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Congratulations, Jerome Powell. This week you have been handed one of the toughest and most important jobs on the planet.

As the new chair of the U.S. Federal Reserve, you will have to pilot the world's most powerful central bank as it attempts to restore normalcy to a global economy still bearing scars from the financial crisis of a decade ago.

To make your task even more difficult, you will take over at a time when some prominent voices are questioning fundamental tenets of central banking.

The doubters are asking whether anyone really understands what causes inflation or how to control it. If the skeptics are right, the Federal Reserve, the Bank of Canada and other key regulators are flying blind when it comes one of their most crucial tasks.

The people who are raising such questions aren't wild-eyed radicals. They're establishment figures such as Claudio Borio of the Bank for International Settlements, who said in a recent speech, "If one is completely honest, it is hard to avoid the question: How much do we really know about the inflation process?"

Mr. Borio, who heads the monetary and economic department at the influential Swiss-based international financial organization, says inflation has been exceptionally weak since the great recession for reasons that aren't well understood.

The global economy is picking up speed and labour markets are tightening but, so far anyway, inflation has barely budged. In Canada, the consumer price index is only inching higher. In the United States and the euro zone, key inflation gauges also remain stubbornly low.

This is not how things are usually assumed to work. As unemployment falls and the economy gets closer to its productive capacity, inflation is supposed to ratchet up as employers bid against one another for increasingly scarce labour and other vital resources. But this time around, the expected link between diminishing economic slack and higher inflation doesn't appear to be operating.

The missing link raises disturbing questions for central banks, like the Fed and the Bank of Canada, that have put inflation targets at the centre of their planning over the past generation. Borrowers and savers have come to rely upon the belief that regulators can fiddle with interest rates and other economic levers to reliably hit an inflation goal of, say, 2 per cent a year. But if central banks can no longer achieve those goals in practice – or even explain how they can hit them in theory – then the whole edifice of central bank planning comes into doubt.

For now, anyway, central bankers find themselves operating in a baffling world that is the reverse of what their predecessors faced in the 1970s and 1980s. "They used to struggle to bring inflation down or keep it under control; now they toil to push it up," Mr. Borio said. "They used to fear wage increases; now they urge them on."

It's a humbling turnaround for monetary planners, who once prided themselves on being able to fine-tune inflation by moving interest rates in response to unemployment and other measures of slack in the economy.

Recent experience suggests they vastly overestimated their powers. Consider Japan, where years of rock-bottom interest rates have failed to ignite any inflationary spark and where the linkage between output capacity and inflation appears to have fallen apart. Unemployment has plunged to 2.8 per cent in Japan, its lowest level in more than 20 years, but inflation remains barely above zero despite the drum-tight labour market.

"Could it be that we know less than we think?" Mr. Borio asks. "Might we have overestimated our ability to control inflation, or at least what it would take to do so?"

Mr. Borio and others are worried because the low interest rates that go hand in hand with low inflation have encouraged an epic wave of borrowing and helped to drive up the prices of assets ranging from stocks to real estate.

The result, according to the worriers, is a debt-heavy, bubble-prone global economy that appears unusually vulnerable to bad shocks. If a new downturn were to hit, central banks would face a fresh problem: How do you stimulate an economy by chopping interest rates when rates are already unusually low?

Policy makers are becoming increasingly frank about expressing at least some of their misgivings. "Our framework for understanding inflation dynamics could be mis-specified in some fundamental way," current Fed chair Janet Yellen acknowledged in September.

In October, Daniel Tarullo, a former Fed governor, wrote a remarkably candid account of his years at the U.S. central bank in which he argued the Fed no longer has a workable theory about how to manage key aspects of the economy. "We do not, at present, have a theory of inflation dynamics that works sufficiently well to be of use for the business of real-time monetary policy making," he asserted. The title of his presentation – "Monetary policy without a working theory of inflation" – sums up his viewpoint.

Much of the debate centres on the so-called Phillips curve, a relationship between unemployment and wage inflation that was first documented by economist William Phillips in the 1950s. According to the Phillips curve and its successors, a fall in unemployment is typically linked to higher wages and also higher inflation in general.

Central banks have relied for decades upon some version of the Phillips curve to help manage inflation. The problem is that the Phillips curve appears to have flattened considerably since the 1970s and recent evidence shows only a weak relationship between a country's unemployment level and its inflation rate.

Explanations abound for this fading relationship. One theory is that central banks have attained so much credibility as inflation fighters that people no longer build much of an inflation hedge into wage negotiations. According to this school of thought, expectations are so firmly anchored that inflation is hard to budge despite changes in the real economy.

Maybe so. But, as Mr. Tarullo argues, inflation expectations are awfully hard to measure. It's even less clear how you change them. Furthermore, pinning everything on some grand notion of expected inflation doesn't match up with first-person accounts of how wage settlements are reached. In the real world, most people say they're striving to get as much as the market can bear, not trying to match their demands to some model of forecast inflation.

So maybe the core problem isn't frozen expectations, but globalization. The entry of China, India and the ex-Soviet bloc into the world economy in the 1990s effectively doubled the global labour pool from 1.5 billion workers to 3 billion, according to the Bank of England. The sudden addition of a huge new army of workers amounted to a massive disinflationary shock: Producers in developed countries no longer had to bid up wages for workers at home but could simply move the work to a cheaper foreign locale. Perhaps it was that effect that weakened the link between domestic unemployment and domestic inflation.

Mr. Borio is fond of this explanation. He and others also point to the pervasive impact of technology. The internet and other advances allowed work to be moved more easily to other locations. In addition, the growth of online shopping restrained the ability of retailers to raise prices. Meanwhile, the expansion of the gig economy through companies such as Uber and Airbnb tapped unused pockets of part-time workers and other resources. All those factors probably helped put a lid on inflation.

To be sure, the economy may already be adjusting to all these changes. The Federal Reserve Bank of San Francisco argues in a recent note, co-written by Sylvain Leduc of the Bank of Canada, that the Phillips curve has only flattened in the United States since the financial crisis. The flattening reflects the long recovery from the downturn, the authors say. If so, the Phillips curve is probably not dead, merely dormant. According to this view, the relationship between falling unemployment and rising inflation is likely to reassert itself.

Perhaps. What is certain is that central bankers can no longer feel confident about some of their profession's most cherished notions. If they get things wrong – or simply mis-time them – the implications could be severe for the global economy.

Mr. Powell, let us sincerely wish you the best of luck at your new job.

President Donald Trump on Thursday tapped Federal Reserve Governor Jerome Powell to become head of the U.S. central bank, promoting a soft-spoken centrist to replace Janet Yellen when her term expires in February.

Reuters

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