diff --git a/matlab/model_inversion.m b/matlab/model_inversion.m
index 8560568b0..f67288cc1 100644
--- a/matlab/model_inversion.m
+++ b/matlab/model_inversion.m
@@ -15,7 +15,7 @@ function [endogenousvariables, exogenousvariables] = model_inversion(constraints
 %
 % REMARKS
 
-% Copyright (C) 2018 Dynare Team
+% Copyright (C) 2018-2019 Dynare Team
 %
 % This file is part of Dynare.
 %
@@ -44,7 +44,7 @@ if ~isdseries(exogenousvariables)
     error('model_inversion: Second input argument must be a dseries object!')
 end
 
-if ~isdseries(initialconditions)
+if ~isempty(initialconditions) && ~isdseries(initialconditions)
     error('model_inversion: Third input argument must be a dseries object!')
 end
 
@@ -68,8 +68,10 @@ if exogenousvariables.vobs>constraints.vobs
     observed_exogenous_variables_flag = true;
 end
 
-% Add auxiliary variables in initialconditions object.
-[initialconditions, info] = checkdatabase(initialconditions, DynareModel, true, false);
+if DynareModel.maximum_lag
+    % Add auxiliary variables in initialconditions object.
+    initialconditions = checkdatabase(initialconditions, DynareModel, true, false);
+end
 
 % Get the list of endogenous and exogenous variables.
 endo_names = DynareModel.endo_names;
@@ -77,10 +79,17 @@ exo_names = DynareModel.exo_names;
 
 % Use specidalized routine if the model is backward looking.
 if ~DynareModel.maximum_lead
-    [endogenousvariables, exogenousvariables] = ...
-        backward_model_inversion(constraints, exogenousvariables, initialconditions, ...
-                                 endo_names, exo_names, freeinnovations, ...
-                                 DynareModel, DynareOptions, DynareOutput);
+    if DynareModel.maximum_lag
+        [endogenousvariables, exogenousvariables] = ...
+            backward_model_inversion(constraints, exogenousvariables, initialconditions, ...
+                                     endo_names, exo_names, freeinnovations, ...
+                                     DynareModel, DynareOptions, DynareOutput);
+    else
+        [endogenousvariables, exogenousvariables] = ...
+            static_model_inversion(constraints, exogenousvariables, ...
+                                     endo_names, exo_names, freeinnovations, ...
+                                     DynareModel, DynareOptions, DynareOutput);
+    end
     return
 end
 
diff --git a/matlab/static_model_for_inversion.m b/matlab/static_model_for_inversion.m
new file mode 100644
index 000000000..9e3ba56bb
--- /dev/null
+++ b/matlab/static_model_for_inversion.m
@@ -0,0 +1,38 @@
+function [r, J] = static_model_for_inversion(z, dynamicmodel, ycur, x, params, ModelInversion)
+
+% Copyright (C) 2019 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 <http://www.gnu.org/licenses/>.
+
+% Set up y
+y = zeros(ModelInversion.nyfree+ModelInversion.nyctrl, 1);
+
+y(ModelInversion.y_constrained_id) = ycur;
+if ModelInversion.nyfree
+    y(ModelInversion.y_free_id) = z(1:ModelInversion.nyfree);
+end
+
+% Update x
+x(ModelInversion.x_free_id) = z(ModelInversion.nyfree+(1:ModelInversion.nxfree));
+
+if nargout>1
+    [r, Jacobian] = feval(dynamicmodel, y, x, params, [], 1);
+else
+    r = feval(dynamicmodel, y, x, params, [], 1);
+    return
+end
+
+J = Jacobian(:,ModelInversion.J_id);
diff --git a/matlab/static_model_inversion.m b/matlab/static_model_inversion.m
new file mode 100644
index 000000000..e47d05f29
--- /dev/null
+++ b/matlab/static_model_inversion.m
@@ -0,0 +1,122 @@
+function [endogenousvariables, exogenousvariables] = static_model_inversion(constraints, exogenousvariables, endo_names, exo_names, freeinnovations, DynareModel, DynareOptions, ~)
+
+% 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.
+%
+% OUTPUTS
+% - endogenous          [dseries]
+% - exogenous           [dseries]
+%
+% REMARKS
+
+% Copyright (C) 2019 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 <http://www.gnu.org/licenses/>.
+
+% Get indices for the calibrated and free innovations.
+freeinnovations_id = zeros(length(freeinnovations), 1);
+if length(freeinnovations)<DynareModel.exo_nbr
+    for i=1:length(freeinnovations)
+        freeinnovations_id(i) = find(strcmp(freeinnovations{i}, exo_names));
+    end
+    calibratedinnovations_id = setdiff(transpose(1:length(exo_names)), freeinnovations_id);
+else
+    freeinnovations_id = transpose(1:length(exo_names));
+    calibratedinnovations_id = [];
+end
+
+nxfree = length(freeinnovations_id);
+nxcalb = length(calibratedinnovations_id);
+
+% Get indices for the the controlled and free endogenous variables.
+controlledendogenousvariables_id = zeros(length(freeinnovations), 1);
+if length(freeinnovations)<DynareModel.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);
+
+% Get indices of variables appearing at time t-1.
+% should be empty. iy1 = find(DynareModel.lead_lag_incidence(1,:)>0);
+
+% Get indices of variables appearing at time t.
+% all variables appear at time t in a static model. iy0 = find(DynareModel.lead_lag_incidence(2,:)>0);
+
+% Build structure to be passed to the objective function.
+ModelInversion.nyfree = nyfree;
+ModelInversion.nyctrl = nyctrl;
+ModelInversion.nxfree = nxfree;
+ModelInversion.nxcalb = nxcalb;
+ModelInversion.y_constrained_id = vec(DynareModel.lead_lag_incidence(controlledendogenousvariables_id));
+ModelInversion.y_free_id = vec(DynareModel.lead_lag_incidence(freeendogenousvariables_id));
+ModelInversion.x_free_id = freeinnovations_id;
+ModelInversion.J_id = [ModelInversion.y_free_id ; sum(DynareModel.lead_lag_incidence(:)>0)+ModelInversion.x_free_id];
+
+% Get the name of the dynamic model routines.
+model_dynamic = str2func([DynareModel.fname,'.dynamic']);
+model_stransf = str2func('static_model_for_inversion');
+
+% Initialization of the returned simulations (endogenous variables).
+Y = NaN(DynareModel.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));
+DynareOptions.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, failed] = dynare_solve(model_stransf, z, DynareOptions, model_dynamic, ycur, X(itx, :), DynareModel.params, ModelInversion);
+    if failed
+        error('Enable to solve the system of equations!')
+    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);
\ No newline at end of file