  We apply Feshbach-Krein-Schur renormalization techniques in the hierarchical
Anderson model to establish a criterion on the single-site distribution which
ensures exponential dynamical localization as well as positive inverse
participation ratios and Poisson statistics of eigenvalues. Our criterion
applies to all cases of exponentially decaying hierarchical hopping strengths
and holds even for spectral dimension $d > 2$, which corresponds to the regime
of transience of the underlying hierarchical random walk. This challenges
recent numerical findings that the spectral dimension is significant as far as
the Anderson transition is concerned.
