Load an Inter-Country Input-Output Table

Reads the raw ICIO matrices and precomputes everything the decompositions need, returning an 'icio' class object. This is the entry point for all decompositions.

Usage

load_icio(
  inter,
  final,
  countries,
  industries,
  output = NULL,
  va = NULL,
  null_inventory = FALSE
)

Arguments

inter: intermediate demand table supplied as a numeric matrix of dimensions GN x GN (G = no. of countries, N = no. of industries). Both rows and columns should be arranged first by country, then by industry (e.g. C1I1, C1I2, ..., C2I1, C2I2, ...) and should match (symmetry), such that rows and columns refer to the same country-industries. Alternatively, an Input-Output Table object of class 'iot' can be passed here - a list with elements 'inter', 'final', 'countries', 'industries' and (optionally) 'output' - in which case the remaining table arguments are taken from it. See leather.
final: final demand table supplied as a numeric matrix of dimensions GN x GM (M = no. of final demand categories recorded for each country). The rows of final need to match the rows of inter, and the columns should also be arranged first by country, then by final demand category (e.g. C1FD1, C1FD2, ..., C2FD1, C2FD2, ...) with the order of the countries the same as in inter.
countries: character. A vector of country or region names of length G, arranged in the same order as they occur in the rows and columns of inter and final.
industries: character. A vector of industry names of length N, arranged in the same order as they occur in the rows and columns of inter and the rows of final.
output: numeric. A vector of gross outputs for each country-industry matching the rows of inter and final. If not provided it will be computed as rowSums(inter) + rowSums(final).
va: numeric. A vector of value added for each country-industry matching the columns of inter. If not provided it will be computed as output - colSums(inter), which is what the Stata icio command does.
null_inventory: logical. TRUE sets the inventory (last final demand category for each country) to zero.

Value

An 'icio' class object - a list with the following elements:

A			Input coefficients matrix (`inter` column-normalized by `output`), including the domestic blocks.
B			Leontief Inverse matrix $(I - A)^{-1}$.
Lb			List of `G` domestic (local) Leontief Inverse blocks $(I - A_{gg})^{-1}$, one `N x N` matrix per country.
E			Total Exports (output of each country-industry servicing foreign production or foreign final demand).
ESR			Total Exports by destination country.
Vc			Value added content of output (`va / output`).
G			Number of countries.
N			Number of industries.
GN			Number of country-industries.
k			Vector of country names.
i			Vector of industry names.
X			Total Output ( `= output`).
Y			Total Final Demand by destination country.
Yd			Domestic Final Demand.
Ym			Foreign Final Demand.

The country-industry names identifying the rows and columns are available as names(x$Vc) or dimnames(x$B)[[1L]].

Details

Only A and B are dense GN x GN matrices. The masked and block-diagonal variants of them that the decompositions require ($A$ with the domestic blocks zeroed, the domestic and foreign parts of $B$) are derived on the fly by the functions that need them, being either recoverable from A and B in a few operations or, in the case of the domestic Leontief inverse, block-diagonal and thus $1 - 1/G$ structural zeros.

Value added defaults to the column residual of the table (output - colSums(inter)), which reproduces the Stata icio command exactly. Supplying a va that differs from it makes the column sums of $V B$ deviate from 1, so identities such as GEXP = DC + FC may no longer hold exactly - faithful to the supplied data.

Author

Sebastian Krantz, Bastiaan Quast. Adapted from code by Fei Wang.

Examples

# Load example data
data(leather)

# Create intermediate object (class 'icio') from an 'iot' object
m <- load_icio(leather)

# Equivalent: passing the matrices directly
m <- load_icio(leather$inter, leather$final, leather$countries, leather$industries)

# Examine the object
str(m)
#> List of 15
#>  $ A  : num [1:9, 1:9] 0.20721 0.03089 0.01158 0.01416 0.00386 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:9] "Argentina.Agriculture" "Argentina.Textile_and_Leather" "Argentina.Transport_Equipment" "Turkey.Agriculture" ...
#>   .. ..$ : chr [1:9] "Argentina.Agriculture" "Argentina.Textile_and_Leather" "Argentina.Transport_Equipment" "Turkey.Agriculture" ...
#>  $ B  : num [1:9, 1:9] 1.2764 0.0562 0.0197 0.035 0.0244 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:9] "Argentina.Agriculture" "Argentina.Textile_and_Leather" "Argentina.Transport_Equipment" "Turkey.Agriculture" ...
#>   .. ..$ : chr [1:9] "Argentina.Agriculture" "Argentina.Textile_and_Leather" "Argentina.Transport_Equipment" "Turkey.Agriculture" ...
#>  $ Lb :List of 3
#>   ..$ : num [1:3, 1:3] 1.2691 0.0492 0.0192 0.1305 1.1666 ...
#>   ..$ : num [1:3, 1:3] 1.212 0.0957 0.0586 0.174 1.3128 ...
#>   ..$ : num [1:3, 1:3] 1.2537 0.0709 0.1246 0.2619 1.3253 ...
#>  $ E  : Named num [1:9] 33.2 28.5 2.6 45.9 59.2 8.5 38.7 31 77.9
#>   ..- attr(*, "names")= chr [1:9] "Argentina.Agriculture" "Argentina.Textile_and_Leather" "Argentina.Transport_Equipment" "Turkey.Agriculture" ...
#>  $ ESR: num [1:9, 1:3] 0 0 0 10.7 12.1 1.6 14.9 10.3 31.6 14 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:9] "Argentina.Agriculture" "Argentina.Textile_and_Leather" "Argentina.Transport_Equipment" "Turkey.Agriculture" ...
#>   .. ..$ : chr [1:3] "Argentina" "Turkey" "Germany"
#>  $ Vc : Named num [1:9] 0.673 0.569 0.321 0.619 0.509 ...
#>   ..- attr(*, "names")= chr [1:9] "Argentina.Agriculture" "Argentina.Textile_and_Leather" "Argentina.Transport_Equipment" "Turkey.Agriculture" ...
#>  $ G  : int 3
#>  $ N  : int 3
#>  $ GN : int 9
#>  $ k  : chr [1:3] "Argentina" "Turkey" "Germany"
#>  $ i  : chr [1:3] "Agriculture" "Textile_and_Leather" "Transport_Equipment"
#>  $ X  : Named num [1:9] 77.7 58.3 19 112.7 124.6 ...
#>   ..- attr(*, "names")= chr [1:9] "Argentina.Agriculture" "Argentina.Textile_and_Leather" "Argentina.Transport_Equipment" "Turkey.Agriculture" ...
#>  $ Y  : num [1:9, 1:3] 21.5 16.2 11 7.5 8.9 1.2 9.2 7.9 25.1 6.1 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:9] "Argentina.Agriculture" "Argentina.Textile_and_Leather" "Argentina.Transport_Equipment" "Turkey.Agriculture" ...
#>   .. ..$ : chr [1:3] "Argentina" "Turkey" "Germany"
#>  $ Yd : num [1:9, 1:3] 21.5 16.2 11 0 0 0 0 0 0 0 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:9] "Argentina.Agriculture" "Argentina.Textile_and_Leather" "Argentina.Transport_Equipment" "Turkey.Agriculture" ...
#>   .. ..$ : chr [1:3] "Argentina" "Turkey" "Germany"
#>  $ Ym : num [1:9, 1:3] 0 0 0 7.5 8.9 1.2 9.2 7.9 25.1 6.1 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:9] "Argentina.Agriculture" "Argentina.Textile_and_Leather" "Argentina.Transport_Equipment" "Turkey.Agriculture" ...
#>   .. ..$ : chr [1:3] "Argentina" "Turkey" "Germany"
#>  - attr(*, "class")= chr "icio"

A			Input coefficients matrix (`inter` column-normalized by `output`), including the domestic blocks.
B			Leontief Inverse matrix \((I - A)^{-1}\).
Lb			List of `G` domestic (local) Leontief Inverse blocks \((I - A_{gg})^{-1}\), one `N x N` matrix per country.
E			Total Exports (output of each country-industry servicing foreign production or foreign final demand).
ESR			Total Exports by destination country.
Vc			Value added content of output (`va / output`).
G			Number of countries.
N			Number of industries.
GN			Number of country-industries.
k			Vector of country names.
i			Vector of industry names.
X			Total Output ( `= output`).
Y			Total Final Demand by destination country.
Yd			Domestic Final Demand.
Ym			Foreign Final Demand.