GPS observations of ocean tide loading displacements can help infer the regional anelastic properties of the asthenosphere. We estimate M$_2$ ocean tide loading displacements at 170 GPS sites in New Zealand and compare these to modeled values using a range of numerical tide and radially symmetric (1D) elastic and anelastic Earth models. Regardless of the model combination we are unable to reduce the strong spatial coherence of the M$_2$ residuals across the North Island where they reach 0.4 mm (2\%). The best fit in the North Island is obtained when combining the FES2014b tide model with spatially-variable ocean density and water compressibility, and the STW105 Earth model. The residuals exhibit a change of $\sim$0.3 mm in magnitude between the Taupo Volcanic Zone and the east coast ($\sim$100 km), suggesting that this region’s laterally-varying, shallow rheological structure may need to be considered to explain these observations.