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.
Arguments
- Im
A Leontief inverse matrix created by
leontief_inverse_create().
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.
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)
#> iotables_row agriculture_group industry_group construction trade_group
#> 1 backward linkages 1.704922 1.841421 1.813747 1.603712
#> business_services_group other_services_group
#> 1 1.594974 1.378375
# 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)
#> sector A B C
#> 1 backward linkages 1 1 1