diff --git a/matlab/backward/dynamic_static_model_for_simulation.m b/matlab/backward/dynamic_static_model_for_simulation.m
new file mode 100644
index 000000000..8ce608333
--- /dev/null
+++ b/matlab/backward/dynamic_static_model_for_simulation.m
@@ -0,0 +1,29 @@
+function [r, J] = dynamic_static_model_for_simulation(z, dynamicmodel, x, params, steady_state, it_)
+
+% Copyright © 2021 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/>.
+
+% NOTE: It is assumed that all variables appear at time t in the model.
+
+if nargout>1
+    % Compute residuals and jacobian of the full dynamic model.
+    [r, J] = feval(dynamicmodel, z, x, params, steady_state, it_);
+    J = J(:,1:rows(J)); % Remove derivatives with respect to shocks.
+else
+    % Compute residuals.
+    r = feval(dynamicmodel, z, x, params, steady_state, it_);
+end
\ No newline at end of file
diff --git a/matlab/perfect-foresight-models/perfect_foresight_solver.m b/matlab/perfect-foresight-models/perfect_foresight_solver.m
index e675b7fec..37bf898f9 100644
--- a/matlab/perfect-foresight-models/perfect_foresight_solver.m
+++ b/matlab/perfect-foresight-models/perfect_foresight_solver.m
@@ -70,14 +70,15 @@ if ~oo_.deterministic_simulation.status && ~options_.no_homotopy
         fprintf('Switching to a homotopy method...\n')
     end
 
-    if ~M_.maximum_lag
+    if ~M_.maximum_lag && M_.maximum_lead>0
         disp('Homotopy not implemented for purely forward models!')
         disp('Failed to solve the model!')
         disp('Return with empty oo_.endo_simul.')
         oo_.endo_simul = [];
         return
     end
-    if ~M_.maximum_lead
+
+    if ~M_.maximum_lead && M_.maximum_lag>0
         disp('Homotopy not implemented for purely backward models!')
         disp('Failed to solve the model!')
         disp('Return with empty oo_.endo_simul.')
@@ -85,6 +86,14 @@ if ~oo_.deterministic_simulation.status && ~options_.no_homotopy
         return
     end
 
+    if ~M_.maximum_lead && ~M_.maximum_lag
+        disp('Homotopy not implemented for purely static models!')
+        disp('Failed to solve the model!')
+        disp('Return with empty oo_.endo_simul.')
+        oo_.endo_simul = [];
+        return
+    end
+
     % Disable warnings if homotopy
     warning_old_state = warning;
     warning off all
diff --git a/matlab/perfect-foresight-models/perfect_foresight_solver_core.m b/matlab/perfect-foresight-models/perfect_foresight_solver_core.m
index 3dac602f6..a1896890e 100644
--- a/matlab/perfect-foresight-models/perfect_foresight_solver_core.m
+++ b/matlab/perfect-foresight-models/perfect_foresight_solver_core.m
@@ -75,12 +75,15 @@ else
             oo_.deterministic_simulation.status = false;
         end
     else
-        if M_.maximum_endo_lead == 0 && ~options_.lmmcp.status % Purely backward model
+        if M_.maximum_endo_lead == 0 && M_.maximum_endo_lag>0 && ~options_.lmmcp.status % Purely backward model
             [oo_.endo_simul, oo_.deterministic_simulation] = ...
                 sim1_purely_backward(oo_.endo_simul, oo_.exo_simul, oo_.steady_state, M_, options_);
-        elseif M_.maximum_endo_lag == 0 && ~options_.lmmcp.status % Purely forward model
-        [oo_.endo_simul, oo_.deterministic_simulation] = ...
-            sim1_purely_forward(oo_.endo_simul, oo_.exo_simul, oo_.steady_state, M_, options_);
+        elseif M_.maximum_endo_lag == 0 && M_.maximum_endo_lead>0 && ~options_.lmmcp.status % Purely forward model
+            [oo_.endo_simul, oo_.deterministic_simulation] = ...
+                sim1_purely_forward(oo_.endo_simul, oo_.exo_simul, oo_.steady_state, M_, options_);
+        elseif M_.maximum_endo_lag == 0 && M_.maximum_endo_lead == 0 && ~options_.lmmcp.status % Purely static model
+            [oo_.endo_simul, oo_.deterministic_simulation] = ...
+                sim1_purely_static(oo_.endo_simul, oo_.exo_simul, oo_.steady_state, M_, options_);
         else % General case
             switch options_.stack_solve_algo
               case 0
diff --git a/matlab/perfect-foresight-models/sim1_purely_backward.m b/matlab/perfect-foresight-models/sim1_purely_backward.m
index 3f155325f..06e5f005c 100644
--- a/matlab/perfect-foresight-models/sim1_purely_backward.m
+++ b/matlab/perfect-foresight-models/sim1_purely_backward.m
@@ -19,15 +19,8 @@ function [endogenousvariables, info] = sim1_purely_backward(endogenousvariables,
 % You should have received a copy of the GNU General Public License
 % along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
 
-if size(M.lead_lag_incidence,1) > 1
-    ny0 = nnz(M.lead_lag_incidence(2,:));    % Number of variables at current period
-    nyb = nnz(M.lead_lag_incidence(1,:));    % Number of variables at previous period
-    iyb = find(M.lead_lag_incidence(1,:)>0); % Indices of variables at previous period
-else
-    ny0 = nnz(M.lead_lag_incidence(1,:));    % Number of variables at current period
-    nyb = 0;
-    iyb = [];
-end
+ny0 = nnz(M.lead_lag_incidence(2,:));    % Number of variables at current period
+iyb = M.lead_lag_incidence(1,:)>0;       % Logical vector (for lagged variables)
 
 if ny0 ~= M.endo_nbr
     error('All endogenous variables must appear at the current period!')
@@ -43,13 +36,8 @@ dynamicmodel_s = str2func('dynamic_backward_model_for_simulation');
 info.status = true;
 
 for it = M.maximum_lag + (1:options.periods)
-    if M.maximum_lag==0 && it==1
-        y = endogenousvariables(:,it);        % Values at previous period, also used as guess value for current period
-        ylag = [];        
-    else
-        y = endogenousvariables(:,it-1);        % Values at previous period, also used as guess value for current period
-        ylag = y(iyb);
-    end
+    y = endogenousvariables(:,it-1);        % Values at previous period, also used as guess value for current period
+    ylag = y(iyb);
     if ismember(options.solve_algo, [12,14])
         [tmp, check] = dynare_solve(dynamicmodel_s, y, options, M.isloggedlhs, M.isauxdiffloggedrhs, M.endo_names, M.lhs, ...
                                     dynamicmodel, ylag, exogenousvariables, M.params, steadystate, it);
diff --git a/matlab/perfect-foresight-models/sim1_purely_static.m b/matlab/perfect-foresight-models/sim1_purely_static.m
new file mode 100644
index 000000000..ec03a848a
--- /dev/null
+++ b/matlab/perfect-foresight-models/sim1_purely_static.m
@@ -0,0 +1,50 @@
+function [endogenousvariables, info] = sim1_purely_static(endogenousvariables, exogenousvariables, steadystate, M, options)
+
+% Performs deterministic simulation of a purely static model
+
+% Copyright © 2021 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/>.
+
+if nnz(M.lead_lag_incidence(1,:)) ~= M.endo_nbr
+    error('All endogenous variables must appear at the current period!')
+end
+
+if ismember(options.solve_algo, [12,14]) && ~M.possible_to_use_solve_algo_12_14
+    error(M.message_solve_algo_12_14)
+end
+
+dynamicmodel = str2func([M.fname,'.dynamic']);
+dynamicmodel_s = str2func('dynamic_static_model_for_simulation');
+
+info.status = true;
+
+y = endogenousvariables(:,1);
+
+for it = 1:options.periods
+    if ismember(options.solve_algo, [12,14])
+        [tmp, check] = dynare_solve(dynamicmodel_s, y, options, M.isloggedlhs, M.isauxdiffloggedrhs, M.endo_names, M.lhs, ...
+                                    dynamicmodel, exogenousvariables, M.params, steadystate, it);
+    else
+        [tmp, check] = dynare_solve(dynamicmodel_s, y, options, ...
+                                    dynamicmodel, exogenousvariables, M.params, steadystate, it);
+    end
+    if check
+        info.status = false;
+    end
+    endogenousvariables(:,it) = tmp;
+    y = endogenousvariables(:,it);
+end
\ No newline at end of file
diff --git a/tests/Makefile.am b/tests/Makefile.am
index 52052c2e2..7f66c697b 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -332,6 +332,7 @@ MODFILES = \
 	deterministic_simulations/purely_forward/ar1.mod \
 	deterministic_simulations/purely_forward/nk.mod \
 	deterministic_simulations/purely_backward/ar1.mod \
+	deterministic_simulations/purely_static/toto.mod \
 	deterministic_simulations/rbc_det1.mod \
 	deterministic_simulations/rbc_det2.mod \
 	deterministic_simulations/rbc_det3.mod \
diff --git a/tests/deterministic_simulations/purely_static/toto.mod b/tests/deterministic_simulations/purely_static/toto.mod
new file mode 100644
index 000000000..21f76c702
--- /dev/null
+++ b/tests/deterministic_simulations/purely_static/toto.mod
@@ -0,0 +1,25 @@
+var x y;
+
+varexo ex ey;
+
+model;
+  y = x*x/2 + ey;
+  x = ex;
+end;
+
+initval;
+  y = 0;
+  x = 0;
+  ex = 0;
+  ey = 0;
+end;
+
+steady;
+
+shocks;
+    var ex;
+    periods 1 2 3 4;
+    values 1 .5 .25 .125;
+end;
+
+simul(periods=4);