Steady state values of a DSGE model variables


When we solve a DSGE model analyticaly we calculate steady state of the model variables such as Y C I G L W P MC and etc based on the model parameters such as \alpha , \beta , \delta and etc. Can we use steady state of variables with real data mean ?

For example steady state of consumption is mean of LnC_{t}. Or we should obtain steady state values based on the model parameters compeletly.In some DSGE models calculation of steady state for some variables is difficult.

I don’t seem to understand your question. The parameters, in general, are chosen in order to match, some, real data outcomes in steady state or their shares. So this is already what is done.
You cannot imply a model’s steady state that you would like to have and then solve for it. If you have problems calculating it, maybe numerical methods can help.

I work with a Log-linear DSGE model. means are zero or near zero and steady state values are zero. After simulation of the model we compare model moments such as standard deviations. Therefore my question is that can we use real data means as steady state values of the model? For example in Log-linear DSGE models in Dynare when we use Log-linear equations in some equations we need steady state values for solving the model or local variables in the model block.

For example suppose that market equilibrium condition in a Log-linear form is :

\overline Y \hat Y = \overline C \hat C + \overline I \hat I +\overline G \hat G

Y_{ss} \hat Y = C_{ss} \hat C + I_{ss} \hat I + G_{ss} \hat G

We need steady state of consumption or \overline C or C_{ss} and Y_{ss} , I_{ss} , G_{ss} otherwise we can not solve the model in Log-linear form.

Can we use mean of real data consumption for C_{ss} or we should calculate it based on the model parameters ?

No, you cannot just use means of real data, since the steady states that are needed for log-linearising your model are the model specific steady states that do depend on the parameters used. Any other number, including real data means, do (with a very high probability) not overlap with the model steady states and so you wouldn’t log-linearise around the true model steady state. You cannot just skip the step of calculating the steady state by using other values for log-linearisation.
The steady state of your model depends on the parameters chosen, thus this is how you can try to match some outcomes, not the other way round.

Why do you have to log-linearise your model to begin with?

I solve my DSGE model in a Log-linear form. Therefore according to your comments we can not use real data moments such as mean in the model and we should calculate them based on the model parameters.

Please carefully read @DoubleBass’s reply.

Parameters and data moments need to be consistent. You cannot simply use C_ss from the data without adjusting the parameters accordingly. Also note that in models with constant returns to scale, the levels can be arbitrarily scaled with TFP. So you would also need to fix technology to be consistent with the data even if you went down that route.