Distance-decayed market access

Market access of each origin as the sum of destination mass discounted by distance, \(MA_i = \sum_{j \neq i} m_j d_{ij}^{-\theta}\). This is the standard reduced-form measure used in economic geography and in the remote-sensing literature on rural connectivity, where access rather than raw distance is the quantity that predicts economic outcomes.

Usage

island_market_access(
  x,
  mass,
  to = NULL,
  theta = 1,
  which = c("point", "capital"),
  unit = c("km", "mi", "nmi"),
  self = NULL
)

Arguments

x

A character vector of ISO codes or country names: the origins.

mass

Numeric vector of destination mass. If named, names are resolved the same way as x and matched to the destinations, so the vector may be in any order and may cover more territories than are used. If unnamed, it must be the same length as the destinations and in the same order.

to

Optional character vector of destinations. Defaults to NULL, meaning the destinations are x itself (access within the set).

theta

Positive distance-decay elasticity. Default 1.

which

Coordinate to use: "point" (representative landmass point, the default) or "capital".

unit

Distance unit the decay operates on: "km" (default), "mi", or "nmi". Changing it rescales the result by a constant factor, so it matters for levels but not for rankings.

self

Optional internal distance, in unit, used to include each origin's own mass as m_i * self^-theta. A single number, or one per element of x. NULL (default) excludes own mass.

Value

A named numeric vector of market access, one element per element of x, named by iso_code. Origins that cannot be resolved, or that carry no coordinate, return NA. Destinations with missing mass or missing coordinates are dropped from the sum rather than propagating.

Details

The package supplies the geometry, not the mass. Population, GDP, tourist arrivals, and trade volumes are all time-varying and contested, so mass is always user-supplied and the reference year is the caller's to document. theta is likewise a modelling choice: values near 1 are conventional for trade gravity, higher values concentrate weight on near neighbours.

Own mass is excluded by default, because the internal distance of a territory to itself is undefined at this resolution. Supply self to include it under an explicit internal-distance assumption.

Distances are great-circle, computed by island_distance. See the "Profiling the world's small island developing states" vignette for what that does and does not represent for archipelagos.

See also

island_distance, island_coords

Examples

# Illustrative population masses (thousands) for the Dutch Caribbean six.
# Supply your own sourced figures in real work.
pop <- c(AW = 108, CW = 156, SX = 43, "BQ-BO" = 25, "BQ-SE" = 3, "BQ-SA" = 2)
round(island_market_access(names(pop), pop), 3)
#>    AW    CW    SX BQ-BO BQ-SE BQ-SA 
#> 1.464 1.284 0.403 2.759 1.081 1.304 

# Stronger decay concentrates weight on the nearest neighbours, separating
# the ABC and SSS groups sharply.
round(island_market_access(names(pop), pop, theta = 2), 6)
#>       AW       CW       SX    BQ-BO    BQ-SE    BQ-SA 
#> 0.011295 0.012056 0.001956 0.032294 0.013507 0.021399 

# Access to the wider region rather than to each other. Illustrative
# population in thousands.
region <- c(US = 335000, CO = 52000, VE = 28000, DO = 11000)
round(island_market_access(c("AW", "CW", "SX"), region, to = names(region)), 2)
#>     AW     CW     SX 
#> 179.73 181.30 145.18