But what exactly is meant when we talk about "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 recent 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:

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

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.

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