WITH stock markets in turmoil and market-implied inflation expectations tumbling, is it time to conclude that the Federal Reserve's interest rate rise in December was premature? My colleague R.A thinks so. The Fed, according to doves, moved too soon to raise rates because it feared, wrongly, that a wage-price spiral might take off. Here is R.A:

Why might the Fed need to tighten abruptly? The only reason to do so would be for fear that tightening gradually in the face of rising inflation would not prevent the emergence of an inflationary spiral between wages and prices, pushed ahead by rising inflation expectations. Most of the members of the Fed's monetary-policy committee began their professional careers in the 1970s or early 1980s, a period characterised by high inflation—and, eventually, by Fed-induced recessions intended to wring inflationary pressures out of the economy.

This is a little harsh on the Fed. It is true that Janet Yellen, the Fed's chair, emphasises the labour market in her assessment of future inflationary pressure. But she does not refer to wage-price spirals. Instead, she makes a simpler­­­­—and harder to dispute­­­­—claim: that the amount of slack in the economy is a leading indicator of inflation.

This distinction is important, because inflation can emerge abruptly without wage growth being responsible. Indeed, the evidence that wage inflation causes price inflation is weak. Causation probably runs the other way: recently, cheap oil and a strong dollar has boosted real wages, holding down the need for cash-terms pay rises in spite of a tight labour-market. In November David Mericle of Goldman Sachs estimated that recent low inflation has knocked about 0.2 percentage points off wage growth.

The full dynamics of inflation are a puzzle. Yet the evidence for Ms Yellen's simple claim—that slack predicts inflation—is strong. Indeed, domestic slack is more important than global deflationary pressure for American prices. More recent work by Mr Mericle "finds no evidence that a global inflation factor helps to explain US core inflation after controlling for domestic slack". His finding is consistent with academic work, including some by Ms Yellen herself. When it comes to slack, what happens inside American borders is most important. With unemployment low, that means inflation should rise once commodity price declines and dollar appreciation halt.

There is another factor that might justify earlier rate rises: a flattening Phillips curve (which plots the relationship between slack and inflation). At the meetings of the American Economic Association last week in San Francisco, Olivier Blanchard presented work suggesting that a one percentage-point fall in unemployment now leads to only 0.2 percentage-points more inflation. Mr Blanchard noted that the old "accelerationist" (ie, wage-price spiral) model seems broken; high unemployment after the crisis did not lead to deflation.

A flatter Phillips curve makes reducing inflation costlier. If the Fed overshot, it would need to engineer a deeper recession and more unemployment to return to target. It might take unemployment fully 5 percentage points higher to get inflation down from just 3% to 2%. That is a sobering thought.