Federal Reserve Board Chair Janet Yellen. REUTERS/Kevin Lamarque Falling oil prices may be good news for consumers who have seen prices at the pump start falling and the prices of other goods starting to drop as well, but it could prove a headache for Federal Reserve Board Chair Janet Yellen.

That's because the US, which just posted an astonishing 5% gain in GDP, is now flirting with deflation.

The Fed is thus facing a bizarre economic dilemma: It has runaway growth and collapsing prices at the same time. The weapons available to Yellen to fight deflation are flimsy. Normally, the Fed would want to lower interest rates. But they are already at zero — there is nowhere left to go. And, of course, house-on-fire economic growth usually calls for higher interest rates, which would only exacerbate the deflation side of the problem.

The Fed most recently faced this problem in the 1980s, when low oil prices spurred runaway growth. The Fed took its eye off the ball at the time, leading to nearly 5% inflation by 1990.

Both Brent and West Texas Intermediate (WTI) crude oil prices have fallen by more than half since June as the US shale oil boom increased the supply of the commodity and signs that emerging-market growth is slowing weighed on demand. The rout was also compounded by the surprising decision by OPEC in November not to cut production in response to falling prices.

Those falls in oil prices are pushing inflation below the Federal Reserve's 2% target, potentially delaying the likelihood of rate hikes despite a buoyant economy.

Personal consumption expenditures inflation. Goldman Sachs

As Jan Hatzius, chief economist at Goldman Sachs, writes in a recent note: "It is not inconceivable that Fed officials will hike even if core inflation ends up close to 1%, as long as they are convinced that the weakness is entirely due to temporary factors such as energy prices and oil. But the hurdle for how convincing other data need to be in this case would increase significantly."

That is, the Fed may put its 2% target aside if the Federal Open Market Committee (FOMC) decides that prices are being depressed by short-term factors that will eventually stabilize or reverse, pushing inflation back toward target. The International Monetary Fund forecasts 3.1% growth in the US over 2015, while the country's unemployment rate was 5.8% in November, around the level that many economists consider the "natural rate" below which wage gains would be expected to start pushing up prices.

This would imply that labor-market indicators would become critical to the FOMC's analysis of when to raise rates — and in particular wage growth. As Yellen put it in August last year, "since wage movements have historically been sensitive to tightness in the labor market, the recent behavior of both nominal and real wages point to weaker labor market conditions than would be indicated by the current unemployment rate."

That is, rate hikes may be put on hold until people start seeing the benefits of growth in their take-home pay. Moreover, with global fears over the prospect of deflation gripping much of the developed world, the FOMC body could find itself under pressure to hold off rate hikes while inflation remains below target.

But there are big risks to this strategy. If the dip in inflation due to commodity-price falls helps to mask the underlying strength of the US economy, once they stop falling inflation could come surging back and be much more difficult to control.

Below is a chart showing Barclay's forecasts for headline inflation. As you can see, after dipping into negative territory, Barclay's expects CPI to head above 2% by the end of 2015.

Headline US inflation. Haver Analytics, BLS, Barclays Research

If the FOMC holds off for too long and expectations of higher inflation take hold, then it could be much more difficult for the Fed to bring it back to target over the medium term.

Moreover, Yellen has also indicated that sluggish wage growth may not prove a sufficient reason to hold rates down. Sluggish wage growth could reflect "pent-up wage deflation" that could be holding back the pace of gains, labor's share of income could be structurally lower than it has been in the past (firms are spending a larger proportion of their money on e.g. dividends to shareholders and investment than on employees than in the past), and people who are unemployed finding it more difficult than expected to return to the workforce.

If those warnings prove accurate, prices may start to rise before wage growth picks up substantially, implying that the Fed may need to increase rates earlier.

There have indeed been numerous predictions of runaway inflation over the past few years, all of which have proved painfully wide of the mark. Nevertheless, the balance of risks has been shifting as the US continues to recover from the crisis and close the remaining economic gap it left behind.

The Fed is charged with working out a safe exit strategy from its emergency policies, which many credit with having rescued the country from economic disaster. However, the collapse in oil prices has served only to make this difficult job even harder.