### Capacity and Capacity Utilization Methodology

The Federal Reserve Board's capacity indexes attempt to capture the concept of sustainable maximum output, the greatest level of output a plant can maintain within the framework of a realistic work schedule after factoring in normal downtime and assuming sufficient availability of inputs to operate the capital in place. The concept itself generally conforms to that of a full-input point on a production function, with the qualification that capacity represents a sustainable maximum, rather than some higher unsustainable short-term maximum.

In general, to calculate an individual capacity index, preliminary, implied end-of-year indexes of industrial capacity are calculated by dividing a production index by a utilization rate obtained from a survey for that end-of-year period. These ratios are expressed, like the indexes of industrial production, as percentages of production in a comparison base year, currently 2007, and they give the general level and trend of the capacity estimates. Each implied capacity index number is an estimate of a sustainable maximum level of output expressed as a percentage of actual output in 2007. Thus, if in December 2007 the production index is 100 and a related utilization rate from a survey is 80 percent, then the implied capacity index is 100/0.8 = 125.

#### Summary of Methods

The individual capacity indexes for a year are derived from (1) preliminary, implied end-of-year indexes of capacity obtained by dividing a production index for an industry by a corresponding utilization rate obtained from a survey and (2) additional measures that, for most industries, are economic determinants of an industry's annual capacity growth. The capacity indexes, like the IP indexes, are expressed as percentages of production in 2007. Once the preliminary, implied capacity indexes are calculated, they are related to the additional measures in a regression model. The final capacity indexes for a year are derived from the fitted values of these regressions. The preliminary, implied capacity indexes thus give the general level and trend of annual changes from one year to the next. For most manufacturing industries, estimates of industry capital input and a variable related to the average age of the industry's capital stock are used as the additional measures.[1] For mining, utilities, and selected manufacturing industries, measures of physical capacity are available and are used to determine the final capacity indexes.[2]

The capital input figures are estimates of the flow of services derived from an industry's net stocks of physical assets; the net stocks are developed principally from investment data reported in issues of the Annual Survey of Manufactures and Census of Manufactures. Also used are estimates of business investment and price deflators by asset type, as well as the composition of an industry's capital spending by asset type, all from the Bureau of Economic Analysis.

#### Editing and Current Estimates

In general, the capacity indexes are estimated from annual data. Estimates for the current year are largely extrapolations. The monthly capacity estimates are interpolated between the year-end estimates and are rarely adjusted. Monthly utilization is derived by dividing a production index by a capacity index. The utilization ratio is not adjusted. If the utilization rate published by the Federal Reserve begins to diverge from a related utilization rate recently reported by a trade source, such as the American Iron and Steel Institute, the appropriate capacity estimate may be revised and notice is given in the G.17 release.

#### Source Data and Updating

Capacity indexes for industries that account for about 20 percent of total industry capacity are based on capacity and output data reported in physical units from government and trade sources, primarily in mining and electric utilities. In manufacturing, most capacity indexes are based on responses to the Census Bureau's Quarterly Survey of Plant Capacity; these industries account for a bit less than 75 percent of total industry capacity. Capacity estimates in physical units are available for significant portions of several major industries, however; these include paper, industrial chemicals, petroleum refining, primary metals, and motor vehicles. In the absence of utilization data for a few mining series, capacity is based on trends through peaks in production (roughly 5 percent of total industry capacity). Overall, capacity indexes are constructed for 89 detailed industries (71 in manufacturing, 16 in mining, and two in utilities), which mostly correspond to industries at the three- and four-digit North American Industry Classification System level.

With a spring annual revision schedule, an initial estimate of capacity for a year is released in February, and then the annual revision to capacity is issued in with the annual revision to IP, which is usually targeted for late March.

In compiling the estimates of manufacturing capacity from 1972 on, every effort has been made to achieve continuity with the estimates before 1972. The McGraw-Hill/DRI survey was the primary determinant of the level of utilization series in manufacturing from 1955 through the mid-1970s. Continuity is achieved by applying a level adjustment to series whose data source changed from the McGraw-Hill/DRI survey to the Census survey to maintain consistency with the historical levels based on the earlier survey. (The two surveys overlapped for 14 years.) Generally, utilization rates from the Census survey, now the main source for manufacturing utilization rates, were lower, on average, than those of the discontinued McGraw-Hill/DRI survey; thus, the Federal Reserve's utilization rates for major industry totals and subtotals differ from those issued by the Census Bureau.

[1] The age variable is the ratio of the age of an industry's capital stock relative to its expected service life, given the mix of assets that compose the stock. A fuller description of the models that are used to develop the Federal Reserve's capacity estimates was reported in Gilbert, Morin, and Raddock, "Industrial Production and Capacity Utilization: Recent Developments and the 1999 Revision," Volume 86, March 2000, pp. 194–97.