We study federated learning (FL), which enables mobile devices to utilize their local datasets to collaboratively train a global model with the help of a central server, while keeping data localized. At each iteration, the server broadcasts the current global model to the devices for local training, and aggregates the local model updates from the devices to update the global model. Previous work on the communication efficiency of FL has mainly focused on the aggregation of model updates from the devices, assuming perfect broadcasting of the global model. In this paper, we instead consider broadcasting a compressed version of the global model. This is to further reduce the communication cost of FL, which can be particularly limited when the global model is to be transmitted over a wireless medium. We introduce a lossy FL (LFL) algorithm, in which both the global model and the local model updates are quantized before being transmitted. We analyze the convergence behavior of the proposed LFL algorithm assuming the availability of accurate local model updates at the server. Numerical experiments show that the proposed LFL scheme, which quantizes the global model update (with respect to the global model estimate at the devices) rather than the global model itself, significantly outperforms other existing schemes studying quantization of the global model at the PS-to-device direction. Also, the performance loss of the proposed scheme is marginal compared to the fully lossless approach, where the PS and the devices transmit their messages entirely without any quantization.