Abstract
This article introduces an R package, , that simplifies the analysis of trade in value added with international input-output tables. It provides a full set of commands for data extraction, matrix creation and manipulation, decomposition of value added in gross exports (using alternative methodologies) and a straightforward calculation of many value added indicators. It can handle both raw data from well-known public input-output databases and custom data. It has a wide sector and geographical flexibility and can be easily expanded and adapted to specific economic analysis needs, facilitating a better understanding and a wider use of the available statistical resources to study globalization.
The analysis of trade in value added involves the use of international input-output tables and intensive matrix manipulation. Some trade databases, such as the OECD Trade in Value Added Database (TiVA), offer a web interface, but cannot be customized and lack some key indicators developed in recent literature, especially indicators of bilateral trade in value added and participation in global value chains. This makes recourse to raw data almost inevitable and creates the need for software capable of performing complex matrix analysis in a user-friendly environment.
This is the gap pretends to fill. It has been designed as a package for R with a triple purpose: as an international input-output table general analysis tool (with commands to extract raw data and produce and manipulate large matrices), as a way to decompose value added in exports using alternative methodologies, and as a tool to easily produce complex tailor-made value added indicators with flexible sector and geographical customization.
To our knowledge, there are no equivalent software tools available. There are some input-out analysis tools, like (Wade and Sarmiento-Barbieri 2020), but they cannot properly handle OECD’s ICIO-type data (with some countries divided in industrial areas). The package (Quast and Kummritz 2015) produces a decomposition of value added in exports, but only according to the methodology of Wang, Wei, and Zhu (2013).
Outside of the R ecosystem, the module
icio (Belotti, Borin, and Mancini
2021) for the software Stata (StataCorp 2021) provides the more modern (and
methodologically sounder) decomposition method of Borin and Mancini (2023). However,
icio is a closed-source module, it does not allow complex
sector analysis and customization, direct handling of input-output
tables nor detailed decompositions (for instance, distinguishing between
value added exported induced by inputs and by final goods).
can therefore be used as all-purpose tool, both to facilitate the
extraction and manipulation of input-output matrices and to obtain
detailed and customized indicators of trade in value added, facilitating
research on global value chains, globalization, and its economic
effects. In the following sections, we will describe the methodological
background of , in particular the international input-output table
framework and its use to calculate value added induced by gross exports.
Then we will explain the creation of the three basic objects of : a list
of basic input-output tables (the wio class), a list with
the different matrix components of a decomposition of value added in
exports (the exvadec class) and a list with a detailed
origin and destination of value added (the exvadir class).
We will then explain the commands to fully exploit the information
included in the aforementioned classes. Along the way we will produce
examples of use.
can be installed from the CRAN repository and made available for the current session following the usual procedure:
install.packages("exvatools")
library(exvatools)Analyzing the value added in exports requires the previous extraction of a series of basic input-output matrices in a standardized format. We will consider a typical international input-output framework with \(G\) countries and \(N\) sectors. Each country \(s\) provides goods and services from each sector \(i\) to each sector \(j\) in country \(r\), and sources its goods and services from the sectors of each country \(t\).
| Input | \(1\) | \(2\) | \(\dots\) | \(G\) | \(1\) | \(2\) | \(\dots\) | \(G\) | ||
| \(1\) | \(\mathbf{Z}_{11}\) | \(\mathbf{Z}_{12}\) | \(\dots\) | \(\mathbf{Z}_{G1}\) | \(\mathbf{Y}_{11}\) | \(\mathbf{Y}_{12}\) | \(\dots\) | \(\mathbf{Y}_{G1}\) | \(\mathbf{X}_{1}\) | |
| Intermediate | \(2\) | \(\mathbf{Z}_{21}\) | \(\mathbf{Z}_{22}\) | \(\dots\) | \(\mathbf{Z}_{G2}\) | \(\mathbf{Y}_{21}\) | \(\mathbf{Y}_{22}\) | \(\dots\) | \(\mathbf{Y}_{G2}\) | \(\mathbf{X}_{2}\) |
| inputs | … | \(\dots\) | \(\dots\) | \(\dots\) | \(\dots\) | \(\dots\) | \(\dots\) | \(\dots\) | \(\dots\) | \(\dots\) |
| \(G\) | \(\mathbf{Z}_{G1}\) | \(\mathbf{Z}_{G2}\) | \(\dots\) | \(\mathbf{Z}_{GN}\) | \(\mathbf{Y}_{G1}\) | \(\mathbf{Z}_{G2}\) | \(\dots\) | \(\mathbf{Y}_{GN}\) | \(\mathbf{X}_{G}\) | |
| Value Added | \(\mathbf{VA}_{1}\) | \(\mathbf{VA}_{2}\) | \(\dots\) | \(\mathbf{VA}_{G}\) | ||||||
| Input | \(\mathbf{X}_{1}\) | \(\mathbf{X}_{2}\) | \(\dots\) | \(\mathbf{X}_{G}\) |
In a typical international input-output table (which is a matrix composed of block matrices) \(\mathbf{Z}\) is the matrix of intermediate inputs (dimension \(GN \times GN\)), with each sub-matrix \(\mathbf{Z}_{sr}\) (dimension \(N \times N\)) elements \(z_{sr}^{ij}\) representing the deliveries of intermediate inputs from sector \(i\) in country \(s\) to sector \(j\) in country \(r\). \(\mathbf{Y}\) is the matrix of final demand, of dimension \(GN \times G\) (aggregated by country for practical purposes from an original \(\mathbf{Yfd}\) matrix with \(FD\) demand components). \(\mathbf{X}\) is the production matrix, of dimension \(GN \times 1\), and \(\mathbf{VA}\) the value added demand, of dimension \(1 \times GN\).
The typical demand model, which dates back to Leontief (1936), assumes that the inputs from sector \(i\) of country \(s\) to sector \(j\) of country \(r\) are a constant proportion of the output of sector \(j\) in country \(r\). From there we obtain a matrix of coefficients \(\mathbf{A}\) whose elements are the proportion of intermediate inputs over total production, \(a_{sr}^{ij} = z_{sr}^{ij} / {x_{r}^{j}}\). Then the relations in the international input-output table can be expressed as \(\mathbf{AX}+\mathbf{Y}=\mathbf{X}\), from where we deduct a relation between production and final demand:
\[\begin{equation} \mathbf{X}=\left(\mathbf{I}-\mathbf{A}\right)^{-1}\mathbf{Y}=\mathbf{BY} (\#eq:XBY) \end{equation}\]
Here the matrix \(\mathbf{B}\) (inverse of \(\mathbf{I} -\mathbf{A}\), where \(\mathbf{I}\) is the identity matrix) collects the backward linkages that the final demand \(\mathbf{Y}\) induces on production. Each element of \(\mathbf{B}\), \(b_{sr}^{ij}\), can be expressed as the increase of production of sector \(i\) in country \(s\), when the final demand of sector \(j\) in country \(r\) increases by one unit.
If the ratio between inputs and production is constant, then the ratio between value added (i.e., the value of production minus the value of inputs) and production can also be considered constant, so we can define vector \(\mathbf{V}\) as the value added by unit of output \(\mathbf{X}\) and express the value added in terms of global demand as \(\mathbf{V} \mathbf{X} = \mathbf{V} \mathbf{BY}\). More specifically, for a given country \(s\):
\[\begin{equation} \mathbf{V}_s \mathbf{X}_s = \mathbf{V}_s \sum_{j}^{G}\sum_{r}^{G}{\mathbf{B}_{sj} \mathbf{Y}_{jr}} (\#eq:VBY) \end{equation}\]
that we can break down into the value added produced and absorbed in \(s\) and the value added produced in \(s\) and absorbed abroad:
\[\begin{equation} \mathbf{V}_s \sum_{j}^{G}{\mathbf{B}_{sj}\mathbf{Y}_{js}} + \mathbf{V}_s \sum_{j}^{G} \sum_{r\neq s}^{G} {\mathbf{B}_{sj}\mathbf{Y}_{jr}} (\#eq:VADVAX) \end{equation}\]
The second term in @ref(eq:VADVAX) is usually referred to as value added exported \({\mathbf{VAX}}_s\) (Johnson and Noguera 2012). In aggregated terms, value added absorbed abroad coincides with value added exported, but this is not true in bilateral terms. In fact, \({\mathbf{VAX}}_{sr}\) is the value added produced in \(s\) and absorbed in \(r\), but regardless of the export destination. To obtain the value added exported to \(r\) regardless of the absorption country we need to calculate the value added induced not by final demand, but by the demand of gross exports.
For that, knowing that each column of the matrix product \(\mathbf{V} \mathbf{B}\) is a linear combination whose sum is a unit vector \(\boldsymbol{\iota}\), we can break down the linkage effects over the production of any country \(s\) into those derived of domestic inputs and those derived of foreign components.
\[\begin{equation} \boldsymbol{\iota} = \sum_{t}^{G}{{\mathbf{V}}_t\mathbf{B}_{ts}} = {\mathbf{V}}_s \mathbf{B}_{ss} + \sum_{t\neq s}^{G} {{\mathbf{V}}_t\mathbf{B}_{ts}} (\#eq:sumVB) \end{equation}\]
If we multiply both terms of equation @ref(eq:sumVB) by the demand of gross exports of country \(s\), \(\mathbf{E}_s\), we obtain a basic decomposition of the content of value added in exports into domestic and foreign content.
\[\begin{equation} \boldsymbol{\iota} \mathbf{E}_{s} = \sum_{t}^{G} {{\mathbf{V}}_t\mathbf{B}_{ts}\mathbf{E}_{s}} = {\mathbf{V}}_s \mathbf{B}_{ss} \mathbf{E}_{s} + \sum_{t\neq s}^{G}{{\mathbf{V}}_t \mathbf{B}_{ts} \mathbf{E}_{s}} (\#eq:content) \end{equation}\]
Expression @ref(eq:content) reflects that the demand of gross exports of \(s\) can only be satisfied with domestic value added or with foreign value added (with inputs being value added of other sectors). This is also valid for the bilateral exports of \(s\), \(\mathbf{E}_{sr}\) (the sum being in this case the total gross bilateral exports).
We have so far overlooked the sector distribution of exports. It we wanted to preserve the sector information, we should use a diagonalized version of matrix \(\mathbf{V}\), \(\hat{\mathbf{V}}\), with the resulting product \(\hat{\mathbf{V}} \mathbf{B}\) reflecting the sector of origin of value added. If we opted instead (as it normally the case) to reflect the value-added exporting sector, then the products \({\hat{\mathbf{V}}}_s \mathbf{B}_{ss}\) and \({\hat{\mathbf{V}}}_t \mathbf{B}_{ts}\) should be diagonalized as \(\widehat{{\mathbf{V}}_s \mathbf{B}_{ss}}\) and \(\widehat{{\mathbf{V}}_t \mathbf{B}_{ts}}\), respectively.
The decomposition of value added in exports essentially consists in analyzing the elements of Equation @ref(eq:content), extracting the elements that are not really value added (double counted) as well as those that are not really exports (flows eventually re-imported and absorbed domestically).
The basic matrices of a Leontief demand-induced model can be easily
obtained from raw data with the command make_wio():
make_wio(wiotype = "icio2023", year = NULL,
src_dir = NULL, quiet = FALSE)where:
wiotype is a string specifying the type of
international input-output table to be used (and therefore the source
zip file to be looked for in the source directory
src_dir).year is an integer specifying the reference year. If
missing, make_wio() will use the last available year for
that database (e.g., 2020 for "icio2023" or 2014 for
"wiod2016").src_dir is the source directory where the raw data is
located. If data is stored in the current working directory, this
argument can be omitted.quiet is a boolean, with TRUE opting for a
silent output.produces basic input-output tables from three types of data: public international input-output databases, custom data and sample data.
Public international input-output databases can be directly downloaded from the web pages of their respective institutions. Three sources are currently supported:
The default wiotype is "icio2023",
corresponding to the OECD ICIO Tables, version 2023 (years 1995 to
2020), available as zip files that can be downloaded from the ICIO
web page. Older versions of OECD ICIO ("icio2021",
"icio2018" and "icio2016") are provided for
backward compatibility (for example, to reproduce examples in literature
using those databases). For WIOD Tables, versions included are
"wiod2016" (version 2016, years 2000 to 2014),
"wiod2013" and "lrwiod2022" (long-run WIOD
tables, version 2022, for years 1965 to 2000). All of them are available
at the University of Groningen’s Growth and Development
Centre web page. FIGARO tables, whether industry-by-industry
("figaro2022i") or product-by-product
("figaro2022p") are available at the Eurostat
web page.
The advantage of these databases is threefold: they are widely used
in the economic literature, they are quite rich in terms of countries
and sectors, and they are directly downloadable from the web page of
their supporting institutions, typically as zipped files containing
comma-delimited files (.csv), Excel files
(.xlsx) or R data files (.RData). In any case,
can be easily extended to other available international input-output
databases like the Eora database (Lenzen et al.
2013) or the ADB Multi-Regional Input Output (ADB-MRIO) Database
(Asian Development Bank 2023).
For instance, if we want to use with the 2023 edition of the OECD
ICIO tables (with data up to 2020), we must first download the source
file “ICIO_2016-2020-extended.zip” (92 MB) from the ICIO
web page. Then we will use the command make_wio(),
specifying the edition, the year and the folder where the source zip
file is saved (just the directory). For instance, if the file was
located in C:\Users\Username\Documents\R and we wanted the
year 2020:
wio <- make_wio("icio2023", year = 2020,
src_dir = "C:/Users/Username/Documents/R")and will take care of the rest: it will extract the .csv
files from the zip file and produce the basic input-output matrices.
Alternatively, can use custom data to create basic input-output
matrices. In this case, we just need as input a numeric matrix or data
frame with the intermediate inputs \(\mathbf{Z}\) and the final demand \(\mathbf{Yfd}\), plus a vector with the
names of the countries. In this case, we will use an alternative
command, make_custom_wio().
wio <- make_custom_wio(df, g_names = c("C01", "C02", "C03"))If we just want to check the features of , there is no need to
download any data. The package includes two sets of fictitious data,
wiotype = "iciotest" (an ICIO-type data sample, with Mexico
and China disaggregated) and wiotype = "wiodtest" (a
WIOD-type data sample). Both can be directly used in
make_wio(), with no need to specify year or source
directory.
As the dimension of publicly available input-output matrices is big,
here we will use here ICIO-type fictitious data made with
make_wio("iciotest").
wio <- make_wio("iciotest")The newly created wio class, which can be easily checked
with summary(wio), includes the following elements:
Additionally, the main dimensions are provided in the list
dims, such as the number of countries \(G\), the number of countries including
disaggregated countries \(GX\), the
number of sectors \(N\), the number of
final demand components \(FD\), or
combinations thereof (\(GN\), \(GXN\), \(GFD\)). A list names is also
provided, including the names of countries (ISO codes of 3 characters),
the names of sectors, (from D01 to D99 for tables based in ISIC revision
4, and from C01 to C99 for tables based in ISIC revision 3), the names
of demand components, and two additional metadata: the type of source
database ("icio2023", "wiod2016", etc.) and
the year.
Although was initially conceived as a trade analysis software, it
also includes a series of commands that facilitate the manipulation of
international input-output tables for any other purposes. Thus, we can
multiply a diagonal matrix by an ordinary one with dmult(),
an ordinary by a diagonal with multd(), or make a
block-by-block Hadamard product of matrices with hmult().
We can also easily obtain a block diagonal matrix with
bkd(), a block off-diagonal matrix with
bkoffd(), or a diagonal matrix with the sums of all columns
with diagcs().
Additionally, as always operates with named rows and columns (names
of countries and sectors), several commands are included to consolidate
matrices, preserving the matrix format and optionally providing names
for the resulting rows or columns: rsums() to sum rows,
csums() to sum columns, sumnrow() to sum every
nth row of a matrix, sumncol() to sum every
nth column, sumgrows() to sum groups of rows of a
particular size, sumgcols() to do the same with columns,
etc.
On the other hand, the OECD ICIO tables have a particular feature:
two big industrial countries, China and Mexico, are broken down into two
regions each. Calculations must initially be done with disaggregated
data, but later consolidated under the name of the country. The command
meld() takes care of that.
Let us, for instance, check that the production \(\mathbf{X}\) is equivalent to the product of the global Leontief inverse matrix \(\mathbf{B}\) and the final demand \(\mathbf{Y}\):
BY <- wio$B %*% wio$YWe can sum the rows (with rsums(), naming the result as
"BY") and check that it coincides with the production
vector:
BY <- rsums(BY, "BY")
print(cbind(head(BY, 10), head(wio$X, 10)))## BY X
## ESP_01T09 1378.568 1378.568
## ESP_10T39 1914.607 1914.607
## ESP_41T98 2113.699 2113.699
## FRA_01T09 1848.173 1848.173
## FRA_10T39 1799.486 1799.486
## FRA_41T98 1608.004 1608.004
## MEX_01T09 0.000 0.000
## MEX_10T39 0.000 0.000
## MEX_41T98 0.000 0.000
## USA_01T09 1895.742 1895.742Now let us calculate the value added absorbed abroad. For that we need to multiply the value added coefficients matrix \(\hat{\mathbf{V}}\) (represented here as \(\mathbf{W}\)) by the global inverse matrix \(\mathbf{B}\) by the final demand matrix \(\mathbf{Y}\), and then exclude the value added absorbed domestically. This can be easily done with a few commands.
To calculate all value added induced by final demand:
VBY <- dmult(wio$W, wio$B) %*% wio$Y
VBY## ESP FRA MEX USA CHN ROW
## ESP_01T09 33.25239 33.04328 29.13415 39.26315 44.36171 40.26254
## ESP_10T39 105.86567 99.40932 118.73322 139.90848 115.91495 126.97831
## ESP_41T98 221.93642 191.16663 158.37563 173.76610 145.22181 168.64254
## FRA_01T09 48.48628 66.62310 51.62458 49.45643 47.66424 70.97642
## FRA_10T39 120.80031 104.64030 128.78920 102.79096 97.91708 99.78527
## FRA_41T98 134.74749 129.14500 99.99938 88.70168 86.75694 101.79354
## MEX_01T09 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
## MEX_10T39 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
## MEX_41T98 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
## USA_01T09 175.01545 130.46673 128.74728 107.71747 102.20179 117.94400
## USA_10T39 102.29790 84.03672 79.60012 121.89497 66.60450 100.75615
## USA_41T98 115.50508 118.18725 129.51719 122.16680 95.86500 111.98916
## CHN_01T09 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
## CHN_10T39 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
## CHN_41T98 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
## ROW_01T09 82.22487 42.82585 45.01008 60.06683 46.78138 51.62906
## ROW_10T39 90.44372 97.64510 80.63597 95.00232 91.33130 91.05473
## ROW_41T98 62.56171 51.01318 42.64560 58.70599 41.40437 50.09897
## MX1_01T09 173.85507 180.14952 154.43342 149.69601 164.13090 149.43125
## MX1_10T39 119.84480 74.11099 117.78742 97.93871 142.64384 121.97803
## MX1_41T98 49.45281 29.23090 35.52473 39.69653 36.67997 31.42076
## MX2_01T09 96.85254 83.89485 70.55941 97.36493 80.35587 66.40230
## MX2_10T39 138.50490 86.35272 92.84516 108.88726 99.24637 102.95958
## MX2_41T98 82.91973 67.68778 62.14849 77.03372 65.06803 75.12146
## CN1_01T09 109.94070 114.47837 91.18810 152.37369 127.84703 118.37641
## CN1_10T39 119.64017 127.22095 126.45021 165.70116 164.43470 128.00251
## CN1_41T98 109.34845 93.91197 106.67385 115.50129 111.77386 119.86482
## CN2_01T09 84.74417 83.13258 69.33664 86.84078 80.88526 72.00972
## CN2_10T39 73.17244 54.76049 43.08188 56.11525 70.19744 78.67920
## CN2_41T98 158.98841 103.45062 108.60598 136.04997 128.63627 109.93866The rows for Mexico and China are disaggregated. We can easily meld
them with meld():
VBY <- meld(VBY)
VBY## ESP FRA MEX USA CHN ROW
## ESP_01T09 33.25239 33.04328 29.13415 39.26315 44.36171 40.26254
## ESP_10T39 105.86567 99.40932 118.73322 139.90848 115.91495 126.97831
## ESP_41T98 221.93642 191.16663 158.37563 173.76610 145.22181 168.64254
## FRA_01T09 48.48628 66.62310 51.62458 49.45643 47.66424 70.97642
## FRA_10T39 120.80031 104.64030 128.78920 102.79096 97.91708 99.78527
## FRA_41T98 134.74749 129.14500 99.99938 88.70168 86.75694 101.79354
## MEX_01T09 270.70761 264.04436 224.99283 247.06094 244.48677 215.83355
## MEX_10T39 258.34970 160.46370 210.63258 206.82598 241.89021 224.93762
## MEX_41T98 132.37254 96.91869 97.67322 116.73025 101.74800 106.54222
## USA_01T09 175.01545 130.46673 128.74728 107.71747 102.20179 117.94400
## USA_10T39 102.29790 84.03672 79.60012 121.89497 66.60450 100.75615
## USA_41T98 115.50508 118.18725 129.51719 122.16680 95.86500 111.98916
## CHN_01T09 194.68487 197.61095 160.52474 239.21447 208.73229 190.38614
## CHN_10T39 192.81261 181.98144 169.53209 221.81640 234.63214 206.68171
## CHN_41T98 268.33686 197.36260 215.27984 251.55127 240.41013 229.80349
## ROW_01T09 82.22487 42.82585 45.01008 60.06683 46.78138 51.62906
## ROW_10T39 90.44372 97.64510 80.63597 95.00232 91.33130 91.05473
## ROW_41T98 62.56171 51.01318 42.64560 58.70599 41.40437 50.09897We just want the value added absorbed abroad. For that we need the
block off-diagonal matrix of \(\mathbf{\hat{V}BY}\), that we can produce
with bkoffd():
vax <- bkoffd(VBY)
head(vax, 10)## ESP FRA MEX USA CHN ROW
## ESP_01T09 0.00000 33.04328 29.13415 39.26315 44.36171 40.26254
## ESP_10T39 0.00000 99.40932 118.73322 139.90848 115.91495 126.97831
## ESP_41T98 0.00000 191.16663 158.37563 173.76610 145.22181 168.64254
## FRA_01T09 48.48628 0.00000 51.62458 49.45643 47.66424 70.97642
## FRA_10T39 120.80031 0.00000 128.78920 102.79096 97.91708 99.78527
## FRA_41T98 134.74749 0.00000 99.99938 88.70168 86.75694 101.79354
## MEX_01T09 270.70761 264.04436 0.00000 247.06094 244.48677 215.83355
## MEX_10T39 258.34970 160.46370 0.00000 206.82598 241.89021 224.93762
## MEX_41T98 132.37254 96.91869 0.00000 116.73025 101.74800 106.54222
## USA_01T09 175.01545 130.46673 128.74728 0.00000 102.20179 117.94400Equation @ref(eq:content) showed a basic decomposition of the value of gross exports into its domestic and foreign content. However, matrix \(\mathbf{B}\) in that equation is the result of successive rounds of production induced by demand, therefore incurring in double counting. To differentiate between true value added and double counting we must specify a spatial perimeter and a sequential perimeter. The spatial perimeter (or perspective) will delimit the border that has to be crossed a specific number of times for a transaction to be considered as value added, and the the sequential perimeter (or approach) will delimit the number of border crossings for a transaction to be considered as value added.
The most consistent decomposition methods employ for the spatial perimeter the exporting country’s border (country perspective) and for the sequential perimeter the first border crossing (source-based approach). As a result, export flows are considered as value added the first time they cross the exporting country’s border, with ulterior flows being considered as double counting.
Once we have identified export flows that are double counted (and therefore do not constitute real value added), we must also differentiate the export flows that eventually return to be absorbed in the exporting country (and therefore do not constitute true exports). The methodology to calculate value added in exports is not univocal, and has led to a considerable amount of discussion in the past few years, following Daudin, Rifflart, and Schweisguth (2011); Johnson and Noguera (2012); Foster-McGregor and Stehrer (2013); Wang, Wei, and Zhu (2013); Koopman, Wang, and Wei (2014); Los, Timmer, and Vries (2016) and Los and Timmer (2018); Nagengast and Stehrer (2016); Johnson (2018); Arto et al. (2019); Miroudot and Ye (2021) and Borin and Mancini (2023).
The most recent decomposition methods, including those of Borin and Mancini (2023) or Miroudot and Ye (2021), involve the calculation of a coefficient matrix \(\mathbf{A}\) that excludes the linkage effects of exported inputs. Thus, for a given country \(s\) we will define an extraction matrix \(\mathbf{A}^{xs}\) as a global coefficient matrix whose coefficients corresponding to the exports of inputs of \(s\) are equal to zero.
\[\begin{equation} \mathbf{A}^{xs} = \left[ \begin{matrix} \mathbf{A}_{11} & \mathbf{A}_{12} & \cdots & \mathbf{A}_{1s} & \cdots & \mathbf{A}_{1G} \\ \mathbf{A}_{21} & \mathbf{A}_{22} & \cdots & \mathbf{A}_{2s} & \cdots & \mathbf{A}_{2G} \\ \vdots & \vdots & \ddots & \vdots & \vdots & \vdots \\ 0 & 0 & \cdots & \mathbf{A}_{ss} & \cdots & 0 \\ \vdots & \vdots & \vdots & \vdots & \ddots & \vdots \\ \mathbf{A}_{G1} & \mathbf{A}_{G2} & \cdots& \mathbf{A}_{Gs}& \cdots& \mathbf{A}_{GG} \\ \end{matrix} \right] (\#eq:Anots) \end{equation}\]
The global inverse Leontief matrix \(\mathbf{B}^{xs}\) derived of this extraction matrix will collect the value added induced by exports excluding intermediate goods. Therefore, the double counting will be the difference between the Leontief inverse global matrix \(\mathbf{B}\) and the Leontief inverse global extraction matrix \(\mathbf{B}^{xs}\), from where we can break down the components of equation @ref(eq:content) into the domestic value added \({\mathbf{V}}_s \mathbf{B}^{xs}_{ss} \mathbf{E}_{sr}\), the double counted domestic value added \({\mathbf{V}}_s (\mathbf{B}_{ss} - \mathbf{B}^{xs}_{ss}) \mathbf{E}_{sr}\), the foreign value added \(\sum_{t\neq s}^{G}{{\mathbf{V}}_t \mathbf{B}^{xs}_{ts} \mathbf{E}_{sr}}\), and the foreign double counting \(\sum_{t\neq s}^{G}{{\mathbf{V}}_t (\mathbf{B}_{ts} - \mathbf{B}^{xs}_{ts}) \mathbf{E}_{sr}}\)
Then, after expressing exports in terms of final demand, we we will
be able to separate the exports that eventually return home to be
absorbed, called reflection. Figure @ref(fig:decomposition) shows the
process carried out by make_exvadec(), first separating
Domestic Content (DC) and Foreign Content (FC), then identifying
Domestic Value Added (DVA) and Foreign Value added (FVA), separating
them from Domestic Double Counting (DDC) and Foreign Double Counting
(FDC), and finally dividing Domestic Value Added between Value Added
Exported (VAX) and Reflection (REF).
Decomposition of value added in gross exports
Using these indicators (or parts thereof) we can obtain additional indicators to measure the participation of countries in global value chains, whether in the form of foreign inputs used in the domestic production of exports (backward vertical specialization) or in the form of domestic inputs exported to be used in the production of foreign exports (forward vertical specialization). In case these indicators are available, the denomination will be global value chain participation (GVC), divided in global value chain participation backwards (GVCB) and forward (GVCF).
The command make_exvadec() (export value added
decomposition) provides, from a wio object, the full
decomposition of the value added in exports for every country or for a
particular country or country group, according to different
methodologies. The command syntax is as follows:
make_exvadec(wio_object, exporter = "all", method = "bm_src",
output = "standard", quiet = TRUE)with the following arguments:
wio_object is an object of class wio
obtained through the command make_wio.exporter is a string with the code for the exporting
country. Default is "all" (producing an output of dimension
\(GN \times G\)), but can be the code
of a country, e.g., "ESP", or country group, e.g.,
"EU27" (producing an output of dimension \(N \times G\)).method is a string specifying the decomposition
method.output is a string specifying the desired output
type.quiet is a boolean indicating whether to produce output
silently (default is FALSE).The available methods and outputs are summarized in Table
@ref(tab:methodoutput). Selecting "bm_src" will produce a
Borin and Mancini (2023) source-based
decomposition (from our point of view, the most methodologically sound),
"bm_snk" a Borin and Mancini
(2023) sink-based decomposition, "my" a Miroudot and Ye (2021) decomposition,
"wwz" a Wang, Wei, and Zhu
(2013) decomposition, "kww" a Koopman, Wang, and Wei (2014) decomposition and
"oecd" a basic OECD decomposition.
| Method | Description | Perimeters | Outputs |
|---|---|---|---|
bm_src |
Borin and Mancini (2019), source | Source-based approach, various perspectives | basic, standard,
terms |
bm_snk |
Borin and Mancini (2019), sink | Sink-based approach, country perspective | standard, terms |
my |
Miroudot and Ye (2021) | Source-based approach, various perspectives | standard, terms,
terms2 |
wwz |
Wang et al. (2013) | Mix of both | standard, terms,
terms2 |
kww |
Koopman et al. (2014) | Sink-based approach, mixed perspective | standard, terms |
oecd |
OECD (2021) (not a decomposition) | Not applicable | standard, terms,
tiva |
The "standard" output of make_exvadec()
will include a series of matrices of dimension \(GN \times G\) (when exporter is
"all") or of dimension \(N \times
G\) (when the exporting country is specified, e.g.,
"USA"), with breakdown by exporting country and sector, and
by importer (country of destination), plus additional metadata:
In some cases, indicators reflecting the participation in global value chains (vertical specialization) will be provided, mainly foreign value added that eventually takes part in the domestic production of exports (\(\mathbf{GVCB}\) or global value chain participation backwards) or domestic value added that eventually takes part in the foreign production of exports (\(\mathbf{GVCF}\) or global value chain participation forward).
exvadec objects will inherit metadata of the
wio object they come from, like dims,
names, or source (type), plus the
indication of the decomposition method used and, in case of
individual decompositions, the exporter. The
"standard" output should be enough for most analyses, but
alternative outputs can be specified with the argument
output. The option "terms" will show all the
elements of the decomposition (whose sum is the total value of gross
exports), which is useful if we need to distinguish the value added
induced by intermediate outputs. The Wang, Wei,
and Zhu (2013) decomposition corresponds with the terminology of
their Table A2 (pg. 35), but an additional "terms2" is
provided (with the terminology of their Table E1, pg. 61).
The "kww" and "wwz" methods are, in fact, a
mix of perspectives and approaches. The exporting country perspective
and the source approach should probably be considered as the standard,
but some alternative approaches (like the sink approach, considering
value added all flows prior to the last border crossing) and various
tailored perspectives are provided. Thus, the sector, bilateral or
bilateral-sector perspectives consider double counting all flows out of
those perimeters, and can be calculated for the "bm_src"
and the "my" methods (by using the additional arguments
partner and sector). Additionally, the
"my" method allows a world perspective (using
perim = "WLD"), consider as double counting the crossing of
any border more than once, not only that of the exporting
country.
We have included an additional decomposition called
"oecd", which is not a true full decomposition method, but
represents nevertheless a calculation of several elements of value added
in exports. It includes a "tiva" output to show the most
typical indicators included in the OECD TiVA database. In this
decomposition (unlike in the the rest), the bilateral VAX is just VAX
absorbed in the partner country.
To create create a full decomposition of the value added in the exports of Spain using the method of Borin and Mancini (2023), using a exporting country perspective and a source-based approach, we would type:
exvadec <- make_exvadec(wio, exporter = "ESP", method = "bm_src")## ======================================================================
## DECOMPOSITION OF VALUE ADDED IN EXPORTS OF SPAIN IN 2022
## Sector: All sectors
## Destination: All countries
## ======================================================================
## VA_components USD_MM Percent
## Gross exports of goods and services (EXGR) 4666.96 100.00
## Domestic Content in VA (DC) 2165.17 46.39
## Domestic Value Added (DVA) 1880.60 40.30
## Value Added Exported (VAX) 1624.18 34.80
## Reflection (REF) 256.41 5.49
## Domestic Double Counting (DDC) 284.58 6.10
## Foreign Content in VA (FC) 2501.78 53.61
## Foreign Value Added (FVA) 2176.21 46.63
## Foreign Double Counting (FDC) 325.58 6.98
## Global Value Chain-related trade (GVC) 4034.25 86.44
## GVC-related trade, backward (GVCB) 2786.36 59.70
## GVC-related trade, forward (GVCF) 1247.89 26.74
## ======================================================================
## Method: Borin and Mancini (2023), source-based, standard output
## Exporting country perspective, source approachIf we want to go deeper into the components of this value added, differentiating between final and intermediate exports, we can use:
exvadec.terms <- make_exvadec(wio, exporter = "ESP",
method = "bm_src", output = "terms")## ======================================================================
## DECOMPOSITION OF VALUE ADDED IN EXPORTS OF SPAIN IN 2022
## Sector: All sectors
## Destination: All countries
## ======================================================================
## VA_components USD_MM Percent
## EXGR (Gross exports of goods and services) 4666.96 100.00
## T01 VAX1 (DVA, finals) 534.98 11.46
## T02 VAX2 (DVA, interm. for absorption) 97.73 2.09
## T03 VAX3 (DVA, interm. for final exports) 314.51 6.74
## T04 VAX4 (DVA, interm. for reexport) 676.96 14.51
## T05 REF1 (Reflection, finals) 102.25 2.19
## T06 REF2 (Reflection, intermediates) 154.17 3.30
## T07 DDC (Domestic Double Counting) 284.58 6.10
## T08 FVA1 (FVA, finals) 631.12 13.52
## T09 FVA2 (FVA, interm. for absorption) 112.29 2.41
## T10 FVA3 (FVA, interm. for final exports) 478.65 10.26
## T11 FVA4 (FVA, interm. for reexport) 954.15 20.44
## T12 FDC (Foreign Double Counting) 325.58 6.98
## ======================================================================
## Method: Borin and Mancini (2023), source-based, terms output
## Exporting country perspective, source approachIf we want to get a list of common trade indicators (exports,
imports, value added, production) similar to those of the TiVA database,
we could just use make_exvadec() with the method
"oecd" and output = "tiva".
tiva <- make_exvadec(wio, exporter = "ESP",
method = "oecd", output = "tiva")## ======================================================================
## DECOMPOSITION OF VALUE ADDED IN EXPORTS OF SPAIN IN 2022
## Sector: All sectors
## Destination: All countries
## ======================================================================
## VA_components USD_MM Percent
## Gross exports of goods and services (EXGR) 4666.96 100.00
## Gross exports, finals (EXGR_FNL) 1343.03 28.78
## Gross exports, intermediates (EXGR_INT) 3323.92 71.22
## Gross imports (IMGR) 5292.12 113.40
## Gross imports, finals (IMGR_FNL) 2386.14 51.13
## Gross imports, intermediates (IMGR_INT) 2905.98 62.27
## Domestic absorption (DOM) 739.92 15.85
## Domestic absorption, finals (DOM_FNL) 224.26 4.81
## Domestic absorption, interm. (DOM_INT) 515.66 11.05
## Gross balance (BALGR) -625.17 -13.40
## Domestic Content in VA (EXGR_DVA) 2165.17 46.39
## Direct domestic VA content (EXGR_DDC) 1757.25 37.65
## Indirect domestic VA content (EXGR_IDC) 123.34 2.64
## Reimported domestic VA content (EXGR_RIM) 284.58 6.10
## Value Added in final demand (FD_VA) 1985.24 42.54
## DVA in dom. final dem. (VAD) (DXD_DVA) 361.05 7.74
## DVA in foreign final dem. (VAX) (FFD_DVA) 1624.18 34.80
## FVA in dom. final dem. (VAM) (DFD_FVA) 2249.35 48.20
## Balance of VA (VAX - VAM) (BALVAFD) -625.17 -13.40
## Foreign VA Content (EXGR_FVA) 2501.78 53.61
## Backward participation in GVC (DEXFVAP) 2501.78 53.61
## Forward participation in GVC (FEXDVAP) 3047.87 65.31
## Value added (VA) 1985.24 42.54
## Production (PROD) 5406.87 115.85
## ======================================================================
## Method: OECD (2022), TiVA output
## Country perspective, source approachThe decomposition of make_exvadec() does not distinguish
between the different sources of foreign value added. This is where the
command make_exvadir() might be useful. It provides data on
the direction of value added, i.e., details of both the geographical and
sectoral origin of the value added incorporated in exports and of the
final destination (in gross terms or in terms of final demand). It
allows therefore a thorough analysis of where the value added is
generated and where it ends up (for instance, how EU services are
important for UK’s exports of goods, or the role of China as
intermediate party in the exports of Russia).
The command make_exvadir() produces an output which is
the result of multiplying the value added matrix \(\hat{\mathbf{V}}\) by the global Leontief
inverse matrix \(\mathbf{B}\) by a
matrix of exports \(\mathbf{EXGR}\),
but with a high level of specification of the three matrices. First, the
matrix \(\hat{\mathbf{V}}\) (\(\mathbf{V}\) diagonalized, to preserve the
sector information) will be multiplied by a specific form of \(\mathbf{B}\): regular \(\mathbf{B}\) to obtain the total value
added content, \(\mathbf{B}_d\) to
obtain the domestic value added content and \(\mathbf{B_m}\) to obtain the foreign value
added content; or its equivalents in the form of extraction matrices
\(\mathbf{B}^{xs}\) to obtain the
total, domestic or foreign value added excluding double counting,
according to the methodology of Borin and Mancini
(2023).
Then, depending of the sectoral perspective, the product \(\hat{\mathbf{V}} \mathbf{B}\) will be left as it is (sector of origin) or will be summed up by columns and diagonalized, i.e., as \(\widehat{\mathbf{VB}}\) (default option, exporting sector perspective). The specification of sectors or countries of origin of value added will be done by setting the non-specified values to zero. If the exporter is a group of countries, there is the possibility of considering intra-regional flows as exports or not (by default, intra-regional flows will be excluded).
Finally, the resulting adjusted product \({\mathbf{VB}}\) will be multiplied by a form of export matrix \(\mathbf{EXGR}\). By default, the ordinary gross export matrix will be considered, but the option will be given to express exports in terms of absorption (i.e., final demand), as \(\mathbf{EXGRY}\), giving in this case the possibility of distinguishing between destination of final goods (\(\mathbf{Y_m}\)) and destination of intermediate exports processed as final goods (\(\mathbf{A_m B Y}\): this is the only way of calculating the value added induced by intermediate exports).
Additionally, the possibility will be given to consider exports that go via a specific country, i.e., an intermediate importer (for example, Russian exports to the EU that go via China). If this is the case, \(\widehat{\mathbf{VB}}\) will be multiplied by \(\mathbf{Y}_{sr} + \mathbf{A}_{sr}[\mathbf{BY}]_r\), with \(s\) being the exporter and \(r\) the intermediate importer, and \([\mathbf{BY}]_r\) the rows of product \(\mathbf{BY}\) for country \(r\)), i.e., the exports of \(s\) used in the production of \(r\), that ends up in \(r\) or exported elsewhere.
The syntax of make_exvadir() is:
make_exvadir(wio_object, va_type = "TC", flow_type = "EXGR", exporter,
via = "any", sec_orig = "all", geo_orig = "all",
intra = FALSE, perspective = "exporter")The arguments are as follows:
wio_object is an object of class wio
(required).va_type is a string describing the type of value added:
"TC", the default, is the total content in value added
(matrix \(\mathbf{B}\)), both foreign
and domestic, but we can also select "DC" (the domestic
value added content, using matrix \(\mathbf{B_d}\)) or "FC" (the
foreign value added content, using matrix \(\mathbf{B_m}\)). "TVA" is the
total pure value added, i.e., excluding double counting (matrix \(\mathbf{B}^{xs}\)), and we can also get the
"DVA" (domestic value added, excluding double counting,
matrix \(\mathbf{B_d}^{xs}\)) or the
"FVA" (foreign value added, excluding double counting,
matrix \(\mathbf{B_m}^{xs}\)).flow_type is a string specifying the type of export
flow. Default is gross total exports ("EXGR"). Alternatives
are exports expressed in terms of final demand: total exports
("EXGRY"), final exports ("EXGRY_FIN") or
intermediate exports ("EXGRY_INT"). The latter options will
show where value added exported is eventually absorbed, regardless of
where it was initially exported.exporter is a string reflecting the code of the
exporting country or group of countries.via is a string with the code of the intermediate
importing country or country group. Default is "any". This
option requires flows to be expressed necessarily in terms of final
demand.geo_orig is a string with the code of the country or
country group origin of value added. Default is "all".sec_orig is string with the code of sector of origin of
value added (e.g., "AGR", "MANUF",
"SRVWC"…). Default is "all".intra is a boolean to specify whether to include or not
intra-region exports (default is FALSE, i.e., EU27 exports
will include only extra-EU exports).perspective shows the sectoral perspective of value
added. Default is exporting sector ("exporter") but sector
of "origin" can also be specified.Please note that, compared to make_exvadec(),
make_exvadir() is logically more restricted at decomposing
value added, so in principle calculations will be shown in terms of
domestic and foreign content (DC/FC) or, at most, domestic and foreign
value added (DVA/FVA, excluding double counting), but including
reflection (REF). Also note that the total content in value added from
all origins and all sectors is, precisely, the value of total gross
exports.
We have seen that the foreign content in Spanish exports amounts to
USD 2501.78 million. Where does it come from? The specific geographical
and sector origin of the value added in exports can be obtained using
the command make_exvadir():
exvadir <- make_exvadir(wio, exporter = "ESP", va_type = "FC",
flow_type = "EXGR")
head(exvadir$FC, 10)## ESP FRA MEX USA CHN ROW
## ESP_01T09 0 0.00000 0.00000 0.00000 0.00000 0.00000
## ESP_10T39 0 0.00000 0.00000 0.00000 0.00000 0.00000
## ESP_41T98 0 0.00000 0.00000 0.00000 0.00000 0.00000
## FRA_01T09 0 19.45318 26.47295 15.19438 35.51728 24.42115
## FRA_10T39 0 14.09801 34.93554 23.48504 32.13613 27.09630
## FRA_41T98 0 15.84674 25.71533 14.12113 17.62330 14.63281
## MEX_01T09 0 38.41321 52.27477 30.00356 70.13415 48.22319
## MEX_10T39 0 31.07698 77.01024 51.76931 70.83935 59.72978
## MEX_41T98 0 33.18999 53.85912 29.57581 36.91088 30.64749
## USA_01T09 0 23.35813 31.78700 18.24443 42.64685 29.32333Note that the exvadir object that we have obtained is
different from the exvadec object, in the sense that
‘exporters’ in an exvadir object are the different
countries and sectors of origin of the value added included in the
exports of a specific country (in this case, Spain). We can better
understand this by typing summary(exvadir):
summary(exvadir)##
## ======================================================================
## ORIGIN AND DESTINATION OF VALUE ADDED IN EXPORTS OF SPAIN IN 2022
## ======================================================================
## Value added type: Foreign VA content (FC)
## In type of flow: Total gross exports (EXGR)
## That goes via country: any
## Using inputs from sector: all sectors
## Of country: all countries
## With sector perspective: exporting
## ======================================================================
##
## Available countries of origin of VA (G): 6
## ESP, FRA, MEX, USA, CHN, ROW
##
## Available sectors of origin of VA (N): 3
## D01T09, D10T39, D41T98
##
## Available destinations of VA (G): 6
## ESP, FRA, MEX, USA, CHN, ROW
## Now we will see how to maximize the information given by these objects.
The commands make_wio(), make_exvadec() and
make_exvadir() produce objects that are lists of matrices
will a full breakdown by sector and countries of destination. However,
most analyses require grouping of those variables. The advantage is that
grouping by sector or by destination do not require additional
computing, just an aggregation of variables.
To check the information about sectors, it suffices to print
info_sec():
info_sec("iciotest")##
## ======================================================================
## Test Input Output Table, ICIO-type, 2022 edition
## ======================================================================
##
## Individual sectors:
## PRIMARY: D01T09 (Primary sector), MANUF: D10T39 (Manufacturing),
## SRVWC: D41T98 (Services, including construction)
##
## Sector groups:
## TOTAL: D01T98 (Total goods and services), GOODSWU: D01T39 (Goods,
## total, incl. utilities)To check the information about available countries, the command is
info_geo():
info_geo("iciotest")##
## ======================================================================
## Test Input Output Table, ICIO-type, 2022 edition
## ======================================================================
##
## Individual countries:
## CHN (China), ESP (Spain), FRA (France), MEX (Mexico), USA (United
## States), ROW (Rest of the world)
##
## Groups of countries:
## WLD (World), EUROPE (Europa), EU27 (EU-27), AMERICA (Americas),
## NAMERICA (North America), LATAM (Latin America and Caribbean), ASIA
## (Asia), EASIA (East Asia), ASIAOC (Asia and Oceania), G7 (G7), G20
## (G20), NAFTA (NAFTA), USMCA (USMCA), APEC (APEC), RCEP (RCEP), EU28
## (EU-28), OECD (OECD), EMU (EMU), EMU19 (EMU-19), NONEU28 (Non-EU28),
## NONEU27 (Non-EU27), NONOECD (Non-OECD)These commands do not require to have a wio in the
environment, so we can just check what countries are available in the
OECD’s ICIO tables, 2023 edition.
info_geo("icio2023")##
## ======================================================================
## OECD's Inter-Country Input-Output Table (ICIO), 2023 edition
## ======================================================================
##
## Individual countries:
## ARG (Argentina), AUS (Australia), AUT (Austria), BEL (Belgium), BGD
## (Bangladesh), BGR (Bulgaria), BLR (Belarus), BRA (Brazil), BRN
## (Brunei Darussalam), CAN (Canada), CHE (Switzerland), CHL (Chile),
## CHN (China), CIV (Côte d'Ivoire), CMR (Cameroon), COL (Colombia), CRI
## (Costa Rica), CYP (Cyprus), CZE (Czech Republic), DEU (Germany), DNK
## (Denmark), EGY (Egypt), ESP (Spain), EST (Estonia), FIN (Finland),
## FRA (France), GBR (United Kingdom), GRC (Greece), HKG (Hong Kong,
## China), HRV (Croatia), HUN (Hungary), IDN (Indonesia), IND (India),
## IRL (Ireland), ISL (Iceland), ISR (Israel), ITA (Italy), JOR
## (Jordania), JPN (Japan), KAZ (Kazakhstan), KHM (Cambodia), KOR
## (Korea), LAO (Laos), LTU (Lithuania), LUX (Luxembourg), LVA (Latvia),
## MAR (Morocco), MEX (Mexico), MLT (Malta), MMR (Myanmar), MYS
## (Malaysia), NGA (Nigeria), NLD (Netherlands), NOR (Norway), NZL (New
## Zealand), PAK (Pakistan), PER (Peru), PHL (Philippines), POL
## (Poland), PRT (Portugal), ROU (Romania), RUS (Russia), SAU (Saudi
## Arabia), SEN (Senegal), SGP (Singapore), SVK (Slovak Republic), SVN
## (Slovenia), SWE (Sweden), THA (Thailand), TUN (Tunisia), TUR
## (Turkey), TWN (Chinese Taipei), UKR (Ukraine), USA (United States),
## VNM (Vietnam), ZAF (South Africa), ROW (Rest of the world)
##
## Groups of countries:
## WLD (World), EUROPE (Europa), EU27 (EU-27), EURNONEU (Europe non-EU),
## AFRICA (Africa), NAFRICA (North Africa), SSAFRICA (Sub-Saharan
## Africa), AMERICA (Americas), NAMERICA (North America), LATAM (Latin
## America and Caribbean), ASIA (Asia), CWASIA (Central and West Asia),
## EASIA (East Asia), SASIA (Southern Asia), SEASIA (South-East Asia),
## OCEANIA (Oceania), ASIAOC (Asia and Oceania), G7 (G7), G20 (G20),
## NAFTA (NAFTA), USMCA (USMCA), EEA (EEA), EFTA (EFTA), APEC (APEC),
## ASEAN (ASEAN), RCEP (RCEP), EU28 (EU-28), OECD (OECD), EMU (EMU),
## EMU19 (EMU-19), EU27NONEMU (EU-28 not EMU), EU28NONEMU (EU-27 not
## EMU), NONEU28 (Non-EU28), NONEU27 (Non-EU27), NONOECD (Non-OECD)Additionally, the commands get_geo_codes() and
get_sec_codes() provide details about the components of the
different groups. These commands are also directly applicable for any
available input-output table. For instance, for "wiod2016"
we would have the following components of NAFTA:
get_geo_codes("NAFTA", wiotype = "wiod2016")## [1] "CAN|MEX|USA"And for "icio2023" we have the following components of
the information services sector (INFO):
get_sec_codes("INFO", wiotype = "icio2023")## [1] "D26|D58T60|D61|D62T63"Once we know the sector and geographical disaggregation, we can
discuss how to take advantage of the information contained in
exvatools objects.
Once we have obtained a decomposition, we can play with the results
in terms of sectors and countries of destination just using the command
get_exvadec_bkdown(). For instance, to select the value
added in Spanish exports of services (including construction) to the
United States, we just have to type:
get_exvadec_bkdown(exvadec, exporter = "ESP",
sector = "SRVWC", importer = "USA")## ======================================================================
## DECOMPOSITION OF VALUE ADDED IN EXPORTS OF SPAIN IN 2022
## Sector: Services, including construction (SRVWC)
## Destination: United States (USA)
## ======================================================================
## VA_components USD_MM Percent
## Gross exports of goods and services (EXGR) 276.71 100.00
## Domestic Content in VA (DC) 159.63 57.69
## Domestic Value Added (DVA) 145.95 52.75
## Value Added Exported (VAX) 127.28 46.00
## Reflection (REF) 18.67 6.75
## Domestic Double Counting (DDC) 13.68 4.94
## Foreign Content in VA (FC) 117.08 42.31
## Foreign Value Added (FVA) 101.53 36.69
## Foreign Double Counting (FDC) 15.55 5.62
## Global Value Chain-related trade (GVC) 221.62 80.09
## GVC-related trade, backward (GVCB) 130.76 47.25
## GVC-related trade, forward (GVCF) 90.86 32.84
## ======================================================================
## Method: Borin and Mancini (2023), source-based, standard output
## Exporting country perspective, source approachNote that the bilateral VAX in this case shows the value
added exported to the United States, regardless of the final absorption
country.
We can also produce an exvadec object will all countries
and then select any exporting country and any partner or sector:
exvadec.all <- make_exvadec(wio, exporter = "all", quiet = TRUE)and then:
get_exvadec_bkdown(exvadec.all, exporter = "USA",
sector = "MANUF", importer = "CHN")## ======================================================================
## DECOMPOSITION OF VALUE ADDED IN EXPORTS OF UNITED STATES IN 2022
## Sector: Manufacturing (MANUF)
## Destination: China (CHN)
## ======================================================================
## VA_components USD_MM Percent
## Gross exports of goods and services (EXGR) 400.89 100.00
## Domestic Content in VA (DC) 164.19 40.96
## Domestic Value Added (DVA) 138.36 34.51
## Value Added Exported (VAX) 114.29 28.51
## Reflection (REF) 24.06 6.00
## Domestic Double Counting (DDC) 25.83 6.44
## Foreign Content in VA (FC) 236.70 59.04
## Foreign Value Added (FVA) 204.59 51.03
## Foreign Double Counting (FDC) 32.12 8.01
## Global Value Chain-related trade (GVC) 379.14 94.57
## GVC-related trade, backward (GVCB) 262.53 65.49
## GVC-related trade, forward (GVCF) 116.61 29.09
## ======================================================================
## Method: Borin and Mancini (2023), source-based, standard output
## Exporting country perspective, source approachApart from the console printout, get_exvadec_bkdown()
will output a matrix with the results.
The command get_data() takes an exvatools
object (wio or exvadec) and produces a value
or a matrix of values. It allows a quick extraction of data. The main
advantage of get_data() is that it does not only admit
individual sectoral codes ("MANUF") or destination country
codes ("USA", "NAFTA"), but also lists of
sectors and countries in vector form. Therefore, we can easily produce a
matrix of domestic value added with breakdown by sector and by
destination groups. The syntax of get_data()is as
follows:
get_data(exvatools_object, variable, exporter = NULL,
sector = "TOTAL", importer = "WLD", custom = FALSE)The arguments are as follows:
exvatools_object (required) is an object of class
wio, exvadec or exvadir, and
variable is a string specifying one of the variables
included in the exvatools_object, such as
"EXGR", "VAX", "FVA", etc.exporter is a string vector with one or more codes of
exporters or groups of exporters, such as "ESP",
"EU27", c("WLD", "EU27", "NONEU27"), etc. This
will define the rows in the resulting matrix. Specific exclusions can be
accepted through the excluding code x (lowercase x), so
"EU27xESP" would be EU countries, excluding Spain,
"WLDxEU27" would be total world except EU, and so on. More
than one exception can be specified with the "|" element,
such as in "WLDxESP|FRA|ITA". Available countries and
country group id codes can be checked with the command
info_geo(). The argument exporter is required
in all cases except two: in case of a country-specific
exvadec object, in which the exporter is previously
defined, and in case of an exvadir object, where, by
definition, there is only one exporter. Note that, in the case of an
exvadir object obtained for country \(s\), the argument exporter
does not refer to country \(s\) itself,
but to the \(t = 1 \dots G\) exporters
of value added that is used by country \(s\) to produce its exports. Therefore, if
the exporter argument is missing, the default behavior of
get_data() will be different, depending on the case: for a
country-specific exvadec, it will default to the exporting
country, whereas for an exvadir object it will default to
"WLD" (i.e., sum of all origins of value added).sector is a string vector with one or more codes of
sectors or groups of sectors, such as "MANUF",
"SERVS", "TOTAL",
c("TOTAL", "GOODSWU", "SRVWC"), etc. These will also show
as rows in the result. Specific exclusions can be accepted through the
excluding code x, so "MANUFxPET" would be
manufactures, excluding oil products, "SRVWCxBIZSV" would
be total services (with construction) except business services, and so
on. Available sector id codes can be checked with the command
info_sec(). Default option is "TOTAL" (sum of
all sectors for the specific exporter). The option "all"
can be used to specify all sectors.importer is a character string or vector with one or
more codes of importing countries or groups of countries, such as
"ESP", "EU27",
c("WLD", "EU27", "NONEU27"), etc. This defines the columns
of the result. Default option is "WLD", i.e, the sum of all
importers for the specific exporter (and sector) selection.custom is a boolean specifying whether custom-made
groups of countries or sectors present in the environment should be
looked up by get_data(). For instance, HITECH
could be a specific variable including all high-tech sectors, or
LDC could be a list of least-developed countries. Custom
variables should be referred to as strings in get_data(),
so, for instance,
get_data(exva, "VAX", exporter = "LDC", custom = TRUE)
would look for a variable called LDC in the environment and
would use its codes to extract and group data.We can use get_data() to summarize the foreign content
of Spanish exports, with a breakdown between EU and Non-EU origin
(specifying a few countries) and also distinguishing between goods (with
utilities) and services. We can also break down the destination of those
exports between EU and non-EU countries:
get_data(exvadir, exporter = c("WLD", "EU27", "FRA",
"NONEU27", "USA"),
sector = c("TOTAL", "GOODSWU", "SRVWC"),
importer = c("WLD", "EU27", "NONEU27"))## WLD EU27 NONEU27
## WLD_TOTAL 2501.78421 367.55781 2134.22640
## WLD_GOODSWU 1772.66226 236.16941 1536.49285
## WLD_SRVWC 729.12195 131.38840 597.73355
## EU27_TOTAL 340.74928 49.39794 291.35134
## EU27_GOODSWU 252.80996 33.55120 219.25877
## EU27_SRVWC 87.93932 15.84674 72.09258
## FRA_TOTAL 340.74928 49.39794 291.35134
## FRA_GOODSWU 252.80996 33.55120 219.25877
## FRA_SRVWC 87.93932 15.84674 72.09258
## NONEU27_TOTAL 2161.03493 318.15987 1842.87505
## NONEU27_GOODSWU 1519.85229 202.61821 1317.23408
## NONEU27_SRVWC 641.18263 115.54166 525.64097
## USA_TOTAL 433.65389 64.94868 368.70521
## USA_GOODSWU 286.90179 38.50383 248.39796
## USA_SRVWC 146.75210 26.44485 120.30725If there is not a specific group in the database of sectors or
countries, the user has two options: to create a group and use
get_data() with the option custom = TRUE, or
simply to use a combination of countries or sectors with a vertical line
"|".
In the latter case, for instance, if we want to combine
ESP and MEX in a single group, we can just
type:
get_data(exvadec.all, "VAX", exporter = "ESP|MEX",
sector = c("TOTAL", "MANUF", "SRVWC"),
importer = "USA")## USA
## ESP|MEX_TOTAL 756.1258
## ESP|MEX_MANUF 251.3334
## ESP|MEX_SRVWC 257.0910If the vertical line "|" is used to join, the exception
marker is "x". It allows us, for instance, to calculate
NAFTA exports, both intra-regional and extra-regional, employing
services and non-services, using as extra-regional
"WLDxNAFTA" and as non-services
"TOTALxSRVWC"
get_data(exvadec.all, "EXGR", exporter = "NAFTA",
sector = c("TOTAL", "TOTALxSRVWC", "SRVWC"),
importer = c("WLD", "NAFTA", "WLDxNAFTA"))## WLD NAFTA WLDxNAFTA
## NAFTA_TOTAL 13087.740 2602.338 10485.402
## NAFTA_TOTALxSRVWC 8736.552 1502.340 7234.212
## NAFTA_SRVWC 4351.188 1099.998 3251.189Let us use get_data()to calculate the relative
comparative advantage (RCA) in terms of gross exports and compare it
with that in terms of VAX. The RCA is the relation between the
proportion of exports of sector \(i\)
in country \(s\) to total exports of
\(s\) (\(E_{si}/E_s\)) and the proportion of world
exports of sector \(i\) to total world
exports (\(E_{wi}/E_w\)). If RCA is
more than 1, it means that country \(s\) has a relative specialization (and a
comparative advantage) in sector \(i%\)
compared to the world average.
We will create a function to calculate the RCA so it can be used with
both gross exports (EXGR) and value added exported
(VAX). As we can see, get_data() considerably
simplifies the calculation of country exports and sector exports.
RCA <- function(exva, exvar) {
Esi <- get_data(exva, exvar, exporter = "all", sector = "all")
Es <- get_data(exva, exvar, exporter = "all", sector = "TOTAL")
Es <- rep(as.numeric(Es), each = exva$dims$N)
Ewi <- get_data(exva, exvar, exporter = "WLD", sector = "all")
Ewi <- rep(as.numeric(Ewi), exva$dims$G)
Ew <- as.numeric(get_data(exva, exvar, exporter = "WLD", sector = "TOTAL"))
rca <- (Esi/Es)/(Ewi/Ew)
colnames(rca) <- paste0("RCA", ".", exvar)
return(rca)
}
head(cbind(RCA(exvadec.all, "EXGR"),
RCA(exvadec.all, "VAX")), 10)## RCA.EXGR RCA.VAX
## ESP_01T09 0.7981206 0.4575154
## ESP_10T39 1.1110328 1.0953243
## ESP_41T98 1.0883393 1.3971980
## FRA_01T09 1.0378051 0.7268141
## FRA_10T39 1.0686493 1.1512224
## FRA_41T98 0.8963249 1.0970064
## MEX_01T09 1.0752922 1.3324652
## MEX_10T39 0.9908369 1.0324864
## MEX_41T98 0.9356388 0.6658469
## USA_01T09 1.0464957 1.2057567We can see that some relative advantage (RCA > 1) in terms of gross exports disappear when calculated in terms of VAX, while some other appear.
Another useful application is the calculation of bilateral balances. We can see that there are considerable difference in bilateral balances when calculated in terms of value added compared to the same balances using gross exports.
EXGR <- get_data(exvadec.all, "EXGR", "all", importer = "all")
IMGR <- bkt(EXGR)
VAX <- get_data(exvadec.all, "VAX", "all", importer = "all")
VAM <- bkt(VAX)
BALGR <- round(EXGR - IMGR, 0)
BALVA <- round(VAX - VAM, 0)
as.data.frame(cbind(BALGR, " "=" ", BALVA),
row.names = exvadec.all$names$g_names)## ESP FRA MEX USA CHN ROW ESP FRA MEX USA CHN ROW
## ESP 0 8 -394 -130 -158 49 0 30 -151 -34 -92 111
## FRA -8 0 53 -290 -544 173 -30 0 -28 -127 -253 96
## MEX 394 -53 0 263 189 459 151 28 0 84 68 279
## USA 130 290 -263 0 -570 -19 34 127 -84 0 -297 74
## CHN 158 544 -189 570 0 464 92 253 -68 297 0 319
## ROW -49 -173 -459 19 -464 0 -111 -96 -279 -74 -319 0 provides several additional commands, some of them resulting from
the mere combination of make_exvadir() and
get_data() with specific default arguments. Of course, it
would be easy to create other custom combinations.
The command get_va_exgr() provides a detailed sector and
geographical origin and destination of value added.
get_va_exgr(wio_object, va_type = "FC",
geo_orig = "all", sec_orig = "TOTAL",
geo_export, sec_export = "TOTAL", as_numeric = TRUE)It allows to analyze, for instance, the percentage of services (both domestic and foreign) embedded in Spanish exports of manufactures, i.e. the so-called ‘servicification’ of Spanish exports:
get_va_exgr(wio, va_type = "TC",
geo_orig = c("ESP", "WLDxESP"), sec_orig = "SRVWC",
geo_export = "ESP", sec_export = "MANUF",
as_numeric = FALSE)## WLD
## ESP_MANUF 84.95594
## WLDxESP_MANUF 263.71717On the other hand, if we wanted the value added in services of the US incorporated in the Spanish exports of manufactures, i.e., the Spanish dependence of US services to produce exports of manufactures:
get_va_exgr(wio, geo_orig = "USA", sec_orig = "SRVWC",
geo_export = "ESP", sec_export = "MANUF")## [1] 51.31605Sometimes we are not only interested in the origin, but also in the
country of final absorption. For that we have the command
get_va_exgry(). This is equivalent to the OECD’s Gross
Exports by Origin of Value Added and Final destination
(FD_EXGR_VA, FD_EXGRFNL_VA and
FD_EXGRINT_VA), but with much more flexible geographical
and sector options. Since the OECD TiVA database no longer provides this
indicator in their online version, this command becomes particularly
useful.
get_va_exgry(wio_object, va_type = "TC", flow_type = "EXGRY",
geo_orig = "WLD", geo_export, sec_export = "TOTAL",
geo_fd = "WLD", as_numeric = TRUE)Here flow_type are exports (expressed in terms of final
demand), whether total ("EXGRY"), final
("EXGRY_FIN") or intermediate ("EXGRY_INT"),
and geo_fd is the country or region of final demand.
This allows, for instance, to calculate what part of US value added incorporated in China’s exports of manufactures ends up absorbed back in the US.
get_va_exgry(wio, geo_orig = "USA", geo_export = "CHN",
sec_export = "MANUF", geo_fd = "USA")## [1] 53.81984also provides a simple command to obtain details of both the geographical and sector origin of the value added incorporated in exports induced by final demand.
get_va_fd(wio_object, va_type = "TOTAL",
geo_orig = "WLD", sec_orig = "TOTAL",
geo_fd = "WLD", sec_fd = "TOTAL", intra = FALSE)This would allow, for instance, the calculation of the Chinese total value added (or GDP) induced by US final demand for manufactures:
get_va_fd(wio, geo_orig = "CHN", sec_orig = "TOTAL",
geo_fd = "USA", sec_fd = "MANUF")## WLD
## CHN_TOTAL 229.385We have presented the package for decomposition of value added in exports using international-input out tables in R. provides a convenient tool for calculating and manipulating international input-output matrices, and simplifies the decomposition of value added in exports (using alternative methodologies). It also allows a straightforward calculation of custom value added indicators.
The purpose of is to provide the scientific community with tools to take advantage of the valuable statistical resources that are the international input-output tables, facilitating the analysis of the complex interaction between trade in goods and services and between economic sectors in different countries.