The log canonical model conjecture for big log canonical divisors

Let $(X,\Delta)$ be a projective log canonical pair of dimension $n$. Log canonical model conjecture. If $K_X+\Delta$ is big, then $(X,\Delta)$ has a log canonical model. The source presents this as a generalisation of its main theorem and notes that, in dimension $n+1$, it would seem to imply the abundance conjecture.