We have studied a model polymer solution based on 1,4-polybutadienes (PBD) to explore the origin of negative intrinsic viscosity in polymer solutions where the polymer has typically a lower glass transition temperature than that of the solvent. Viscoelastic measurements are carried out to show that the PBD solutions possess smaller viscosity than that of the solvent at low temperatures. DSC analysis shows that the incorporation of the 1,4-PBD into a butadiene-based solvent of higher glass transition temperature depresses the solution glass transition temperature below that of the solvent. By designing a reference system with the same glass transition characteristics as the solution, we recover the positive effect of the polymer hydrodynamic contribution to the solution viscosity, suggesting that the conventional molecular theories for polymer solutions can be phenomenologically remedied by incorporating the polymer plasticization effect.