I see little reason to believe that we have entered, or are about to enter, such a period of stagflation.  For one thing, although current data on growth and inflation have departed from desirable levels, matters looked far worse 30 years ago than they do now. 

At a time when commodity prices are rising as rapidly as they are, inflation is a concern. [Those price hikes, especially for energy and food, are taking] a huge toll on households.

From press Q&A as reported by Reuters

Determining appropriate policy necessarily involves more than figuring out the neutral real federal funds rate. This reality is especially obvious at present. Inflation has been elevated for some time and prices of commodities are surging. I find these trends particularly vexing at a time when global demand growth, most likely, has slowed.

In the near term, headline inflation is likely to continue to be boosted by the direct effects of the recent increases in the prices of energy and food. If, as futures markets suggest, those prices level off later this year, prospects seem reasonably good for headline inflation to move back in line over time with core inflation. And I expect core inflation to ease off slowly as commodity prices level out and as economic slack creates competitive conditions that inhibit increases in labor costs and prices

My expectations for moderating inflation and limited spillover effects from commodity price increases depend critically on the continued stability of inflation expectations. In that regard, year-ahead inflation expectations of households have increased this year in response to the jump in headline inflation. Of greater concern, some measures of longer-term inflation expectations appear to have edged up. If longer-term inflation expectations were to become unmoored--whether because of a protracted period of elevated headline inflation or because the public misinterpreted the recent substantial policy easing as suggesting that monetary policy makers had a greater tolerance for inflation than previously thought--then I believe that we would be facing a more serious situation.

The Federal Open Market Committee will be monitoring inflation developments closely for any sign that our longer-run objective of promoting price stability is threatened.

We expect inflation to abate somewhat in the second half and going into 2009 based upon our forecast of weak economic growth. ... There is some early indication that the strength of inflation has softened.

From Q&A as reported by Bloomberg News.

[Inflation is increasing] to what I call unacceptable levels.

As reported by Bloomberg News

I think there is a real danger and the psychology around inflation is beginning to change. Expectations about inflation are beginning to change and that is a major concern to me.

Once people start passing this on, start thinking about inflation as a way of life, behaviors change

As reported by Market News International and Reuters

There still is growth in the world economy, even if we slow down. It's difficult for me to see a supply response that will feed into that demand to relieve all the price pressures we see on oil.

As reported by Reuters

I consider the current level of monetary accommodation to be appropriate. That, together with the fiscal package, should be sufficient to promote a gradual step up to moderate economic growth later this year. Likewise, I would expect that inflation will moderate in coming quarters, as more slack in labor and product markets emerges and as commodity prices level off.

In the 1970s and early 1980s, the wage-price spiral was spun from the pass-through of rising food and energy prices to inflation, which was in turn passed along to wages and, then again, through to final goods prices. Fueling the movement were expectations that monetary policy would allow inflation to continue to rise for the foreseeable future.

I see little reason to believe that we have entered, or are about to enter, such a period of stagflation. For one thing, although current data on growth and inflation have departed from desirable levels, matters looked far worse 30 years ago than they do now.

For another, there is no evidence that wages have started to spiral up, as broad measures of compensation have expanded quite moderately over the past year. Moreover, productivity growth has been fairly robust, and, after incorporating its effects, unit labor costs were up by only ¼ of 1 percent over the past year. In addition, the slack in labor and product markets stemming from the weakening in economic activity that seems likely should put somewhat greater downward pressure on inflation going forward. Therefore, my forecast of the most likely outcome over the next couple of years is that total and core inflation will moderate from present levels.

The substantial easing of monetary policy to date, combined with ongoing measures to foster market liquidity, should help to promote growth over time and to mitigate risks to economic activity. I know that some observers are saying that this strategy introduces other risks. For example, some individuals question whether by lowering our policy rate in the face of price pressures, we put at risk our goal of keeping inflation low and stable over the long term.

While even the core price measures in the United States are rising somewhat faster than I would prefer, and inflation presents a key risk to my outlook, I believe that the Federal Reserve’s policy strategy remains compatible with a low and stable inflation rate.

Inflation was disappointing as well last year. The price index for personal consumption expenditures rose by 3.6 percent during 2007, compared to 2.3 percent the year before. Rapid increases in food and energy prices were the obvious culprits, but that provides little comfort to this central banker. The Federal Reserve is responsible for keeping total inflation low and stable—including food and energy prices. While the effects of unexpected commodity price increases are difficult to offset rapidly, an appropriate monetary policy would ensure that such shocks even out over time and do not impart a persistent inflation bias—either up or down.

Summing all of these factors, we think conditions will improve in the second half of this year, but not enough to prevent economic activity from still running at a relatively sluggish pace. We expect real GDP growth will return close to potential as we move through 2009.

...

Regarding the outlook for inflation, we project improvement over the medium term, with core inflation in the range of 1-1/2 to 2 percent by 2010. This forecast assumes that the resource slack being generated by the current weakness in the real economy will work to offset the cost pressures from higher energy and commodity prices ...

Our forecast also assumes—in line with current readings from futures markets—that energy and commodity prices will stabilize some time over the medium term.

Some would dismiss these rising inflationary pressures as temporary.  I believe they are more serious.  Energy prices have been trending up for the past five years, and there are good reasons for thinking that higher food and commodity prices are not being entirely driven by temporary supply and demand imbalances.  However, the bigger concern is that these increases are beginning to generate an inflation psychology to an extent that I have not seen since the 1970s and early 1980s.  Measures of inflation expectations in surveys and financial markets are moving higher, and businesses are increasingly passing on higher input and commodity prices to consumers and business customers.  In this environment, in my opinion, there is a significant risk that higher inflation will become embedded in the economy and require significant monetary policy tightening to reduce it.