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Foster-Greer-Thorbecke (FGT) poverty measures

Source: R/fgt_poverty.R
fgt_poverty.Rd

Calculates the FGT metrics, a family of poverty measures originally proposed by Foster et al. (1984) that capture the extent and severity of poverty within an accessibility distribution. The FGT family is composed of three measures that differ based on the \(\alpha\) parameter used to calculate them (either 0, 1 or 2) and which also changes their interpretation. Please see the details section for more information on the interpretation of the measures.

Usage

fgt_poverty(
  accessibility_data,
  sociodemographic_data,
  opportunity,
  population,
  poverty_line,
  group_by = character(0)
)

Arguments

accessibility_data

A data frame. The accessibility levels whose poverty levels should be calculated. Must contain the columns id and any others specified in opportunity.

sociodemographic_data

A data frame. The distribution of sociodemographic characteristics of the population in the study area cells. Must contain the columns id and any others specified in population.

opportunity

A string. The name of the column in accessibility_data with the accessibility levels to be considerend when calculating accessibility poverty.

population

A string. The name of the column in sociodemographic_data with the number of people in each cell. Used to weigh accessibility levels when calculating poverty.

poverty_line

A numeric. The poverty line below which individuals are considered to be in accessibility poverty.

group_by

A character vector. When not character(0) (the default), indicates the accessibility_data columns that should be used to group the poverty estimates by. For example, if accessibility_data includes a race column that specifies the racial category of the population (e.g. "black" and "white") that each entry refers to, passing "race" to this parameter results in poverty estimates grouped by race.

Value

A data frame containing the three poverty estimates (FGT0, FGT1 and FGT2) for the study area.

Interpretation of FGT measures

The interpretation of each FGT measure depends on the \(\alpha\) parameter used to calculate it:

  • with \(\alpha = 0\) (FGT0) the measure captures the extent of poverty as a simple headcount - i.e. the proportion of people below the poverty line;

  • with \(\alpha = 1\) (FGT1) the measure, also know as the "poverty gap index", captures the severity of poverty as the average percentage distance between the poverty line and the accessibility of individuals below the poverty line;

  • with \(\alpha = 2\) (FGT2) the measure simultaneously captures the extent and the severity of poverty by calculating the number of people below the poverty line weighted by the size of the accessibility shortfall relative to the poverty line.

FGT values range from 0 to 1. A value of 0 indicates that every individual is above the poverty line. When every individual is below the poverty line, however, FGT0 value is 1 and FGT1 and FGT2 values approach 1.

References

Foster J, Greer J, Thorbecke E (1984). “A Class of Decomposable Poverty Measures.” Econometrica, 52(3), 761–766. ISSN 0012-9682, doi:10.2307/1913475 , 1913475.

Examples

if (FALSE) { # identical(tolower(Sys.getenv("NOT_CRAN")), "true")
data_dir <- system.file("extdata", package = "accessibility")
travel_matrix <- readRDS(file.path(data_dir, "travel_matrix.rds"))
land_use_data <- readRDS(file.path(data_dir, "land_use_data.rds"))

access <- cumulative_cutoff(
  travel_matrix,
  land_use_data,
  cutoff = 30,
  opportunity = "jobs",
  travel_cost = "travel_time"
)

poverty <- fgt_poverty(
  access,
  opportunity = "jobs",
  sociodemographic_data = land_use_data,
  population = "population",
  poverty_line = 95368
)
poverty
}