Federal Reserve Chair Kevin Warsh heads into Wednesday's Consumer Price Index (a key U.S. inflation gauge) report with economists debating whether cooling price pressures will keep the Fed on hold or whether renewed inflation could revive the case for a rate increase instead of cuts. Former Fed economist Claudia Sahm said inflation news since her July analysis had been favorable, after she earlier assigned a 60% chance to the Fed holding rates and a 40% chance to a hike based on scenarios in the June FOMC minutes. The Fed kept its benchmark rate unchanged at 3.50%-3.75% in July for a fifth straight meeting, though three officials dissented in favor of a 25-basis-point increase. Consensus forecasts call for headline inflation to cool to 3.4% from 3.5%, with core inflation (excluding volatile food and energy prices) at 2.5%. Economist Mohamed El-Erian said markets will watch whether energy price gains since February are feeding into core inflation and how persistent services inflation remains. The policy debate is also unfolding as national debt exceeds $39.89 trillion, a backdrop Peter Schiff said makes higher rates harder even as it increases the need for them, while Cato Institute economist Jai Kedia told Benzinga that only a serious inflation shock would likely have a lasting effect on stocks because markets are already pricing in a worse report than June.