Simulation Unit Root with drift

Dynare help (legacy posts)
1

Hi, I have a unit root process with drift. The policy function looks fine, but when I want to simulate de process using dynare it seems to be without the drift, does anyone know why the simulated variable is not trending???
best,

var y_bar ;
unit_root_vars y_bar;
parameters D_y_bar ;
varexo sh_y_bar;

D_y_bar = 0.04 ; %% drift

model;
y_bar/y_bar(-1) = exp( D_y_bar + sh_y_bar );
end;

steady_state_model;
y_bar = 1;
end;

check;

shocks;
var sh_y_bar ; stderr 0.01;
end;

stoch_simul(order=1,irf=40, periods=1000);

plot(oo_.endo_simul(1,:)’);legend(‘unit root drift?’);

2

The point is that your model does not have a steady state. The value that you declare in steady_state_model is not a steady state of the model, so you misled Dynare.
More generally, models with unit root but no drift have an infinity of steady states, but models with unit roots and a drift have no steady state. Dynare can only handle the former, not the latter, since it needs a steady state.