NEW YORK, May 3 (Reuters) - A falling dollar may complicate the U.S. inflation outlook, creating another headache for the Federal Reserve as it attempts to gauge whether stubbornly high inflation will be tamed.

The Fed has historically put less weight on exchange rates compared with its central bank peers in some Asian and European countries, because the impact from trade on prices and on the U.S. economy usually has been relatively limited.

But the Fed may have less room for complacency now.

The dollar’s recent decline comes at a time when the labor market has remained surprisingly tight -- “gangbusters” as one policy-maker put it -- in spite of sluggish growth.

“A weaker dollar could become more of an inflation factor,” said Michael Feroli, an economist at J.P. Morgan in New York. “At the margin, a weakening dollar makes it difficult to be sure that inflation comes under control.”

The dollar has fallen considerably over the past year, hitting life-time lows against the euro and 26-year lows against sterling last week.

At the same time, a Fed index that measures the trade-weighted value of the dollar against a basket of seven major currencies hit the lowest level in its 34-year history.

A declining dollar could increase inflationary pressure through various channels. Higher import prices could feed into retail costs and lessen the competitive pressures domestic firms face, giving them greater leeway to raise prices.

Recent signs suggest some easing in inflationary pressures. A report this week showed the Fed’s favorite core inflation gauge held steady in March, with the year-on-year rate easing to a 2.1 percent gain, just above the 1 percent to 2 percent range many officials have described as their “comfort zone.”

But the Fed expects growth to pick up later this year, and policy-makers may not be convinced prices will steadily fall until there is more slack in the labor market

In March, the jobless dipped to 4.4 percent from an already low 4.5 percent, even though the economy posted a sluggish 1.3 percent annual growth rate in the first quarter.

PASS-THROUGH

A staff report by the New York Federal Reserve Bank last April that measured the impact shifts in exchange rates have on domestic inflation in 21 countries, which are members of the Organization for Economic Cooperation and Development, found the United States to be the least sensitive.

The ‘sensitivity’ of the U.S. consumer price index was less than 5 percent, while the average for the 21 countries was 15 percent. For Germany and France, it was around 20 percent.

So far, Fed policy-makers have not addressed the issue of a weaker dollar.

When asked last week about the impact of a declining dollar on monetary policy, San Francisco Federal Reserve Bank President Janet Yellen said only that it was difficult to predict exchange rates, adding: “The Fed is focused on the dual mandate” of price stability and maximum employment.

In contrast, some euro zone policy-makers have suggested currencies have become more of a policy risk. The euro hit a record high of $1.3683 against the dollar on Friday.

“The euro is one of the very important factors in our considerations,” European Central Bank Governing Council member Klaus Liebscher told Reuters in an interview on Monday.

A stronger euro could lessen the need for further rate increases, as it would ease inflationary pressures in the euro zone by cutting the import cost of dollar-denominated oil and commodities and depressing the costs of consumer goods from overseas.

But others played down the effect of the euro on the economy. The EU’s Economic and Monetary Affairs Commissioner Joaquin Almunia on Thursday said the euro’s gains in recent years have not damaged exports from the nations using the single currency.

Many analysts expect the dollar to remain under pressure, as U.S. interest rates look set to stay steady amid a slowing economy and still high prices, while rates in other major economies such as Britain and the euro zone look set to rise as policy-makers attempt to rein in inflation amid robust growth.

Such narrowing of interest rate differentials make dollar-denominated assets less attractive for investors and reduce demand for the greenback.