  We investigate a model of the interacting holographic dark energy with cold
dark matter (CDM). If the holographic energy density decays into CDM, we find
two types of the effective equation of state. In this case we have to use the
effective equations of state ($\omega^{\rm eff}_{\rm \Lambda}$) instead of the
equation of state ($\omega_{\rm \Lambda})$. For a fixed ratio of two energy
densities, their effective equations of state are given by the same negative
constant. Actually, the cosmic anti-friction arisen from the vacuum decay
process may induce the acceleration with $\omega^{\rm eff}_{\rm \Lambda}<-1/3$.
For a variable ratio, their effective equations of state are slightly
different, but they approach the same negative constant in the far future.
Consequently, we show that such an interacting holographic energy model cannot
accommodate a transition from the dark energy with $\omega^{\rm eff}_{\rm
\Lambda}\ge-1$ to the phantom regime with $\omega^{\rm eff}_{\rm \Lambda}<-1$.
