One of the benefits of grouping is that it enables us to derive measures of density and diversity; here are just a few…
Location Quotient
The LQ for industry i in zone z is the share of employment for i in z divided by the share of employment of i in the entire region R. \[
LQ_{zi} = \dfrac{Emp_{zi}/Emp_{z}}{Emp_{Ri}/Emp_{R}}
\]
High Local Share
Low Local Share
High Regional Share
\[\approx 1\]
\[< 1\]
Low Regional Share
\[> 1\]
\[\approx 1\]
Herfindahl-Hirschman index
The HHI for an industry i is the sum of squared market shares for each company in that industry: \[
H = \sum_{i=1}^{N} s_{i}^{2}
\]
Concentration Level
HHI
Monopolistic: one firm accounts for 100% of the market
\[1.0\]
Oligopolistic: top five firms account for 60% of the market
\[\approx 0.8\]
Competitive: anything else?
\[< 0.5\]?
Shannon Entropy
Shannon Entropy is an information-theoretic measure: \[
H(X) = - \sum_{i=1}^{n} P(x_{i}) log P(x_{i})
\]
