In Starr's paper https://www.math.stonybrook.edu/~jstarr/papers/moduli4.pdf the folk result that the fibred category of pairs $(X\to S, L)$, where $S$ is an affine scheme, $X\to S$ is flat proper finitely presented morphism of algebraic spaces and $L$ is a relatively ample line bundle on $X$, is an algebraic stack is proven.
This made me wonder:
Is the fibred category of pairs $(X\to S,L)$, where $X\to S$ is flat proper finitely presented and $L$ is a relatively big line bundle on $X$, an algebraic stack?
I couldn't find an answer in the stacks project.