That’s because rate changes immediately redistribute interest income
BIS 21 – Bank for International Settlements
“2021 Annual Economic Report,” Bank for International Settlements, June 2021, https://www.bis.org/publ/arpdf/ar2021e.pdf
Monetary policy stance and inequality
Changes in the stance of monetary policy inevitably have some short-run distributional effects. Every time the central bank adjusts interest rates, changes its lending terms or purchases assets, distributional consequences follow. For example, any such adjustment redistributes interest income between debtors and creditors and influences asset prices, which reallocate income and wealth in the population depending on holdings (see Box II.C for a detailed analysis of this point). But the more important influence of monetary policy on inequality is through its impact on inflation, employment and economic activity. These are the main macroeconomic factors that shape inequality over the business cycle.