Inflation rose 0.4% in April and 4.7% from a year ago, according to key gauge for the Fed

Inflation stayed stubbornly high in April, potentially reinforcing the chances that interest rates could stay higher for longer, according to a gauge released Friday that the Federal Reserve follows closely.

The personal consumption expenditures price index, which measures a variety of goods and services and adjusts for changes in consumer behavior, rose 0.4% for the month excluding food and energy costs, higher than the 0.3% Dow Jones…