The U.S. central bank's decision to cut interest rates by half a percentage point leaves open the risk of a resurgence in inflation, a former Kansas City Federal Reserve president said on Thursday.

Having all but tamed inflation, the Federal Reserve is poised to do something Wednesday it hasn’t done in more than four years: Cut its benchmark interest rate, a step that should lead to lower borrowing costs for consumers and businesses.

For more than two years, we've heard a steady drumbeat of news highlighting inflation and its impact on interest rates. The correlation seems clear, but the issue is actually more complex.