Near-infrared absorption in transparent conducting oxides (TCOs) is usually caused by electronic intraband transition at high doping levels. Improved infrared transparency is commonly explained by enhanced drift mobility in these TCOs. Here, an alternative cause behind the high infrared transparency of La-doped barium stannate (LBSO) transparent electrodes is presented. Following the Drude model formalism, we reconstructed spectrally resolved dielectric permittivity for a set of thin films with different free electron concentrations. A comparison of optical properties of LBSO with the tin-doped indium oxide thin films with identical carrier concentrations suggests that the redshift of the screened plasma wavelength for LBSO originates from its large high-frequency dielectric constant of 4.4, one of the highest reported for the s-orbital-based TCOs. Moreover, our measurements confirm an optical mobility significantly higher (>300 cm2/V s) than the drift mobility, effectively suppressing the free carrier absorption. These factors enable high infrared transparency of LBSO films and motivate further exploration of LBSO as broadband TCOs for solar cells and nanophotonics.