Understanding the shock process in this DSGE model

I’m looking at the model proposed in Hansen2020. The unlinearized model features an exogenous process looking like this:

A_t = \bar{A}*e^{\epsilon_t} , where \bar{A} is the steady state of A_t and \epsilon_t the exogenous variable.

I don’t understand how a shock equation like this can determine the models steady state, since in the steady state the equation just becomes 1=1. If I run the model in Dynare I can find a steady state for whatever value of A I suggest to Dynare (which makes sense to me, cause it’s not determined). Now for A=1 the steady state makes the most sense (reasonable values, consumption nonnegative), but I can’t see how this is determined.

The shock process in steady state is completely determined, given \bar A. The latter is a parameter determined by the model builder.

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I see, thank you. But shouldn’t \bar{A} in that case be reported in the calibration section with the other parameters?

I guess it isn’t reported, because the parameter doesn’t appear in the log-linearized model anymore. However, the log-linearized model contains steady-state variables and for those I need to solve for the unlinearized models steady-state, which I can’t do, because \bar{A} isn’t reported. Does that mean I can’t replicate the model (or only by guessing) or am I missing something here?

It’s often forgotten to report in papers because people simply normalize it to \bar A=1.