  Building on the first variational formula of the calculus of variations, one
can derive the energy-momentum conservation laws from the condition of the Lie
derivative of gravitation Lagrangians along vector fields corresponding to
generators of general covariant transformations to be equal to zero. The goal
is to construct these vector fields. In gauge gravitation theory, the
difficulty arises because of fermion fields. General covariant transformations
fail to preserve the Dirac spin structure $S_h$ on a world manifold $X$ which
is associated with a certain tetrad field $h$. We introduce the universal Dirac
spin structure $S\to\Sigma\to X$ such that, given a tetrad field $h:X\to
\Sigma$, the restriction of $S$ to $h(X)$ is isomorphic to $S_h$. The canonical
lift of vector fields on $X$ onto $S$ is constructed. We discover the
corresponding stress-energy-momentum conservation law. The gravitational model
in the presence of a background spin structure also is examined.
