  The Gromov-Witten invariants of a smooth, projective variety $V$, when
twisted by the tautological classes on the moduli space of stable maps, give
rise to a family of cohomological field theories and endow the base of the
family with coordinates. We prove that the potential functions associated to
the tautological $\psi$ classes (the large phase space) and the $\kappa$
classes are related by a change of coordinates which generalizes a change of
basis on the ring of symmetric functions. Our result is a generalization of the
work of Manin--Zograf who studied the case where $V$ is a point. We utilize
this change of variables to derive the topological recursion relations
associated to the $\kappa$ classes from those associated to the $\psi$ classes.
