Question about correction/constant

I have a question about the correction term in my second order approximation. I have a model with stochastic volatility that I am trying to approximate. The model has an error term that is being multiplied by an endogenous variable. The endogenous variable follows a log AR(1) process with a shock. When I use the approximation in Dynare, I find that changing the variance of the shock to the AR(1) process does not change the correction term. When I calculate the correction term on my own, I find that the correction term changes as the variance changes. Am I making a mistake in my coding in Dynare, or is the result I am getting correct in Dynare? (It’s entirely possible that my calculation is correct.)

I have attached a mod file with a simplified version of my code. The “sig” variable is allowed to change over time when there are shocks to “u.” When I change the variance of “u” (in line 27) I don’t find that the correction term (and therefore the constant) for the approximation to “y” does not change like when I calculate this on my own. In this case, with var u=2, by my calculation the correction should be 1.4923 instead of 0.206612. I am wondering if I have a problem in my coding in the .mod file or if this is a type of model that isn’t supported by Dynare or if this is indeed correct and my calculation is incorrect. Any help is appreciated.

Thanks in advance
simplesv.mod (371 Bytes)

Has anyone had a chance to look at this? Any input is appreciated. Thanks.

Could you tell me how you computed the supposed outcome?