Not long ago, we posted a commentary discussing the difficulty of interpreting GDP data. The problem is one of extracting the true signal of economic growth from the noisy way that we measure output.

This signal extraction problem is generic in economics (and other sciences that use statistics). Indeed, one of us began his professional career trying to discern the trend of U.S. inflation. It was 1980 and the inflation numbers were hitting a peak of nearly 20%. The standard operating procedure at the time was to take things like food, energy and some housing-related items out of the index and recalculate them. But that meant removing only the components that had gone up more than average! How could you justify that? [Here’s a three-part blog post by Mike Bryan of the Atlanta Fed that recounts a similarly unsatisfying experience, as well as his thoughtful reactions over the years.]

Leading central banks today target inflation. To do so, they must measure it. That turns out to be no small feat. For years, people have been trying to figure out how to best use the information we have to estimate the medium-term trend in inflation. There are two issues. The first is scope: what should we include in the price measure? The Federal Reserve targets the rate of change of the price index of personal consumption expenditures (PCE), which is broader than the consumer price index (CPI), but the difference is not all that critical.

The second question policymakers have to answer is how to treat the monthly data as it comes in. In order to discern a trend, do you pay close attention to monthly changes in prices, or to some long-term average? And, do you look at the whole index or just pieces of it? That is, how can we figure out if a recent rise or fall in inflation is just transitory, or if it will persist? Is it merely statistical noise, or a useful signal of things to come?

In the 1970s, around the time that oil prices were skyrocketing for the first time (they rose from less than $4 a barrel in 1973 to nearly $40 in 1980), analysts started to compute measures of inflation that excluded food and energy prices. The logic was that these were short-lived movements that did not represent changes in the medium-term inflation trend. But from the beginning, researchers questioned the wisdom of this approach. Were some parts of the price index always completely uninformative about the future?

These doubts led to a different approach to measuring trend or *core *inflation: namely, the application of simple statistical filters designed to extract the signal from the noisy price data. For example, early work by one of us in this area explored the median CPI and the trimmed mean CPI as measures of trend. For those of you with an appetite for the technical details, you can find them here and here (as well as the links in Mike Bryan’s post). These statistical methods reduce the weight on those index components that show extreme movements in a particular month.

Are these statistical filters useful? Let’s look at the data to see. The two charts below are based on the monthly CPI data. The top one computes monthly percentage changes at annual rates. Some of the changes are so large that the chart truncates them. What you see is that the headline (all-items) CPI is extremely noisy. The blue line has lots of numbers that are very big and short-lived, both up and down.

**Comparing Measures of Inflation**

Now, turning to the other three lines – the CPI ex-food and energy (labeled “Core”), along with the median CPI and the trimmed mean published monthly by the Cleveland Fed. These three series are quite a bit more stable than the headline CPI. While it may be hard to see it on the chart, looking over the last 20 years (since 1994), it is the median that has the smallest standard deviation – nearly 20 percent lower than the CPI excluding food & energy!

The bottom graph plots 12-month percentage changes. Looking at the two pictures, you can see immediately why few people pay attention to the top version: it’s too noisy. Even in the bottom panel, the headline CPI still fluctuates quite a bit more than the other three indices, which track each other pretty well. But, if you look closely, you’ll see that when the median diverges from the traditional core measure, the CPI excluding food and energy, the core usually reverts to the median over time. In other words, the median CPI looks like a pretty good measure of the medium-term trend.

So, which items in the CPI are most frequently picked out as the median component? Put differently, which CPI components are particularly useful as guides for the medium-term inflation trend? It turns out that two bits are more informative than the rest. The first is something called “owner-equivalent rent” (OER) and the second is “food away from home.” OER is a strange animal. In order to ensure that homeowners and renters are treated equally, national statisticians pretend that homeowners rent their homes from themselves, and then they proceed to estimate this fictional rent. Calculation of OER is pretty complicated, involving a survey of rental units that are matched to the homes people live in and some averaging over time. Importantly, the OER seems to do a pretty good job of tracking the medium-term trend. [For more on the role of OER and its dynamics, see this recent post.)

Food away from home captures a microcosm of the overall economy. Why? Running a restaurant requires renting space, hiring employees (who receive a salary and benefits), outsourcing things like laundry, paying your utility bill, and buying raw materials that are normally delivered. As a result, the price of eating out roughly mirrors the aggregate price level itself.

What does all of this mean for inflation and for current monetary policy? In a previous post, we suggested that current Fed policy appears consistent with an eventual overshoot of its 2% inflation objective. But, so far, the inflation data don't show it. Over the past 12 months, the median CPI is up by 2.2%. However, annual PCE inflation, which the Fed targets, typically averages 0.5 percentage points *less than* CPI inflation. With its inflation target still intact, the Fed is willing to maintain a very stimulative policy, even if that makes an eventual inflation overshoot likely. Doing so buys them insurance against a downside economic surprise at a time when – with short-term interest rates stuck at the zero bound – they can’t cut the policy interest rate.