  In models where dark matter and dark energy interact non-minimally, the total
amount of matter in a fixed comoving volume may vary from the time of
recombination to the present time due to energy transfer between the two
components. This implies that, in interacting dark energy models, the
fractional matter density estimated using the cosmic microwave background
assuming no interaction between dark matter and dark energy will in general be
shifted with respect to its true value. This may result in an incorrect
determination of the equation of state of dark energy if the interaction
between dark matter and dark energy is not properly accounted for, even if the
evolution of the Hubble parameter as a function of redshift is known with
arbitrary precision. In this paper we find an exact expression, as well as a
simple analytical approximation, for the evolution of the effective equation of
state of dark energy, assuming that the energy transfer rate between dark
matter and dark energy is described by a simple two-parameter model. We also
provide analytical examples where non-phantom interacting dark energy models
mimic the background evolution and primary cosmic microwave background
anisotropies of phantom dark energy models.
