# Initial value as arbitrary point

Hi all,

I want to investigate the shape of the transition from an arbitrary initial point, different from the steady state, but I still get a jump in the variables as if there was a shock going on. I don’t want to shock the system, I just want to see the smooth transition to the ss without any jumps.

For that purpose, I remove the “steady” command after the “initval” block but still get unwanted jumps in the simulation. I quote from the User Guide: “…if you wanted to begin your soulution path from an arbitrary point, you would enter those values in your initival block, followed by the command steady…”

I paste the short code below:

var k Q c m;

varexo pop;

parameters alpha mu beta;
alpha=0.3;
// eta=0.04;
mu=0.8;
beta=0.9;

model;
(pop/c)=beta*((pop/c(+1))(1+alphak^(alpha-1))-popmualphak^(alpha-1)/c(+1));
(1/c)=beta
((1/Q)+(1/c(+1)));
k=k(-1)^(alpha)+k(-1)-c-m;
Q=Q(-1)+pop*(m-mu*k(-1)^(alpha));
end;

initval;
pop=1; // 2 IS THE VALUE FOR POPULATION FOR WHICH Q_RSS IS BELOW THE THRESHOLD AND IT’S STABLE, GIVEN THE PARAMETER VALUES WE ASSIGNED. WE CAN MAKE A NICE GRAPH OUT OF THIS.
k=0.5;
Q=1.4;
c=((1-mu)^(1/(1-alpha)))*((beta/(1-beta))*alpha)^(alpha/(1-alpha));
m=k^(alpha)-c;
end;

// Check that this is indeed the steady state

// Check the Blanchard-Kahn conditions
/* check;

endval;
pop=1;
k=((beta/(1-beta))(alpha(1-mu)))^(1/(1-alpha));
c=((1-mu)^(1/(1-alpha)))((beta/(1-beta))alpha)^(alpha/(1-alpha));
Q=(beta/(1-beta))
((1-mu)^(1/(1-alpha)))
((beta/(1-beta))*alpha)^(alpha/(1-alpha));
m=k^(alpha)-c;
end;