I scaled down a video, but the bit rate does not change I have a 3000 by 3000 VR video encoded in H264. I scaled down the video by

ffmpeg -i input.mp4 -vf scale=2160:2160 output.mp4


To my surprise, the bit rate of output.mp4 did not decrease (in fact, it increased a little bit).

Is not a scaled down video supposed to have lower bit rate than the original video? What is the mechanism of -vf scale=***?
The scale filter has no effect on the encoder's bitrate control. 

Yes, a scaled down video should have a lower bitrate if it is encoded with the same encoder settings as the source. In your command, since no encoder parameters are explicitly set, ffmpeg defaults to encoder x264 with rate-control mode CRF with value 23. Apparently, this results in the same bitrate as the full-sized source. Set a higher value to reduce size.

ffmpeg -i input.mp4 -vf scale=2160:2160 -crf 26 output.mp4