  We propose a novel method to estimate M_*/M_BH, the ratio of stellar mass
(M_*) to black hole mass (M_BH), at various redshifts using two recent
observational results: the correlation between the bolometric luminosity of
active galactic nuclei (AGN) and the star formation rate (SFR) in their host
galaxies, and the correlation between SFR and M_* in star-forming (SF)
galaxies. Our analysis is based on M_BH and L_bol measurements in two large
samples of type-I AGN at z~1 and z~2, and the measurements of M_*/M_BH in
0.05<z<0.2 red galaxies. We find that M_*/M_BH depends on M_BH at all
redshifts. At z~2, M_*/M_BH 280 and ~40 for M_BH=10^8 and M_BH=10^9 M_sol,
respectively. M_*/M_BH grows by a factor of ~4-8 from z~2 to z~0 with extreme
cases that are as large as 10-20. The evolution is steeper than reported in
other studies, probably because we treat only AGN in SF hosts. We caution that
estimates of M_*/M_BH evolution which ignore the dependence of this ratio on
M_BH can lead to erroneous conclusions.
