leontief | R Documentation |
The Leontief decomposition of gross flows (exports, final demand, output) into their value added origins.
leontief(x, post = c("exports", "output", "final_demand", "none"), long = TRUE)
x |
an object of class decompr. |
post |
post-multiply the value added multiplier matrix [VB = V(I-A)^{-1}] with something to deduce the value added origins thereof.
The default is |
long |
logical. Transform the output data into a long (tidy) data set or not, default is |
The Leontief decomposition is obtained by pre-multiplying the flow measure (e.g. exports) with the value added multiplier matrix [VB = V(I-A)^{-1}], obtained by pre-multiplying the Leontief Inverse matrix [B = (I-A)^{-1}] with a diagonal matrix [V] containing the direct value added share in each industries output.
V is obtained as diag(v / o)
where o
is total industry output. v
is either supplied to load_tables_vectors
or computed as o - colSums(x)
with x
the raw IO matrix.
If o
is not supplied to load_tables_vectors
, it is computed as rowSums(x) + rowSums(y)
where y
is the matrix of final demands. If both o
and v
are not supplied to load_tables_vectors
, this is equivalent to computing V as diag(1 - colSums(A))
, with A is the row-normalized IO matrix also used to compute the Leontief Inverse [B].
If long = TRUE
a molten data frame containing the elements of the decomposed flows matrix in the final column, preceded by several identifier columns.
If long = FALSE
the decomposed flows matrix is simply returned.
Bastiaan Quast
Leontief, W. (Ed.). (1986). Input-output economics. Oxford University Press.
Hummels, D., Ishii, J., & Yi, K. M. (2001). The nature and growth of vertical specialization in world trade. Journal of international Economics, 54(1), 75-96.
Wang, Zhi, Shang-Jin Wei, and Kunfu Zhu (2013). Quantifying international production sharing at the bilateral and sector levels (No. w19677). National Bureau of Economic Research.
kww
, wwz
, decompr-package
# Load example data data(leather) # Create intermediate object (class 'decompr') decompr_object <- load_tables_vectors(leather) # Perform the Leontief decomposition of each country-industries # exports into their value added origins by country-industry leontief(decompr_object)
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