Federal Reserve officials might raise interest rates soon because they have a theory: Falling unemployment pushes up prices and wages, requiring tighter credit to keep inflation in check. What they don’t have is proof that the theory has worked consistently in the past, or evidence it is working now.  The U.S. unemployment rate was 5.3% in July, just above the 5% to 5.2% range that Fed officials expect in the long run. But annual inflation readings have remained below the Fed’s 2% target, while pay raises seem stuck in low gear.  Fed Chairwoman Janet Yellen and her colleagues face a tough decision at their Sept. 16-17 policy meeting. They can assume inflation will ramp up, and raise interest rates at the risk of smothering modest economic growth, or they could wait for evidence of an inflation uptick and risk seeing prices rise too fast.  Their trust in the late economist A.W. Phillips, whose work on the relationship between the job market and wages remains popular but controversial four decades after his death, might matter as much as hard data on consumer prices and worker pay.  “We haven’t lost faith in the framework” described by Mr. Phillips and his successors, that a tight labor market generates higher inflation, said David Altig, research director at the Atlanta Fed. But “the numbers that you would plug into that framework and the exact levels at which the pressures begin to emerge, we’re not so clear on those.”  The murky links among unemployment, wages and prices will be in the mountain air this week at the central bank’s annual retreat in Jackson Hole, Wyo. Fed officials will join central bankers and economists from around the world to discuss inflation dynamics and monetary policy, the apt topic of this year’s conference.  Mr. Phillips may come up in the conversations. In an influential 1958 paper, he hypothesized that employers would bid up wages when workers are scarce, but feel little pressure to raise pay when unemployment is high and many workers are available. Data on the U.K. economy from 1861 to 1957 backed him up: High unemployment generally corresponded with low or negative wage growth; low unemployment was reflected in faster wage growth.  The sloped line depicting that relationship was embraced by many economists in the following decades to help explain how the economy works. Increasingly sophisticated versions of the so-called Phillips curve use measures of economic slack, model prices as well as wages and incorporate concepts like inflation expectations. One such model is embedded in the Fed’s workhorse simulation of the U.S. economy.  Ms. Yellen has been a longtime booster, citing it as a Fed governor during policy discussions in the 1990s and telling lawmakers in 2010 that despite some shortcomings, “the Phillips curve model provides a coherent and useful framework for thinking about the influence of monetary policy on inflation.”  But the simple link between U.S. unemployment and inflation described by the Phillips curve appeared to break down after the 1960s. High inflation coexisted with high unemployment in the 1970s. In the 1990s, the jobless rate fell as price pressures weakened. Over the past three years, inflation has declined despite a falling jobless rate.  Critics including Milton Friedman argued the Phillips curve’s suggested trade-off between unemployment and inflation was only temporary. In other words, the Fed couldn’t permanently lower unemployment by accepting higher inflation. Today, the curve’s advocates acknowledge that, but maintain a relationship exists in the short run. Yet even this pattern has proved ever more elusive. By 2007, Fed officials had come to believe that because the public’s expectations of inflation were so stable, it took much larger changes in unemployment than before to alter how prices and wages were set. Other forces, such as commodity prices, can have a bigger impact on inflation, but one that quickly fades.  The practical value of the curve as a tool to predict the future or fine-tune policy can rightly be questioned since economists don’t know how low unemployment can go before it crosses the theoretical threshold when inflation will start to rise, or how fast inflation will respond.  At their July policy meeting, several Fed officials “noted that higher rates of resource utilization appeared to have had only very limited effects to date on wages and prices, and underscored the uncertainty surrounding the inflation process as well as the role and dynamics of inflation expectations,” according to minutes released Wednesday.  Still, a Wall Street Journal survey this month found two-thirds of economists believed the link exists and lower unemployment will eventually lead to higher inflation.  “Everyone knows it’s a bad model,” said David Stockton, senior fellow at the Peterson Institute for International Economics and a former top economist at the Fed. “The problem is, no one has put a better one on the table that outperforms it.”  Indeed, it is at the heart of the Fed’s thinking as it prepares to raise its benchmark short-term interest rate, which has been pinned near zero since December 2008. Officials say they will act when they become “reasonably confident” that inflation will move up toward their 2% target, and they’ve seen “some further improvement” in the labor market.  Ms. Yellen told reporters in June she would “need to see additional strength in the labor market…in order to have confidence that inflation will move back up to 2%.” In other words, the Fed could begin to raise rates even if wage and price data stay weak.  “In the absence of direct evidence that inflation is in fact converging to the target and in the absence of compelling or convincing direct evidence, I think a policy maker has to act on the view that the basic relationship in the Phillips curve between inflation and employment will assert itself in a reasonable period of time as the economy tightens up,” Atlanta Fed President Dennis Lockhart told the Journal this month.  Write to Ben Leubsdorf at ben.leubsdorf@wsj.com
As the Federal Reserve ponders raising rates, one of the economic theories it is relying on is the Phillips curve, which holds that as the jobless rate falls, inflation rises. But the link has been elusive in U.S. data after the 1960s.