Modify companion matrix if VAR model has a constant.

matlab/get_companion_matrix.m

@@ -42,7 +42,8 @@ if nargin < 2
 end
 
 if strcmp(auxiliary_model_type, 'var')
-    [AR, ~] = feval(sprintf('%s.varmatrices', M_.fname), auxiliary_model_name, M_.params, M_.var.(auxiliary_model_name).structural);
+    [AR, ~, Constant] = feval(sprintf('%s.varmatrices', M_.fname), auxiliary_model_name, M_.params, M_.var.(auxiliary_model_name).structural);
+    isconstant = any(abs(Constant)>0);
 elseif strcmp(auxiliary_model_type, 'trend_component')
     [AR, A0, A0star] = feval(sprintf('%s.trend_component_ar_a0', M_.fname), auxiliary_model_name, M_.params);
 else
@@ -57,11 +58,17 @@ n = length(M_.(auxiliary_model_type).(auxiliary_model_name).lhs);
 
 switch auxiliary_model_type
   case 'var'
-    oo_.var.(auxiliary_model_name).CompanionMatrix = zeros(n*p);
-    oo_.var.(auxiliary_model_name).CompanionMatrix(1:n,1:n) = AR(:,:,1);
+    oo_.var.(auxiliary_model_name).CompanionMatrix = zeros(n*p+isconstant);
+    oo_.var.(auxiliary_model_name).CompanionMatrix(isconstant+(1:n),isconstant+(1:n)) = AR(:,:,1);
     for i = 2:p
-        oo_.var.(auxiliary_model_name).CompanionMatrix(1:n,(i-1)*n+(1:n)) = AR(:,:,i);
-        oo_.var.(auxiliary_model_name).CompanionMatrix((i-1)*n+(1:n),(i-2)*n+(1:n)) = eye(n);
+        oo_.var.(auxiliary_model_name).CompanionMatrix(isconstant+(1:n),isconstant+(i-1)*n+(1:n)) = AR(:,:,i);
+        oo_.var.(auxiliary_model_name).CompanionMatrix(isconstant+(i-1)*n+(1:n),isconstant+(i-2)*n+(1:n)) = eye(n);
+    end
+    if isconstant
+        oo_.var.(auxiliary_model_name).CompanionMatrix(1,1) = 1;
+        for i=1:n
+            oo_.var.(auxiliary_model_name).CompanionMatrix(1+i,1) = Constant(i);
+        end
     end
     M_.var.(auxiliary_model_name).list_of_variables_in_companion_var = M_.endo_names(M_.var.(auxiliary_model_name).lhs);
     if nargout

preprocessor @ e1f7d8c7

-Subproject commit 15d7432105578c749cd5a81b2ab09fe8bf01d1b7
+Subproject commit e1f7d8c73556398a774ab55c8dc578c79ebb6c3b

tests/var-expectations/11/example1.mod

@@ -21,16 +21,17 @@ var_expectation_model(model_name = varexp, expression = diff(log(x)), auxiliary_
 
 model;
 [ name = 'X' ]
-diff(log(x)) = b*diff(z) + a*diff(log(x(-1))) + (1-a)*diff(log(x(-2))) + c*diff(z(-2)) + e_x;
+diff(log(x)) = b*diff(z) + a*diff(log(x(-1))) + b*(1-a)*diff(log(x(-2))) + c*diff(z(-2)) + e_x;
 [ name = 'Z' ]
-diff(z) = f*(diff(z(-1))-diff(log(x)))+c*diff(z(-2)) + e_z;
+diff(z) = .1 + f*(diff(z(-1))-diff(log(x)))+c*diff(z(-2)) + e_z;
 [ name = 'Y' ]
 log(y) = diff(log(x)) + d*log(y(-2)) + e*diff(z(-1)) + e_y;
 
 foo = var_expectation(varexp);
 end;
 
-[ar, a0] = example1.varmatrices('toto', M_.params);
+% Evaluate strutural VAR matrices
+[ar, a0, const] = example1.varmatrices('toto', M_.params);
 
 assert(isequal(diag(a0), ones(3,1)), 'Diagonal of a0 is wrong.')
 
@@ -41,6 +42,19 @@ assert(a0(2,3)==0, 'Element (2,3) in A0 is wrong.')
 assert(a0(3,1)==f, 'Element (3,1) in A0 is wrong.')
 assert(a0(3,2)==0, 'Element (3,1) in A0 is wrong.')
 
-assert(isequal(ar(:,:,1), [a 0 0; 0 0 e; 0 0 f]), 'First autoregressive matrix is wrong');
-assert(isequal(ar(:,:,2), [1-a 0 c; 0 d 0; 0 0 c]), 'Second autoregressive matrix is wrong');
+assert(isequal(ar(:,:,1), [a 0 0; 0 0 e; 0 0 f]), 'First autoregressive matrix is wrong')
+assert(isequal(ar(:,:,2), [(1-a)*b 0 c; 0 d 0; 0 0 c]), 'Second autoregressive matrix is wrong')
 
+assert(isequal(const, [.0;.0;.1]), 'Constant vector is wrong.')
+
+% Evaluate reduced form VAR matrices
+[AR, ~, CONST] = example1.varmatrices('toto', M_.params, true);
+
+assert(all(all(abs(AR(:,:,1)-a0\ar(:,:,1))<1e-9)), 'Reduced form is wrong (first lag)')
+assert(all(all(abs(AR(:,:,2)-a0\ar(:,:,2))<1e-9)), 'Reduced form is wrong (second lag)')
+assert(all(abs(CONST-a0\const)<1e-9), 'Reduced form is wrong (constant)')
+
+% Test get_companion_matrix when the VAR model has a constant.
+get_companion_matrix('toto', 'var');
+
+assert(all(all(abs(oo_.var.toto.CompanionMatrix-[1, zeros(1, 6); CONST, AR(:,:,1), AR(:,:,2); zeros(3,1), eye(3), zeros(3)])<1e-9)), 'Companion matrix is wrong')