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Inflation can be pure too

Here is a discussion of work showing that constructed measures of ‘pure inflation’ differ markedly from standard measures. For example, pure inflation is uncorrelated with real output – just as neoclassical economics says it should be.

Everyone seems to care about inflation. Policymakers worry about controlling it; journalists demand answers to why it just went up or down; the public rates it in surveys as a major social problem; and academic economists use measures of inflation as much as any other number. (Try opening an issue of any general interest economics journal and count how many articles use a measure of inflation to deflate something.) Inflation is the rare economic concept that deserves an entry in the dictionary, which typically goes something like “inflation is the overall increase in prices.”

A key step in turning this definition into something concrete is choosing how to add up all the price changes into a single number. The answers to this “price index” problem have typically fallen into two well-separated groups. One group studies indices as statistical estimators, and focuses attention on probability models, sampling uncertainty, and so forth. Another group focuses on the economic fundamentals behind the index, like consumer or producer behaviour, economic welfare, or some predicted correlation with key observables. This tight separation leaves all of these measures exposed to criticism: the first group for having little to do with economics, the second with typically being too tightly linked to modeling specifics and details.

There is one measure of inflation, though, in which statistics and economics meet. And luckily, it is one that is pretty central to economics. In almost all introductory economics courses, the time comes when the teacher tells the following story: “Imagine that every price in the economy exogenously doubled. What used to cost €1 now costs €2, those who were paid €15 per hour now are paid €30, and what was worth €100 now is worth €200. Crucially, no relative prices change. Therefore, because people care about trade-offs in making choices, no one will behave any differently. There is no ‘money illusion’ in that changes in the unit of account don’t change anything real at all.” Students then hear this result again, when they take microeconomic theory and learn that demand functions are homogeneous of degree zero in prices and income, when they take macroeconomics and learn about long-run vertical Phillips curves, and when they take history of economic thought and learn about David Hume.

Central to this economic story with its sharp prediction is a measure of inflation defined by two statistical properties: (i) all prices increase in exactly the same proportion, and (ii) the change is unrelated to any relative-price movements. The extent to which (ii) holds is what we might call the 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 that economists tell their students.

While authors as far back as David Hume or Francis Edgeworth discussed pure inflation, the concept went through most of the XXth century without much notice. The exception is a short and (unfairly) neglected article by Michael Bryan and Stephen Cecchetti published in 1993. They had the key insight that the methods of factor analysis are well-suited to extract pure inflation, because these methods give a straightforward way to measure the common component in price changes that affects all equiproportionately.

In 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.

When we did this for the United States, we 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. Most of the time, pure inflation and CPI inflation are broadly related, but there are interesting exceptions. For instance in the late 1990s and early 2000s, CPI and core inflation were relatively low, but pure inflation was actually quite high. Favourable relative-price shocks seem to have accounted for most of what was seen back then as surprisingly low and stable inflation in spite of loose monetary policy.

With our measure of pure inflation, we can also check the claim that there is “no money illusion”. Dating back at least to Phillips and his famous curve, economists have found that measures of inflation are robustly correlated with measures of real activity. Most theories explain this as a result of relative price changes. In sticky-price models, for instance, when monetary policymakers intervene, some firms change their prices while others do not. Because there is a change in the relative price of the goods sold by these two types of firms, consumption and production plans change and so quantities change. However, since economists only have crude measures of relative price changes, this explanation of the correlation between real activity and inflation has not been directly tested. A worrying alternative is that, in fact, there is money illusion, and the story that pervades our teaching of economics is just wrong.

Armed with our measure of relative-price changes and pure inflation, we re-examined the Phillips correlations. What we found was reassuring. After controlling for relative price changes, the correlation between inflation (or 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. Neoclassical economics seems to have this one right.


Bryan, Michael F. and Stephen G. Cecchetti (1993). “The Consumer Price Index as a Measure of Inflation.” Federal Reserve Bank of Cleveland Economic Review, pp. 15-24.

Reis, Ricardo and Mark Watson (2007). “Relative Goods’ Prices and Pure Inflation” CEPR 6593, December. http://www.cepr.org/pubs/dps/DP6593.asp

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