  Calculations of the two-loop $\beta$-function for N=1 supersymmetric
electrodynamics are compared for regularizations by higher derivatives and by
the dimensional reduction. The renormalized effective action are found to be
the same for both regularizations. However, unlike the dimensional reduction,
the higher derivative regularization does not lead to anomaly puzzle, because
it allows to perform correct calculation of diagrams with insertions of
counterterms. In particular, using this method a contribution of diagrams with
insertions of counterterms is calculated exactly to all orders. This
contribution appears to be 0 if the theory is regularized by the dimensional
reduction. We argue, that this result follows from mathematical inconsistency
of the dimensional reduction and is responsible for the anomaly puzzle.
