To the extent that households that participate actively in financial transactions typically have higher income, then this channel also implies that consumption inequality should rise after expansionary monetary policy shocks.
The third is the “portfolio channel”: if low-income households tend to hold relatively more cash and fewer financial assets than high-income households, then potentially inflationary actions on the part of the central bank would represent a transfer from low- to high-income households. Again, this would tend to increase consumption inequality.