This is another one of those months when you could report pretty much any number you like to summarize the current inflation rate, and, as William Polley noted, newspapers did. At times like these, the concept of “core inflation” can be very helpful.
Inspired by Macroblog’s as always excellent discussion, I took a look at the annual change in the major expenditure categories of the CPI as reported today by the Bureau of Labor Statistics. The histogram below records the fraction of the typical U.S. urban household’s expenditures devoted to items that went up in price over the last year by the amount indicated on the horizontal axis. For example, the graph reveals that 4.8% of household expenditures (corresponding to communication and women’s and girl’s apparel) fell in categories that exhibited a decline in prices between -1.5% and -2.5% over the last year.
If you were to show this distribution to a statistician and ask for a single number that summarized the central tendency of this data set, what would they say? I think most statisticians would try to persuade you that summarizing these numbers with any single statistic could be very misleading. For example, the median of these data would indicate a 2.2% annual inflation rate, whereas the mean would suggest a 3.7% annual inflation rate. These correspond (with slight numerical differences) to the median CPI inflation of 2.3% reported by the Federal Reserve Bank of Cleveland and the 3.6% CPI inflation reported by the Bureau of Labor Statistics, repectively. The differences between my numbers and theirs are due to the fact that I’m using coarser expenditure categories and a less complete data set than either Cleveland or the BLS.
The reason that the mean and median are so different for this data set is because of the extreme outliers. Motor fuel costs (accounting for 4.0% of household expenditures) are up 31.3% over the last year and fuel oil (a less important 0.3%) was up 33.3%. Many statisticians might conclude that there is a central tendency for a subset of the price data that is perhaps well summarized by the median of the entire sample, and a separate set of numbers that are likely responding to a very different set of influences from the rest of the data.
The Federal Reserve bears ultimate responsibility for one interpretation of the central tendency of such price data, specifically, the Fed is responsible for the purchasing power of a dollar. Although very dramatic changes in the rate at which the Fed allows dollar bills to get into circulation may affect the variance or skew of the price-change distribution, for the most part the latter come from events beyond the Fed’s control. The Fed isn’t in the business of getting oil out of the Gulf of Mexico and refining it for consumers. This is one reason that it really makes more sense for the Fed to focus on the median rather than the mean at times like these.
Barry Ritholtz expressed his usual healthy skepticism of any alteration of the statistics that makes them come out more favorable. But, as I noted here, there is another good reason for preferring a measure like the median CPI to the usual CPI, now and at any time. Numerous studies (e.g., ,
, ) have concluded that, if your interest is in trying to predict the value that the usual CPI (a mean-based statistic) will assume over the next few years, you’ll actually get a better forecast if you base it on something like the median CPI.
But what about those consumers who have to pay not just for the “central tendency” of this distribution, but cover all the family’s bills? For them I offer this modest consolation. I predicted on Monday that U.S. retail gasoline prices could easily fall 30 cents a gallon over the next few weeks, and in fact they’ve come down 10 cents a gallon already since then. With the October unleaded gasoline futures contract down today to $1.79 a gallon on NYMEX, and the average U.S. retail price at $2.85, another 30 cents down in retail prices from today looks like an equally safe bet. But if that indeed comes to pass, don’t thank Alan Greenspan– he had nothing to do with it.