# The Shannon-Weaver Index of Economic Diversity: An Overview and Descriptive Analysis

## INTRODUCTION

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 a regional economy dominated by a single sector is likely to be closely tied to the performance of that sector, which can become a liability for the region if the core industry suffers a national or regional downturn (Fitchen, 1995). Economic diversity is thought to enhance economic performance by shielding a region from the adverse effects of economic shocks and increasing the proportion of goods and services that can be produced locally (whether for intermediate or final demand), thereby slowing the leakage of money out of the local economy.

## DESCRIPTION OF THE SHANNON-WEAVER INDEX

The Shannon-Weaver (S-W) entropy function (Shannon and Weaver, 1949) has been used to calculate indices of economic diversity (Attaran, 1986). The S-W Index measures the economic diversity of a region against a uniform distribution of employment where the norm is equi-proportional 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.

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 therefore varies by region and year, and can prove very useful for mapping trends. For example, the figure below shows the changing economic diversity of U.S. counties, as measured by the S-W index, from 2001 to 2019.

## 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 Industry Employment Industry Employment 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.

Another consideration relates to the comparison of S-W indices over time. In order for a year-over-year comparison to be valid, the S-W indices must have been calculated from data using the same sectoring scheme. Because the IMPLAN sectoring scheme changes when new BEA Benchmark I-O tables are published (roughly every five years), the number of IMPLAN sectors changes, which influences the S-W index calculation, and thus, the S-W index values. Thus, to compare S-W indices over time, one should use the time series data in IMPLAN’s online Data Library, in which all IMPLAN data dating back to 2001 have been re-estimated using the same, latest IMPLAN sectoring scheme, using current best practices and revised raw data where available.

Another consideration related to comparisons over time is that a loss of employment in a highly concentrated industry, all else equal, will cause a region’s S-W index to increase; yet no one would argue that the loss of employment was a good thing. In such a case, the increase in S-W index is not due to the region expanding into new industries or growing its fledgling industries, but rather the shrinkage of a dominant industry.

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.

As the above notes make clear, interpreting S-W index values over time or across geographies is not always straightforward due to the influence of many factors on the S-W calculation. As such, it is best to investigate S-W index changes in the context of any changes in the underlying employment data. In light of this, as well as times and places where a certain degree of specialization is appropriate and desirable, the S-W index should not be used in isolation to proclaim a region’s economic health or prospects for future economic growth. Nonetheless, the S-W index can serve as a useful tool when considered alongside other metrics, both economic and non-economic.

## OTHER IMPORTANT NOTES

While the S-W Index displayed in IMPLAN uses 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.

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 that the proprietor data are place-of-residence-based, while wage and salary employment data are place-of-work based.

## RESOURCES

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