  Mid-infrared optical Hall effect measurements are used to determine the free
charge carrier parameters of an unintentionally doped wurtzite-structure
$c$-plane oriented In$_{0.33}$Ga$_{0.67}$N epitaxial layer. Room temperature
electron effective mass parameters of $m^{*}_{\bot}=(0.205 \pm 0.013)~m_0$ and
$m^{*}_{\parallel}=(0.204 \pm 0.016)~m_0$ for polarization perpendicular and
parallel to the $c$-axis, respectively, were determined. The free electron
concentration was obtained as $(1.7 \pm 0.2)\times 10^{19}~$cm$^{-3}$. Within
our uncertainty limits we detect no anisotropy for the electron effective mass
parameter and we estimate the upper limit of the possible effective mass
anisotropy is 7$\%$. We discuss the influence of band nonparabolicity on the
electron effective mass parameter as a function of In content. The effective
mass parameter is consistent with a linear interpolation scheme between the
conduction band mass parameters in GaN and InN when the strong nonparabolicity
in InN is included. The In$_{0.33}$Ga$_{0.67}$N electron mobility parameters
were found to be anisotropic supporting previous experimental findings for
wurtzite-structure GaN, InN, and Al$_{x}$Ga$_{1-x}$N epitaxial layers with
$c$-plane growth orientation.
