iotables (version 0.9.4)

leontief_inverse_create: Create the Leontief inverse

Description

Compute the Leontief inverse from a technology-coefficient matrix.

Usage

leontief_inverse_create(technology_coefficients_matrix, digits = NULL)
leontieff_inverse_create(technology_coefficients_matrix, digits = NULL)

Value

A data.frame with the original key column and the Leontief inverse in the remaining columns. If digits is provided, values are rounded.

Arguments

technology_coefficients_matrix

A technology-coefficient matrix created by input_coefficient_matrix_create().

digits

Optional integer. Precision for rounding. Default NULL (no rounding).

Details

The Leontief inverse is defined as \(L = (I - A)^{-1}\), where \(A\) is the input-coefficient matrix created by input_coefficient_matrix_create().

In the Eurostat Manual of Supply, Use and Input–Output Tables (Beutel, 2008), this formulation appears in Chapter 15 (see equations (19), (43), etc.). The UN Handbook on Supply and Use Tables and Input–Output Tables with Extensions and Applications (2018, Rev. 1) also uses this standard definition (see pp. 619–621).

For the analogous inverse from output coefficients, see ghosh_inverse_create().

See Also

Other analytic object functions: ghosh_inverse_create(), input_flow_get(), leontief_matrix_create(), output_coefficient_matrix_create()

Examples

# A tiny 2x2 system with hand-calculable inverse
minimal_matrix <- data.frame(
  sector = c("A", "B"),
  A = c(0.2, 0.4),
  B = c(0.1, 0.2)
)

leontief_inverse_create(minimal_matrix, digits = 3)

# With a full example from the package
tm <- input_flow_get(
  data_table = iotable_get(),
  households = FALSE
)
leontief_inverse_create(technology_coefficients_matrix = tm)