  One of the main advantages of super-renormalizable higher derivative quantum
gravity models is the possibility to derive exact beta functions, by making
perturbative one-loop calculations. We perform such a calculation for the
Newton constant by using the Barvinsky-Vilkovisky trace technology. The result
is well-defined in a large class of models of gravity in the sense that the
renormalization group beta functions do not depend on the gauge-fixing
condition. Finally, we discuss the possibility to apply the results to a large
class of nonlocal gravitational theories which are free of massive ghost-like
states at the tree-level.
