iotables (version 0.9.4)

backward_linkages: Backward Linkages

Description

Compute the backward linkages of each industry or product sector from a Leontief inverse matrix. Backward linkages indicate how strongly a sector is interconnected on the demand side: when a sector increases its output, it will increase intermediate demand on all other sectors.

Usage

backward_linkages(Im)

Value

A one-row data.frame containing the backward linkage values for each column (industry or product) of the Leontief inverse. The first column is the sector key column, and the remaining columns correspond to the linkage values.

Arguments

Im

A Leontief inverse matrix created by leontief_inverse_create().

Details

Backward linkages are defined as the column sums of the Leontief inverse, in line with the Eurostat Manual of Supply, Use and Input–Output Tables (pp. 506–507) and the United Nations Handbook on Supply and Use Tables and Input–Output Tables with Extensions and Applications (p. 636).

See Also

Other linkage functions: forward_linkages()

Examples

de_coeff <- input_coefficient_matrix_create(iotable_get(), digits = 4)
I <- leontief_inverse_create(de_coeff)
backward_linkages(I)

# Trivial example: identity matrix gives linkages = 1
I <- diag(3)
colnames(I) <- rownames(I) <- c("A", "B", "C")
I_df <- data.frame(sector = rownames(I), I, check.names = FALSE)
backward_linkages(I_df)