The first argument, represented in this this piece by Laurence Meyer is purely statistical. The Fed should pay no attention to food and energy prices, as movements in these prices tend to be transitory. Further, in recent data, as supported by this study for example, core inflation tends to predict headline inflation, so if we want to control headline inflation, ultimately we should be controlling core inflation anyway.
The second argument in favor of using core inflation measures, comes from New Keynesian (NK) theory. In NK models, welfare losses arise from relative price distortions, but the problem arises only for the sticky prices, not for the more-volatile flexible prices. Therefore, according to the argument, monetary policy should confine attention to only the sticky prices, for example what is in the Atlanta Fed's sticky price index.
Now, this speech by Charles Plosser got me thinking, in particular this passage:
Some fear that the strong rise in commodity and energy prices will lead to a more general sustained inflation. Yet, at the end of the day, such price shocks don’t create sustained inflation, monetary policy does. If we look back to the lessons of the 1970s, we see that it is not the price of oil that caused the Great Inflation, but a monetary policy stance that was too accommodative. In an attempt to cushion the economy from the effects of higher oil prices, accommodative policy allowed the large increase in oil prices to be passed along in the form of general increases in prices, or greater inflation. As people and firms lost confidence that the central bank would keep inflation low, they began to expect higher inflation and those expectations influenced their decisions, making it that much harder to reverse the rise. Thus, it was accommodative monetary policy in response to high oil prices that caused the rise in general inflation, not the high oil prices per se. As much as we may wish it to be so, easing monetary policy cannot eliminate the real adjustments that businesses and households must make in the face of rising oil or commodity prices. These are lessons that we cannot forget.There is an interesting idea in here. In general, which prices are volatile and which are not will depend on the monetary policy regime and what the central bank is attempting to target.
To make the argument more precise (though it's still pretty rough - just a sketch really), I need some symbols, which I can't put in the body of this post, so I'll direct you to these notes. Here's the basic idea. Suppose that all prices are flexible, and that the Fed can control the price level, but only imprecisely due to errors related to measurement, the loose link between policy and prices, or even sheer stupidity. Suppose that there are essentially two kinds of goods, "volatile-price" goods, and "smooth-price" goods, with the relative price of these two types of goods fluctuating randomly.
Now, suppose the Fed chooses to target the price of the smooth-price goods, in dollars. As a result, the prices of volatile-price goods are indeed volatile, both due to policy errors and because of the relative price variability. As well, the prices of smooth-price goods, which are indeed smooth, are an excellent tool for forecasting the future price level, as fluctuations around the price level target are due only to current innovations coming from policy errors and innovations to relative prices.
But, the Fed could choose instead to target the prices of volatile-price goods. Then, everything is turned on its head. The volatile prices are now smooth, the smooth prices are volatile, and the good forecasting tool for the future price level is the volatile price.
But, if you are a firm believer in sticky prices, you will now say: "But if the Fed attempted to target the non-sticky prices, we would have a problem, in that we would get inefficient fluctuations in real GDP. Further, the Bils and Klenow data, and Klenow-Malin work tell us something important about the stickiness of prices across goods and services." To which my reply is: "This evidence tells us only about the observed behavior of particular prices, and tells us nothing about how the pricing behavior depends on monetary policy. For that, we need a theory, and perhaps a structural model of price-setting that we can fit to the data. Indeed, I think I (or someone else) could write down a model with flexible prices where, under particular monetary regimes, the model delivers the features of the data. Indeed, this paper, by Head/Liu/Menzio/Wright does something like that."
To say how a central bank should be responding to particular observed price movements, we need some solid theory concerning the welfare effects of inflation, how monetary policy affects inflation, and some solid measurement to tell us about the quantitative effects. I don't see anything solid that justifies the Fed's focus on core inflation measures. Indeed, one could, I think, make a better case for looking at headline inflation measures.