There is a lot of buzz around inflation these days. Some people are explaining why we shouldn‘t worry and some people why we should, but regardless – it’s a topic of conversation for the first time in ages. And despite this (or rather, because of it, because I find myself very busy these days), I haven’t written in a long time despite the fact that I have a few things worth writing about. I keep trying, though.

Today I am cheating a bit and taking a column from the quarterly inflation outlook that my company (Enduring Investments) just sent to customers. But I think it is fair to include it here because the musing was provoked by a recent exchange I had on Twitter while doing my monthly CPI analysis/tweetstorm (follow me @inflation_guy).

As readers know, I tend to focus on Median CPI, rather than Core CPI, as my forecast target variable. The reason is that price changes are rarely distributed randomly. If they were, then the choice of core or median CPI would be irrelevant because they would normally be the same or roughly the same. But when a distribution has long tails, the ends of the distribution exert a lot of pressure on the average and so median can differ substantially from the mean simply because one tail is much longer than the other even if most of the distribution is similar.

Consider a playground see-saw and imagine that on one side of the see-saw are seated several small children. Think of the “average” of the see-saw system as the point where the see-saw balances. Well, there are lots of ways to balance the system with weight on the other side of the see-saw: a very large weight close to the fulcrum will do it. But the further away from the fulcrum one places the weight, the smaller the weight necessary to balance the scale. As Archimedes said, “give me a lever long enough, and a place to stand, and I can move the world.” The point is that influence far from the middle of the distribution can have a very significant effect on the average because it is far away from the distribution:  the effect on the mean is (weight * distance from the mean).

Example: the mean of 98% of a distribution is 12. The remaining 2% of the distribution is 28. The weighted average is [(12 * 0.98) + (118 * .02)] / (0.98 + 0.02) = 14.12.  That little 2% caused the mean to go from 12, without the tail, to 14.12 with the tail…a movement of 17.7%! Notice that .02 * 118 = 2.12, which is the amount the mean moved. And if that tail is 228 rather than 118, the mean goes to 16.32. So you see, the length of the tail matters. In both cases, the median was 12, which I would argue is a better indicator of the “central tendency” of the distribution.

(If the distribution is approximately normal, then the tails roughly balance and so the mean and median are about the same. But many economic indicators are not normally distributed, especially ones like income or home prices which are bound by zero on one side. Thus, for many economic series the median, rather than mean, is a better measure. Even though CPI is not bound by zero, it is not normal because prices are not set in a continuous process but instead to have jump-discontinuities.)

The chart below, which I often show in my CPI tweetstorm, shows the see-saw of CPI, where I’ve broken up the index into its lowest-level components and placed those weights on a number line representing the most-recent year-over-year changes. The height of the bar indicates the amount of the basket that sits in that bucket. As you can see, nearly half of the CPI is inflating faster than 3% (which is why Median CPI is 2.8%), and the mode of the distribution is between 3.5% and 4.0%. But because of the far left tail, the mean – which is what core CPI is – is just barely over 2%. Because we have much longer left-hand tails than right-hand tails, the average is biased lower relative to median.

But is this “normal?” Some people have occasionally accused me of picking Median CPI because it tends to be higher, and so the number makes it look like there is more inflation. If the spread were constant, then it would be a bit academic which we chose as the forecast variable, and in fact, Core would have a better claim since after all, as consumers purchasing that basket we are in fact paying the average price and not the median.

In fact, though, I think that the tendency of core in recent years to trade below median really is its own interesting story about how prices evolve. If we have 3% inflation, it does not mean that all prices are going up at 3% per year, 0.75% per quarter, 0.25% per month. The price of any given good doesn’t move smoothly but rather episodically, sporadically, spastically. When we are in a disinflationary period, or anyway a low-inflation period, what is happening is that those episodes involve periods of slower prices and “transitory factors” that tend to be on the downside.[1] In that sense, it may be that the Fed, and me/Enduring, both err when they try to look through ‘transitory factors’ because transitory factors may be part of the process. The argument for that perspective is similar to the argument I myself make about why “ex-items” measures make sense when you are looking at an individual company’s earnings but not when you look at the aggregate earnings of the economy. Because bad stuff, or “items,” are always happening to someone somewhere. You can throw them out of anyone analysis but if you own the index, you’ll get some of those “items.” You just don’t know from where. Perhaps inflation is the same way.

However, I should point out that median inflation is not always below core. The chart below shows median and core CPI going back to 1983, which is when the Cleveland Fed’s series for Median CPI begins. Notice that from 1983 until 1993, Median CPI was generally lower than core CPI. In 1994, this changed and it has been the opposite ever since.

The year 1994 is significant because that is also the year that most models for inflation that are calibrated on pre-1994 data break down (or, conversely, it is the year prior to which a model calibrated on post-1994 data breaks down). I have written previously about this phenomenon and the fact that the Fed believes this is when inflation expectations abruptly became “anchored,” whatever that means – but *I* believe that this discontinuity is when globalization kicked into high gear with an explosion in the number of bilateral and multilateral trade agreements. It strikes me as plausible that these items are related. When markets are suddenly opened to global competition, affected markets will suddenly show slower price appreciation due to the pressure from that competition (and the replacement of high-cost domestic goods with lower-cost imports). But which market is currently being affected will not stay constant, but change over time. In other words, I think the fact that core has been persistently below median for a long time is a symptom of the globalization “dividend.”

If I am right, and if I am also right about the arrow of globalization changing direction, then it follows that core and median might flip positions at some point over the next couple of years. And then the “transitory effects” will be mostly on the high side.

[1] It could also be indicative of a bias from the measures that their improved methods are always looking for lower inflation – not in the “the BLS is making up this *@&$^” sense but in the sense that for lots of reasons the CPI appears to be overstated because of technical details about the functional form, the way measurement errors happen, etc. And so researchers may spend more time looking for ways that inflation is overstated. I don’t think that research bias is actually much of a problem. But I figured I ought to mention that that is one possible interpretation.