Added specialized code for the inversion of backward models.
Stéphane Adjemian (Charybdis)
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function [endogenousvariables, exogenousvariables] = backward_model_inversion(constraints, exogenousvariables, initialconditions, endo_names, exo_names, freeinnovations, DynareModel, DynareOptions, DynareOutput)
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% INPUTS
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% - constraints [dseries] with N constrained endogenous variables from t1 to t2.
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% - exogenousvariables [dseries] with Q exogenous variables.
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% - initialconditions [dseries] with M endogenous variables starting before t1 (M initialcond must contain at least the state variables).
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% - endo_names [cell] list of endogenous variable names.
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% - exo_names [cell] list of exogenous variable names.
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% - freeinstruments [cell] list of exogenous variable names used to control the constrained endogenous variables.
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%
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% OUTPUTS
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% - endogenous [dseries]
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% - exogenous [dseries]
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%
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% REMARKS
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% Copyright (C) 2017 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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% Get indices for the calibrated and free innovations.
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freeinnovations_id = zeros(length(freeinnovations), 1);
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if length(freeinnovations)<DynareModel.exo_nbr
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for i=1:length(freeinnovations)
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freeinnovations_id(i) = strmatch(freeinnovations{i}, exo_names, 'exact');
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end
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calibratedinnovations_id = setdiff(transpose(1:length(exo_names)), freeinnovations_id);
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else
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freeinnovations_id = transpose(1:length(exo_names));
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calibratedinnovations_id = [];
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end
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nxfree = length(freeinnovations_id);
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nxcalb = length(calibratedinnovations_id);
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% Get indices for the the controlled and free endogenous variables.
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controlledendogenousvariables_id = zeros(length(freeinnovations), 1);
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if length(freeinnovations)<DynareModel.endo_nbr
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for i=1:length(freeinnovations)
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controlledendogenousvariables_id(i) = strmatch(constraints.name{i}, endo_names, 'exact');
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end
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freeendogenousvariables_id = setdiff(transpose(1:length(endo_names)), controlledendogenousvariables_id);
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else
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controlledendogenousvariables_id = transpose(1:length(endo_names));
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freeendogenousvariables_id = [];
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end
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nyfree = length(freeendogenousvariables_id);
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nyctrl = length(controlledendogenousvariables_id);
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% Get indices of variables appearing at time t-1.
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iy1 = find(DynareModel.lead_lag_incidence(1,:)>0);
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% Get indices of variables appearing at time t.
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iy0 = find(DynareModel.lead_lag_incidence(2,:)>0);
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% Set indices for trust_region algorithm.
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idx = 1:DynareModel.endo_nbr;
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jdx = 1:(nyfree+nxfree);
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% Build structure to be passed to the objective function.
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ModelInversion.nyfree = nyfree;
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ModelInversion.nyctrl = nyctrl;
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ModelInversion.nxfree = nxfree;
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ModelInversion.nxcalb = nxcalb;
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ModelInversion.y_constrained_id = vec(DynareModel.lead_lag_incidence(2,controlledendogenousvariables_id));
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ModelInversion.y_free_id = vec(DynareModel.lead_lag_incidence(2,freeendogenousvariables_id));
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ModelInversion.x_free_id = freeinnovations_id;
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ModelInversion.J_id = [ModelInversion.y_free_id ; sum(DynareModel.lead_lag_incidence(:)>0)+ModelInversion.x_free_id];
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% Get the name of the dynamic model routines.
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model_dynamic = str2func([DynareModel.fname,'_dynamic']);
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model_dtransf = str2func('dynamic_model_for_inversion');
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% Initialization of vector y (free endogenous variables and free innovations).
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y = NaN(nyfree+nxfree);
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% Initialization of the returned simulations (endogenous variables).
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Y = NaN(DynareModel.endo_nbr, nobs(constraints)+1);
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initialconditions
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constraints.dates(1)
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Y(:,1) = initialconditions(constraints.dates(1)-1).data(1:DynareModel.endo_nbr);
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for i=1:nyctrl
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Y(controlledendogenousvariables_id(i),2:end) = transpose(constraints.data(:,i));
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end
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% Initialization of the returned simulations (exogenous variables).
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X = exogenousvariables{exo_names{:}}.data;
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% Inversion of the model, solvers for the free endogenous and exogenous variables (call a Newton-like algorithm in each period).
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for it = 2:nobs(constraints)+1
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% Set the lagged values of the endogenous variables.
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ylag = Y(iy1,it-1);
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% Set the current values of the constrained endogenous variables.
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ycur = Y(controlledendogenousvariables_id,it);
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% Vector z gather the free endogenous variables (initialized with lagged
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% values) and the free exogenous variables (initialized with 0).
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z = [Y(freeendogenousvariables_id,it-1); zeros(nxfree, 1)];
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% Solves for z.
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z = dynare_solve(model_dtransf, z, DynareOptions, model_dynamic, ylag, ycur, X, DynareModel.params, DynareOutput.steady_state, it, ModelInversion);
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% Update the matrix of exogenous variables.
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X(it,freeinnovations_id) = z(nyfree+1:end);
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% Update the matrix of endogenous variables.
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Y(freeendogenousvariables_id,it) = z(1:nyfree);
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end
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endogenousvariables = dseries(Y', constraints.dates(1)-1, endo_names);
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exogenousvariables = dseries(X(2:end,:), constraints.dates(1), exo_names);
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@ -0,0 +1,39 @@
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function [r, J] = dynamic_model_for_inversion(z, dynamicmodel, ylag, ycur, x, params, steady_state, it_, ModelInversion)
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% Copyright (C) 2017 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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% Set up y
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y = zeros(length(ylag)+ModelInversion.nyfree+ModelInversion.nyctrl,1);
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y(1:length(ylag)) = ylag;
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y(ModelInversion.y_constrained_id) = ycur;
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if ModelInversion.nyfree
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y(ModelInversion.y_free_id) = z(1:ModelInversion.nyfree);
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end
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% Update x
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x(it_, ModelInversion.x_free_id) = transpose(z(ModelInversion.nyfree+(1:ModelInversion.nxfree)));
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if nargout>1
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[r, Jacobian] = feval(dynamicmodel, y, x, params, steady_state, it_);
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else
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r = feval(dynamicmodel, y, x, params, steady_state, it_);
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return
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end
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J = Jacobian(:,ModelInversion.J_id);
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@ -1,12 +1,13 @@
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function [endogenousvariables, exogenousvariables] = model_inversion(constraints, exogenousvariables, initialconditions, DynareModel)
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global oo_
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function [endogenousvariables, exogenousvariables] = model_inversion(constraints, ...
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exogenousvariables, ...
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initialconditions, DynareModel, DynareOptions, DynareOutput)
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% INPUTS
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% - constraints [dseries] with N constrained endogenous variables from t1 to t2.
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% - exogenousvariables [dseries] with Q exogenous variables.
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% - initialconditions [dseries] with M endogenous variables starting before t1 (M initialcond must contain at least the state variables).
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% - DynareModel [struct] M_, Dynare global structure containing informations related to the model.
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% - DynareOptions [struct] options_, Dynare global structure containing all the options.
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%
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% OUTPUTS
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% - endogenous [dseries]
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@ -31,7 +32,7 @@ global oo_
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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 ~isequal(nargin, 4)
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if ~isequal(nargin, 6)
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error('model_inversion: This routine require six input arguments!')
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end
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@ -71,6 +72,15 @@ end
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endo_names = cellstr(DynareModel.endo_names);
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exo_names = cellstr(DynareModel.exo_names);
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% Use specidalized routine if the model is backward looking.
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if ~DynareModel.maximum_lead
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[endogenousvariables, exogenousvariables] = ...
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backward_model_inversion(constraints, exogenousvariables, initialconditions, ...
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endo_names, exo_names, freeinnovations, ...
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DynareModel, DynareOptions, DynareOutput);
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return
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end
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% Initialize fplan
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fplan = init_plan(crange);
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@ -93,10 +103,4 @@ end
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f = det_cond_forecast(fplan, initialconditions, crange);
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endogenousvariables = f{endo_names{:}};
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exogenousvariables = f{exo_names{:}};
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%if observed_exogenous_variables_flag
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% for i=1:length(list_of_observed_exogenous_variables)
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% exogenousvariables{list_of_observed_exogenous_variables{i}} = observed_exogenous_variables{list_of_observed_exogenous_variables{i}};
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% end
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%end
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exogenousvariables = f{exo_names{:}};
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