Understanding the Shannon Weaver Index PDF Print Email

shannon weaver

 industry colors

 

This indicator is a measurement of the “diversity” of the regional economy. The most diverse economy is one in which all industries exist and have an equal share of economic activity. If a region has 100 industries and each of those industry sectors had – e.g., 10 employees, then the index would be the maximum of 1.0.

Conversely, if the region only had one industry, of the possible 100, with a total employment of 1000, then the index would be the minimum of 0.0. For the index, in IMPLAN, the economic activity is measured in terms of employment – as opposed to using value added, labor income or industry output. Generally, a diverse economy is a healthy economy. But remember that any indicator by itself may be misleading. If a region is dominated by a single industry, it is not diverse and indeed may be subject to the caprices of that single industry – but is the region better off by closing down that industry, thereby increasing “diversity”?

 

What are the Shannon-Weaver economic indices?*

If economic diversity is defined as “the presence in an area of a great number of different types of industries” or “the extent to which the economic activity of a region is distributed among a number of categories”, then it is useful to have a summary statistic to describe the diversity of an area and compare it to other areas.

 

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

As it is applied to the regional estimate of employment data, the entropy measure of industrial diversity D is defined as:

  

where

D(E1, E2,…En)=-∑Eilog2Ei

                         n

 

n = the number of industries, and 

E = the proportion of total employment of the region that is located in the ith industry.

The indices contained in these databases have been normalized with respect to the maximum possible index for a given domain of industries (n). As a result, all indices range between 0 (no diversity) and 1.0 (perfect diversity). Specifically, the indices in these databases were computed as:

  

where

D(E1, E2,…En)=-∑Eilog2Ei/MAX (D(E1, E2,…En))

                         n

n = 440 (IMPLAN Sectoring).

Two important properties of the index are:

1.The maximum value ofD is attained when the E are all equal. This is the case where the region is totally diversified in the sense that all industries contribute equally to the region’s employment. Also, the greater the number of industries sharing the region’s economic activity, the greater the value of D.

2.D = 0 when only one of the E = 1 and the remaining are 0. This is an extreme case where the economic activity of a region is concentrated in only one industry; therefore, economic diversity is totally absent.

 

 

Shannon, C.E. and W. Weaver. 1949. “The Mathematical Theory of Communication, The University of Illinois Press, Urbana, IL. Attaran, M. 1986. “Industrial Diversity and Economic Performance in U.S. Areas”, Annals of Regional Science, Vol. 20, No. 2:44-55. 

* From the US Forest Service website www.fs.fed.us