Dear Johannes,
First thank you very much for your previous guidance, I am grateful.
This is a common specification of preference shock in a utility function:
Utility=Vp*(lnC+ln(1-L))
C is consumption, L is labour
Vp=(1-rho) * Vp_bar+rho * Vp(-1)+e
rho is autoregressive parameter, Vp_bar is a constant and steady state of Vp
I find usually Up is called as preference shock
However, some literature call e innovation, while some literature call e structural shock. Which one do you think is more often be used? call e innovation or structural shock ?
I would also like to know in dynare historical shock decomposition, does ‘shock’ refer to structural shock/innovation (e) or shock (Vp)？
Thank you very much and look forward to hearing from you.
Best Regards,
Jesse
The confusion may come from the Dynare language. In your example e is the innovation of the autoregressive process Vp which, wrt the model, is an exogenous variable (since its definition is independent of the core of the model). But in Dynare e is declared with the varexo statement.
The historical shock decomposition in Dynare is a decomposition with respect to the (structural) innovations.
It is not just Dynare. Vp in your example is a preference shock process, while e is the actual shock/innovation to preferences. The historical shock decomposition will provide you with the total effect of all e that happened over time. which is essentially the same as the contribution of Vp.