Single-zone synchrotron self-Compton and external Compton models are widely used to explain broad-band Spectral Energy Distributions (SEDs) of blazars from infrared to gamma-rays. These models bear obvious similarities to the homogeneous synchrotron cloud model which is often applied to explain radio emission from individual components of parsec-scale radio jets. The parsec-scale core, typically the brightest and most compact feature of blazar radio jet, could be the source of high-energy emission. We report on ongoing work to test this hypothesis by deriving the physical properties of parsec-scale radio emitting regions of twenty bright Fermi blazars using dedicated 5-43 GHz VLBA observations and comparing these parameters to results of SED modeling.