Economic diversity is believed to enhance economic stability and growth by limiting the number of imports a local economy needs to sustain its current production and by providing increased availability of locally produced final demand purchases. The Shannon–Weaver (S-W) Diversity Index measures economic diversity on the basis of the number of Industries in a region and the distribution of employment across those Industries.
Generally, entropy methods measure the order or disorder found in the data. The S-W Index is an entropy method that measures the economic diversity of a region against a uniform distribution of employment; where the norm is equal employment in all Industries.
In other words, it is a measure of the extent to which the employment of a region is evenly distributed among its Industries. It ranges in value from zero to one, with zero indicating minimum diversity and a value of one indicating maximum diversity. A value of zero (complete specialization) occurs when the economic activity of a region is concentrated in only one Industry. A value of one (perfect diversity) occurs when all industries are present in the region, with employment spread equally among them.
DESCRIPTION OF THE SHANNON-WEAVER INDEX
In order for an economy to withstand supply and demand shocks, it must either maintain its competitive advantage or have enough variety of industries to reemploy displaced workers (Malizia and Ke, 1993). While economic specialization takes advantage of economies of scale (Skyes, 1950) and competitive advantage (Diamond and Simon, 1990), the performance of an area dominated by one sector is likely to be closely tied to the performance of that sector, which can become a liability for the area if the core industry suffers a national or regional downturn (Fitchen, 1995). Economic diversity is thought to enhance economic performance by 1) shielding a region from the adverse effects of idiosyncratic economic shocks and 2) increasing the proportion of intermediate and final demand that can be supplied locally, thereby slowing the leakage of money out of the local economy.
Without denying the value of specialization and competitive advantage, the focus of this article is on economic diversity and one measure of economic diversity in particular: the Shannon-Weaver (S-W) Index. The S-W Index is an entropy method that measures the economic diversity of a region against a uniform distribution of employment where the norm is equal employment in all industries. In other words, it is a measure of the extent to which the employment of a region is evenly distributed among its industries. It ranges in value from zero to one, with zero indicating minimum diversity and a value of one indicating maximum diversity. A value of zero (complete specialization) occurs when the economic activity of a region is concentrated in only one industry. A value of one (perfect diversity) occurs when all industries are present in the region, with employment spread equally among them.
The S-W Index has been calculated and displayed by the IMPLAN data and software system for economic impact analysis since their 1999 data set. In IMPLAN, the S-W Index for a region is calculated as follows:
where Ei is employment in industry i, E is total employment in the region, and N is the number of possible industries. Although the equation is here written with logarithms of base 2, the base of the logarithm used when calculating the S-W Index can be chosen freely, though comparing S-W values across time or place requires that they are all calculated with the same log bases. Shannon and Weaver (1948) discuss logarithm bases 2, 10 and e, and these have since become the most popular bases in applications that use the S-W Index.
The S-W Index can be very useful for graphing trends across time or mapping differences across geographies, such as in Figure 1.
Shannon-Weaver Indices of Continental U.S. Counties, 2014
LIMITATIONS OF THE SHANNON-WEAVER INDEX
Keep in mind, however, that the S-W Index does not account for the fact that many of the industries in a region may be closely related and would therefore provide little protection were one of the other closely-related industries to suffer a major decline. For example, a given region would receive the same S-W Index if its 1,000 employees were spread in either of the two hypothetical patterns shown in Table 1. While both cases have 1,000 employees and five industries, with employment spread evenly amongst the five industries, it should be apparent that Case 1 represents a much more diverse economy than Case 2. This subtle difference between the two cases is not reflected in the S-W Index, which would give the same value to both cases. Wagner and Deller (1993) discuss this issue and propose an alternative measure of economic diversity.
Two Sample Industry Mixes Resulting in the same S-W Index Values.
|Case 1||Case 2|
|Grain farming||250||Automobile manufacturing||250|
|Petroleum refineries||250||Light truck and utility vehicle manufacturing||250|
|Motor vehicle body manufacturing||250||Motor vehicle body manufacturing||250|
|Wholesale - Household appliances and electrical and electronic goods||250||Motor vehicle gasoline engine and engine parts manufacturing||250|
|Legal services||250||Motor vehicle metal stamping||250|
One might expect that aggregating closely related sectors together (e.g., aggregating all the sectors in Case 2 in Table 1 in a single “Auto industry”) would improve the S-W Index by treating like sectors as a single sector, rather than as distinct sectors. Yet the S-W Index as currently calculated actually increases when the employment data are aggregated into a smaller number of related sectors. This occurs for two reasons: when a region’s employment data are aggregated into fewer sectors, a) there are fewer sectors with zero employment and b) the employment appears to be more evenly spread amongst those aggregated sectors; the aggregated sector smooths out the variation between the individual industries within the aggregated industry.
Related to this issue of sector aggregation is the issue of comparing S-W indices over time. Because the IMPLAN sectoring scheme changes periodically (in reflection of the BEA’s Benchmark I-O tables, which are released roughly every five years), the number of sectors will change, which will influence the S-W Index calculation, rendering year-to-year comparisons imperfect when comparing across years with different sectoring schemes. One solution is to use the time series version of the IMPLAN data, which currently span from 2001 to 2019 and are all in the 546 sectoring scheme. This time series data set also addresses the issue of consistency pointed out by the State of Hawaii’s Department of Business, Economic Development and Tourism (2008).
While the S-W Index displayed in IMPLAN Pro and IMPLAN Online use Employment as the factor of choice, it is certainly possible to use other factors, such as Employee Compensation, as the factor of choice to give an alternate view and additional insight into the region’s economic diversity. This could be useful if the industries in a given region vary widely in their levels of Employee Compensation, in which case even if employment were perfectly evenly spread amongst all industries, the Employee Compensation would not be.
In the case of bedroom community counties (i.e., counties in which most residents commute to another county to work), a relatively low S-W Index may represent less of a concern since for these counties, it is the economic strength of the county in which its residents work which is of most importance (see the example of Lancaster County, PA below).
As IMPLAN currently measures S-W Index based on total employment, note that this includes both wage and salary workers and proprietors. It may be instructive to investigate the changes in S-W Index when just wage and salary employees are considered. This may be an important factor given the proprietor data are residence based, while wage and salary employment data are place of work based.
Due to the limitations of the S-W Index as well as to the fact that there are times and places where a certain degree of specialization is appropriate, the S-W Index should not be used in isolation to claim a particular region’s overall economic health or prospects for future economic growth. Nonetheless, it can serve as a useful tool when considered alongside other metrics, both economic and non-economic.
Diamond, C.A. and Simon, C.J. 1990. Industrial Specialization and the Returns to Labor. Journal of Labor Economics, 8(2): 175-201.
Fitchen, J.M. 1995. Why Rural Poverty is Growing Worse: Similar Causes in Diverse Settings. In The Changing American Countryside, edited by E.N. Castle, Lawrence, KS: University Press of Kansas.
Malizia, E.E. and S. Ke. 1993. The Influence of Economic Diversity on Unemployment and Stability. Journal of Regional Science, 33(2): 221-35.
Shannon, C. E. and Weaver W. 1948. A Mathematical Theory of Communication. The Bell System Technical Journal, 27, 623–656.
Skyes, J. 1950. Diversification of Industry. The Economic Journal, 60 (240): 697-714.
State of Hawaii Research and Economic Analysis Division. 2008. Measuring Economic Diversification in Hawaii. Department of Business, Economic Development and Tourism, http://files.hawaii.gov/dbedt/economic/data_ reports/EconDiversification/Economic_Diversification_ Report_Final%203-7-08.pdf.
Thorvaldson, J. & Squibb, J. (2017). An Expanded Look into the Role of Economic Diversity on Unemployment. The Journal of Regional Analysis & Policy, 42, 2, pp 137-153.
Wagner, J.E. & Deller, S.C. (1993). A Measure of Economic Diversity: An Input-Output Approach. USDA Forest Service and the University of Wisconsin-Extension. Retrieved January 17, 2020. Available: https://pdfs.semanticscholar.org/b055/c0b4a52b599c3bba36a69e87235e3b2b3757.pdf.
Updated February 22, 2021