That proposition was put to the test after Paul Volcker became Fed chairman in 1979.
Mr Volcker was set on getting inflation down.
As it turned out, he would need to prove his mettle.
His tight monetary policies—the federal funds rate reached almost 20% in 1981—contributed to a double-dip recession, which pushed unemployment above 10%.
It got the job done; inflation tumbled.
Since Mr Volcker's time at the Fed, it has rarely exceeded 5%.
To this day, some economists point to the Volcker recessions as proof that inflation expectations are adaptive.
The public did not believe inflation would fall just because the Fed said it would.
America had to suffer high unemployment to bring inflation down.
Policymakers had to grapple with a short-term Phillips curve after all, as Friedman and Phelps had argued.
Yet the experience of the 1980s would not be repeated.
In the decades that followed, central banks committed to inflation targets.
As they gained credibility, the trade-off between inflation and unemployment weakened.
Economists wrote “New Keynesian” models incorporating rational expectations.
By the mid-2000s some of these models showed a “divine coincidence” : targeting the best possible path for inflation, after an economic shock, would also result in the best possible path for unemployment.
Few economists think the divine coincidence holds in practice.
New Keynesian models usually struggle to explain reality unless they are tweaked to incorporate, for example, at least some people with adaptive expectations.
A cursory examination of the data suggests expectations follow inflation (they sank, for instance, after oil prices fell in late-2014).