Model unable to pin down a SS value for a variable

In general, when we have a model we calibrate it by setting the value of certain ratios of steady state parameters. However, before that usually to have a well defined model, one needs to be able to have a unique solution for each steady state variable.

My question is, what if my steady state cannot pin down a value for a certain parameter. This happens, because I introduce a transaction cost (which is zero in steady state). However, that variable is observable from the data and can easily be calibrated (as a ratio of output) although it can’t be pinned down from the steady state. My question is, is this a problem and why?

P.S: The variable is bonds (gov. debt) with ricardian equivalence broken by the transaction cost assumption.

P.S 2. In other words, one can only pin down steady state debt or steady state taxes, but not both.

From what you describe, your model features a continuum of steady states. In that case, you cannot endogenously compute the steady state, but you can use a steady state file to select one steady state that you desire. The price level in New Keynesian models is such an example. We then often simply set it to 1. See e.g.