Regional Economics Functions — regional

A collection of functions for calculating regional economics indices, including Location Quotient (LQ), Herfindahl-Hirschman Index (HHI), and Ellison-Glaeser Index (EG). These functions are designed for analyzing regional and industrial data to assess spatial concentration and market structure.

Usage

LQ(data, region, total, .cols, .by = NULL)

HHI(x, scaled = FALSE)

EG(data, region, industry, y)

Arguments

data: A data frame containing the necessary data for calculations. For LQ, the first row is assumed to be the national total, with the first two columns specifying the region and total, optionally including a grouping column. For EG, it contains region, industry, and indicator columns (e.g., employment or output).
region: The name of the column in data specifying the region (used in LQ and EG).
total: The name of the column in data specifying the total (used in LQ).
.cols: The columns in data for which to calculate the location quotient (used in LQ).
.by: Optional grouping column for LQ, defaults to NULL (no grouping).
x: A numeric vector for calculating the HHI (used in HHI).
scaled: Logical; if TRUE, the HHI is scaled to account for the number of firms. Defaults to FALSE.
industry: The name of the column in data specifying the industry (used in EG).
y: The name of the column in data specifying the indicator (e.g., employment or output, used in EG).

Value

LQ: A data frame with the region column and calculated location quotients for the specified columns, optionally grouped by .by.
HHI: A numeric value representing the HHI, either scaled or unscaled.
EG: A tibble with two columns: the industry name and the corresponding EG index value.

Details

LQ: Calculates the Location Quotient for multiple columns with optional grouping. The LQ measures the relative concentration of an industry in a region compared to a national benchmark. The data must be arranged so that within each region value (and within each .by group) the FIRST row is the national/total benchmark row, which is dropped by the function; every remaining row is treated as a region. Rows must be pre-arranged accordingly (e.g., with dplyr::arrange()), otherwise the results are silently wrong.
HHI: Calculates the Herfindahl-Hirschman Index, a measure of market concentration based on the squared sum of market shares. If scaled = TRUE, the HHI is normalized to account for the number of firms.
EG: Calculates the Ellison-Glaeser Index, which measures the geographic concentration of an industry while controlling for firm size distribution and random distribution effects. It requires data on regions, industries, and an indicator (e.g., employment or output). The data must contain one row per firm/establishment (multiple rows per region-industry combination); passing region-aggregated data (one row per region-industry) silently produces wrong EG values.

Examples

# Example data
data = data.frame(
  region = c("National", "Region_A", "Region_B"),
  total = c(10000, 4000, 6000),
  industry1 = c(2000, 1000, 1000),
  industry2 = c(6000, 2000, 4000)
)

# Calculate Location Quotient
LQ(data, region, total, starts_with("industry"))
#>     region industry1 industry2
#> 1 Region_A 1.2500000 0.8333333
#> 2 Region_B 0.8333333 1.1111111

# Calculate HHI
x = c(50, 30, 20)
# Calculate the raw HHI
HHI(x)
#> [1] 0.38
# Calculate the standard (scaled) HHI
HHI(x, scaled = TRUE)
#> [1] 0.07

# Example data for EG
eg_data = data.frame(
 region = c("R1", "R1", "R1", "R1", "R2", "R2", "R3", "R3", "R1", "R2", "R2", "R3"),
 industry = c("A", "A", "A", "A", "A", "A", "A", "A", "B", "B", "B", "B"),
 employment = c(250, 200, 150, 100, 20, 15, 10, 5, 50, 200, 150, 50)
)
EG(eg_data, region, industry, y = employment)
#> # A tibble: 2 × 2
#>   industry    EG
#>   <chr>    <dbl>
#> 1 A        0.131
#> 2 B        0.918