumpy dumpyrhog;
+
+rrst = 1.0000;
+pist = 3.2000;
+gamst= 0.5500;
+tau  = 2.0000; 
+nu   = 0.1000;
+kap  = 0.3300;
+phi  = tau*(1-nu)/nu/kap/exp(pist/400)^2;
+cyst = 0.8500;
+psi1 = 1.5000;
+psi2 = 0.1250;
+rhor = 0.7500;
+rhog = 0.9500;
+rhoz = 0.9000;
+sigr = 0.2;
+sigg = 0.6;
+sigz = 0.3;
+dumpy = 0;
+dumpyrhog = 1;
+
+model;
+#pist2 = exp(pist/400);
+#rrst2 = exp(rrst/400);
+#bet   = 1/rrst2;
+#gst   = 1/cyst;
+#cst   = (1-nu)^(1/tau);
+#yst   = cst*gst;
+1 = exp(-tau*c(+1)+tau*c+R-z(+1)-p(+1));
+(1-nu)/nu/phi/(pist2^2)*(exp(tau*c)-1) = (exp(p)-1)*((1-1/2/nu)*exp(p)+1/2/nu) - bet*(exp(p(+1))-1)*exp(-tau*c(+1)+tau*c+dy(+1)+p(+1));
+exp(c-y) = exp(-g) - phi*pist2^2*gst/2*(exp(p)-1)^2;
+R = rhor*R(-1) + (1-rhor)*psi1*p + (1-rhor)*psi2*(y-g) + sigr*e_r;
+g = dumpyrhog*rhog*g(-1) + sigg*e_g;
+z = rhoz*z(-1) + sigz*e_z;
+YGR = gamst+100*(dy+z);
+INFL = pist+400*p;
+INT = pist+rrst+4*gamst+400*R;
+dy = y - y(-1);
+end;
+
+shocks;
+var e_r = 0.6^2;
+var e_g = 0.5^2;
+var e_z = 0.4^2;
+corr e_r, e_g = 0.3;
+corr e_r, e_z = 0.2;
+corr e_z, e_g = 0.1;
+end;
+
+steady_state_model;
+z=0; g=0; c=0; y=0; p=0; R=0; dy=0;
+YGR=gamst; INFL=pist; INT=pist+rrst+4*gamst;
+end;
+
+estimated_params;
+tau,   2,     1e-5, 10,      gamma_pdf,     2,    0.5; 
+
+%these parameters do not enter the linearized solution
+cyst, 0.85,  1e-5, 0.99999, beta_pdf,      0.85, 0.1;
+sigg, 0.6,   1e-8, 5,     inv_gamma_pdf, 0.4,  4;
+rhoz,  0.9,   1e-5, 0.99999, beta_pdf,      0.66, 0.15;
+corr e_r,e_g, 0.3,   1e-8, 5, inv_gamma_pdf, 0.4,  4;
+corr e_z,e_g, 0.3,   1e-8, 5, inv_gamma_pdf, 0.4,  4;
+corr e_z,e_r, 0.3,   1e-8, 5, inv_gamma_pdf, 0.4,  4;
+
+%these parameters could only be identified from the steady state of YGR INFL and INT, however, we observer y pi R instead
+rrst,  1,     1e-5, 10,      gamma_pdf,     0.8,  0.5;
+gamst, 0.55,  -5,   5,       normal_pdf,    0.4,  0.2;
+dumpy, 0, -10, 10, normal_pdf, 0, 1;
+
+%these parameters jointly determine the slope kappa of the linearized new keynesian phillips curve
+pist,  3.2,   1e-5, 20,      gamma_pdf,     4,    2;
+nu,    0.1,   1e-5, 0.99999, beta_pdf,      0.1,  .05;
+phi,   50,    1e-5, 100,     gamma_pdf,     50,   20;
+
+%these parameters are pairwise collinear as one should not use both formulations for the standard error of a shock
+sigz, 0.3,   1e-8, 5,     inv_gamma_pdf, 0.4,  4;
+stderr e_z, 0.3,   1e-8, 5, inv_gamma_pdf, 0.4,  4;
+
+%these parameters are pairwise collinear as they are multiplicative
+rhog,  0.95,  1e-5, 0.99999, beta_pdf,      0.8,  0.1;
+dumpyrhog, 1, -10, 10, normal_pdf, 1, 1;
+
+%these parameters are jointly not identified due to the specification of the Taylor rule
+psi1,  1.5,   1e-5, 10,      gamma_pdf,     1.5,  0.25;
+psi2,  0.125, 1e-5, 10,      gamma_pdf,     0.5,  0.25;
+rhor,  0.75,  1e-5, 0.99999, beta_pdf,      0.5,  0.2;
+stderr e_r, 0.2,   1e-8, 5, inv_gamma_pdf, 0.3,  4;
+
+end;
+
+steady;
+check;
+
+identification(order=3, parameter_set=calibration, grid_nbr=10);