Centering Variables in Interaction with Lagged Dependent Variable

#1
I have to run this regression:

Y (t) = a + b1 X (t-1) + b2 Y (t-1) + b3 X (t-1)*Y (t-1)

Y at time "t" is regressed using as IVs X at time t-1, Y at time t-1 (lagged dependent variable) and the Interaction of X at t-1 and Y at t-1. Both X and Y are continuous variables.

I need to center both X (t-1) and Y (t-1) to reduce collinearity.

My question is:

Should I center also Y (t), the dependent variable at time t, if not for statistical reasons, at least to better interpret the results ??