Dynamic measures of inflation.

• Author: Reis, Ricardo
• Position: Research Summaries

While the definition of inflation is widely agreed upon--"a continuing rise in the general price level" according to Merriam-Webster--turning it into a concrete measure is much more difficult. One key obstacle is figuring out how to combine all of the price changes in the economy into a single number, and this price-index problem has occupied many economists for centuries. (1)

Roughly three approaches have been taken. One is rooted in statistics, seeing price indexes as estimators of an underlying concept, and focusing on probability models of price dynamics and how to deal with sampling uncertainty, consistency, efficiency, and so on. Another approach uses both mathematics and logic, proposing axioms that price indexes should satisfy, and from them deriving the formulas necessary to compute the indexes. A third approach uses models of economic choice, whether of producer or consumer behavior, and derives price indexes as dual measures of changes in welfare.

Across all approaches, most of the work so far has been static. While the price indexes are used to compare two dates, the theory underlying them gives little or no role to time. More recently, a dynamic approach has surfaced, in an attempt to measure inflation and to answer three separate questions. (2)

What are the consequences of central banks targeting different measures of inflation?

Kosuke Aoki and Pierpaolo Benigno began this literature by characterizing optimal monetary policy if there are two sectors in the economy, one where prices are flexibly chosen and another where they are sticky, so the relevant dynamics relate to price adjustment. (3) Michael Woodford already had shown that if there is only one sector with sticky prices, then even though social welfare depends on the volatility of both inflation and an output gap, stabilizing inflation alone achieves both goals (a result that Olivier Blanchard and Jordi Gall would later label "the divine coincidence.") (4) Aoki and Benigno found that, with two sectors, targeting only the sectoral price index in the sticky-price sector maximizes social welfare.

In my work with N. Gregory Mankiw, we set up a simple but general framework to study a stability-price-index (SPI), designed so that by committing to keep it on target, the central bank would stabilize economic activity. (5) We consider an economy with many sectors and four sources of heterogeneity in sectoral characteristics: the sluggishness of price adjustments; the cyclical sensitivity of optimal prices; the sector's size; and the magnitude of sector-specific shocks. Our first result is a generalization of Aoki and Benigno: the stickier are a sector's prices, the larger is its weight on the SPI. By targeting the prices in stickier sectors, the central bank minimizes the forecast errors that these firms make when fixing their prices ex ante.

Our second result justifies the practice of focusing on core measures of inflation, which exclude food and energy prices. We show that if a sector has very volatile specific shocks, like food and energy, then it requires large movement in its relative...