Time To Build Ramsey model

Dynare help (legacy posts)
1

Hello, everyone.
Someone please help me.
I’m newbe of dynare and have questions.

I want to simulate time-to-build ramsey model.
In this model, Law of motion of capital is follow;
k(t+1)-k(t)=f(k(t-1))-δk(t-1)
I know this model require two initial value of capital(k(-1)and k(0)), but I don’t know how I express in dynare.

I write a dynare cord of this model,but I have a syntax error in line19 (K = Kstar)
I don’t know why error occured. Please tell me why this cord is wrong.

[code]var C K;
parameters alpha delta beta rho;

alpha = 0.3;
beta = 0.99;
delta = 0.025;
rho = 0.9;

Cstar = ((1 - beta)/(alpha * beta^2)^(alpha/(alpha - 1)) - delta * ((1 - beta)/(alpha * beta^2)^(1/(alpha - 1));
Kstar = ((1 - beta)/(alpha * beta^2)^(1/(alpha - 1));

model;
C^(-1 * rho) = beta * C(+1)^(-1 * rho) + beta^2 * (alpha * K(+1)^(alpha - 1) - delta) * C(+2)^(-1 * rho);
K(+1) - K = K(-1)^(alpha) - delta * K(-1) - C;
end;

inival;
C = Cstar
K = Kstar
end;

steady;

[Cstar; Kstar][/code]

Thank you for your reading.

2
  1. There are several brackets missing.
  2. It should be initval not inival.
  3. Every line needs to end with a semicolon.
3

Thank you for your great help, Mr.jpfeifer.
Thanks to your perfect comment,I was able to simulate this model.

4

someone please help me. I have another problem.

I want to simulate comparative dynamics in this model, but not work.

I want to move the beta and draw a picture which it affects on dynamic path.
So, I redefined beta from “parameters” to “varexo”.
Code is here.

[code]var C K;
varexo beta;
parameters alpha delta rho;

alpha = 0.3;
delta = 0.025;
rho = 0.9;

model;
C^(-1 * rho) = beta * C(+1)^(-1 * rho) + beta^3 * (alpha * K(+1)^(alpha - 1) - delta) * C(+3)^(-1 * rho);
K(+1) - K = K(-2)^(alpha) - delta * K(-2) - C;
end;

Cstar = ((1 - beta)/(alpha * beta^3)+(delta / alpha))^(alpha/(alpha - 1)) - delta * ((1 - beta)/(alpha * beta^3)+(delta / alpha))^(1/(alpha - 1));
Kstar = ((1 - beta)/(alpha * beta^3)+(delta / alpha))^(1/(alpha - 1));

initval;
C = 10;
K = 100;
beta = 0.99;
end;

endval;
C = Cstar;
K = Kstar;
beta = 0.99;
end;

steady;

shocks;
var beta;
periods 5:45;
values 0.95;
end;

simul(periods=50);

rplot C;
rplot K;
[/code]

5

Always provide the error message you are experiencing. I can run your model with the current Dynare unstable.

6

Thank you for your comment.
I’ll be careful.
The problem is resolved in my own.
Thank you.

7

I simulate another model of time to build.
Simulation doesn’t work well.

please help me.

[code]var C K M pi;
parameters alpha delta beta g gamma;

alpha = 0.3;
beta = 0.99;
delta = 0.025;
g=1.01;
gamma = 0.8;

model;
C^(-1) = beta * C(+1)^(-1) + (beta^3) * (alpha * K(+1)^(alpha - 1) - delta) * C(+3)^(-1);
beta * gamma * M^(-1) = pi(-1)*C(-1)^(-1) - beta * C^(-1);
K(+1) - K = K(-2)^(alpha) - delta * K(-2) - C;
M(+1) = (g/pi(+1)) * M;
end;

Cstar = ((1 - beta)/(alpha * beta^3) + (delta / alpha))^(alpha/(alpha - 1)) - delta * ((1 - beta)/(alpha * beta^3) + (delta / alpha))^(1/(alpha - 1));
Kstar = ((1 - beta)/(alpha * beta^3) + (delta / alpha))^(1/(alpha - 1));
pistar = g;
Mstar = gamma * beta/(g - beta)*((1 - beta)/(alpha * beta^3) + (delta / alpha))^(alpha/(alpha - 1)) - delta * ((1 - beta)/(alpha * beta^3) + (delta / alpha))^(1/(alpha - 1));

initval;
C = 1;
K = 1;
M = 1;
pi = 1.01;
end;

endval;
C = 1.97038;
K = 21.2584;
M = 78.0252;
pi = 1.01;
end;

steady;

simul(periods = 5);

rplot C;
rplot K;
rplot M;
rplot pi;

[/code]

Error message is follow;

error: SIMUL: error in model specification : variable pi doesn’t appear as current variable.

If you need additional information to solve this problem, please reply here.

Thank you.

8

You need to check your model. If inflation does not appear within the current period, there must be something wrong.

9

Thanks for your comment.
I could able to simulate this model, but another problem occur.

I simulate time to build ramsey model.
But,I have another question.
I used check command and I verify the linearized model has some complex number of eigenvalues.
So optimal path should be oscillate.
I could able to simulate this model without error, but optimal path isn’t oscillate.
My scenario is following;
going to steady state from initial value of C and K are 1.

I check my dynare code over ten times, but I was not able to why it occurs.

dynare code is here

var C K;
parameters alpha beta delta rho;

alpha = 0.3;
beta = 0.99;
delta = 0.025;
rho = 0.9;


model;
C^(-1 * rho) = beta * C(+1)^(-1 * rho) + beta^7 * (alpha * K(+1)^(alpha - 1) - delta) * C(+7)^(-1 * rho);
K = K(-1) + K(-6)^(alpha) - delta * K(-6) - C(-1);
end;

initval;
C = 1;
K = 1;
end;

endval;
C = 1.96661;
K = 20.9;
end;

steady;

check;

simul(periods = 30);

rplot C;
rplot K;

dynatype(ram);

and result file is attachment.
X2 means if X(t+1)>X(t), return 1
X(t+1)<X(t), return -1
X(t+1)=X(t), return 0
GOX is growth rate of X.
(X is a variable name)

Thank you for your reading.
lagram.txt (1.74 KB)
ram.txt (1.83 KB)

10

Complex eigenvalues do not automatically mean oscillations. Actually, some complex generalized eigenvalues are common in DSGE models.

11

Thank you.
I found some mistake in my model, and some problems are resolved.