Why there is no such thing as food inflation, or housing inflation, or health care inflation, or any other kind of sector inflation.

Inflation is common to all prices, by definition.

The press have been talking a lot about inflation ever since the rate of inflation picked up in early 2021. The press, however, are not particularly well-educated in economics (including the financial press), and their misuse of economics terminology — here focused on their misuse of the word inflation — is accordingly unsurprising. The misuse of the word inflation (here is a recent example from Reuters) has trickled down to the public, and I’ve heard so many people use the word incorrectly in the last four years that it’s driven me crazy enough to post a quickie about it. Here I want to explain why the word inflation is used incorrectly.

Inflation is, by definition, a change in the general price level in an economy. The lazy (but still true) way to see that there is no such thing as food inflation, or housing inflation, and so forth, is that food and housing and so forth are not general: prices in these sectors are sector-specific (wow), and therefore are not inflation. QED.

A lot of people outside of the economics profession find this unsatisfying, however, especially since they’ve repeatedly heard the press misuse this terminology and have internalized it themselves. So let me express the idea using some simple math. For simplicity, suppose the economy has two goods: good 1, good 2. The change in the price of each good can be decomposed into two components: the common component (inflation or π) and the good-specific component (δ):

\(\begin{align*} \Delta p_1 &= \pi + \delta_1, \\ \Delta p_2 &= \pi + \delta_2. \end{align*}\)

The inflationary term does not have a good-specific subscript because it is common to all goods; the good-specific component has a subscript because it is the price change unique to that good.

When the price of good 1 increases, it can do so for two different reasons: because inflation is positive, or because its good-specific price change is positive. At the extreme, this could be when inflation is zero but good 1 has an idiosyncratic price increase:

\(\pi = 0 \text{ and } \delta_1 > 0 \quad \Rightarrow \quad \Delta p_1 > 0.\)

At the other extreme, this could be when inflation is positive but good 1 has no idiosyncratic price increase:

\(\pi > 0 \text{ and } \delta_1 = 0 \quad \Rightarrow \quad \Delta p_1 > 0.\)

In the first case, the price of good 1 is rising faster than the rate of inflation; in the second case, the price of good 1 is rising exactly at the rate of inflation.

Here is the crucial part for non-economists to grasp: in both cases, I have just discussed the relative price increase of good 1. By comparing the individual price of good 1 to inflation, we are implicitly comparing the individual price of good 1 to that of price 2, because inflation is determined by (and is common to) all price changes. If price 1 increases faster than inflation, then it must be rising relative to price 2.

Here’s a numerical example. Suppose good 1 has increased by 1% and good 2 has increased by 5%. Furthermore, suppose that the two goods are equally weighted so that the rate of inflation is therefore simply the midpoint of 3%. Then we can write the change in the two prices as

\(\begin{align*} \Delta p_1 &= 3\% - 2\% = 1\%, \\ \Delta p_2 &= 3\% + 2\% = 5\%. \end{align*}\)

Using correct terminology, we can say the following:

• The nominal price of good 1 has increased by 1%.

• The nominal price of good 2 has increased by 5%.

• Inflation is 3%.

• The real price of good 1 has fallen by 2% (nominal price change minus inflation).

• The real price of good 2 has increased by 2% (nominal price change minus inflation).

The important takeaway is that the word inflation does not refer to just any old price increase: those are just called, well, price increases, which can be absolute or relative, real or nominal. I just wrote in terms of goods, but the same logic applies to sectors:

• The price of technology has increased by 1%.

• The price of food has increased by 5%.

• Inflation is 3%.

• The real price of technology has fallen by 2%.

• The real price of food has increased by 2%.

There is only one statement made about inflation, and it is not good- or sector-specific!

The thing to keep in mind is that inflation is a fundamentally macroeconomic phenomenon relating to a currency: it is economy-wide and encompasses all prices in the economy, capturing the purchasing power of a currency. As soon as you start talking about sector-specific prices, you are no longer talking about the purchasing power of a currency — and the word inflation is no longer applicable — because you are no longer considering the set of prices that need to be under consideration in order to evaluate the purchasing power of that currency.

Let’s do another numerical example. Suppose price 1 increases by 2% and price 2 decreases by 2%. The rate of inflation is therefore 0%: the purchasing power of a dollar is unchanged. You need more dollars to purchase the same quantity good 1, you need fewer dollars to purchase the same quantity of good 2, and overall you can buy the same quantities of goods 1 and 2 because the price increase and price decrease balance out. Saying “good 1 inflation is 2%” is tantamount to saying that the purchasing power of currency has decreased by 2% in terms of purchasing good 1. But currency isn’t analyzed at that level because the value of a currency is not specific to a single good: it is evaluated against its ability to purchase some combination of all goods. Ergo it is also incorrect to talk about inflation in that context, because inflation is a statement about the purchasing power of currency. The correct thing to say would be “the price of good 1 has increased by 2%” or “good 1 has become 2% more expensive.”

tl;dr: inflation reflects the purchasing power of a currency, not simply whether the price of some things have gone up, and we shouldn’t let the economically illiterate press dictate the usage of economic terminology.