  In this paper we study local error bound moduli for a locally Lipschitz and
regular function via its outer limiting subdifferential set. We show that the
distance of 0 from the outer limiting subdifferential of the support function
of the subdifferential set, which is essentially the distance of 0 from the end
set of the subdifferential set, is an upper estimate of the local error bound
modulus. This upper estimate becomes tight for a convex function under some
regularity conditions. We show that the distance of 0 from the outer limiting
subdifferential set of a lower $\mathcal{C}^1$ function is equal to the local
error bound modulus.
