How Much Do Official Price Indexes Tell Us About Inflation?
Official price indexes, such as the CPI, are imperfect indicators of inflation calculated using ad hoc price formulae different from the theoretically well-founded inflation indexes favored by economists. This paper provides the first estimate of how accurately the CPI informs us about “true” inflation. We use the largest price and quantity dataset ever employed in economics to build a Törnqvist inflation index for Japan between 1989 and 2010. Our comparison of this true inflation index with the CPI indicates that the CPI bias is not constant but depends on the level of inflation. We show the informativeness of the CPI rises with inflation. When measured inflation is low (less than 2.4% per year) the CPI is a poor predictor of true inflation even over 12-month periods. Outside this range, the CPI is a much better measure of inflation. We find that the U.S. PCE Deflator methodology is superior to the Japanese CPI methodology but still exhibits substantial measurement error and biases rendering it a problematic predictor of inflation in low inflation regimes as well.
We have long known that the price indexes constructed by statistical agencies, such as the Consumer Price Index (CPI) and the Personal Consumption Expenditure (PCE) deflator, measure inflation with error. This error arises for two reasons. First, formula biases or errors appear because statistical agencies do not use the price aggregation formula dictated by theory. Second, imperfect sampling means that official price indexes are inherently stochastic. A theoretical macroeconomics literature starting with Svensson and Woodford  and Aoki  has noted that these stochastic measurement errors imply that one cannot assume that true inflation equals the CPI less some bias term. In general, the relationship is more complex, but what is it? This paper provides the first answer to this question by analyzing the largest dataset ever utilized in economics: 5 billion Japanese price and quantity observations collected over a 23 year period. The results are disturbing. We show that when the Japanese CPI measures inflation as low (below 2.4 percent in our baseline estimates) there is little relation between measured inflation and actual inflation. Outside of this range, measured inflation understates actual inflation changes. In other words, one can infer inflation changes from CPI changes when the CPI is high, but not when the CPI close to zero. We also show that if Japan were to shift to a methodology akin to the U.S. PCE deflator, the non-linearity would be reduced but not eliminated. This non-linear relationship between measured and actual inflation has important implications for the conduct of monetary policy in low inflation regimes.