Oo_.mean of an exogenous shock is larger than its steady state

I’m trying to compute the unconditional welfare. However, it turned out that the stochastic mean of unconditional welfare is larger than its deterministic steady state. Then I found something more strange.

In the mod file fabur.mod (753 Bytes)
, an exogenous shock VarPhi follows the rule
log(VarPhi) = (1-0.9)*log(1) + 0.9*log(VarPhi(-1)) + Eps_phi;
Here are four strange things…

  • The steady state of VarPhi is 1, while in oo_.mean the value is 1.026.
  • After I changed + Eps_phi into - Eps_phi, the result was the same.
  • After I changed the rule into VarPhi = (1-0.9)*log(1) + 0.9*VarPhi(-1) - Eps_phi where the steady state is zero now, oo_.mean is still larger than zero.
  • After I raised the variance of Eps_phi, oo_.mean got even larger.

Anyone can explain the above facts? Or how can I fix it?
fabur.mod (753 Bytes)

Your shock process is log-normally distribution. The mean of a lognormal distribution is e^{0+\frac{1}{2}\sigma^2}. That explains the mean shift relative to the steady state of 1.
That mean shift in exogenous processes is often not desired. See e.g. Level specification of exogenous shock

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Thank you so much, Professor Pfeifer!