I have agreed to write something on the history of the Phillips Curve, so I may post on the topic from time to time.
The heyday of the Phillips Curve was 1956-1969. In that fourteen year period:
--unemployment was below 4.25 percent in five years--1956, 1966, 1967, 1968, and 1969. In those years, inflation ranged between 2.8 percent and 5.9 percent, with an average of about 4.0 percent.
--unemployment was between 4.25 and 5.5 percent in four years--1957, 1959, 1964, and 1965. In those years, inflation ranged between 1.2 percent and 3.0 percent, with an average of 1.8 percent.
--unemployment was over 5.5 percent in five years--1958, 1960, 1961, 1962, and 1963. In those years, inflation ranged between 0.7 percent and 1.8 percent, with an average of about 1.3 percent.
It seemed obvious, then, that low unemployment caused high inflation, and high unemployment caused low inflation.
Of course, to Milton Friedman, it was far from obvious. He thought you could have high unemployment with high inflation, if the money supply was growing rapidly. Inflation is a monetary phenomenon.
In the 1970's, we had high unemployment with high inflation. There is a narrative that says that this vindicated Friedman and drove the Phillips Curve out of macroeconomics.
Except that the Phillips Curve did not die. I encountered it just the other day. As for Friedman, there is a fight going on between those who think that he would support the current monetary expansion (e.g., David Beckworth) and others who vehemently disagree (e.g., John Taylor).
On this purely hypothetical issue, I think I side with Taylor. I don't think Friedman would argue for trying to undo a monetary mistake by making a mistake in the opposite direction. If there is no Phillips Curve going forward, then a monetary expansion now will cause more inflation without reducing unemployment.
I do not count myself as a Friedman disciple. But I think the Recalculation Story would suggest that we won't get much out of monetary loosening, other than additional inflation.