Stochastic steady state and deterministic steady state

Dear all,

I estimate a DSGE model with a second moment shock. To solve the model, I use DYNARE and I apply a third-odder approximation. As the later moves the endogenous variables away from their deterministic steady states (DSS), I compute the IRFs by shutting off all shocks until the stochastic steady state (SSS) is reached, and then, IRFs are expressed as the percent deviation from the SSS.

During a talk, someone asks me a question about the discrepancy between the DSS and the SSS. According to her, the larger the difference between the DSS and SSS is, the higher is the “role” played by the uncertainty shock in the economic system. In my simulation, I find that the two are actually very close. Furthermore, the initial guess I provide to DYNARE is the true DSS of the endogenous variables.

Is there really a problem if my SSS and my DSS are very close? If yes, is there some “threshold” indicating that the influence of the volatility shock is significant?

Thank in advance, and sorry, if my questions are unclear. Actually, this little bit technical question

The comment you received is not true in full generality, because it is neither necessary nor sufficient for the SSS and DSS to be close for having big uncertainty effects.

The discrepancy between DSS and SSS reflects the general amount of uncertainty as measured by the shock variances and the nonlinearity of the model.
First the sufficiency case: You can have cases where the level shock has a high variance and the model is strongly nonlinear, while the volatility shock has almost 0 variance. In this case DSS and SSS will be quite far apart. But the volatility shock will not matter, because its size is small.

The “necessary” part makes somewhat more sense. If the DSS and SSS are really close, because the model is very close to being linear, then a mean preserving spread is not going to have a big effect, because there is no amplification. But if the reason is relatively low average volatility in the economy, an uncertainty shock can still have big effects if it increases the volatility by a lot.

There is more chance that I am in the second case.

The standard deviation of my volatility shock is based on empirical data (so I do not have to increase it). However, as my DSS and SSS are very close, maybe my model do not display a lot of non-linearity…

Another question: should the volatility shock be specified in log or in level?

Thanks a lot for your answer

For a clean exercise, you should not use any exp() as you will get Jensen’s Inequality effects. See e.g. Basu/Bundick (2017): Uncertainty Shocks in a Model of Effective Demand.

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