  We reduce Iitaka's subadditivity conjecture for the logarithmic Kodaira
dimension to a special case of the generalized abundance conjecture by
establishing an Iitaka type inequality for Nakayama's numerical Kodaira
dimension. Our proof heavily depends on Nakayama's theory of $\omega$-sheaves
and $\widehat{\omega}$-sheaves. As an application, we prove the subadditivity
of the logarithmic Kodaira dimension for affine varieties by using the minimal
model program for projective klt pairs with big boundary divisor.
