Discuss detrending of lagged trend_var

Consider

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;

from https://forum.dynare.org/t/impulse-responses-with-cointegrated-stochastic-trends/22756 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.