(Adds more of Bostic’s remarks) Aug 9 (Reuters) - Atlanta Federal Reserve Bank President Raphael Bostic said on Monday the U.S. economy is improving faster than expected, with the time when the Fed could start slowing its bond purchases nearing quickly and inflation already at a point that could satisfy one leg of a key test for the beginning of rate hikes. Bostic said he is eyeing the fourth quarter for the start of a bond-purchase taper but is open to an even sooner start if the job market keeps up its recent torrid pace of improvement. Moreover, he said that by his assessment inflation has already achieved the Fed’s 2% threshold. That is one of two requirements to be met before rate hikes can be considered. The Fed official, who has already penciled in late 2022 for the start of the rate hikes, pointed to the five-year annual average for the core personal consumption expenditures index, or core PCE inflation, which by his calculation reached 2% in May. “There are many reasons to think that we may be at that goal target right now,” Bostic told reporters. But he said the committee has yet to agree on the metrics it will use to measure that progress, something policymakers will need to discuss. Bostic’s remarks echoed comments made by St. Louis Fed President James Bullard last month, who said that the current pace of inflation, at 3.5% annually by the Fed’s preferred measure, is well above the central bank’s 2% target, and adequate in his view to make up for past weak inflation as required by the central bank’s new framework. Fed officials agreed to leave interest rates at near zero levels until the labor market reaches maximum employment, and inflation averages 2%, on track to moderately exceed 2% for some time. Policymakers said in December they would continue purchasing government bonds at the current pace of $120 billion a month until there is “substantial further progress” toward the central bank’s goals for inflation and maximum employment. With the elevated inflation levels reached during the pandemic, Bostic said, the Fed has effectively achieved the “substantial further progress” goal for inflation. More progress is still needed in the labor market, but that goal could be accomplished after another month or two of strong job improvement, Bostic said. That puts the Fed on a path to begin trimming purchases between October to December, or sooner, if the gains in August are stronger than expected, he said. Bostic also said he supports a “balanced” approach to tapering asset purchases that reduces mortgage-backed securities and Treasury securities at the same rate and he would be in favor of tapering asset purchases over a shorter period than what the Fed has previously done. “I am in favor of going relatively fast,” Bostic said. (Reporting by Jonnelle Marte and Howard Schneider; Editing by Steve Orlofsky) Our Standards: The Thomson Reuters Trust Principles.