The U.S. Federal Reserve has made its inflation-fighting intentions abundantly clear. Now comes the difficult part: sticking to that commitment as tighter monetary policy restrains the economy and puts millions out of work.

Will the Fed stay the course? I sure hope so, but it will be a long, hard road, which raises doubts.

Over the past month, Fed officials have consistently demonstrated their resolve to push inflation back down to the central bank’s 2% target. Chair Jerome Powell called the commitment “unconditional,” the policy-making Federal Open Market Committee voted unanimously for a 75-basis-point interest-rate increase, and the FOMC’s projections show the federal funds rate reaching a target range of 4.25% to 4.50% by the end of this year and remaining elevated through 2023.

That said, it’s easy to be unified when you’re catching up after being far behind the curve, when the labor market is still strong and when the public views inflation-fighting as a priority. That will all change as the Fed’s inflation-fighting efforts start to take effect, increasing unemployment and likely tipping the economy into recession. Yet, judging from their own projections, Fed officials still haven’t been fully forthcoming about these consequences.

The FOMC’s median September forecast: After a sharp slowdown this year (most of which has already happened), growth picks up over the next three years, with output growing just 0.6 percentage point less than its potential over that period. The resulting increase in the unemployment rate is very modest—to 4.4% in 2023 and 2024, up from 3.7% currently and only slightly above the Fed’s 4.0% estimate of the long-term rate consistent with 2% inflation. Yet this somehow proves sufficient to bring inflation down sharply to 2.3% by 2024.

Albeit more plausible than the “immaculate disinflation” fantasies of March and June, this outlook is still unduly rosy. For one, the unemployment rate will have to go higher: Larry Summers has argued that it might have to be 2 percentage points higher than its long-term equilibrium level just to reduce underlying inflation by 1 percentage point per year. Second, the current relationship between job openings and unemployment, known as the Beveridge curve, suggests that the equilibrium level is actually about 5%. This implies a much higher unemployment rate would be needed to significantly reduce inflation. Third, the Fed’s projections have no precedent: Never has the unemployment rate increased by 0.5% or more without a recession (as the economist Claudia Sahm famously noted), and never in post-war history has it risen by just 0.9 percentage point (after 0.5, the next stop is 2 percentage points).

Another worrisome sign: FOMC members appear to disagree about how long the central bank will stick with its inflation fight. All but one expect the federal funds rate to end 2023 somewhere between 4.25% and 5%, but the range widens to 2.5% to 4.75% at the end of 2024. And this isn’t related to expectations that inflation will be vanquished by 2024. No more than a few forecast that it will have fallen to 2% by then.

So far, people seem to believe Powell’s pledge that the Fed will “keep at it” until the job is done. Longer-term inflation expectations appear well-anchored close to 2%. Prices in the Treasury market, for example, imply an annual inflation rate of 2.4% between 5 and 10 years in the future. Surveys also suggest that consumers’ expectations of long-term inflation have fallen back within their pre-pandemic ranges.

But what will happen when people realize that the job will be harder, and the pain greater, than the Fed has indicated? Support for its policies will probably decline, and it will lose credibility—something crucial to retain to get inflation under control.

Bill Dudley, a Bloomberg Opinion columnist and senior adviser to Bloomberg Economics, is a senior research scholar at Princeton University’s Center for Economic Policy Studies. He served as president of the Federal Reserve Bank of New York from 2009 to 2018, and as vice chairman of the Federal Open Market Committee. He was previously chief U.S. economist at Goldman Sachs.