Short version: If you want to achieve particular values for endogenous variables you will need to calibrate the structural parameters which determine the steady states accordingly. For example, labor supply is often taken as a “proportion of time spent working” and thus calibrated to ~1/3 by, among other things, the choice of a labor supply disutility parameter. Many references probably exist showing this process. Appendix A.2 of one of my working papers [link] goes into detail for the news-shock model of Jaimovich and Rebelo (2009).
Considerably Longer version:
Yes, and you should as well. As you probably know the solution technique in Dynare and in most DSGE modeling involves linearizing the equilibrium conditions. Linearization implies it is being done “around some particular variable constellation”. The convention has been to pick the nonstochastic steady state (of the BGP in a stationary model) as this constellation since this is where the economy will return in the long run.
The steady state values of endogenous variables will be entirely pinned down by the values of parameters. Think, for example, of the simple Keynesian cross from intermediate macroeconomics: the “solution” is output as a function of autonomous expenditure and a multiplier which are both entirely determined by structural parameters; since everything else is a function of output itself (or exogenous), the other endogenous variables will inherit this quality. One can then see how these values adjust in response to alternate parameterizations and choose the one which is “best” in some sense.
This would be simple if you had just a few variables and parameters. But often DSGE models have a large number of both, and changing one parameter might result in a better fit for one variable while sacrificing the fit on another. One very simple way of choosing the values for parameters is through the method of simulated moments (MSM) which compares the moments implied by your model at a given constellation to those of the data and adjusts parameters to minimize the (weighted) sum of forecast errors. You as the modeler must choose (1) the target moments (2) the parameters to vary and (3) the weighting matrix. This is what Beaudry and Portier (2004) [link] do to calibrate a few parameters for which there is little data. They have a footnote providing further references for more technical detail and applications. This discussion on Dynare forums will also help [link].
Finally, a comment on the steady state values you have previously seen: fitting the parameters to the levels for these macroeconomic data might come at a high cost: while you can probably reasonably approximate the levels at some point in time, I suspect this will sacrifice the reasonableness of the transition equations with respect to the data. In that case your simulations might begin reasonably at your somewhat arbitrary beginning period and then diverge from the data.
DSGE models have done fairly well explaining the “stylized facts” for many advanced economies - indeed, this focus on matching stylized facts is one of the main contributions of Kydland and Prescot (1982) [link]. You might consider calibrating the BGP to match features of the BGP e.g. data on growth rates, cross-correlations, and autocorrelations of key macroeconomic variables and then retroactively calculate the implied paths for the variables you want to express in levels.
I am sure others on this board have practical advice for implementing this.