Historical shock decomposition, error in init2shocks option?

Estimation
1

Dear all,

is there any chance there might be an error in the recently introduced init2shocks command that attributes initial values/ conditions to structural shocks? When I run the decomposition for a simple AR(1) process,

log(by/ Pby) = Prho_by * log(by(-1)/Pby) + e_by,

where Pby is the steady state value by, Prho_by gives the persistence of the process, and e_by is the structural shock, I would expect there to be no more initial value component when the init2shocks option is specified.

Instead - find the historical decompositions both with and without the init2shocks option specified below - I get a slowly decaying initial value contribution with an (absolute) period-1 value exactly the size of the period-1 structural shock. I wonder if there’s a problem with double counting here? Any thoughts appreciated! Thanks!

AR1_decomposition.fig (120.4 KB)
AR1_decomposition_init2shocks.fig (121.4 KB)

2

@rattoma You may want to chime in.
My understanding is that there will always be an effect of the initial condition left. The shock contributions refer to e_by, while the initial condition is about the initial conditions for the endogenous states. This initial condition will not simply vanish, but init2shocks allows you to assign that initial condition to a particular state.

3

indeed there seems to be an issue, presumably associated to the shock decomposition option init_state.
the default is =0, and I think that init2shocks works properly only for init_state=1, since the smoother only provides latent states in period 1 (and not in period 0, which would be the required information with init_state=0).
could @a_hatu report what happens using the option init_state=1?