First, data indicate that prices are already rising faster than 2% and have accelerated in recent months. Second, the low rate of short-term unemployment may be creating pressure for faster inflation despite the large total number of unemployed and underemployed individuals. And third, the rhetoric of Fed officials indicates that the central bank may not react quickly and aggressively enough if inflation continues to rise above 2%

The Federal Reserve's preferred measure of inflation—the price of consumer spending excluding food and energy—rose 1.4% over the past 12 months but increased since February at a 2.1% seasonally adjusted annual rate. Producer prices for the same goods and services have been rising over the same time period by 3.6% annually.

These recent price increases may be a temporary surge that will recede in the months ahead. But they could be a response to increased demand as the economy recovers from the sharp downturn at the start of the year. Although the level of real GDP fell from the fourth quarter of 2013 to the first quarter of 2014, in the most recent three months real consumer spending rose at a 4% annual rate.

Will unemployment limit wage inflation? The unemployment rate is still a relatively high 6.3%, but an unusually large one-third of those who are counted as unemployed have been out of work for more than six months. Because the long-term unemployed are less connected with the active job market, they may provide less downward pressure on wage inflation. Recent research by Princeton's Alan Krueger and two of his colleagues indicates that wages respond to the number of short-term unemployed rather than to the total unemployment rate.

More specifically, the Brookings Institutionstudy written with Mr. Krueger's Princeton colleagues Judd Cramer and David Cho implies that the unemployed who have been out of work for six months or more do not affect wage inflation. In contrast, wages begin to rise more rapidly when the unemployment rate among those out for less than six months declines to between 4% and 4.5%. Since the unemployment rate of those out for less than six months was only 4.1% in May, wages may soon begin to rise more rapidly.

Not everyone is convinced by this research. A more recent study by a Federal Reserve staff member suggests that the difference between the inflation effects of the long-term and short-term unemployed may only reflect recent experience and not be a good guide to the future. And William Dudley, president of the New York Fed, argues that the distinction between the effects of short-term and long-term unemployment depends on whether the long-term unemployment is cyclical or reflects structural and demographic changes that will limit their return to work even as markets tighten.

Is the Krueger research an accurate warning that labor markets are now closer to the threshold at which inflation begins to rise despite the substantial total number of people who aren't working? By the time we do know if he's right, it may be much more difficult to contain inflationary pressures.

More generally, Federal Reserve officials have made statements that suggest the Fed may not act quickly and strongly enough to limit a rising rate of inflation. Mr. Dudley expressed a common Fed opinion when he said recently that he believes the federal funds rate will rise relatively slowly from its current near zero level, adding that he expects the equilibrium real short-term interest rate will remain lower than its historic average and less than 2% even when the existing headwinds have dissipated.

The key to the future is how the Fed will respond when prices steadily rise above its 2% target rate while the overall unemployment rate is still relatively high. A misinterpretation of labor-market slack, and a failure to create a positive real federal-funds rate, could put the economy on a path of rapidly rising inflation.

Mr. Feldstein, chairman of the Council of Economic Advisers under President Reagan, is a professor at Harvard and a member of The Wall Street Journal's board of contributors.