WASHINGTON (Reuters) -New Federal Reserve Governor Stephen Miran may not have won converts to his call for steep interest rate cuts at last month's policy meeting, but his inaugural session has stirred fresh debate about how much rates are restricting the economy and the risks involved in getting that assessment wrong.

Minutes of the September 16-17 meeting due out on Wednesday could provide new details on the discussion, which will be central to how far and how fast officials cut rates as they try to assess how to balance inflation risks, with prices still rising at a 2.7% pace, well above their 2% target, against what some see as a weakening job market. 

Though the federal government shutdown delayed release of the September employment report last week, private-sector and other data suggested that hiring continued to be sluggish.

But that may not necessarily translate into higher unemployment due to the limits President Donald Trump has put on immigration and thus on labor supply. Analysts also note that record-high stock prices, ongoing consumer spending and economic growth that is by some measures moving back above trend suggest that Fed policy may not be all that tight at all.

A recently updated Fed staff model analyzing how the federal funds rate, stock prices, corporate bond yields and other metrics influence the economy found that overall financial conditions are boosting - not restraining - economic growth by about a percentage point a year, with the Fed's policy rate contributing slightly to the lift.

Putting too much weight on a job market that may be slowing because of the decline in available foreign-born workers could set the Fed up for a mistake, Jason Thomas, head of global research and investment strategy for the Carlyle Group, wrote on Tuesday.    "The risk today is that the Fed misdiagnoses the fall in payroll employment growth as entirely a demand-side phenomenon and cuts rates to levels that fuel an eventual wage-price spiral in industries grappling with a sudden dearth of available workers," Thomas said. 

The Fed cut its rate by a quarter-of-a-percentage point at its September meeting, a move Fed Chair Jerome Powell and others characterized as a way to leave policy tight enough to still restrain the economy and put downward pressure on inflation, while also providing a looser policy outlook that could help insure against rapid weakening of the job market.

Miran dissented in favor of a larger half-point cut and submitted projections calling for a series of half-point cuts at coming meetings. He said his colleagues had dramatically overestimated both the inflation risks and the rates level needed to keep price pressures at bay.

Historically, the Fed has only cut rates as fast as Miran has suggested - roughly halving the current 4.00% to 4.25% policy rate by year end - in response to a crisis like the pandemic or to try getting ahead of developing risks like those leading to the 2007 to 2009 financial crisis. 

While Miran's is an outlying view, opinions among the other 18 policymakers are also divided. Nine officials in projections issued after the last meeting indicated the need for continued quarter-point rate cuts at their remaining two meetings this year, while seven saw no further cuts needed, a view consistent with worries that inflation seems lodged above the Fed's target.

"The Fed must maintain its credibility on inflation," Kansas City Federal Reserve Bank President Jeffrey Schmid said on Monday, arguing that price increases appeared to be broadening, and that services-sector inflation "seems to have settled in at around 3.5%...higher than has been consistent with the Fed meeting its 2% target."

Services make up the bulk of U.S. consumption, and Dallas Fed President Lorie Logan said recently that work by her staff indicated non-housing services inflation on its own could keep the Fed's preferred price index rising at an above-target 2.4%.

In contrast to concerns about Trump's import tariffs driving up goods prices, sustained services inflation would represent a different problem for the Fed, one where views about the "neutral" rate - the rate which neither helps nor hinders growth - would have even more bearing if officials see the need to keep pressure on the economy. 

Tariffs are now seen by the Fed as likely leading to only one-time price increases, but a take-off of prices in a services sector more sensitive to wages and labor supply could lead to fears of a wage-price spiral and questions about whether immigration limits were feeding inflation as workers become scarce.

Powell said after last month's rate cut that policy remained at a "clearly restrictive level," while remaining noncommittal about further reductions. 

Fed Vice Chair Philip Jefferson, typically cautious when discussing monetary policy, in response to questions last week would say only the rate cut brought the Fed "closer to a more neutral stance" without revealing what he thought the neutral rate might be. Two others, Governor Christopher Waller and Vice Chair for Supervision Michelle Bowman - Trump appointees like Miran - have argued for more cuts out of concern about the job market, though not at the pace Miran has advocated.

To Logan, Schmid and some others, policy may already be close to neutral, a reason to be careful with further cuts until the path of inflation becomes clearer.

"There may be relatively little room to make additional rate cuts without inadvertently moving to an inappropriately accommodative stance," Logan said last week.