Some back-of-the-envelope scribblings:

Let me start with a rounded version of the Rudebusch version of the Taylor rule:

Fed funds target = 2 + 1.5 x inflation - 2 x excess unemployment

where inflation is measured by the change in the core PCE deflator over the past four quarters (currently 1.6), and excess unemployment is the different between the CBO estimate of the NAIRU (currently 4.8) and the actual unemployment rate (currently 9.8).

Right now, this rule says that the Fed funds rate should be -5.6%. So we’re hard up against the zero bound.

Suppose that core inflation stays at 1.6% (although in fact it’s almost sure to go lower.) Then we can back out the unemployment rate at which the target would cross zero, suggesting that tightening should begin: it’s an excess unemployment rate of 2.2, implying an actual rate of 7 percent. That’s a long way from here. If inflation drops to, say, 1 percent, the Fed shouldn’t tighten until unemployment drops to 6.25%.

What would it take to get to that range of unemployment? Okun’s Law suggests that it takes 2 points of GDP growth in excess of potential to reduce unemployment by 1 point. Potential growth is probably around 2.5. So say we have 5 percent growth for the next 2 years — which would be hailed as a stunning boom. Even so, unemployment should fall only 2.5 points, to 7.3. In other words, even with a really strong recovery (which almost nobody expects), the Fed should keep rates on hold for at least two years.

Bear in mind that I’m using entirely standard, conventional analysis here. It’s the people saying that the Fed should start tightening in the near future who are inventing some kind of new, unspecified framework to justify their views.

If we use Krugman's analysis, and the recent CBO projections for the average annual unemployment rate (10.2% in 2010, 9.1% in 2011, and 7.2% in 2012), the Fed would not raise rates until some time in 2012.

Is there a risk that we’ll have inflation after the economy recovers? That’s the claim of those who look at projections that federal debt may rise to more than 100 percent of G.D.P. and say that America will eventually have to inflate away that debt — that is, drive up prices so that the real value of the debt is reduced.

Such things have happened in the past. For example, France ultimately inflated away much of the debt it incurred while fighting World War I.

But more modern examples are lacking. Over the past two decades, Belgium, Canada and, of course, Japan have all gone through episodes when debt exceeded 100 percent of G.D.P. And the United States itself emerged from World War II with debt exceeding 120 percent of G.D.P. In none of these cases did governments resort to inflation to resolve their problems.

So is there any reason to think that inflation is coming? Some economists have argued for moderate inflation as a deliberate policy, as a way to encourage lending and reduce private debt burdens. I’m sympathetic to these arguments and made a similar case for Japan in the 1990s. But the case for inflation never made headway with Japanese policy makers then, and there’s no sign it’s getting traction with U.S. policy makers now.

The all-items CPI is constructed from approximately 8,000 basic indexes, which correspond to 38 geographic areas and 211 item categories. Apples in Chicago and gasoline in San Francisco are examples of these basic CPIs. Since 1978, the BLS has published CPI series that reflect the inflation experiences of two different population groups. The CPI for all urban consumers (CPI-U) and the CPI for urban wage earners and clerical workers (CPI-W) differ only in the relative weights that are attached to the basic item-area index components. For example, the CPI-W has a somewhat higher weight for gasoline than does the CPI-U, because the population of urban wage earners and clerical workers allocates a higher share of its consumption to gasoline than do urban consumers as a whole.

Many consumers feel that their personal inflation experiences are not reflected in the movements of the CPI-U. These experiences can actually be borne out because some consumers spend more than others on items with rapidly increasing prices. The CPI-U is constructed from expenditures averaged over many consumers; as a consequence, some consumers will face a lower rate of inflation than that indicated by the CPI-U, and others will face a higher rate of inflation. For example, earlier it was noted that the wage earner and clerical worker families represented in the CPI-W allocate a higher-than-average share of their expenditures to gasoline. Partly for this reason, the CPI-W rose 4.3 percent over the 12 months ending March 2008, compared with 4.0 percent for the CPI-U. Further, BLS data from the CE show that low-income households spend a greater-than-average percentage of their expenditures on food at home and on gasoline and motor oil. By income quintile, from lowest to highest, 15.3 percent, 14.1 percent, 13.0 percent, 12.1 percent, and 9.2 percent of expenditures are devoted to food at home and to gasoline and motor oil.54 These statistics provide some evidence that the typical household in one of the lower income quintiles may be more adversely affected by current inflation than a typical household in one of the upper quintiles.55

Another reason for the potential difference between the CPI-U and a consumer’s experience of inflation is that the prices of many frequently purchased items, especially necessities such as food and gasoline, recently have been rising more rapidly than the CPI as a whole. Because the CPI is an average of the inflation rates of many different items, if some prices are growing more rapidly than the CPI, then other prices must be growing more slowly. In many cases, the most slowly rising prices are in the categories of consumer durable goods and apparel. In fact, the CPI for durables, which include such items as televisions and computers, fell slightly over the year ending March 2008, as did the index for apparel. Of course, by their nature, those items are purchased less frequently than food and energy items. For a family that had no immediate plans to purchase a new television or computer in March 2008, the price declines of those products over the previous 12 months probably would be less important than the 26.0-percent increase in the price of gasoline, the 48.4-percent rise in the price of fuel oil, the 14.7-percent price increase for bread, and the 13.3-percent price rise for milk. Similarly, although most families purchase apparel during any given year, in many weeks their purchases will be concentrated in food and fuel, and in those weeks they probably experienced price increases higher than the increases reported for the all-items CPI. Nevertheless, the BLS cannot exclude items from the CPI simply because they are purchased infrequently: all goods and services contribute to the CPI in proportion to consumer spending on them, as described earlier.