  It has been conjectured in the literature that renormalizability of the
$\theta$-expanded noncommutative gauge theories improves when one takes into
account full nonuniqueness of the Seiberg-Witten expansion, which relates
noncommutative (`high-energy') with commutative (`low-energy') fields. In order
to check this conjecture we analyze renormalizability of the noncommutative
chiral electrodynamics: we quantize the action which contains all possible
terms implied by the SW map. After renormalization we arrive at a different
theory in which the relation between the coupling constants is changed. This
means that the $\theta$-expanded chiral electrodynamics is not renormalizable:
when fermions are included, the SW expansion is not preserved in quantization.
