The R package decompr implements algorithms for the analysis of Global Value Chains. Two methods for gross export flow decomposition using Inter-Country Input-Output tables are provided. The first method is the Wang-Wei-Zhu (2014) algorithm which splits bilateral gross exports into 16 value added components. These components can broadly be divided into domestic and foreign value added. The second method concerns a source decomposition algorithm. This derives the value added origin of a country-industry???s exports by source country and source industry, by applying the basic Leontief insight to gross trade data. This article summarises the methodology of the algorithms and describes the format of the input and output data.
Global Value Chains (GVCs) have become a central factor in trade and development policy. Policy makers from different countries and institutions have placed them at the center of their agenda and continuously emphasize their growing importance for both international trade and economic development. However, analysing this phenomenon empirically requires complex matrix manipulations, since the relevant data is only available in the form of gross flows. This package enables researchers with little background in matrix algebra and linear programming to easily derive standard GVC indicators for statistical analysis.
As mentioned above, decompr uses Inter-Country Input-Output tables, such as those published by the OECD, WIOD, or national statistics bureaus. These tables state input-output relationships in gross terms between industries within and across countries.
For instance, let us look at the example of the leather used in German manufactured car seats. The ICIOs quantify the value of inputs that the Turkish leather and textiles industry supplies to the German transport equipment industry.
The problem of these gross trade flows, is that they do not reveal how much of the value was added in the supplying industry, and how much of the value was added in previous stages of production, performed by other industries or even countries.
The source decomposition of gross trade flows solves this problem, by reallocating the value of intermediate goods used by industries to the original producers. In our example, the use of Argentinian agricultural produce (raw hides) is subtracted from the Turkish leather industry and added to the Argintinian agricultural industry.
The Wang-Wei-Zhu (henceforth WWZ) decomposition goes a step further by not only revealing the source of the value added, but also breaking down exports into different categories, based on its usage and final destination.
- domestic value added in exports
- foreign value added in exports
- pure double counted terms
The decompr package implements the algorithms for these decompositions as R procedures.
The next section introduces the data as it is used by the package, as well as an example data set provided by the WIOD. Section three summarises the theoretical derivation for the decompositions, and shows how these can be performed in R using the package. After which we conclude with a discussion of potential uses and limitations of this approach.
A sample data set of Input-Output tables is included. In order to save space and speed up computations, the included data set uses regional aggregates, instead of countries.
Load the included data set of WIOD regional Input-Output tables.
data(leather)
A key step in loading the data is making sure that the dimensions of the data inputs are correct, in the sample data we have G = 7 (generally countries, here regions) and N = 34 (number of industries).
length(countries ) # G
## [1] 3
length(industries ) # N
## [1] 3
dim( inter ) # (G*N) x G*N
## [1] 9 9
dim( final ) # (G*N + totals) x G*5
## [1] 9 3
length(out ) # G*N
## [1] 9
- Small derivation
The first step is to load the data and create the elements, there are all stored in a list (of class decompr).
elements <- load_tables_vectors( x = inter,
y = final,
k = countries,
i = industries,
o = out )
- Small derivation
- R demonstration using WIOD data
We can now decompose the elements using the Leontief decomposition.
lt <- leontief( elements )
In addition, a wrapper function called decomp is provided which performs both steps at once. Though it is recomended that the atomic functions be used for large data sets.
lt2 <- decomp( x = inter,
y = final,
k = countries,
i = industries,
o = out,
method = "leontief" )
The output data is as follows
dim(lt )
## [1] 9 9
dim(lt2)
## [1] 9 9
We can now decompose the elements using the Wang-Wei-Zhu decomposition.
w <- wwz( elements )
In addition, a wrapper function called decomp is provided which performs both steps at once. Though it is recomended that the seperate functions be used for large data sets.
w2 <- decomp( x = inter,
y = final,
k = countries,
i = industries,
o = out,
method = "wwz" )
Note that wwz is the default method.
The output data is as follows
str(w )
## num [1:36, 1:25] 0 5.47 7.54 13.01 0 ...
## - attr(*, "dimnames")=List of 2
## ..$ : chr [1:36] "Argentina.Agriculture.Argentina" "Argentina.Agriculture.Turkey" "Argentina.Agriculture.Germany" "sub.TOTAL" ...
## ..$ : chr [1:25] "DVA_FIN" "DVA_INT" "DVA_INTrexI1" "DVA_INTrexF" ...
str(w2)
## num [1:36, 1:25] 0 5.47 7.54 13.01 0 ...
## - attr(*, "dimnames")=List of 2
## ..$ : chr [1:36] "Argentina.Agriculture.Argentina" "Argentina.Agriculture.Turkey" "Argentina.Agriculture.Germany" "sub.TOTAL" ...
## ..$ : chr [1:25] "DVA_FIN" "DVA_INT" "DVA_INTrexI1" "DVA_INTrexF" ...
FNS Fei Wang
Wang, Zhi, Shang-Jin Wei, and Kunfu Zhu. 2014. “Quantifying International Production Sharing at the Bilateral and Sector Levels.” National Bureau of Economic Research.