Dimensionality loss is defined as the channel estimation overhead, which results in a loss of time-frequency resources in pilot-assisted wireless systems. In this paper, the scaling result of dimensionality loss, i.e., the scaling factor, in frequency-division-duplex (FDD) massive multiple-input-multiple-output(MIMO) downlinks is derived. The scaling factor determines the amount of channel estimation overhead, and thus is vital to understand the downlink throughput in FDD massive MIMO systems. Moreover, the transmit diversity of the downlink channel is also derived. In the simulations, we adopt a geometry-based stochastic channel model to validate our analysis. The impact of several assumptions made in our analysis is also investigated.