Document irf_calibration and moment_calibration in the context of estimation

Also adds unit test. Closes #1318

doc/dynare.texi

@@ -5081,8 +5081,6 @@ univariate convergence diagnostic.
 The inefficiency factors are computed as in @cite{Giordano et al. (2011)} based on 
 Parzen windows as in e.g. @cite{Andrews (1991)}.
 
-based on Parzen 
-
 @optionshead
 
 @table @code
@@ -6300,6 +6298,16 @@ all parameters. Note that if @code{mode_compute=6} is used or the @code{posterio
 called @code{scale_file} is specified, the values set in @code{estimated_params}
 will be overwritten.
 
+@customhead{``Endogenous'' prior restrictions}
+
+It is also possible to impose implicit ``endogenous'' priors about IRFs and moments on the model during 
+estimation. For example, one can specify that all valid parameter draws for the model must generate fiscal multipliers that are
+bigger than 1 by specifying how the IRF to a government spending shock must look like. The prior restrictions can be imposed
+via @code{irf_calibration} and @code{moment_calibration} blocks (@pxref{IRF/Moment calibration}). The way it works internally is that 
+any parameter draw that is inconsistent with the ``calibration'' provided in these blocks is discarded, i.e. assigned a prior density of 0. 
+When specifying these blocks, it is important to keep in mind that one won't be able to easily do @code{model_comparison} in this case, 
+because the prior density will not integrate to 1.
+
 @outputhead
 
 @vindex M_.params
@@ -8418,6 +8426,12 @@ Maximum number of lags for moments in identification analysis. Default: @code{1}
 @node IRF/Moment calibration
 @subsection IRF/Moment calibration
 
+The @code{irf_calibration} and @code{moment_calibration} blocks allow imposing implicit ``endogenous'' priors 
+about IRFs and moments on the model. The way it works internally is that 
+any parameter draw that is inconsistent with the ``calibration'' provided in these blocks is discarded, i.e. assigned a prior density of 0. 
+In the context of @code{dynare_sensitivity}, these restrictions allow tracing out which parameters are driving the model to
+satisfy or violate the given restrictions.
+
 IRF and moment calibration can be defined in @code{irf_calibration} and @code{moment_calibration} blocks:
 
 @deffn Block irf_calibration ;

tests/Makefile.am

@@ -32,6 +32,7 @@ MODFILES = \
 	estimation/fs2000_calibrated_covariance.mod \
 	estimation/fs2000_model_comparison.mod \
 	estimation/fs2000_fast.mod \
+	estimation/ls2003_endog_prior_restrict_estimation.mod \
 	estimation/independent_mh/fs2000_independent_mh.mod \
 	estimation/MH_recover/fs2000_recover.mod \
 	estimation/MH_recover/fs2000_recover_2.mod \

tests/estimation/ls2003_endog_prior_restrict_estimation.mod

@@ -0,0 +1,85 @@
+//conducts estimation with an "endogenous" prior restriction specified via irf_calibration and moment_calibration
+
+var y y_s R pie dq pie_s de A y_obs pie_obs R_obs;
+varexo e_R e_q e_ys e_pies e_A;
+
+parameters psi1 psi2 psi3 rho_R tau alpha rr k rho_q rho_A rho_ys rho_pies;
+
+psi1 = 1.54;
+psi2 = 0.25;
+psi3 = 0.25;
+rho_R = 0.5;
+alpha = 0.3;
+rr = 2.51;
+k = 0.5;
+tau = 0.5;
+rho_q = 0.4;
+rho_A = 0.2;
+rho_ys = 0.9;
+rho_pies = 0.7;
+
+
+model(linear);
+y = y(+1) - (tau +alpha*(2-alpha)*(1-tau))*(R-pie(+1))-alpha*(tau +alpha*(2-alpha)*(1-tau))*dq(+1) + alpha*(2-alpha)*((1-tau)/tau)*(y_s-y_s(+1))-A(+1);
+pie = exp(-rr/400)*pie(+1)+alpha*exp(-rr/400)*dq(+1)-alpha*dq+(k/(tau+alpha*(2-alpha)*(1-tau)))*y+k*alpha*(2-alpha)*(1-tau)/(tau*(tau+alpha*(2-alpha)*(1-tau)))*y_s;
+pie = de+(1-alpha)*dq+pie_s;
+R = rho_R*R(-1)+(1-rho_R)*(psi1*pie+psi2*(y+alpha*(2-alpha)*((1-tau)/tau)*y_s)+psi3*de)+e_R;
+dq = rho_q*dq(-1)+e_q;
+y_s = rho_ys*y_s(-1)+e_ys;
+pie_s = rho_pies*pie_s(-1)+e_pies;
+A = rho_A*A(-1)+e_A;
+y_obs = y-y(-1)+A;
+pie_obs = 4*pie;
+R_obs = 4*R;
+end;
+
+shocks;
+	var e_R = 1.25^2;
+	var e_q = 2.5^2;
+	var e_A = 1.89;
+	var e_ys = 1.89;
+	var e_pies = 1.89;
+end;
+
+varobs y_obs R_obs pie_obs dq de;
+
+estimated_params;
+psi1 , gamma_pdf,1.5,0.5;
+psi2 , gamma_pdf,0.25,0.125;
+psi3 , gamma_pdf,0.25,0.125;
+rho_R ,beta_pdf,0.5,0.2;
+alpha ,beta_pdf,0.3,0.1;
+rr ,gamma_pdf,2.5,1;
+k , gamma_pdf,0.5,0.25;
+tau ,gamma_pdf,0.5,0.2;
+rho_q ,beta_pdf,0.4,0.2;
+rho_A ,beta_pdf,0.5,0.2;
+rho_ys ,beta_pdf,0.8,0.1;
+rho_pies,beta_pdf,0.7,0.15;
+stderr e_R,inv_gamma_pdf,(1.2533/3),(0.6551/10);
+stderr e_q,inv_gamma_pdf,(2.5066/3),(1.3103/10);
+stderr e_A,inv_gamma_pdf,(1.2533/3),(0.6551/10);
+stderr e_ys,inv_gamma_pdf,(1.2533/3),(0.6551/10);
+stderr e_pies,inv_gamma_pdf,(1.88/3),(0.9827/10);
+end;
+
+// endogenous prior restrictions
+irf_calibration(relative_irf);
+y(1:4), e_ys, [ -50 50]; //[first year response]
+@#for ilag in 21:40
+R_obs(@{ilag}), e_ys, [0 6]; //[response after 4th year to 10th year]
+@#endfor
+end;
+
+moment_calibration;
+y_obs,y_obs(-(1:4)), +; //[first year acf]
+@#for ilag in -2:2
+y_obs,R_obs(@{ilag}), -; //[ccf]
+@#endfor
+@#for ilag in -4:4
+y_obs,pie_obs(@{ilag}), -; //[ccf]
+@#endfor
+end;
+
+estimation(datafile='../gsa/data_ca1.m',mode_check,first_obs=8,nobs=79,mh_nblocks=1,
+  prefilter=1,mh_jscale=0.0005,mh_replic=5000, mode_compute=4, mh_drop=0.6, bayesian_irf,mcmc_jumping_covariance='identity_matrix') R_obs y;