Moments

[Daniel Bendel]

Dear all Users,

just a short question:

dynare gives me the results of the moments of the model, such as the variance etc.
Is the variance and the standard deviation in percent or do I have to multiply the given number with 100 to get percentage values?

Many greetings,
Daniel

[jpfeifer]

You are confusing something here. The moments are given in model units. If you perform a linearization and not a log-linearization, everything will be in absolute values. Say output is measured in apples and you get a standard deviation of 0.01 this means it fluctuates by 0.01 apples. Now if you did a log-linearization instead, everything will be in log units. So 0.01 output standard deviation would mean 0.01 log units and thus approximately 1%.

This is the short answer. The longer story is that most people use first order approximations, where the solution is invariant to the shock size. If you specify a log process for TFP

Code: Select all

z=rho*z(-1)+eps_z;

and want to set the standard deviation of TFP to 1%, the correct specification would be 0.01 log points;

Code: Select all

shocks;
var eps_z; stderr 0.01;
end;


This will be correct for all orders of approximation. Say this shock size leads to an output variance of 1%. If you perform a log-linearization, this will show up as a variance of 0.01 log points.

But at first order, due to certainty equivalence, you can also say

Code: Select all

shocks;
var epsz; stderr 1;
end;


and interpret this as 1 percent. This change in variance will scale up everything by 100: Output variance will be now 1 log point. But if you interpret everything in percent, this is still correct. A 1% standard deviation TFP shock leads to an output variance of 1%. You just change the interpretation of the numbers. However, at higher orders, this will be wrong due to certainty equivalence not holding.

[Daniel Bendel]

Ah, okay, thanks again for your help!!!