I am currently working with a model explaining economic volatility duing COVID-19. I wonder if my focus is on shock decomposition of key variables and I do not really care about the size of shocks, is it necessary to estimate the standard deviations of shocks? In my understanding, I can just normalize them to unity and the smoother will tell my about how large the shocks are in each period, and I can obtain identical results of shock decomposition as the experiment treating the std devs as parameters to be estimated.
Is my understanding correct? Thanks in advance.