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Producer Price Indexes

## BLS Research Series: Producer Price Indexes Using a Geometric Mean

The U.S. Bureau of Labor Statistics is producing a research series which calculates Producer Price Indexes using a geometric average (PPI geo-mean) at the elementary index level.  This differs from official PPI data, which are calculated using an arithmetic average.

#### Background

Producer price aggregation typically occurs in two stages. First, price changes within a narrowly defined grouping are combined to form an elementary index. Then, these elementary indexes are aggregated into broader measures like the headline PPI for Final Demand. PPI data are currently based on a modified Laspeyres formula at both levels of aggregation. However, in practice the PPI utilizes a formula closer to the Young formula at the elementary calculation level, and a formula closer to a Lowe formula for higher-level aggregations.  At both levels of aggregation, the formula is an arithmetic mean of price changes that fixes quantities in the base period.

The PPI geo-mean research series use a geometric mean, specifically a geometric Young formula rather than an arithmetic mean, to calculate elementary indexes. Rather than fixing quantities, the geometric Young formula fixes revenue shares in the base period. By fixing shares, a geometric Young index captures substitution towards relatively less expensive goods and services. A geometric mean index will be less than or equal to the arithmetic mean index when based on the same weights, and therefore PPI research geo-mean index levels generally will be lower than official PPI index levels when using the geometric Young formula. (Unlike with consumer prices, use of the geometric Young formula for research PPI geo-mean calculations may be less motivated by the issue of substitution.  However, research suggests that although firms have an incentive to substitute production towards higher priced goods and services, this is likely outweighed by other factors like changes in demand resulting in substitution towards lower priced goods.)

A number of countries calculate producer price indexes using a geometric mean formula at the elementary level, and the International Monetary Fund PPI Manual includes geometric mean-based formulas among the possible formulas that can be used to calculate elementary level PPI indexes. The U.S. Consumer Price Index also uses a geometric mean formula at the elementary level for most items.

The geometric Young index may be preferable to the arithmetic Young index because:

• The geometric Young has better axiomatic properties than the arithmetic Young and lower formula bias.
• Price indexes are calculated to estimate specific theoretical targets derived from economic models. The closer an estimate is to the target, the less bias an index has relative to the target. In the case of producer prices, the theoretical target is generally based on a profit maximizing firm given some level of technology and inputs. The geometric Young may be a better approximation of an economic target based on average technology and inputs.

#### Methodology

Other than using a geometric Young formula instead of an arithmetic Young formula at the elementary level of index calculation, the methodology used to calculate these research PPI geo-mean data is generally the same as what is currently used to calculate official PPI data.

#### Limitations

Research PPI geo-mean indexes are calculated outside of the official PPI production system and are at greater risk of calculation errors than official PPI indexes.

Within the wholesale and retail trade sectors, where the PPI measures the average changes in margins (the difference between selling prices and acquisition prices), the geometric Young is particularly sensitive to near-zero margins. Earlier research indicated minor differences in results when imposing bounds on the most extreme price changes and therefore bounds are not imposed in these results.

#### Publication

The publication structure for research PPI geo-mean indexes is identical to the publication structure of official PPI data. Research PPI geo-mean indexes are published in Excel files, and contain select Final Demand-Intermediate Demand indexes, Commodity indexes at the 2-digit level, and Industry indexes at the most aggregate level available (typically the NAICS 3-digit level). Research PPI geo-mean indexes include historical data back to 2011, and are available at the links below: