## September 16, 2005

### Who cares about core inflation?

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., [1], [2], [3]) 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.

Technorati Tags: , , ,

Posted by James Hamilton at September 16, 2005 02:04 PM

digg this | reddit

Listed below are links to weblogs that reference Who cares about core inflation?:

» THE CARNIVAL OF THE CAPITALISTS. from WILLisms.com
Welcome to THE Carnival of the Capitalists. When hosting traveling blog carnivals, it is customary for the host to rank, rate, profile, hide, categorize, and otherwise filter the entries. Sometimes the better posts are near the top or are given... [Read More]

Tracked on September 18, 2005 10:49 PM

You nailed the reason why real inflation matters so much -- the impact on consumer spending.

Until families can figure out how to set their budgets (ex food and energy), real inflation will matter more than the core.

For a more graphic depiction, have a look at Wal Mart's chart -- their clients are amongst the most price sensitive.

http://stockcharts.com/def/servlet/SC.web?c=WMT,uu[m,a]daclyyay[de][pb50!b200][vc60][iUb14!La12,26,9]&pref=G

Posted by: Barry Ritholtz at September 16, 2005 02:41 PM

Excellent post. I think that employing the median makes a great deal of sense in many economic situations. The smart money is already is looking at this question with a more analyitcal eye.

On a related note we probably should look more carefully at how we assemble our stats. The logic that drove us to the mean (conceptual appeal and computational costs) are rapidly falling ...

Posted by: simon at September 16, 2005 04:52 PM

What percent of the general population do you think would agree that inflation of 2%-3% per year accurately reflects their experience in the world?

Posted by: Tim at September 16, 2005 05:33 PM

Thanks, JDH. At least now I see why they say they look at "core inflation".

However, I still tend to quarrel with the use of "core inflation" in politics. It seems dangerous. Once it leaves the technical-analysis domain, it still seems to smack of, "if pigs had hollow bones and feathers and weighed a few grams, pigs could fly." After all, as you say, most folks buy most of the market basket, including the outliers.

Now, suppose one of the outliers keeps trending relentlessly up, up, up, year after year after year. Housing has been doing this for ages. Fuels may go on doing it too, as long as China and others grow fast enough to keep the price of fuel bumping against the ever-increasing marginal costs of supply expansion, and as long as politicians feel obliged to make nods to Kyoto.

Now you find yourself in a world of hurt. After all, the outlier is no longer really an outlier in the normally understood sense of something exhibiting transitory unusual behevior; it is merely a faster-moving part of the basket. And just mathematically, there is no limit to how high such a galloping outlier can jump, but any contervailing outliers moving lower are limited by being highly unlikely to go below zero.

In the world of politics and actual day to day expenditure, it seems that stressing the median risks two improved predictions relative to the mean, not just one. You might more accurately predict the median five or ten years from now. But you might also predict that regulatory action, or an adjustment in tax rates, or for that matter a COLA, based on the picture painted by the median-based deflator instead of the whole basket you have to purchase, will not do what you intended it to do.

Put another way, politicians stressing core inflation will essentially seem to be saying that gasoline, which was \$1 a gallon a few years ago, and now shows little prospect of going below \$2 any time soon, never went up. But outside New York City and downtown San Francisco, nearly everybody buys the stuff. No one cares much about the (real) price in 1980; they had long since adapted to the \$1 level. But folks *are* furious that politicians, yet again, are liars. They are so furious that they have been driving politicians to act counterproductively as you have documented in these pages. And therein lies the danger.

Posted by: PaulS at September 17, 2005 06:22 AM

Hmmm...now that I look again at what I just wrote...on a more technical note, could Fed emphasis on median instead of mean help explain the dot.com and housing bubbles, and Mr. Greenspan's insouciance (most of the time) with respect to them? After all, if you're downweighting or ignoring an exploding component, maybe you're not keeping the money supply in check?

Posted by: PaulS at September 17, 2005 06:28 AM

not to forget the effect on cola.

Posted by: Big Al at September 17, 2005 07:12 AM

"On a related note we probably should look more carefully at how we assemble our stats. The logic that drove us to the mean (conceptual appeal and computational costs) are rapidly falling ..."

I couldn't agree more. We're setting up a new hedge fund, to be called the "Core Return Fund", in which we optimize the median return. We're quite confident of making money nine out of every ten months, and while it's true that about one month out of ten we lose all the money made in the previous nine plus some, we think smart investors should ignore these outliers and instead focus on median returns which are guaranteed to be positive and quite regular. The old fashioned focus on the mean will hopefully soon become a thing of the past.

Posted by: Jeffrey Miller at September 17, 2005 07:29 AM

Jeffrey, even if your objective is to forecast the mean, it may be that statistically you do a better job in achieving that goal by using the median of the sample to predict the mean of the post-sample observations. That at least is the finding of the three studies I mentioned.

Posted by: JDH at September 17, 2005 10:14 AM

Hey, neat. Doesn't that suggest lifestyle changes driven by economics rather than a static-lifestyle notion of inflation?

-t

Posted by: Tom Lord at September 17, 2005 11:43 AM

I gather that the point is that the mean is more affected by outliers. But outliers tend to be noisier. Energy may not look that way now, we imagine that it is on an inexorable upward climb, but historically it has been highly volatile, with sharp increases and decreases from year to year. Food is another area with large swings.

This means that if you use the mean for prediction, it is getting jerked around by food and energy prices. But these are not stable from year to year, so if you use them, your predictions are unstable as well. By ignoring them and using core inflation (or as JDH suggests using the median, which automatically ignores all outliers), you get better predictions even when you are aiming to predict the mean.

The main point though is that although the core rate is a better tool for setting monetary policy, mean inflation is more appropriate for other purposes, such as indexing cost-of-living increases. We need to move to a dual inflation reporting system, one used by monetary analysts and another used for payment adjustments. Core inflation is less relevant for ordinary people, but it is the figure which tends to be more widely reported. We should restrict the use of core inflation to technical monetary analysis and keep the mean inflation rate as the one used for most social purposes.

Posted by: Hal at September 17, 2005 11:56 AM

I have always viewed the choice of central tendency statistics as being dependent on the use to which the data is to put. If one is looking for conclusions about the "typical" member of a population with a skewed dostibution, then the median is the appropriate measure. Examples are house prices and wages.

However, if one is interested in the behavior of the aggregate, then the mean can be a more appropriate measure. For example, the mean is a more appropriate measure when comparing the per capita GDPs of two countries.

The problem with the median CPI is that it is not the inflation experienced by the "typical" household, but it it the "typical" inflation experienced by all households. That makes the median CPI less useful for individual decicion-making in areas such as retirement planning. The solution, provide both mean and median numbers. After all, for optimum decision-making one should use the whole data set, but maybe we could live with just two numbers.

Posted by: RayJ at September 17, 2005 12:40 PM

Hal,
I saw your posting after I submitted mine. You write: "We need to move to a dual inflation reporting system, one used by monetary analysts and another used for payment adjustments."

I agree absolutely!

Posted by: RayJ at September 17, 2005 12:43 PM

JDH,
I would have thought that the median is a biased
estimate, and that in particular is biased down.
The second of the two papers you cite does not seem
to indicate any kind of bias correction and shows
that over the long run the median does not seem
to be biased (surprizing to me at least); the third paper does use a bias correction but doesn't say
how big it is or what the sign is. Do you know?

Posted by: Jeffrey Miller at September 18, 2005 08:05 AM

Jeffrey, it may seem a little surprising when you look at the histogram I plotted, but there does not seem to be much bias. Since 1968, the average value for the usual BLS CPI has been 4.8% inflation per year, which is exactly the same as the average value for the median CPI. The reason is that there will be other months where the outliers show big negative rates of inflation, for which the median CPI is above the mean CPI.

Posted by: JDH at September 18, 2005 08:17 AM

I'm not trying to pick a fight, I'm just curious how you would respond to this question, left unanswered from a couple days ago:

What percent of the general population do you think would agree that inflation of 2%-3% per year accurately reflects their experience in the world?

Posted by: Tim at September 18, 2005 10:19 AM

I'm not sure how people might respond to that survey question, Tim. My guess is that many people notice more when prices on some items go up than when they go down. And of course, some families are spending a much bigger fraction of their budget on gasoline than others.

Posted by: JDH at September 18, 2005 11:12 AM

To answer Tim, I think the most recent consumer sentiment survey of U. of Michigan put the 12-month ahead inflation rate at 4.6%. But that series is pretty volatile, and most of this year, it has been around 3 percent, the top of your range.

Posted by: pat at September 19, 2005 03:33 PM

Good answer, Pat. Thanks a lot.

Posted by: JDH at September 19, 2005 03:40 PM

Academic Economists would do well to stop referring to the cpi as a credible inflation indicator. Adoption of The Boskin Commission hearings recommendations resulted in a highly questionable, full point reduction in the reading. Now, the "Housing Bubble 2" Blog excerpts a 9/22/05 article in "The Economist" explaining why the respected Stephen Roach objects to the use of "core" cpi as an inflation indicator.
"Stephen Roach, the chief economist at Morgan Stanley, worked at the Fed in the 1970s under the then chairman, Arthur Burns. He remembers the dangers of core inflation. When oil prices surged in 1973-74, Burns asked the Fed's economists to strip out energy from the consumer-price index (CPI) to get a less distorted measure. When food prices then rose sharply, they stripped those out too—followed by used cars, children's toys, jewellery, housing and so on, until around half the CPI basket was excluded because it was supposedly “distorted” by exogenous forces. As a result, the Fed failed to spot the breadth of emerging inflationary pressures throughout the economy."

Posted by: bailey at September 22, 2005 01:54 PM

This is late, but an article in the latest Economist (http://www.economist.com/finance/displayStory.cfm?story_id=4425575)
makes my point better than I could:

"Stephen Roach, the chief economist at Morgan Stanley, worked at the Fed in the 1970s under the then chairman, Arthur Burns. He remembers the dangers of core inflation. When oil prices surged in 1973-74, Burns asked the Fed's economists to strip out energy from the consumer-price index (CPI) to get a less distorted measure. When food prices then rose sharply, they stripped those out too, followed by used cars, children's toys, jewellery, housing and so on, until around half the CPI basket was excluded because it was supposedly 'distorted' by exogenous forces. As a result, the Fed failed to spot the breadth of emerging inflationary pressures throughout the economy."

History tends to repeat itself.

Posted by: PaulS at September 26, 2005 07:00 AM