The U-shaped curve of real interest rates in relation to inflation

We document our analysis with the cases of the United States and the euro zone. We believe that real interest rates (short-term and long-term) have a U-shaped profile in their relationship with inflation: If inflation is too low (negative), the economy is in deflation, due to an abnormal rise in real interest rates due to the stickiness of nominal interest rates (around 0); If inflation is too high, real interest rates rise because central banks intervene with an overreaction of nominal interest rates to inflation. This U-shaped curve appears in the United States, but not in the euro zone. This means that real interest rates in the United States are lowest for the intermediate values of inflation, which are those expected from 2021 onwards. At these intermediate levels of inflation, growth is therefore strongly stimulated, but asset prices may rise rapidly and generate bubbles .