Estimation command

i tried to replicate medina/soto model on dynare, i use the Log-linearized model and i estimate my model with Bayesian Approach.
in my dynare code the variables are fractional deviations from their steady state values (for exemple y_hat, c_hat, inv_hat…etc)
my data contains the same variables as in paper (page 16).
for the real variable (gdp, consumption, investement) i use the logarithm of
its first difference, demeaned, (ΔlnYt,ΔlnCt,ΔlnINVt)

in my dinare code these variable are the variable observable of y_hat, c_hat, inv_hat?:

or the observable variable of dy_hat,dc_hat, dinv_hat?

dtbc457.pdf (485 KB)

I don’t fully get your question. If you are asking whether you should match growth rates in the data like ΔlnYt to growth rates of model variables (dy_hat) or to the level of the variable (y_hat), then the former is correct. You need to match growth rates to growth rates.