Dear Professor Jpfeifer,

Thank so much for your response. I recently included learning and using Dynare to solve problems in DSGE models in one of the courses that I am teaching at the University. I visited some few Dynare usersâ€™ websites and drafted those questions for the purpose of teaching and learning. Hence, the problem set is actually from a university course designed to learn, teach and understand modelling DSGE models using Dynare.

I have made an effort to answer few questions via simulation. However, I need someone who is an expert to double check the work to ensure that the work is properly done for me. I have few challenges in the process of trying to solve those questions. How is volatility computed in Dynare? How do we identify forward-looking and backward-looking variables in Dynare? Given a loss function, how is welfare function calculated in Dynare? These are very few challenges that I need help. Meanwhile, I tried to calculate welfare function based on the Mod files I downloaded from your link but I encountered further challenges.

Please find attached the progress I have made. Please assist me to calculate welfare function of this economy. Your assistance on this direction will be highly appreciated.

// Declare variables

var y pi i g mu upsilon;

varexo g1 g2 g3;

parameters sigma beta phip omega alpha kappa rho1 rho2 rho3;

//Value of parameters

sigma = 1;

beta = 0.99;

phip = 1.5;

omega = 0.5;

alpha = 3;

kappa = ((1-omega)*(1-beta*omega)/(alpha*omega));

rho1 = 0.3;

rho2 = 0.8;

rho3 = 0.5;

model;

y = y(+1) - (1/sigma)*(i - pi(+1)) + g;*

pi = betapi(+1) + kappa*y + mu;*

i = phippi + upsilon;

g = rho1*g(-1) + g1;*

mu = rho2mu(-1) + g2;

upsilon = rho3*upsilon(-1) + g3;

end;

initval;

y = 0;

pi = 0;

i = 0;

end;

shocks;

var g1; stderr 1;

var g2; stderr 0.5;

var g3; stderr 1;

end;

stoch_simul(linear,irf=20)i,pi,y;

=======================================================================

// Welfare analysis

// Declare variables

var y pi i g mu upsilon;

@#define Ramsey_policy_timeless=1

@#define Ramsey_policy_t0_optimal=0

@#define discretionary_policy=0

varexo g1 g2 g3;

parameters sigma beta phip omega alpha kappa rho1 rho2 rho3;

//Value of parameters

sigma = 1;

beta = 0.99;

phip = 1.5;

omega = 0.5;

alpha = 3;

kappa = ((1-omega)*(1-beta*omega)/(alpha*omega));

rho1 = 0.3;

rho2 = 0.8;

rho3 = 0.5;

model(linear);

y = y(+1) - 1/sigma*(i - pi(+1)) + g;

pi = beta*pi(+1) + kappa*y + mu;

i = phip*pi + upsilon;*

g = rho1g(-1) + g1;

mu = rho2*mu(-1) + g2;*

upsilon = rho3upsilon(-1) + g3;

end;

initval;

y = 0;

pi = 0;

i = 0;

end;

planner_objective(pi^2 + y^2);

ramsey_model(planner_discount=0.99);

steady;

simul(periods=50);

# shocks;

var g1; stderr 1;

var g2; stderr 0.5;

var g3; stderr 1;

end;

Regards,

Maxwell