Next week, when Federal Reserve officials meet to decide whether to raise interest rates for the first time in nine years, one question will be front and center: How much faith should be placed in a line on a graph first drawn by a New Zealand economist nearly six decades ago, based on data on wages and employment in Britain dating to the 1860s?

That would be the Phillips curve, one of the most important concepts in macroeconomics. It shows how inflation changes when unemployment changes and vice versa. The intuition is simple: When joblessness is low, employers have to pay ever higher wages to attract workers, which feeds through into higher prices more broadly. And inflation is particularly prone to rise when the unemployment rate falls below the “natural rate” at which pretty much everybody who wants a job either has one or can find one quickly.

As the Fed’s chairwoman, Janet L. Yellen, put it in a 2007 speech, the Phillips curve “is a core component of every realistic macroeconomic model.”

Except it doesn’t work. Or at least, it hasn’t worked very well in the last few decades in the United States. And it has proved particularly problematic to try to use that historical relationship to predict where inflation is going.