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function [endogenousvariables, exogenousvariables] = static_model_inversion(constraints, exogenousvariables, endo_names, exo_names, freeinnovations, M_, options_, oo_)
% [endogenousvariables, exogenousvariables] = static_model_inversion(constraints, exogenousvariables, endo_names, exo_names, freeinnovations, M_, options_, oo_)
% INPUTS
% - constraints [dseries] with N constrained endogenous variables from t1 to t2.
% - exogenousvariables [dseries] with Q exogenous variables.
% - endo_names [cell] list of endogenous variable names.
% - exo_names [cell] list of exogenous variable names.
% - freeinstruments [cell] list of exogenous variable names used to control the constrained endogenous variables.
% - M_ [structure] Definition of the model
% - options_ [structure] Options
% - oo_ [structure] Storage of results
%
% OUTPUTS
% - endogenous [dseries]
% - exogenous [dseries]
%
% REMARKS
% Copyright © 2019-2023 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
% Get indices for the free innovations.
freeinnovations_id = zeros(length(freeinnovations), 1);
if length(freeinnovations)<M_.exo_nbr
for i=1:length(freeinnovations)
freeinnovations_id(i) = find(strcmp(freeinnovations{i}, exo_names));
end
else
freeinnovations_id = transpose(1:length(exo_names));
end
nxfree = length(freeinnovations_id);
% Get indices for the the controlled and free endogenous variables.
controlledendogenousvariables_id = zeros(length(freeinnovations), 1);
if length(freeinnovations)<M_.endo_nbr
for i=1:length(freeinnovations)
controlledendogenousvariables_id(i) = find(strcmp(constraints.name{i}, endo_names));
end
freeendogenousvariables_id = setdiff(transpose(1:length(endo_names)), controlledendogenousvariables_id);
else
controlledendogenousvariables_id = transpose(1:length(endo_names));
freeendogenousvariables_id = [];
end
nyfree = length(freeendogenousvariables_id);
nyctrl = length(controlledendogenousvariables_id);
% Build structure to be passed to the objective function.
ModelInversion.nyfree = nyfree;
ModelInversion.nyctrl = nyctrl;
ModelInversion.nxfree = nxfree;
ModelInversion.y_constrained_id = controlledendogenousvariables_id;
ModelInversion.y_free_id = freeendogenousvariables_id;
ModelInversion.x_free_id = freeinnovations_id;
ModelInversion.J_id = [M_.endo_nbr+ModelInversion.y_free_id ; 3*M_.endo_nbr+ModelInversion.x_free_id];
% Get function handles to the dynamic model routines.
dynamic_resid = str2func([M_.fname '.sparse.dynamic_resid']);
dynamic_g1 = str2func([M_.fname '.sparse.dynamic_g1']);
% Initialization of the returned simulations (endogenous variables).
Y = NaN(M_.endo_nbr, nobs(constraints));
for i=1:nyctrl
Y(controlledendogenousvariables_id(i),1:end) = transpose(constraints.data(:,i));
end
% Exogenous variables.
X = exogenousvariables.data;
% Inversion of the model, solvers for the free endogenous and exogenous variables (call a Newton-like algorithm in each period).
ity = 1;
itx = find(exogenousvariables.dates==constraints.dates(1));
options_.solve_algo=4;
for t = 1:nobs(constraints)
% Set the current values of the constrained endogenous variables.
ycur = Y(controlledendogenousvariables_id,ity);
% Vector z gather the free endogenous variables (initialized with lagged
% values) and the free exogenous variables (initialized with 0).
z = [Y(freeendogenousvariables_id,ity); zeros(nxfree, 1)];
% Solves for z.
[z, errorflag, ~, ~, errorcode] = dynare_solve(@static_model_for_inversion, z, options_.simul.maxit, options_.dynatol.f, options_.dynatol.x, ...
options_, dynamic_resid, dynamic_g1, ycur, X(itx, :), M_.params, oo_.steady_state, M_.dynamic_g1_sparse_rowval, M_.dynamic_g1_sparse_colval, M_.dynamic_g1_sparse_colptr, ModelInversion);
if errorflag
error('Enable to solve the system of equations (with error code %i).', errorcode)
end
% Update the matrix of exogenous variables.
X(itx,freeinnovations_id) = z(nyfree+(1:nxfree));
% Update the matrix of endogenous variables.
if nyfree
Y(freeendogenousvariables_id,ity) = z(1:nyfree);
end
% Increment counters
ity = ity+1;
itx = itx+1;
end
endogenousvariables = dseries(Y', constraints.dates(1), endo_names);
exogenousvariables = dseries(X(find(exogenousvariables.dates==constraints.dates(1))+(0:(nobs(constraints)-1)),:), constraints.dates(1), exo_names);
function [r, J] = static_model_for_inversion(z, dynamic_resid, dynamic_g1, ycur, x, params, steady_state, sparse_rowval, sparse_colval, sparse_colptr, ModelInversion)
endo_nbr = ModelInversion.nyfree+ModelInversion.nyctrl;
% Set up y
y = NaN(3*endo_nbr, 1);
y(endo_nbr+ModelInversion.y_constrained_id) = ycur;
if ModelInversion.nyfree
y(endo_nbr+ModelInversion.y_free_id) = z(1:ModelInversion.nyfree);
end
% Update x
x(ModelInversion.x_free_id) = z(ModelInversion.nyfree+(1:ModelInversion.nxfree));
[r, T_order, T] = dynamic_resid(y, x, params, steady_state);
if nargout>1
Jacobian = dynamic_g1(y, x, params, steady_state, sparse_rowval, ...
sparse_colval, sparse_colptr, T_order, T);
J = Jacobian(:, ModelInversion.J_id);
end
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