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 populations.
In our case, the population-interaction index (PII) for a single
location (grid cell) is defined as follows:
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 PII
can 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 "population-interaction zone."
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 four-category classification:
- 1 = rural (little or no urban-related population interaction)
- 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 available for
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. More general discussion of the methods
used to create the index and classifications is available in the Land Use, Value, and Management briefing
room.
Footnotes:
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 concentrations]."
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.
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