Added one variable (LM) and one equation to ensure that the Lagrange multiplier is positive.

It appeared that the Lagrange  multiplier simulated by EP is positive,
but the series simulated by SEP are most of the time negative.

tests/ep/rbcii.mod

-@#define extended_path_version = 1
+@#define extended_path_version = 0
 
-var Capital, Output, Labour, Consumption, Efficiency, efficiency, ExpectedTerm, LagrangeMultiplier;
+var Capital, Output, Labour, Consumption, Efficiency, efficiency, ExpectedTerm, LM, LagrangeMultiplier;
 
 varexo EfficiencyInnovation;
 
@@ -50,8 +50,11 @@ model(block,bytecode,cutoff=0);
 
   // Eq. n°7:
   (Capital==(1-delta)*Capital(-1))*(Output-Consumption) + (1-(Capital==(1-delta)*Capital(-1)))*LagrangeMultiplier = 0;
-  
+
   // Eq. n°8:
+  (LM<0)*(LM+LagrangeMultiplier) + (1-(LM<0))*(LM-LagrangeMultiplier) = 0;
+  
+  // Eq. n°9:
   ExpectedTerm = beta*(((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)*(alpha*((Output/Capital(-1))^(1-psi))+(1-delta))-(1-delta)*LagrangeMultiplier);
 
 end;

tests/ep/rbcii_steadystate.m

@@ -38,12 +38,11 @@ SteadyStateCapital=SteadyStateLabour/Labour_per_unit_of_Capital;
 SteadyStateOutput=Output_per_unit_of_Capital*SteadyStateCapital;
 
 % Fill returned argument ys with steady state values.
-ys(2)=SteadyStateOutput;
-ys(4)=SteadyStateConsumption;
+ys = zeros(9,1);
 ys(1)=SteadyStateCapital;
+ys(2)=SteadyStateOutput;
 ys(3)=SteadyStateLabour;
+ys(4)=SteadyStateConsumption;
 ys(5)=M_.params(8);
-ys(6)=0;
 ys(7)=M_.params(1)*((((SteadyStateConsumption^M_.params(2))*((1-SteadyStateLabour)^(1-M_.params(2))))^(1-M_.params(3)))/SteadyStateConsumption)* ...
-      (M_.params(4)*((SteadyStateOutput/SteadyStateCapital)^(1-M_.params(5)))+1-M_.params(6));
-ys(8)=0;
\ No newline at end of file
+      (M_.params(4)*((SteadyStateOutput/SteadyStateCapital)^(1-M_.params(5)))+1-M_.params(6));
\ No newline at end of file