diff --git a/doc/manual/source/the-model-file.rst b/doc/manual/source/the-model-file.rst
index 86eb7b36a2867284340812824bfa82ff009c8996..4b3e8ee4d6e4376d28939bcfc19428fcc80fdad6 100644
--- a/doc/manual/source/the-model-file.rst
+++ b/doc/manual/source/the-model-file.rst
@@ -11399,6 +11399,14 @@ Optimal Simple Rules (OSR)
future release of Dynare. Use ``optim`` instead to set
optimizer-specific values. Default: ``1e-7``.
+ .. option:: analytic_derivation
+
+ Triggers estimation with analytic gradient of the objective function.
+
+ .. option:: analytic_derivation_mode = INTEGER
+
+ See :opt:analytic_derivation_mode.
+
.. option:: silent_optimizer
See :opt:`silent_optimizer`.
diff --git a/matlab/+osr/objective.m b/matlab/+osr/objective.m
index 3f9306a2916e414b37e34479f9703ba1477ea10c..758d17738068bbdf46af65ce98036e4a265290a2 100644
--- a/matlab/+osr/objective.m
+++ b/matlab/+osr/objective.m
@@ -1,5 +1,6 @@
-function [loss,info,exit_flag,vx,junk]=objective(x,M_, oo_, options_,i_params,i_var,weights)
-% objective function for optimal simple rules (OSR)
+function [loss,info,exit_flag,df,vx]=objective(x,M_, oo_, options_,i_params,i_var,weights)
+% [loss,info,exit_flag,df,vx]=objective(x,M_, oo_, options_,i_params,i_var,weights)
+% Objective function for optimal simple rules (OSR)
% INPUTS
% x vector values of the parameters
% over which to optimize
@@ -14,9 +15,8 @@ function [loss,info,exit_flag,vx,junk]=objective(x,M_, oo_, options_,i_params,i_
% loss scalar loss function returned to solver
% info vector info vector returned by resol
% exit_flag scalar exit flag returned to solver
+% df vectcor Analytic Jacobian
% vx vector variances of the endogenous variables
-% junk empty dummy output for conformable
-% header
%
% SPECIAL REQUIREMENTS
% none
@@ -37,19 +37,18 @@ function [loss,info,exit_flag,vx,junk]=objective(x,M_, oo_, options_,i_params,i_
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
-junk = [];
exit_flag = 1;
vx = [];
-% set parameters of the policiy rule
+df=NaN(length(i_params),1);
+% set parameters of the policy rule
M_.params(i_params) = x;
-% don't change below until the part where the loss function is computed
-[dr,info] = resol(0,M_,options_,oo_);
+[oo_.dr,info] = resol(0,M_,options_,oo_);
if info(1)
if info(1) == 3 || info(1) == 4 || info(1) == 5 || info(1)==6 ||info(1) == 19 ||...
- info(1) == 20 || info(1) == 21 || info(1) == 23 || info(1) == 26 || ...
- info(1) == 81 || info(1) == 84 || info(1) == 85
+ info(1) == 20 || info(1) == 21 || info(1) == 23 || info(1) == 26 || ...
+ info(1) == 81 || info(1) == 84 || info(1) == 85
loss = 1e8;
info(4)=info(2);
return
@@ -60,5 +59,26 @@ if info(1)
end
end
-vx = osr.get_variance_of_endogenous_variables(M_,options_,dr,i_var);
-loss = full(weights(:)'*vx(:));
\ No newline at end of file
+if ~options_.analytic_derivation
+ vx = osr.get_variance_of_endogenous_variables(M_,options_,oo_.dr,i_var);
+ loss = full(weights(:)'*vx(:));
+else
+ totparam_nbr=length(i_params);
+ oo_.dr.derivs = get_perturbation_params_derivs(M_, options_, [], oo_, i_params, [], [], 0); %analytic derivatives of perturbation matrices
+
+ pruned_state_space = pruned_state_space_system(M_, options_, oo_.dr, i_var, 0, 0, 1);
+ vx = pruned_state_space.Var_y + pruned_state_space.E_y*pruned_state_space.E_y';
+ dE_yy = pruned_state_space.dVar_y;
+ for jp=1:length(i_params)
+ dE_yy(:,:,jp) = dE_yy(:,:,jp) + pruned_state_space.dE_y(:,jp)*pruned_state_space.E_y' + pruned_state_space.E_y*pruned_state_space.dE_y(:,jp)';
+ end
+
+ model_moments_params_derivs = reshape(dE_yy,length(i_var)^2,totparam_nbr);
+
+ df = NaN(totparam_nbr,1);
+ loss = full(weights(:)'*vx(:));
+
+ for jp=1:length(i_params)
+ df(jp,1) = sum(weights(:).*model_moments_params_derivs(:,jp));
+ end
+end
\ No newline at end of file
diff --git a/preprocessor b/preprocessor
index bd0ba65a61c0d97e3f537194136e3cdad0f4f3b2..5a2b3e052f3fc5d0fa1379227ee2ab7cdfcd7466 160000
--- a/preprocessor
+++ b/preprocessor
@@ -1 +1 @@
-Subproject commit bd0ba65a61c0d97e3f537194136e3cdad0f4f3b2
+Subproject commit 5a2b3e052f3fc5d0fa1379227ee2ab7cdfcd7466
diff --git a/tests/Makefile.am b/tests/Makefile.am
index 6f5b2ab4a35b86afa3dec4e41849269181a6b736..9aecc2bafedce657eb5660b1e20dde8055ce14d0 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -120,6 +120,7 @@ MODFILES = \
irfs/example1_unit_std.mod \
optimal_policy/OSR/osr_example.mod \
optimal_policy/OSR/osr_example_objective_correctness.mod \
+ optimal_policy/OSR/osr_objective_correctness_anal_deriv.mod \
optimal_policy/OSR/osr_example_obj_corr_non_stat_vars.mod \
optimal_policy/OSR/osr_example_param_bounds.mod \
optimal_policy/OSR/osr_obj_corr_algo_1.mod \
diff --git a/tests/optimal_policy/OSR/osr_example.mod b/tests/optimal_policy/OSR/osr_example.mod
index 538d142f9de8779820b416a16912663cd587b941..d0b3e61ead69f5600348384f10b8795b224a8d31 100644
--- a/tests/optimal_policy/OSR/osr_example.mod
+++ b/tests/optimal_policy/OSR/osr_example.mod
@@ -10,6 +10,12 @@ kappa = 0.18;
alpha = 0.48;
sigma = -0.06;
+gammarr = 0;
+gammax0 = 0.2;
+gammac0 = 1.5;
+gamma_y_ = 8;
+gamma_inf_ = 3;
+
model(linear);
y = delta * y(-1) + (1-delta)*y(+1)+sigma *(r - inflation(+1)) + y_;
@@ -28,14 +34,11 @@ end;
optim_weights;
inflation 1;
y 1;
+y,inflation 0.1;
end;
osr_params gammax0 gammac0 gamma_y_ gamma_inf_;
-gammarr = 0;
-gammax0 = 0.2;
-gammac0 = 1.5;
-gamma_y_ = 8;
-gamma_inf_ = 3;
-
osr;
+osr(analytic_derivation,opt_algo=4);
+osr(analytic_derivation,opt_algo=1,optim=('DerivativeCheck','on','FiniteDifferenceType','central'));
\ No newline at end of file
diff --git a/tests/optimal_policy/OSR/osr_example_objective_correctness.mod b/tests/optimal_policy/OSR/osr_example_objective_correctness.mod
index be67fa10a09f7a1e7c04aad721ac37ad5d6da684..d35ca9fbad085c4e58276d5067abdce1b9ffb664 100644
--- a/tests/optimal_policy/OSR/osr_example_objective_correctness.mod
+++ b/tests/optimal_policy/OSR/osr_example_objective_correctness.mod
@@ -26,7 +26,6 @@ end;
options_.nograph=1;
options_.nocorr=1;
-options_.osr.tolf=1e-20;
osr_params gammax0 gammac0 gamma_y_ gamma_inf_;
@@ -42,7 +41,7 @@ gammac0 = 1.5;
gamma_y_ = 8;
gamma_inf_ = 3;
-osr;
+osr(optim=('TolFun',1e-20));
%compute objective function manually
objective=oo_.var(strmatch('y',M_.endo_names,'exact'),strmatch('y',M_.endo_names,'exact'))+oo_.var(strmatch('inflation',M_.endo_names,'exact'),strmatch('inflation',M_.endo_names,'exact'))+oo_.var(strmatch('dummy_var',M_.endo_names,'exact'),strmatch('dummy_var',M_.endo_names,'exact'));
diff --git a/tests/optimal_policy/OSR/osr_objective_correctness_anal_deriv.mod b/tests/optimal_policy/OSR/osr_objective_correctness_anal_deriv.mod
new file mode 100644
index 0000000000000000000000000000000000000000..1a9b351891a8e7f36752d14557b0cf3fa0ad2924
--- /dev/null
+++ b/tests/optimal_policy/OSR/osr_objective_correctness_anal_deriv.mod
@@ -0,0 +1,109 @@
+// Example of optimal simple rule
+var y inflation r dummy_var;
+varexo y_ inf_;
+
+parameters delta sigma alpha kappa gammax0 gammac0 gamma_y_ gamma_inf_;
+
+delta = 0.44;
+kappa = 0.18;
+alpha = 0.48;
+sigma = -0.06;
+
+
+model(linear);
+y = delta * y(-1) + (1-delta)*y(+1)+sigma *(r - inflation(+1)) + y_;
+inflation = alpha * inflation(-1) + (1-alpha) * inflation(+1) + kappa*y + inf_;
+dummy_var=0.9*dummy_var(-1)+0.01*y;
+r = gammax0*y(-1)+gammac0*inflation(-1)+gamma_y_*y_+gamma_inf_*inf_;
+end;
+
+shocks;
+var y_;
+stderr 0.63;
+var inf_;
+stderr 0.4;
+end;
+
+options_.nograph=1;
+options_.nocorr=1;
+osr_params gammax0 gammac0 gamma_y_ gamma_inf_;
+
+
+optim_weights;
+inflation 1;
+y 1;
+dummy_var 1;
+end;
+
+
+gammax0 = 0.2;
+gammac0 = 1.5;
+gamma_y_ = 8;
+gamma_inf_ = 3;
+
+osr(analytic_derivation,optim=('TolFun',1e-20));
+%compute objective function manually
+objective=oo_.var(strmatch('y',M_.endo_names,'exact'),strmatch('y',M_.endo_names,'exact'))+oo_.var(strmatch('inflation',M_.endo_names,'exact'),strmatch('inflation',M_.endo_names,'exact'))+oo_.var(strmatch('dummy_var',M_.endo_names,'exact'),strmatch('dummy_var',M_.endo_names,'exact'));
+
+if abs(oo_.osr.objective_function-objective)>1e-8
+ error('Objective Function is wrong')
+end
+
+%redo computation with covariance specified
+optim_weights;
+inflation 1;
+y 1;
+dummy_var 1;
+y,inflation 0.5;
+end;
+
+osr(analytic_derivation);
+%compute objective function manually
+objective=oo_.var(strmatch('y',M_.endo_names,'exact'),strmatch('y',M_.endo_names,'exact'))+oo_.var(strmatch('inflation',M_.endo_names,'exact'),strmatch('inflation',M_.endo_names,'exact'))+oo_.var(strmatch('dummy_var',M_.endo_names,'exact'),strmatch('dummy_var',M_.endo_names,'exact'))+0.5*oo_.var(strmatch('y',M_.endo_names,'exact'),strmatch('inflation',M_.endo_names,'exact'));
+if abs(oo_.osr.objective_function-objective)>1e-8
+ error('Objective Function is wrong')
+end
+
+gammax0=1.35533;
+gammac0=1.39664;
+gamma_y_=16.6667;
+gamma_inf_=9.13199;
+
+%redo computation with double weight on one covariance
+optim_weights;
+inflation 1;
+y 1;
+dummy_var 1;
+y,inflation 1;
+end;
+
+osr(analytic_derivation);
+%compute objective function manually
+objective=oo_.var(strmatch('y',M_.endo_names,'exact'),strmatch('y',M_.endo_names,'exact'))+oo_.var(strmatch('inflation',M_.endo_names,'exact'),strmatch('inflation',M_.endo_names,'exact'))+oo_.var(strmatch('dummy_var',M_.endo_names,'exact'),strmatch('dummy_var',M_.endo_names,'exact'))+1*oo_.var(strmatch('y',M_.endo_names,'exact'),strmatch('inflation',M_.endo_names,'exact'));
+if abs(oo_.osr.objective_function-objective)>1e-8
+ error('Objective Function is wrong')
+end
+oo_covar_single=oo_;
+
+%redo computation with single weight on both covariances
+
+optim_weights;
+inflation 1;
+y 1;
+dummy_var 1;
+y,inflation 0.5;
+inflation,y 0.5;
+end;
+
+osr(analytic_derivation);
+%compute objective function manually
+objective=oo_.var(strmatch('y',M_.endo_names,'exact'),strmatch('y',M_.endo_names,'exact'))+oo_.var(strmatch('inflation',M_.endo_names,'exact'),strmatch('inflation',M_.endo_names,'exact'))+oo_.var(strmatch('dummy_var',M_.endo_names,'exact'),strmatch('dummy_var',M_.endo_names,'exact'))+0.5*oo_.var(strmatch('y',M_.endo_names,'exact'),strmatch('inflation',M_.endo_names,'exact'))+0.5*oo_.var(strmatch('inflation',M_.endo_names,'exact'),strmatch('y',M_.endo_names,'exact'));
+if abs(oo_.osr.objective_function-objective)>1e-8
+ error('Objective Function is wrong')
+end
+if abs(oo_.osr.objective_function-oo_covar_single.osr.objective_function)>1e-8
+ error('Objective Function is wrong')
+end
+if max(abs(cell2mat(struct2cell(oo_.osr.optim_params))-cell2mat(struct2cell(oo_covar_single.osr.optim_params))))>1e-5
+ error('Parameters should be identical')
+end