Log linearization Help!

Dear all,

I need some advice whether I correctly linearized the equation for capital evoluation with a multiplicative investment efficiancy shock:

K(t) = (1-delta)*K(t-1) + i(t)*I(t) where i(t) is an investment efficiency shock

I log linerized this equation arount the steady state and got the following: Khat = (1-delta)Khat(-1) + deltaIhat + ihat;

Am I correct in that?



I think there is a delta missing in front of the efficiency shock. It is multiplicative with I and should thus have the same prefactor.