Add display of theoretical moments at order=3 with pruning
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@ -3817,7 +3817,8 @@ Computing the stochastic solution
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:mvar:`oo_.conditional_variance_decomposition_ME`). The
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variance decomposition is only conducted, if theoretical
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moments are requested, *i.e.* using the ``periods=0``-option.
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In case of ``order=2``, Dynare provides a second-order accurate
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Only available at ``order<3``. In case of ``order=2``,
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Dynare provides a second-order accurate
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approximation to the true second moments based on the linear
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terms of the second-order solution (see *Kim, Kim,
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Schaumburg and Sims (2008)*). Note that the unconditional
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@ -4013,9 +4014,10 @@ Computing the stochastic solution
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|br| After a run of ``stoch_simul``, contains the
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variance-covariance of the endogenous variables. Contains
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theoretical variance if the ``periods`` option is not present (or
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an approximation thereof for ``order=2``), and simulated variance
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otherwise. The variables are arranged in declaration order.
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theoretical variance if the ``periods`` option is not present and simulated variance
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otherwise. Only available for ``order<4``. At ``order=2`` it will be be
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a second-order accurate approximation. At ``order=3``, theoretical moments
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are only available with ``pruning``. The variables are arranged in declaration order.
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.. matvar:: oo_.var_list
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@ -4042,9 +4044,10 @@ Computing the stochastic solution
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number of the matrix in the cell array corresponds to the order of
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autocorrelation. The option ar specifies the number of
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autocorrelation matrices available. Contains theoretical
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autocorrelations if the ``periods`` option is not present (or an
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approximation thereof for ``order=2``), and simulated
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autocorrelations otherwise. The field is only created if
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autocorrelations if the ``periods`` option is not present and simulated
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autocorrelations otherwise. Only available for ``order<4``. At ``order=2`` it will be be
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a second-order accurate approximation. At ``order=3``, theoretical moments
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are only available with ``pruning``. The field is only created if
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stationary variables are present.
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The element ``oo_.autocorr{i}(k,l)`` is equal to the correlation
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@ -4082,9 +4085,10 @@ Computing the stochastic solution
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If a second order approximation has been requested,
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contains the vector of the mean correction terms.
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In case ``order=2``, the theoretical second moments are a
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second order accurate approximation of the true second
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moments, see conditional_variance_decomposition.
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Only available at ``order<4``. In case ``order=2``, the
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theoretical second moments are a second order accurate
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approximation of the true second moments. See conditional_variance_decomposition.
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At ``order=3``, theoretical moments are only available with ``pruning``.
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.. matvar:: oo_.variance_decomposition
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@ -4152,8 +4156,10 @@ Computing the stochastic solution
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|br| After a run of ``stoch_simul`` with the
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``contemporaneous_correlation option``, contains theoretical
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contemporaneous correlations if the ``periods`` option is not
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present (or an approximation thereof for ``order=2``), and
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simulated contemporaneous correlations otherwise. The variables
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present, and simulated contemporaneous correlations otherwise.
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Only available for ``order<4``. At ``order=2`` it will be be
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a second-order accurate approximation. At ``order=3``, theoretical moments
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are only available with ``pruning``. The variables
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are arranged in declaration order.
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.. matvar:: oo_.SpectralDensity
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@ -0,0 +1,126 @@
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function oo_=disp_th_moments_order3(dr,M_,options_,i_var,oo_)
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% oo_=disp_th_moments_order3(dr,M_,options_,i_var,oo_)
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% Display theoretical moments of variables based on (third order) pruned
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% state-space
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%
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% INPUTS:
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% dr : Dynare decision rules structure
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% M_ : Matlab's structure describing the Model (initialized by dynare, see @ref{M_}).
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% options_ : Matlab's structure describing the options (initialized by dynare, see @ref{options_}).
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% i_var : Index of requested variables in declaration order
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% oo_ : Matlab's structure describing the Model (initialized by dynare, see @ref{M_}), containing
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%
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% OUTPUTS:
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% oo_ : Matlab's structure describing the Model (initialized by dynare, see @ref{M_}), containing
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% gamma_y [cell] Matlab cell of nar+1 arrays, where nar is the order of the autocorrelation function.
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% gamma_y{1} [double] Covariance matrix.
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% gamma_y{i+1} [double] Autocorrelation function (for i=1,...,options_.ar).
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% mean [vector] Unconditional mean
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% var [matrix] Unconditional covariance matrix
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% autocorr [cell] Cell storing the theoretical autocorrelation
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% contemporaneous_correlation [matrix] matrix of contemporaneous correlations
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%
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% Copyright (C) 2020 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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if options_.one_sided_hp_filter || options_.hp_filter || options_.bandpass.indicator
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error(['disp_th_moments:: theoretical moments incompatible with filtering. Use simulated moments instead'])
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end
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nvars=length(i_var);
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obs_var=NaN(nvars,1);
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for i=1:nvars
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obs_var(i,1) = find(strcmp(M_.endo_names(i_var(i),:), M_.endo_names(dr.order_var)));
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end
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pruned_state_space = pruned_state_space_system(M_, options_, dr, obs_var, options_.ar, 1, 0);
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m = pruned_state_space.E_y;
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oo_.gamma_y{1} = pruned_state_space.Var_y;
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i1 = find(abs(diag(oo_.gamma_y{1})) > 1e-12);
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s2 = diag(oo_.gamma_y{1});
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sd = sqrt(s2);
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z = [ m sd s2 ];
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oo_.mean = m;
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oo_.var = oo_.gamma_y{1};
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if ~options_.noprint %options_.nomoments == 0
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title='THEORETICAL MOMENTS BASED ON PRUNED STATE SPACE';
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headers={'VARIABLE','MEAN','STD. DEV.','VARIANCE'};
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labels = M_.endo_names(i_var,:);
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lh = cellofchararraymaxlength(labels)+2;
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dyntable(options_,title,headers,labels,z,lh,11,4);
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if options_.TeX
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labels = M_.endo_names_tex(i_var,:);
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lh = cellofchararraymaxlength(labels)+2;
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dyn_latex_table(M_,options_,title,'th_moments',headers,labels,z,lh,11,4);
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end
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end
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if isempty(i1)
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disp_verbose(' ',~options_.noprint)
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disp_verbose('All endogenous are constant or non stationary, not displaying correlations and auto-correlations',~options_.noprint)
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disp_verbose(' ',~options_.noprint)
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return;
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end
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if options_.nocorr == 0 % && size(stationary_vars, 1) > 0
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corr=pruned_state_space.Corr_y;
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if options_.contemporaneous_correlation
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oo_.contemporaneous_correlation = corr;
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end
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if ~options_.noprint
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skipline()
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title='MATRIX OF CORRELATIONS BASED ON PRUNED STATE SPACE';
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labels = M_.endo_names(i_var,:);
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headers = ['Variables';labels];
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lh = cellofchararraymaxlength(labels)+2;
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dyntable(options_,title,headers,labels,corr,lh,8,4);
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if options_.TeX
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labels = M_.endo_names_tex(i_var,:);
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headers=['Variables';labels];
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lh = cellofchararraymaxlength(labels)+2;
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dyn_latex_table(M_,options_,title,'th_corr_matrix',headers,labels,corr,lh,8,4);
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end
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end
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end
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if options_.ar > 0 %&& size(stationary_vars, 1) > 0
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z=NaN(length(i1),options_.ar);
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for i=1:options_.ar
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oo_.gamma_y{i+1} = pruned_state_space.Corr_yi(:,:,i);
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oo_.autocorr{i} = oo_.gamma_y{i+1};
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z(:,i) = diag(oo_.gamma_y{i+1}(i1,i1));
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end
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if ~options_.noprint
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skipline()
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title='COEFFICIENTS OF AUTOCORRELATION BASED ON PRUNED STATE SPACE';
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labels = M_.endo_names(i_var(i1),:);
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headers = ['Order ';cellstr(int2str([1:options_.ar]'))];
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lh = cellofchararraymaxlength(labels)+2;
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dyntable(options_,title,headers,labels,z,lh,8,4);
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if options_.TeX
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labels = M_.endo_names_tex(i_var(i1),:);
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lh = cellofchararraymaxlength(labels)+2;
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dyn_latex_table(M_,options_,title,'th_autocorr_matrix',headers,labels,z,lh,8,4);
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end
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end
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end
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@ -189,9 +189,11 @@ if ~options_.nomoments
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if PI_PCL_solver
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PCL_Part_info_moments(0, PCL_varobs, oo_.dr, i_var);
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elseif options_.periods == 0
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% There is no code for theoretical moments at 3rd order
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if options_.order <= 2
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oo_=disp_th_moments(oo_.dr,var_list,M_,options_,oo_);
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elseif options_.order == 3 && options_.pruning
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% There is no code for theoretical moments at 3rd order without pruning
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oo_=disp_th_moments_order3(oo_.dr,M_,options_,i_var,oo_);
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end
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else
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oo_=disp_moments(oo_.endo_simul,var_list,M_,options_,oo_);
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@ -116,6 +116,6 @@ options_.solve_tolf=1E-12;
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steady(solve_algo=3);
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check;
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stoch_simul(order=3,pruning,irf=0,nocorr,nofunctions,nomoments) C I Y H r D K lambda phi;
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stoch_simul(order=3,pruning,irf=0,nofunctions,contemporaneous_correlation,TeX) C I Y H r D K lambda phi;
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comparison_policy_functions_dynare_mathematica;
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