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Diffusion Indexes of Industrial Production

Beginning July 1991, the Federal Reserve will resume publication of diffusion indexes of indus-trial production (IP) in its monthly statistical release, Industrial Production and Capacity Uti-lization-, diffusion indexes previously were pub-lished from July 1979 to March 1990. Like all diffusion indexes, those for IP summarize the direction of change over a given time period in a set of disaggregated data.1 Thus, their purpose is to provide a measure of the breadth of change in the aggregate series.2

Output changes in the 250 series that constitute the total industrial production index form the basis for the calculation of the diffusion indexes.3

The value of the diffusion index is equal to the proportion of series that increased over a given time period, referred to as the "span" of the

1. Besides those for industrial production, diffusion in-dexes are calculated, for example, by the Bureau of Labor Statistics for payroll employment and by the Bureau of Economic Analysis for the indexes of leading, coincident, and lagging indicators. The diffusion indexes of payroll em-ployment are described in Patricia M. Getz and Mark G. Ulmer, "Diffusion indexes: a barometer of the economy," Monthly Labor Review (April 1990), pp. 13-21. The diffusion indexes of leading, coincident, and lagging indicators are published in the Survey of Current Business.

2. The idea of studying the breadth of movements in economic time series was central to the Work of Arthur Burns and Wesley Mitchell. See Arthur F. Burns and Wesley C. Mitchell, Measuring Business Cycles, National Bureau of Economic Research (New York, 1946). The uses and inter-pretation of diffusion indexes are discussed in, for example, Geoffrey H. Moore, Business Cycles, Inflation, and Fore-casting, Ballinger Publishing Company for the National Bu-reau of Economic Research (Cambridge, Mass., 1980); H.O. Stekler, "Diffusion Index and First Difference Forecasting," Review of Economics and Statistics, vol. 43 (May 1961), pp. 201-208; Geoffrey H. Moore, "Diffusion Indexes: A Com-ment," The American Statistician, vol. 9 (October 1955), pp. 13-17, 30; and Arthur L. Broida, "Diffusion Indexes," The American Statistician, vol. 9 (June 1955), pp. 7-16.

3. The number of series in the total IP index has changed over time, and the calculation of the diffusion indexes reflects these changes. Specifically, from 1968 to 1971, the index comprised 238 series; from 1972 to 1976, 256 series; and since 1977, 250 series. The industrial production index is described in Kenneth Armitage and Dixon A. Tranum, "Industrial Production: 1989 Developments and Historical Revision," Federal Reserve Bulletin, vol. 76 (April 1990), pp. 187-204.

Diffusion indexes of industrial production Percent

— 1 One-month span

i i i i i i i i i i i i i i i ii i i i i i i i

Three-rr H i i i

onth span A i i i i

w 1 1 1 1 1 1 1

/vw 1 ll 1 1 1 1 1 1 1

Six-month span nA i i i . i i i i

fN i i i i i i i

v/VN 1970 1975 1980 1985 1990

The shaded areas denote periods of business recession as defined by the National Bureau of Economic Research.

diffusion index, plus one-half of the proportion that was unchanged. The precise computation of a diffusion index is as follows: If an individual series increases over the span of the diffusion index, it receives a value of 100; if it declines, it receives a value of 0; and if it is unchanged, it receives a value of 50. The diffusion index is then calculated by summing these values for each of the components and dividing the result by the number of series included in the diffusion index. Diffusion indexes of IP for spans of one, three, and six months are available for the period beginning July 1967.

The interpretation of diffusion indexes is straightforward: A value of 50 indicates that over the interval spanned by the diffusion index the proportion of series posting increases was equal to the proportion that declined, whereas a read-ing of more than 50 means that more series rose than declined. As indicated in the chart, the

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July 1991

Diffusion Indexes of Industrial Production 535

Diffusion indexes of industrial production for spans of one, three, and six months, 1967-90

Year January February March April May June July August September October November December

One-month span

1967 51.1 66.7 53.2 67.1 63.3 60.3 1968 60.3 44.3 62.9 55.3 50.6 71.7 57.8 52.3 58.6 59.1 59.5 61.2 1969 57.4 58.2 57.4 62.9 46.0 57.0 59.9 55.7 51.1 52.3 49.4 42.2 1970 34.2 51.1 46.4 43.0 43.9 45.1 60.8 43.5 46.4 38.4 44.3 54.9 1971 56.1 40.9 49.8 59.9 59.5 54.4 56.5 51.5 62.4 62.9 57.0 54.9 1972 70.9 58.4 64.7 66.7 45.5 55.7 56.1 65.9 60.4 66.7 63.9 65.9 1973 52.2 65.5 52.5 52.5 54.1 59.6 62.0 51.8 57.6 58.0 56.9 39.2 1974 41.6 45.5 52.9 45.5 63.9 53.3 48.6 49.4 42.7 37.3 31.8 22.4 1975 35.3 34.9 33.7 56.9 45.1 62.7 59.2 58.8 61.6 53.3 55.7 58.8 1976 60.4 60.4 45.5 51.8 63.1 47.8 56.1 59.6 47.1 56.9 59.6 55.3 1977 54.5 57.6 63.5 65.5 70.3 62.7 49.2 56.0 48.0 54.0 54.4 50.8 1978 53.6 54.0 59.6 76.3 51.2 63.1 51.2 58.4 53.2 56.4 53.6 59.6 1979 45.2 62.0 56.4 44.8 63.9 47.6 52.4 44.0 49.6 57.6 45.2 49.2 1980 56.4 49.2 44.4 34.1 27.3 45.2 39.2 63.9 63.5 61.2 64.7 59.2 1981 47.2 50.8 50.0 49.2 55.2 52.8 55.2 48.0 35.7 35.7 35.3 37.3 1982 40.8 68.3 35.7 39.2 48.4 50.8 39.2 48.0 43.2 40.0 48.8 39.2 1983 68.7 52.0 67.5 63.5 71.5 60.0 68.7 58.4 68.3 64.3 52.0 52.4 1984 69.1 58.8 57.6 57.2 54.8 55.6 51.2 44.4 50.0 45.6 51.2 47.2 1985 50.0 55.2 59.2 50.0 52.8 52.8 49.2 57.2 57.6 40.0 53.2 56.4 1986 60.0 43.6 40.8 61.6 46.4 50.0 50.0 60.0 50.0 54.8 56.4 60.8 1987 43.6 67.5 53.2 56.8 65.9 56.8 66.3 51.2 50.0 63.5 55.6 52.0 1988 63.1 51.6 56.0 57.2 60.4 58.0 66.7 51.6 46.8 57.2 56.8 53.6 1989 60.8 43.6 48.0 65.5 40.0 55.2 48.8 55.2 41.2 51.6 51.2 45.6 1990 56.0 52.8 47.6 49.6 58.4 56.8 57.0 49.2 45.2 37.3 34.5 36.5

Three-month span

1967 44.7 66.2 64.6 65.8 65.0 69.2 1968 69.2 61.2 62.0 51.1 58.2 63.3 67.5 65.8 57.8 60.3 62.0 67.5 1969 65.4 62.4 61.6 68.4 57.8 59.1 51.5 62.0 60.3 52.3 48.9 48.1 1970 34.2 41.4 38.0 43.5 42.2 39.2 49.8 53.2 51.9 40.1 43.0 46.0 1971 53.6 48.9 48.5 48.5 57.4 62.9 58.6 60.3 62.0 65.4 65.8 65.4 1972 71.7 74.3 75.9 69.8 71.4 65.1 55.7 69.0 68.6 73.3 72.2 75.7 1973 61.2 69.4 56.9 61.2 54.9 62.4 63.5 60.8 62.4 58.4 60.4 47.1 1974 40.4 33.7 44.7 45.9 55.3 60.0 55.7 50.2 43.1 41.6 27.5 18.0 1975 17.3 21.2 25.9 35.7 44.7 57.6 56.9 69.0 66.7 61.6 67.5 62.7 1976 68.2 71.8 68.2 57.3 62.7 60.4 62.7 57.6 59.6 59.6 60.0 63.1 1977 58.4 60.0 67.8 70.7 74.3 75.9 69.1 59.6 48.4 53.6 46.8 56.0 1978 49.6 47.6 58.4 78.3 78.3 75.9 56.0 63.9 56.4 61.2 62.0 65.9 1979 51.6 56.4 54.8 53.6 54.4 52.8 56.0 43.6 46.0 50.0 53.2 51.2 1980 52.0 52.4 51.6 35.7 27.7 28.5 28.9 48.8 60.4 71.9 74.7 69.1 1981 60.8 53.2 49.2 52.0 54.4 54.0 60.4 53.6 46.0 32.9 30.9 31.3 1982 30.9 45.6 50.4 55.2 34.5 40.0 42.0 43.6 40.0 45.6 45.6 38.8 1983 61.2 57.6 69.5 65.9 81.5 73.5 77.1 73.1 77.1 75.1 70.3 61.6 1984 65.5 71.9 75.9 63.9 64.3 57.6 51.6 48.8 46.4 41.6 46.4 44.0 1985 46.4 51.6 57.6 57.2 58.0 52.8 46.4 50.8 55.2 52.0 50.8 51.6 1986 64.3 58.4 49.2 46.8 47.2 58.0 44.0 58.0 54.0 58.4 60.4 63.5 1987 58.4 59.6 58.0 62.7 66.7 67.1 75.5 72.3 62.7 62.4 64.3 65.1 1988 65.9 58.0 64.7 56.0 63.5 63.1 68.7 63.9 67.9 56.8 58.8 62.0 1989 63.1 55.2 48.4 56.0 56.4 59.2 48.4 50.0 48.8 50.8 47.6 49.6 1990 53.6 52.8 57.6 51.2 54.8 59.8 65.5 59.6 51.4 39.6 32.1 28.1

Six-month span

1967 40.9 59.9 64.1 62.9 73.8 71.3 1968 71.3 68.8 64.6 69.2 62.9 69.2 62.4 64.6 64.6 69.6 69.2 69.2 1969 66.2 66.2 72.6 71.7 65.4 65.4 67.1 65.0 62.0 56.1 59.9 54.9 1970 38.8 38.4 39.7 36.3 37.6 35.0 46.0 43.5 46.8 43.5 48.1 48.5 1971 52.3 48.5 48.1 56.1 59.1 63.3 57.8 62.0 65.4 70.5 64.6 66.7 1972 73.0 74.7 74.7 82.7 77.6 77.6 65.5 76.1 76.1 72.5 77.3 75.3 1973 73.7 72.5 72.5 68.6 70.2 64.3 66.3 59.6 64.7 65.1 63.1 54.1 1974 44.7 46.7 40.8 38.8 42.0 47.1 53.7 56.1 51.0 51.4 29.4 15.7 1975 18.4 18.0 14.9 20.8 25.1 41.2 47.8 58.4 62.7 64.3 72.2 72.2 1976 72.2 76.9 69.4 68.6 71.8 67.8 60.4 61.6 63.1 63.9 57.3 60.8 1977 62.7 62.0 72.9 72.9 79.2 78.4 74.7 76.3 69.1 63.1 54.0 50.0 1978 52.4 48.0 56.0 71.1 70.7 73.9 78.3 77.9 71.5 57.2 67.9 66.3 1979 59.6 60.8 62.4 55.2 57.2 51.2 55.6 48.8 48.8 52.4 48.0 48.8 1980 51.2 53.2 48.8 37.3 30.5 28.5 28.1 30.5 34.9 45.2 61.2 72.7 1981 71.1 68.3 62.0 61.2 53.6 51.2 56.8 54.8 48.4 40.0 34.9 33.3 1982 27.7 34.5 31.3 30.5 37.3 46.0 47.6 36.9 40.0 40.4 43.2 36.1 1983 54.4 53.2 63.1 66.7 75.1 80.3 75.9 85.9 87.1 85.5 78.3 72.3 1984 75.9 77.5 75.1 73.1 75.1 71.1 59.2 55.2 55.6 48.0 46.0 44.0 1985 42.8 44.0 48.8 50.8 53.6 57.6 54.0 54.4 54.0 51.6 51.6 56.4 1986 64.3 60.0 49.2 60.0 52.0 52.4 47.6 57.2 57.2 56.8 60.4 64.7 1987 62.0 66.3 67.9 66.7 67.9 65.5 73.9 77.9 75.5 84.3 75.9 70.3 1988 68.7 67.1 67.9 67.9 67.9 63.5 70.7 72.3 66.3 71.9 65.1 66.7 1989 64.7 57.6 52.8 66.7 58.8 54.8 51.2 56.4 55.6 44.0 51.6 45.2 1990 51.2 52.8 54.4 52.8 58.4 59.6 61.6 60.4 56.8 54.4 44.4 37.3

Indexes are based on seasonally adjusted data.

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536 Federal Reserve Bulletin • July 1991

average level of each of the diffusion indexes was greater than 50 from July 1967 to December 1990, which simply indicates that more industries re-corded production advances than declines during this period.

The three- and six-month diffusion indexes are substantially smoother from month to month than the one-month index. This pattern occurs because transitory shocks to production that result from, for example, unseasonable weather or strikes can buffet the one-month diffusion index. In contrast, because they are calculated over longer periods, the three- and six-month indexes are better insulated from such factors.

Relationships between diffusion indexes of in-dustrial production and percentage changes in the industrial production index are examined in James E. Kennedy, "Empirical Relationships between the Total Industrial Production Index and Its Diffusion Indexes," Finance and Eco-nomics Discussion Series 163 (Board of Gover-nors of the Federal Reserve System, Divisions of Research and Statistics and Monetary Affairs, July 1991).4

4. This paper may be obtained on request from The Editor, Finance and Economics Discussion Series, Division of Re-search and Statistics, mail stop 89, Board of Governors of the Federal Reserve System, Washington, D.C. 20551.

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July 1991