The additivity conjecture for Kodaira dimension in smooth families

Let $f\colon X\to Y$ be a smooth algebraic fiber space between smooth projective varieties, and let $F$ be its general fiber. The additivity conjecture. One should have

$$\kappa(X)=\kappa(F)+\kappa(Y).$$

This follows formally from the proposed superadditivity statement together with Iitaka's subadditivity conjecture. It is therefore known in the cases where those ingredients are established, but remains open in general.