In order to address this question, we consider a simple renormalizable and gauge invariant model in which the Z′ only has couplings to the electron and muon and their associated neutrinos, arising from mixing with a heavy vectorlike fourth family of leptons. Within this model we discuss the contributions to the electron and muon anomalous magnetic moments from Z′ exchange, subject to the constraints from μ → e γ and neutrino trident production. Using analytic and numerical arguments, we find that such a Z′ model can account for either the electron or the muon g − 2 anomalies, but not both, while remaining consistent with the experimental constraints from μ → eγ and neutrino trident production.