  In our previous work, by using Kolyvagin derivatives of elliptic units, we
constructed ideals C_i of the Iwasawa algebra, and proved that the ideals C_i
become "upper bounds" of the higher Fitting ideals of the one and two variable
p-adic unramified Iwasawa module X over an abelian extension field K_0 of an
imaginary quadratic field K. In this article, by using "non-arithmetic"
specialization arguments, we prove that the ideals C_i also become "lower
bounds" of the higher Fitting ideals of X. In particular, we show that the
ideals C_i determine the pseudo-isomorphism class of X. Note that in this
article, we also treat the cases when the p-part of the equivariant Tamagawa
number conjecture (ETNC)_p is not proved yet.
  In the cases when (ETNC)_p is proved, stronger results have already been
obtained by Burns, Kurihara and Sano: under the assumption of (ETNC)_p and
certain conditions on the character $\psi$ on the Galois group of K_0/K, they
have given a complete description of the higher Fitting ideals of the
\psi-component of X by using Rubin--Stark elements. In our article, we also
prove that the $\psi$-part of C_i coincide with the ideals constructed by
Burns, Kurihara and Sano in certain cases when (ETNC)_p is proved. As a
corollary of this comparison results, we also deduce that the annihilator ideal
of the $\psi$-part of the maximal pseudo-null submodule of X coincides with the
initial Fitting ideal in certain situations.
