A Population-Interaction Index (PII)
The PIZA codes are derived from a classification scheme that
indexes small geographic areas according to the size and proximity
of population concentrations. Designation of the zones begins with
use of common GIS software to assign an index number to each of
many small (five-kilometer) grid cells laid out (figuratively)
across the contiguous 48 States. These "population-interaction
indexes" (PII) are designed to provide a cardinal measure of the
potential interaction between nearby urban-related population and
agricultural production activities in each grid cell. (By a
cardinal measure, we mean that the codes effectively rank each
location or area on a continuous scale.) The population-interaction
indexes are based on the regional economist's or geographer's
concept of a "gravity" model, which provides measures of
accessibility to population concentrations (Shi, Phipps, and
Colyer, 1997).1 This model measures
population interaction by accounting for the size of all
populations in the proximity of a given location or grid cell and
the distance of that location or grid cell from those
In our case, the population-interaction index
(PII) for a single location (grid cell) is defined
PIIij = Pj / Dij
where PIIij is the computed index number
representing the influence on cell i of population located in cell
j, Pj is the population of cell j, and Dij is the distance from
cell i to cell j.
In order to assess the effect of proximity to multiple
population concentrations, the index is aggregated across a number
(N) of possible locations (cells). In an aggregate form, the index
used in this study is given by:
PIIi = S (Pj / Dij) where the summation is over
j = 1 to N,
where the index j represents one of N grid cells within a 50
mile radius of cell i.
Essentially, the population-interaction index provides a
continuous measure of proximity to nearby population
concentrations, accounting for both population size (within a
50-mile radius in our study) and location of the parcel relative to
the population (distance).2 The index
increases as population increases, (since population is in the
numerator) and/or as distance to the population decreases (since
distance is in the denominator).
The first step in constructing the population-interaction index
was to develop a nationwide grid of population density. This was
accomplished by assigning the geographic centroid of each census
block to a 5-km grid cell, then using GIS techniques to add up the
population in each grid cell, and then dividing grid-cell
population by the area of the grid cell.
The next step involved using GIS software to calculate the
population-interaction index for each grid cell using the formula
described above. Our construction of the population-interaction
index is calculated on the basis of population within a 50-mile
radius of each grid cell. Essentially, population (or,
equivalently, in our case, population density) is weighted by the
inverse of distance. With readily available GIS software, the
population-influence indexes for any latitude/longitude in the U.S.
can be obtained. By aggregation within the GIS system, a PIIcan be
calculated for any specified region.
Using Population-Interaction Indexes to Classify Agricultural
Land: PIZA Codes
In order to classify grid cells into either a "rural" zone or a
"population-interaction" zone, regional thresholds were established
based on index levels in the most rural areas of each region. Index
numbers below a threshold represent rural (background) levels of
population interaction, which exist even in the absence of
urban-related population interaction. Any grid cell whose index
exceeds the rural threshold set for its region is classified into a
The rural or background level includes population that supports
an active commercial farming industry, including employees of input
and output industries that support production agriculture as well
as other population associated with the rural-community
infrastructure. That background level can be expected to vary
regionally due to differences in the productivity of farmland.
Consequently, we established thresholds for each of the twenty U.S.
Department of Agriculture regions called Land Resource Regions
(LRRs) (USDA Agricultural Handbook #296).
In order to establish the rural thresholds for each region, we
examined levels of the PII in areas that clearly had not been
subject to nonfarm-related population influence. Cromartie (200l)
and Cromartie and Swanson (1996) identify Census tracts that are
"totally rural," which are based on 1990 commuting data and U.S.
Census Bureau geographic definitions. The term totally rural means
that the tract does not contain any part of a town of 2,500 or more
residents and the primary commuting pattern was to sites within the
tract. (These are category 10 in the RUCA codes.) Thresholds for
individual LRRs were established at the 95th percentile of the
distribution of PII for 5-kilometer grid cells in the set of
totally rural tracts in the LRR.
Grid cells initially classified into the population-interaction
zone were further classified into one of three categories
representing increasingly higher levels of population interaction.
Thresholds to distinguish the three categories were set at levels
of the index that split the original sample into three sets
containing equal numbers of sample observations. The resulting
Population-Interaction Zones for Agriculture (PIZA) consist of a
- 1 = rural (little or no urban-related population
- 2 = population interaction, low
- 3 = population interaction, medium
- 4 = population interaction, high
The indexes (PII) and zone codes (PIZA), which can be used to
classify any geographic point in the 48 contiguous states, are
download. GIS software is necessary, however, to retrieve the
indexes and zone codes and relate them to any given geographic
point (latitude/longitude) or 5-km grid cell. A complementary
scheme similarly indexes and classifies the geographic center of
U.S. counties, providing a county-level version of both.
1The concept of a
"gravity" model evolved from marketing analysis, where it was first
used to assess the attraction of consumers to retail markets (as
described in Shi, Phipps, and Colyer). Recently the concept has
been applied in the agricultural and resource economics literature.
Shi, Phipps, and Colyer describe the gravity model as a
"parsimonious method for capturing urban influence in a single
variable that combines [population] size and distance [from urban
2In Shi, Phipps, and
Colyer and in Hardie, Narayan, and Gardner, distance is accounted
for using the square of D. Based on results reported in Song, we
used D rather than D2.