Added test mod file for the extended path approach (with steady state file and a routine computing

the mean preserving spread correction): Real Business Cycle model with endogenous labour and CES
production function.

tests/ep/mean_preserving_spread.m

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+function m = mean_preserving_spread(autoregressive_parameter)
+% Computes the mean preserving spread for first order autoregressive process.
+%
+% The mean preserving spread m is a constant such that the mean of the process
+%
+%   X_t = X^{\star} * e^{x_t - m}
+%   x_t = \rho x_{t-1} + \varepsilon_t
+%   \varepsilon_t \sim N(0,\sigma^2)
+%
+% is X^{\star}. This constant is such that the unconditional expectation of X_t is equal
+% to the deterministic steady state of X_t
+%
+% AUTHOR(S) 
+%  stephane DOT adjemian AT univ DASH lemans DOT fr
+%  frederic DOT karame AT univ DASH evry DOT fr
+global M_
+
+m = M_.Sigma_e/(1-autoregressive_parameter*autoregressive_parameter);

tests/ep/rbc.mod

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+var Capital, Output, Labour, Consumption, Efficiency, efficiency;
+
+varexo EfficiencyInnovation;
+
+parameters beta, theta, tau, alpha, psi, delta, rho, effstar, sigma2;
+
+/*
+** Calibration
+*/
+
+
+beta    =  0.990;
+theta   =  0.357;
+tau     =  2.000;
+alpha   =  0.450;
+psi     = -0.500;
+delta   =  0.020;
+rho     =  0.950;
+effstar =  1.000;
+sigma2  =  0.001;
+
+external_function(name=mean_preserving_spread);
+
+model(block,bytecode);
+
+  // Eq. n°1:
+  efficiency = rho*efficiency(-1) + EfficiencyInnovation;
+
+  // Eq. n°2:
+  Efficiency = effstar*exp(efficiency-mean_preserving_spread(rho));
+
+  // Eq. n°3:
+  Output = Efficiency*(alpha*(Capital(-1)^psi)+(1-alpha)*(Labour^psi))^(1/psi);
+
+  // Eq. n°4:
+  Consumption + Capital - Output - (1-delta)*Capital(-1);
+
+  // Eq. n°5:
+  ((1-theta)/theta)*(Consumption/(1-Labour)) - (1-alpha)*(Output/Labour)^(1-psi);
+
+  // Eq. n°6:
+  (((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption - beta*((((Consumption(1)^theta)*((1-Labour(1))^(1-theta)))^(1-tau))/Consumption(1))*(alpha*((Output(1)/Capital)^(1-psi))+1-delta);
+
+end;
+
+shocks;
+var EfficiencyInnovation = sigma2;
+end;
+
+steady;
+
+ts = extended_path([],100);

tests/ep/rbc_steadystate.m

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+function [ys, info] = rbc_steadystate(ys, exogenous)
+% Steady state routine for rbc.mod (Business Cycle model with endogenous labour and CES production function)
+
+
+% AUTHOR(S) 
+%  stephane DOT adjemian AT univ DASH lemans DOT fr
+%  frederic DOT karame AT univ DASH evry DOT fr    
+
+% Output_per_unit_of_Capital = (((1/beta)-1+delta)/alpha)^(1/(1-psi));
+% Consumption_per_unit_of_Capital = Output_per_unit_of_Capital - delta;
+% Labour_per_unit_of_Capital = (((Output_per_unit_of_Capital/effstar)^psi-alpha)/(1-alpha))^(1/psi);
+% Output_per_unit_of_Labour = Output_per_unit_of_Capital/Labour_per_unit_of_Capital;
+% Consumption_per_unit_of_Labour = Consumption_per_unit_of_Capital/Labour_per_unit_of_Capital;
+% SteadyStateLabour = 1/(1 + Consumption_per_unit_of_Labour/((theta*(1-alpha)/(1-theta))*(Output_per_unit_of_Labour^(1-psi))));
+% SteadyStateConsumption = Consumption_per_unit_of_Labour*SteadyStateLabour;
+% SteadyStateCapital = SteadyStateLabour/Labour_per_unit_of_Capital;
+% SteadyStateOutput =  Output_per_unit_of_Capital*SteadyStateCapital;
+% ShareOfCapital = alpha/(alpha+(1-alpha)*Labour_per_unit_of_Capital^psi);
+    
+global M_
+    
+info = 0;
+
+% Compute steady state ratios.
+Output_per_unit_of_Capital=((1/M_.params(1)-1+M_.params(6))/M_.params(4))^(1/(1-M_.params(5)));
+Consumption_per_unit_of_Capital=Output_per_unit_of_Capital-M_.params(6);
+Labour_per_unit_of_Capital=(((Output_per_unit_of_Capital/M_.params(8))^M_.params(5)-M_.params(4))/(1-M_.params(4)))^(1/M_.params(5));
+Output_per_unit_of_Labour=Output_per_unit_of_Capital/Labour_per_unit_of_Capital;
+Consumption_per_unit_of_Labour=Consumption_per_unit_of_Capital/Labour_per_unit_of_Capital;
+
+% Compute steady state share of capital.
+ShareOfCapital=M_.params(4)/(M_.params(4)+(1-M_.params(4))*Labour_per_unit_of_Capital^M_.params(5));
+
+% Compute steady state of the endogenous variables.
+SteadyStateLabour=1/(1+Consumption_per_unit_of_Labour/((1-M_.params(4))*M_.params(2)/(1-M_.params(2))*Output_per_unit_of_Labour^(1-M_.params(5))));
+SteadyStateConsumption=Consumption_per_unit_of_Labour*SteadyStateLabour;
+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(1)=SteadyStateCapital;
+ys(3)=SteadyStateLabour;
+ys(5)=M_.params(8);
+ys(6)=0;