Discuss detrending of lagged trend_var
var gd, gu; trend_var(growth_factor=gu) Bu; trend_var(growth_factor=gd) Bd; varexo vd,vu; parameters gamu,gamd,thetadu; gamu=.01; gamd=.003; thetadu=0.3; model; log(gu)=log(1+gamu)+vu; log(gd)=log(1+gamd)+thetadu*log(Bu(-1)/Bd(-1))+thetadu*log((1+gamu)/(1+gamd))+vd; end; initval; gu=1.01; gd=1.003; vd = 0; vu=0; end; steady; check; shocks; var vd; stderr 0.02; var vu; stderr 0.02; end; write_latex_dynamic_model; collect_latex_files; stoch_simul(irf=150,order=1) gu gd;
Internally, we replace the lagged
trend_var Bu, i.e.
Bu(-1), by its definition
Bu/gu. The problem is that we then use the normalization
Bu=1, i.e. we fix today's value of the trend and have
gu implicitly determine the predetermined value yesterday. As a consequence, the variable
gd on the left suddenly reacts contemporaneously to
gu, although in the original equation everything on the right was predetermined. My understanding is that for a stochastic
growth_factor this detrending approach is problematic as we are violating predeterminedness. What is the solution to this issue? Normalizing an endogenous object at time
t to 1 seems to be poor practice. At a minimum, we need to document the current behavior.