Interpretation of shocks

var logdv_Y;
parameters sig_Z rho_Z;
varexo eps_Z;

sig_Z = 0.01;
rho_Z = 0.5;

logdv_Y = logdv_Z + logdv_L;
logdv_Z = rho_Z*logdv_Z(-1) + sig_Z*eps_Z; //shock process

var eps_Z; stderr 1;

I have all my structural equations in log-linearized form (log-deviations). So let’s say I want to see the effect of a 0.01 standard deviation tech shock (I just simplified the system of equations just to show the interaction between Y and Z).


0.009935 for the effect of esp_Z on logdv_Y, can I interpret as

“a percent shock to technology brings about a 0.0099% increase in output”? I am trying to see if I can interpret “one standard deviation shock” as “one percent shock” if the equations are log-linearized, and how the coefficient should be interpreted accordingly.

I am not sure I understand.

  1. The effect of a shock is the coefficient on eps_Z, not the lag of logdv_Z
  2. If logdv_Z is in logs, then a one-percent shock happens when sig_Z*eps_Z=0.01. If logdv_Y is also in logs, its IRF will be the percent response of Y to a one percent shock to Z.

My mistake, so yes I meant to say the coefficient on eps_Z in the policy function is 0.009935. So a percent shock to Z will create a 0.009935% increase in Y? Is this the right way to interpret?

Usually, that is correct.