Dynare forums

Hello,
I have a problem. I get different forecasts for the same model and I do not know why. They only differ in the way, the consumption tax is introduced (mathematically, it is equivalent):

In model 1, I use the expression (e_c+t) in all equations.
In model 2, I use the expression t_c in all equations. t_c is later defined as e_c+t.

Model 1 (wrong forecasts):

Code: Select all

%----------------------------------------------------------------
% 1. Defining variables
%----------------------------------------------------------------

var  w d k n y x c z t s;
varexo_det e_c;
varexo e;

parameters beta alpha delta phi rho;

%----------------------------------------------------------------
% 2. Calibration
%----------------------------------------------------------------

phi    = 0.38;
beta   = 0.99;
delta  = 0.0175;
alpha  = 0.319;
rho    = 0.95;

%----------------------------------------------------------------
% 3. Model
%----------------------------------------------------------------

model;
// Household 
((1-alpha)/alpha)*(c/(1-n)) = w/(1+e_c+t);         /*consumption-leisure tradeoff*/
  alpha*c^(-1)/(1+e_c+t) = beta*(alpha*(c(+1))^(-1)*(1+d(+1)-delta))/(1+e_c(+1)+t(+1));  /*Euler equation*/
  (1+e_c+t)*c + x = s + n*w + d*k(-1);          /*budget constraint*/
  k = k(-1)*(1-delta) + x;             /*capital accumulation*/

// Firm
  y = exp(z)*(k(-1)^phi)*n^(1-phi);
  w = (1-phi)*y/n;
  d = phi*y/k(-1);

// Government
  t = 0.2;
  s = (e_c+t)*c;  /*Tax revenues from consumption taxation are redistributed through transfers s */


// Shocks (not important)
  z = rho*z(-1) + e;

end;



%----------------------------------------------------------------
% 4. Computation
%----------------------------------------------------------------

initval;
  w = 3.09316;
  d = 0.027601;
  k = 16.6054;
  n = 0.241758;
  y = 1.20612;
  x = 0.290595;
  c = 0.915528;
  z = 0;
  t = 0.2;
  s = 0.183106;
 end;

shocks;
 var e = 0;
 var e_c;
 periods 21:500;
 values -0.01;
end;

steady;

stoch_simul(periods = 501, order = 1);
forecast;

Model 2 (right forecasts):

Code: Select all

%----------------------------------------------------------------
% 1. Defining variables
%----------------------------------------------------------------

var  w d k n y x c z  t s t_c;
varexo_det e_c;
varexo e;

parameters beta alpha delta phi rho;

%----------------------------------------------------------------
% 2. Calibration
%----------------------------------------------------------------

phi    = 0.38;
beta   = 0.99;
delta  = 0.0175;
alpha  = 0.319;
rho    = 0.95;

%----------------------------------------------------------------
% 3. Model
%----------------------------------------------------------------

model;
// Household 
((1-alpha)/alpha)*(c/(1-n)) = w/(1+t_c);         /*consumption-leisure tradeoff*/
  alpha*c^(-1)/(1+t_c) = beta*(alpha*(c(+1))^(-1)*(1+d(+1)-delta))/(1+t_c(+1));  /*Euler equation*/
  (1+t_c)*c + x = s + n*w + d*k(-1);          /*budget constraint*/
  k = k(-1)*(1-delta) + x;             /*capital accumulation*/

// Firm
  y = exp(z)*(k(-1)^phi)*n^(1-phi);
  w = (1-phi)*y/n;
  d = phi*y/k(-1);

// Government
  t_c = t + e_c; /*t_c is defined as in model 1*/
     t = 0.2;
    s = t_c*c; /*Tax revenues from consumption taxation are redistributed through transfers s */

// Shocks (not important)
  z = rho*z(-1) + e;

end;



%----------------------------------------------------------------
% 4. Computation
%----------------------------------------------------------------

initval;
 w = 3.09316;
  d = 0.027601;
  k = 16.6054;
  n = 0.241758;
  y = 1.20612;
  x = 0.290595;
  c = 0.915528;
  z = 0;
  t = 0.2;
  s = 0.183106;
 end;

shocks;
 var e = 0;
 var e_c;
 periods 21:500;
 values -0.01;
end;

steady;

stoch_simul(periods = 501, order = 1);
forecast;

Does anyone know why Dynare computes different forecasts?

I am thankful for any help,

best regards,

Niklas