Observed stellar mass and luminosity functions used in this work. Top panel: observed AGN luminosity function, ϕ_AGN(L_Bol(M_*, z)) at different redshifts from the X-ray data of Aird et al. (2015) and using the bolometric correction of Runnoe et al. (2012) to convert X-ray luminosity to bolometric luminosity. Lower panel: stellar mass functions compiled from the latest WINGS (Vulcani et al. 2011, z ∼ 0) and COSMOS (Davidzon et al. 2017, z ∼ 0.2 − 5) survey data converted into the equivalent ϕ_SMF(L_Bol) by using the relation between L_Bol and M_* via M_BH.