leontief_matrix_create: Create a Leontief matrix

Description

Build the Leontief matrix \((I - A)\) from a technology coefficients matrix \(A\). This is the step used before computing the Leontief inverse, see leontief_inverse_create().

Usage

leontief_matrix_create(technology_coefficients_matrix)
leontieff_matrix_create(technology_coefficients_matrix)

Value

A data.frame whose first column is the key and whose remaining columns contain the Leontief matrix \((I - A)\).

Arguments

technology_coefficients_matrix: A technology coefficients matrix created by input_coefficient_matrix_create() or output_coefficient_matrix_create(). The first column must be a key; remaining columns must be numeric.

Details

In Eurostat terminology (Manual of Supply, Use and Input-Output Tables), the technology coefficients matrix \(A\) is formed by dividing each column of the inter-industry flows by the output of that industry. The Leontief matrix is then \(I - A\).

This function removes any detected TOTAL rows/columns (e.g. "total", "cpa_total") before forming \(I - A\), and returns a data frame with the original key column followed by the numeric block of \(I - A\).

Examples

Run this code

# From input coefficients (usual case)
tm <- input_coefficient_matrix_create(
  data_table = iotable_get(),
  households = FALSE
)
L <- leontief_matrix_create(technology_coefficients_matrix = tm)