Measuring spatial concentration and diversity

by Prof. Kilkenny 8/18/2003

for ECON 376: Rural, Urban, and Regional Economics

A city or urban area is a spatial concentration of a large number of people and economic activity. Rural areas are the complement to urban areas. Rural areas are characterized by low population densities, dependence on natural-resource based industries, and are often remote. All countries and national economies are composed of urban and rural places, varying concentrations of population, and diverse specializations. This note is about how spatial concentration or dispersion and the degree of diversity are measured, calculated, and used to describe regions.

1. People: population density shows how many persons there are per unit area. Population density = POP_r/mi² or, POP_r/km² .

use subscript "r" as a generic label for “region”

location codes for states and counties: http://www.census.gov/pub/epcd/cbp/download/geocode.txt

2. Economic activity: employment in industry "i" in location or region "r" = E_ir.

"i" industry codes, North American Industry Classification System (“NAICS”): http://www.census.gov/pub/epcd/cbp/download/naics.ref

"i" industry codes, Standard Industrial Classification (SIC) system, until 1997: http://www.census.gov/pub/epcd/cbp/download/industry.ref

Compare the new NAICS system to the old system: http://www.census.gov/epcd/ec97brdg/

A. Where to obtain regional employment data to measure E_ir :

E_ir r=zip areas: Zip Code Statistics: http://censtats.census.gov/cbpnaic/cbpnaic.shtml

E_ir i=non-farm, r=counties and states: County Business Pattern (CBP) data: http://censtats.census.gov/cbpnaic/cbpnaic.shtml

E_ir CBP for downloading: http://www.census.gov/pub/epcd/cbp/download/cbpdownload.html

B. Use the E_ir data to show the significance of each industry in a location. The percent share (%E_ir) of industry i in a region's total employment is the ratio of the i^th industry’s employment in that place to the sum employment over all the industries (sum over i = Σ_i ) in the place:

%E_ir = 100 ∙ E_ir / Σ_i E_ir

Because service industries employ the largest share of people in most regions, a sector’s percent share is not very informative about what’s special in a region.

C. To show what’s special about a region, use E_ir data to calculate Location Quotients for the place. A Location Quotient (LQ_ir) shows the relative industrial specialization of a location. It compares the share of employment by sector in the region to an economy wide or national average sectoral employment share:

LQ_ir = %E_ir / %E_i•

where the denominator %E_i• in the LQ ratio is the percent share of the industry in total national employment: %E_i• = 100 ∙ Σ_r E_ir / Σ_rΣ_i E_ir .

An LQ_Xr equal to 1 indicates that industry i=”X” is equally significant in location r as it is economy wide. An LQ_Xr larger than 1 (+ standard deviation) indicates that industry X is more significant in region r than economy wide. An LQ_Xr smaller than 1 (- standard deviation) indicates that industry X is less significant in region r than economy wide. Thus, region r relatively specializes in industry X if LQ_Xr is significantly greater than 1. Furthermore, in free market economies, region r’s comparative advantage industries usually have LQ_irs significantly larger than 1.

D. The Hirschman-Herfindal Index (HHI_r) shows the industrial concentration of a region. It is the sum of the squared percent shares of employment:

HHI_r = Σi (%E_ir)².

Note that if all employment is in one sector, HHI= 1. A high HHI (closer to one) indicates that the region has a concentrated industrial pattern. A low HHI indicates there is more sectoral diversity in the region.