Relative prices and inflation (updated)

A recent discussion on twitter went as follows:

The basic point is that relative prices changes and inflation are not the same thing despite the fact that the way we calculate inflation makes them look as though they are.

To quote the Federal Reserve Bank Of Cleveland

Relative Price Changes Are Not Inflation

Relative-price changes, like inflation, can cause price pressure in an economy. We experience them every day much like we experience inflation, and they cause changes in standard price indexes. But there the similarity ends. Relative-price changes are not a monetary phenomenon. They arise in market economies as individual prices adjust to the ebb and flow of the supply and demand for various goods. Relative-price movements convey important information about the scarcity of particular goods and services. A rising relative price indicates that demand is outstripping supply (or that supply is falling behind demand), while a falling relative price denotes just the opposite. A rising relative price induces consumers to conserve on the good in question and to look for substitutes. A rising relative price also, by increasing profit opportunities, entices producers to bring more of the good in question to market.

In this way, relative-price changes—no matter how uncomfortable they are for consumers or producers—transmit vital information necessary for the efficient allocation of resources throughout any market economy. Inflation, by contrast, contributes no information useful to our consumption, production, or labor choices. If anything, inflation can temporarily distort vital relative-price signals, leading people to make unsound economic choices. It can even cause people to shift their time and resources away from activities that foster production and long-term economic growth to activities intended to protect their wealth rather than expand it.

Recently, the relative prices of petroleum, agricultural goods, and some other commodities have risen sharply. One factor responsible for much of these increases is the world’s unprecedented economic performance in recent years. Between 2004 and 2007, world output expanded an average of 4.8 percent each year, according to IMF data. While emerging markets, notably China and India, appear to have led the way, nearly every nation on earth shared in the expansion. This growth and development, which itself stems from an increasing willingness of countries to embrace globally integrated markets, has placed greater demand on world resources, leading to sharp increases in the relative prices of commodities. Foods imported into the United States, for example, have increased 4 percent on average each year since 2002 relative to other goods, while the relative prices of imported industrial commodities have increased 17 percent over the same period. Meanwhile, the relative price of petroleum increased 28 percent each year on average—and because petroleum is required to produce food and industrial commodities, its hike fed into their prices as well.

What we need to keep in mind is the difference between what may be called "true or pure inflation" and "relative price changes". One thing that seems odd about much discussion of inflation is the failure to make this distinction.

As noted by the Cleveland Fed changes in relative prices are important because it is relative prices that direct resource allocation. These are the price signals that are important for the smooth functioning of the economy, they provide the incentives for people to change their behaviour. As Cowen and Crampton (2002: 5) put it [t]he Canadian plumber's knowledge of substitutes for copper piping influences the French electrician's choice of home wiring through its effect on the market price of copper. "Pure inflation", on the other hand, is signal jamming noise which can result in the misallocation of resources. One of the major problems with inflation is the fact that people can't tell the difference between changes in relative prices and pure inflation. This is, in part, because the standard measures of inflation, eg changes in the CPI, contain both components: relative price changes and "pure inflation". Sorting these two factors out however is far from easy.

But what exactly is meant when we talk about "true or pure inflation"? Imagine an economy in which every price exogenously doubled. What used to cost $1 now costs $2, those who were paid $10 per hour now are paid $20, and what was worth $100 now is worth $200 and so on. Note that there has been no relative prices changes here. Thus, because people care about trade-offs when making choices, no one will behave any differently in the new "high price" world than they did previously. We would say, there is no "money illusion" in that changes in the unit of account don’t change anything real at all. (In microeconomic theory you learn this when you are told that demand functions are homogeneous of degree zero in prices and income.) Such an equiproportional price level increase, in the example just given the price level has doubled, is what can be called pure inflation.

In a paper - Relative Goods' Prices and Pure Inflation by Ricardo Reis and Mark Watson, CEPR 6593, December 2007 - it is pointed out that central to the story told above is a measure of inflation which is defined by two properties:

1. all prices increase in exactly the same proportion, and
2. the change is unrelated to any relative-price movements.

Reis and Watson argue that the extent to which (2) holds is an inflation measure's "purity." A measure of inflation is purer the more it has been stripped from relative-price changes and so it is closer to the thought experiment carried out above. How then to purify a measure of inflation?

Reis and Watson note that,

[i]n our own work, we noticed that factor analysis also gave a natural way to purify the measure of inflation. Factor analysis produces a set of components (or factors) that explain why prices move together. One of these factors is the equiproportional change in prices that Bryan and Cecchetti emphasised. But the other factors are just as interesting. These factors are measures of relative-price changes due to some common source (say productivity, fiscal, or monetary shocks), and it turns out that a few of these alone account for a great deal of the variability of price changes. Therefore, we can use them to statistically purify our measure of inflation from these main sources of relative price movements.

Using US data Reis and Watson found that

... most of the movements in conventional measures of inflation like the Consumer Price Index (CPI), its core version, or the GDP deflator are due to relative-price changes. Only around 15-20% of the movements in these measures of inflation correspond to pure inflation.

Given that they had measures of relative price changes and pure inflation Reis and Watson could look for evidence of money illusion in their data. They found that once they controlled for relative price changes, the correlation between (pure) inflation and real activity is essentially zero. So,

... when we see that high inflation typically comes with low unemployment or high output, this is indeed driven by the change in relative prices hidden within the inflation measure. When there is pure inflation, that is when all prices increase in the same proportion independently from any relative price changes, nothing happens to quantities.

Update: In a related blog post Michael Reddell at the Croaking Cassandra blog asks What to make of the CPI?