Global Value Chain Decomposition with icio

icio implements four gross-export decompositions from the Global Value Chain (GVC) literature. All decompositions operate on an inter-country input-output (ICIO) table and answer the question: where does the value added embodied in a country’s exports ultimately originate?

Function	Reference	Level	Terms
`leontief()`	Hummels, Ishii & Yi (2001)	country-industry origin	continuous shares
`kww()`	Koopman, Wang & Wei (2014)	country	9
`wwz()`	Wang, Wei & Zhu (2013)	bilateral country-industry	16
`bm()`	Borin & Mancini (2019)	country / sector / bilateral	up to 13

bm() is the recommended decomposition. Its world/sink perspective also provides a corrected version of the biased KWW decomposition.

The leather dataset

The package ships with leather, a minimal 3-country × 3-industry ICIO table covering the leather GVC for Argentina, Turkey, and Germany.

library(icio)
data(leather)

leather$countries
#> [1] "Argentina" "Turkey"    "Germany"
leather$industries
#> [1] "Agriculture"         "Textile_and_Leather" "Transport_Equipment"

# Intermediate demand matrix (9 × 9)
leather$inter
#>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#>  [1,] 16.1  5.1  1.8  3.2  4.3  0.4  3.1  2.8  4.9
#>  [2,]  2.4  8.0  3.2  0.1  3.2  1.6  1.2  3.9 11.5
#>  [3,]  0.9  0.5  4.0  0.0  0.1  0.3  0.0  0.4  0.5
#>  [4,]  1.1  1.9  0.2 18.0 13.2  6.1  9.0  3.1  8.9
#>  [5,]  0.3  2.8  0.1  6.1 28.1  6.3  2.1  2.5 25.6
#>  [6,]  0.0  0.1  0.3  4.1  3.2  8.9  0.2  0.0  1.8
#>  [7,]  1.2  4.2  0.3  4.1  1.2  0.6 29.0 19.5 17.9
#>  [8,]  1.3  1.1  0.0  3.2  4.8  2.6  5.1 29.1 24.1
#>  [9,]  2.1  1.4  3.0  4.1  3.1  3.9 11.3  8.1 51.3

# Final demand matrix (9 × 3)
leather$final
#>       [,1] [,2] [,3]
#>  [1,] 21.5  6.1  8.4
#>  [2,] 16.2  1.9  5.1
#>  [3,] 11.0  0.5  0.8
#>  [4,]  7.5 29.5 14.2
#>  [5,]  8.9 24.9 16.9
#>  [6,]  1.2 18.5  4.9
#>  [7,]  9.2 17.9 51.2
#>  [8,]  7.9 10.1 38.5
#>  [9,] 25.1 35.2 68.4

# Gross output vector (length 9)
leather$out
#> [1]  77.7  58.3  19.0 112.7 124.6  43.2 156.3 127.8 217.0

The rows and columns of inter and the rows of final are ordered by country first, then industry — 9 country-industry combinations in total.

Building an `icio` object

load_icio() parses the raw ICIO matrices and pre-computes what the decompositions need: the input coefficients A, the Leontief inverse B, the G blocks Lb of the domestic Leontief inverse, value-added coefficients Vc, final demand (Y, Yd, Ym) and exports (E, ESR). Only A and B are dense GN x GN matrices; the masked and block-diagonal variants the decompositions use are derived on the fly.

Inverting (I - A) is by far the most expensive step, so build the object once and reuse it across decompositions.

x <- load_icio(leather)
class(x)
#> [1] "icio"
names(x)
#>  [1] "A"   "B"   "Lb"  "E"   "ESR" "Vc"  "G"   "N"   "GN"  "k"   "i"   "X"   "Y"   "Yd" 
#> [15] "Ym"

An iot-class list like leather is detected automatically; equivalently you can pass the matrices directly as load_icio(inter, final, countries, industries). Tables in the CSV format of the Stata icio command are read with load_icio_csv().

The key scalars:

x$G  # number of countries
#> [1] 3
x$N  # number of industries
#> [1] 3

The value-added coefficient vector Vc = v / o gives the direct value-added share of each country-industry’s gross output:

round(x$Vc, 3)
#>         Argentina.Agriculture Argentina.Textile_and_Leather Argentina.Transport_Equipment 
#>                         0.673                         0.569                         0.321 
#>            Turkey.Agriculture    Turkey.Textile_and_Leather    Turkey.Transport_Equipment 
#>                         0.619                         0.509                         0.289 
#>           Germany.Agriculture   Germany.Textile_and_Leather   Germany.Transport_Equipment 
#>                         0.610                         0.457                         0.325

Total exports by country-industry:

round(x$E, 2)
#>         Argentina.Agriculture Argentina.Textile_and_Leather Argentina.Transport_Equipment 
#>                          33.2                          28.5                           2.6 
#>            Turkey.Agriculture    Turkey.Textile_and_Leather    Turkey.Transport_Equipment 
#>                          45.9                          59.2                           8.5 
#>           Germany.Agriculture   Germany.Textile_and_Leather   Germany.Transport_Equipment 
#>                          38.7                          31.0                          77.9

Leontief decomposition

leontief() pre-multiplies the Leontief inverse by the value-added coefficient matrix and post-multiplies by exports. The result gives the value-added origin (rows) of each exporting country-industry (columns).

leo <- leontief(x)
head(leo, 12)
#>     Source_Country     Source_Industry Using_Country      Using_Industry       FVAX
#>             <fctr>              <fctr>        <fctr>              <fctr>      <num>
#>  1:      Argentina         Agriculture     Argentina         Agriculture 28.5227814
#>  2:      Argentina         Agriculture     Argentina Textile_and_Leather  2.7939513
#>  3:      Argentina         Agriculture     Argentina Transport_Equipment  0.3560669
#>  4:      Argentina         Agriculture        Turkey         Agriculture  1.8106696
#>  5:      Argentina         Agriculture        Turkey Textile_and_Leather  3.1173841
#>  6:      Argentina         Agriculture        Turkey Transport_Equipment  0.3590113
#>  7:      Argentina         Agriculture       Germany         Agriculture  1.2364172
#>  8:      Argentina         Agriculture       Germany Textile_and_Leather  1.3028380
#>  9:      Argentina         Agriculture       Germany Transport_Equipment  4.1208736
#> 10:      Argentina Textile_and_Leather     Argentina         Agriculture  1.0620694
#> 11:      Argentina Textile_and_Leather     Argentina Textile_and_Leather 19.1205319
#> 12:      Argentina Textile_and_Leather     Argentina Transport_Equipment  0.4181392

Each row identifies a source country-industry, a using country-industry, and the amount of value added from the source embodied in the using sector’s exports. Setting long = FALSE returns the underlying matrix directly.

Koopman-Wang-Wei (KWW) decomposition

kww() aggregates to the country level and splits exports into 9 components: domestic value added (DVA), foreign value added (FVA), and various double-counting terms.

kww(x)
#>      Country  DVA_FIN  DVA_INT DVA_INTrex   RDV_FIN   RDV_INT       DDC   FVA_FIN
#>       <fctr>    <num>    <num>      <num>     <num>     <num>     <num>     <num>
#> 1: Argentina 19.34940 18.97119   8.411491  5.259501 0.8259724 0.8723949  3.450595
#> 2:    Turkey 43.39461 26.20678   7.740053 10.475795 2.0075781 2.6369363 10.205386
#> 3:   Germany 78.73101 15.23967   2.748464  5.689669 4.4335916 4.4481800 26.668992
#>     FVA_INT      FDC
#>       <num>    <num>
#> 1: 3.388617 3.770832
#> 2: 5.359698 5.573163
#> 3: 4.455024 5.185401

Note: The KWW decomposition contains a known systematic bias — it underestimates foreign value added by conflating some of it with domestic double-counting. Use bm(perspective = "world", approach = "sink") for the Borin-Mancini correction (see below).

Wang-Wei-Zhu (WWZ) decomposition

wwz() operates at the bilateral country-industry level and decomposes exports into 16 value-added and double-counting terms by importing country.

wz <- wwz(x)
dim(wz)
#> [1] 27 29
names(wz)
#>  [1] "Exporting_Country"  "Exporting_Industry" "Importing_Country"  "DVA_FIN"           
#>  [5] "DVA_INT"            "DVA_INTrexI1"       "DVA_INTrexF"        "DVA_INTrexI2"      
#>  [9] "RDV_INT"            "RDV_FIN"            "RDV_FIN2"           "OVA_FIN"           
#> [13] "MVA_FIN"            "OVA_INT"            "MVA_INT"            "DDC_FIN"           
#> [17] "DDC_INT"            "ODC"                "MDC"                "texp"              
#> [21] "texpint"            "texpfd"             "texpdiff"           "texpdiffpercent"   
#> [25] "texpfddiff"         "texpfddiffpercent"  "texpintdiff"        "texpintdiffpercent"
#> [29] "DViX_Fsr"

The result is a long-format data.table with one row per (exporting country-industry, importing country) pair and one column per term, preceded by three identifier columns (Exporting_Country, Exporting_Industry, Importing_Country). Columns beyond the 16 decomposition terms are accounting diagnostics (texp, texpint, texpfd, etc.).

# DVA_FIN for all exporters into Germany
subset(wz, Importing_Country == "Germany",
       select = c(Exporting_Country, Exporting_Industry, DVA_FIN))
#>    Exporting_Country  Exporting_Industry    DVA_FIN
#>               <fctr>              <fctr>      <num>
#> 1:         Argentina         Agriculture  7.5385668
#> 2:         Argentina Textile_and_Leather  3.9470004
#> 3:         Argentina Transport_Equipment  0.5655083
#> 4:            Turkey         Agriculture 11.8896593
#> 5:            Turkey Textile_and_Leather 13.7238725
#> 6:            Turkey Transport_Equipment  3.4331870
#> 7:           Germany         Agriculture  0.0000000
#> 8:           Germany Textile_and_Leather  0.0000000
#> 9:           Germany Transport_Equipment  0.0000000

wwz2kww() maps the 16-term result to the 9-term KWW format when both are needed:

wwz2kww(wz)
#>     Exporting_Country  Exporting_Industry Importing_Country    DVA_FIN    DVA_INT
#>                <fctr>              <fctr>            <fctr>      <num>      <num>
#>  1:         Argentina         Agriculture         Argentina  0.0000000  0.0000000
#>  2:         Argentina         Agriculture            Turkey  5.4744354  3.8177127
#>  3:         Argentina         Agriculture           Germany  7.5385668  5.5186109
#>  4:         Argentina Textile_and_Leather         Argentina  0.0000000  0.0000000
#>  5:         Argentina Textile_and_Leather            Turkey  1.4704511  2.1258430
#>  6:         Argentina Textile_and_Leather           Germany  3.9470004  6.9894309
#>  7:         Argentina Transport_Equipment         Argentina  0.0000000  0.0000000
#>  8:         Argentina Transport_Equipment            Turkey  0.3534427  0.1740197
#>  9:         Argentina Transport_Equipment           Germany  0.5655083  0.3455755
#> 10:            Turkey         Agriculture         Argentina  6.2797497  1.5433344
#> 11:            Turkey         Agriculture            Turkey  0.0000000  0.0000000
#> 12:            Turkey         Agriculture           Germany 11.8896593  9.6316330
#> 13:            Turkey Textile_and_Leather         Argentina  7.2273648  1.5079152
#> 14:            Turkey Textile_and_Leather            Turkey  0.0000000  0.0000000
#> 15:            Turkey Textile_and_Leather           Germany 13.7238725 12.6338776
#> 16:            Turkey Transport_Equipment         Argentina  0.8407805  0.2002353
#> 17:            Turkey Transport_Equipment            Turkey  0.0000000  0.0000000
#> 18:            Turkey Transport_Equipment           Germany  3.4331870  0.6897811
#> 19:           Germany         Agriculture         Argentina  7.8610949  2.3022565
#> 20:           Germany         Agriculture            Turkey 15.2949565  2.1766743
#> 21:           Germany         Agriculture           Germany  0.0000000  0.0000000
#> 22:           Germany Textile_and_Leather         Argentina  6.5544233  0.9105603
#> 23:           Germany Textile_and_Leather            Turkey  8.3797057  3.8771798
#> 24:           Germany Textile_and_Leather           Germany  0.0000000  0.0000000
#> 25:           Germany Transport_Equipment         Argentina 16.9168288  2.5557476
#> 26:           Germany Transport_Equipment            Turkey 23.7239990  3.4172517
#> 27:           Germany Transport_Equipment           Germany  0.0000000  0.0000000
#>     Exporting_Country  Exporting_Industry Importing_Country    DVA_FIN    DVA_INT
#>                <fctr>              <fctr>            <fctr>      <num>      <num>
#>     DVA_INTrex    RDV_FIN     RDV_INT        DDC    FVA_FIN    FVA_INT        FDC
#>          <num>      <num>       <num>      <num>      <num>      <num>      <num>
#>  1: 0.00000000 0.00000000 0.000000000 0.00000000  0.0000000 0.00000000 0.00000000
#>  2: 1.91423181 1.05270347 0.168614730 0.13657989  0.6255646 0.29795523 0.51220221
#>  3: 2.25638080 1.49085043 0.241349852 0.18525099  0.8614332 0.56826533 0.53929167
#>  4: 0.00000000 0.00000000 0.000000000 0.00000000  0.0000000 0.00000000 0.00000000
#>  5: 0.97828407 0.49764336 0.078969730 0.11147587  0.4295489 0.46604144 0.64174252
#>  6: 3.05664120 2.09237473 0.317887034 0.39076543  1.1529996 1.86007577 1.89282497
#>  7: 0.00000000 0.00000000 0.000000000 0.00000000  0.0000000 0.00000000 0.00000000
#>  8: 0.06316755 0.02665282 0.004631660 0.01428238  0.1465573 0.06372476 0.05352109
#>  9: 0.14278535 0.09927627 0.014519380 0.03404037  0.2344917 0.13255405 0.13124912
#> 10: 0.45133063 0.35653406 0.154036261 0.17412451  1.2202503 0.21802578 0.30261437
#> 11: 0.00000000 0.00000000 0.000000000 0.00000000  0.0000000 0.00000000 0.00000000
#> 12: 2.56760596 3.79670949 0.693923875 0.89342675  2.3103407 1.76685578 1.64984520
#> 13: 0.43629173 0.33247312 0.151185856 0.17073721  1.6726352 0.24266827 0.35872865
#> 14: 0.00000000 0.00000000 0.000000000 0.00000000  0.0000000 0.00000000 0.00000000
#> 15: 4.03417638 5.65394247 0.950059562 1.25226053  3.1761275 2.76149698 2.91418651
#> 16: 0.02727863 0.02065283 0.008562439 0.02353095  0.3592195 0.08088699 0.03885285
#> 17: 0.00000000 0.00000000 0.000000000 0.00000000  0.0000000 0.00000000 0.00000000
#> 18: 0.22337011 0.31548308 0.049810123 0.12285637  1.4668130 0.28976398 0.30893521
#> 19: 0.34078859 0.70328136 0.820750168 0.70338439  1.3389051 0.34277710 0.48676190
#> 20: 0.49276219 1.00222535 0.736949683 0.63274282  2.6050435 0.34681668 0.51182895
#> 21: 0.00000000 0.00000000 0.000000000 0.00000000  0.0000000 0.00000000 0.00000000
#> 22: 0.17961089 0.31779378 0.309465907 0.27378632  1.3455767 0.16256206 0.24622074
#> 23: 0.81073626 1.74521177 1.222414373 1.13900048  1.7202943 0.75356998 1.05188736
#> 24: 0.00000000 0.00000000 0.000000000 0.00000000  0.0000000 0.00000000 0.00000000
#> 25: 0.29897730 0.51188531 0.436904740 0.57733715  8.1831712 1.20835270 0.91079521
#> 26: 0.62558843 1.40927173 0.907106729 1.12192882 11.4760010 1.64094572 1.97790686
#> 27: 0.00000000 0.00000000 0.000000000 0.00000000  0.0000000 0.00000000 0.00000000
#>     DVA_INTrex    RDV_FIN     RDV_INT        DDC    FVA_FIN    FVA_INT        FDC
#>          <num>      <num>       <num>      <num>      <num>      <num>      <num>

Borin-Mancini (BM) decomposition

bm() is the most flexible decomposition. It supports three aggregation levels ("country", "sector", "bilateral") and two accounting perspectives ("exporter" with 13 terms, or "world" with 9 terms).

Country level (exporter perspective, 13 terms)

bm(x)
#>    Exporting_Country  GEXP        DC       DVA      VAX    DAVAX       REF       DDC
#>               <fctr> <num>     <num>     <num>    <num>    <num>     <num>     <num>
#> 1:         Argentina  64.3  53.68996  52.81756 46.73209 34.79877  6.085473 0.8723949
#> 2:            Turkey 113.6  92.46175  89.82482 77.34144 65.50360 12.483373 2.6369363
#> 3:           Germany 147.6 111.29058 106.84240 96.71914 89.31689 10.123261 4.4481800
#>          FC      FVA       FDC      GVC     GVCB     GVCF
#>       <num>    <num>     <num>    <num>    <num>    <num>
#> 1: 10.61004 10.43484 0.1752063 29.50123 11.48244 18.01879
#> 2: 21.13825 20.55564 0.5826050 48.09640 23.77518 24.32122
#> 3: 36.30942 35.06489 1.2445289 58.28311 40.75760 17.52551

The 13 terms break gross exports (GEXP) into domestic content (DC) and foreign content (FC), and further into value-added and double-counting components. GVC participation is measured by GVC = GEXP - DAVAX, split into backward (GVCB) and forward (GVCF) linkages.

Sector level

bm(x, aggregation = "sector")
#>    Exporting_Country  Exporting_Industry  GEXP        DC       DVA       VAX     DAVAX
#>               <fctr>              <fctr> <num>     <num>     <num>     <num>     <num>
#> 1:         Argentina         Agriculture  33.2 29.795288 29.493900 26.540382 20.385155
#> 2:         Argentina Textile_and_Leather  28.5 22.056767 21.569374 18.582499 13.084653
#> 3:         Argentina Transport_Equipment   2.6  1.837902  1.754288  1.609208  1.328962
#> 4:            Turkey         Agriculture  45.9 38.432068 37.469257 32.468054 27.673077
#> 5:            Turkey Textile_and_Leather  59.2 48.074157 46.789941 39.702280 33.025635
#> 6:            Turkey Transport_Equipment   8.5  5.955528  5.565619  5.171110  4.804889
#> 7:           Germany         Agriculture  38.7 33.067867 32.402844 29.139637 26.657741
#> 8:           Germany Textile_and_Leather  31.0 25.719889 25.082406 21.487520 18.915931
#> 9:           Germany Transport_Equipment  77.9 52.502827 49.357153 46.091985 43.743217
#>          REF        DDC        FC        FVA        FDC       GVC       GVCB      GVCF
#>        <num>      <num>     <num>      <num>      <num>     <num>      <num>     <num>
#> 1: 2.9535185 0.30138767  3.404712  3.3423229 0.06238937 12.814845  3.7060999  9.108745
#> 2: 2.9868748 0.48739312  6.443233  6.3486717 0.09456147 15.415347  6.9306263  8.484721
#> 3: 0.1450801 0.08361414  0.762098  0.7438425 0.01825550  1.271038  0.8457122  0.425326
#> 4: 5.0012037 0.96281049  7.467932  7.2556717 0.21226046 18.226923  8.4307426  9.796180
#> 5: 7.0876610 1.28421633 11.125843 10.8426216 0.28322154 26.174365 12.4100595 13.764306
#> 6: 0.3945085 0.38990949  2.544472  2.4573486 0.08712297  3.695111  2.9343811  0.760730
#> 7: 3.2632066 0.66502295  5.632133  5.4445468 0.18758643 12.042259  6.2971562  5.745103
#> 8: 3.5948858 0.63748284  5.280111  5.1021480 0.17796309 12.084069  5.9175939  6.166475
#> 9: 3.2651685 3.14567421 25.397173 24.5181932 0.87897942 34.156783 28.5428469  5.613936

Bilateral sector level

bm(x, aggregation = "bilateral")
#>     Exporting_Country  Exporting_Industry Importing_Country  GEXP         DC        DVA
#>                <fctr>              <fctr>            <fctr> <num>      <num>      <num>
#>  1:            Turkey         Agriculture         Argentina  10.7  8.9591095  8.7346635
#>  2:            Turkey Textile_and_Leather         Argentina  12.1  9.8259679  9.5634845
#>  3:            Turkey Transport_Equipment         Argentina   1.6  1.1210406  1.0476459
#>  4:           Germany         Agriculture         Argentina  14.9 12.7315559 12.4755135
#>  5:           Germany Textile_and_Leather         Argentina  10.3  8.5456405  8.3338317
#>  6:           Germany Transport_Equipment         Argentina  31.6 21.2976809 20.0216436
#>  7:         Argentina         Agriculture            Turkey  14.0 12.5642780 12.4371868
#>  8:         Argentina Textile_and_Leather            Turkey   6.8  5.2626672  5.1463769
#>  9:         Argentina Transport_Equipment            Turkey   0.9  0.6361968  0.6072535
#> 10:           Germany         Agriculture            Turkey  23.8 20.3363108 19.9273303
#> 11:           Germany Textile_and_Leather            Turkey  20.7 17.1742484 16.7485744
#> 12:           Germany Transport_Equipment            Turkey  46.3 31.2051464 29.3355095
#> 13:         Argentina         Agriculture           Germany  19.2 17.2310098 17.0567133
#> 14:         Argentina Textile_and_Leather           Germany  21.7 16.7940996 16.4229968
#> 15:         Argentina Transport_Equipment           Germany   1.7  1.2017051  1.1470343
#> 16:            Turkey         Agriculture           Germany  35.2 29.4729584 28.7345939
#> 17:            Turkey Textile_and_Leather           Germany  47.1 38.2481890 37.2264561
#> 18:            Turkey Transport_Equipment           Germany   6.9  4.8344878  4.5179730
#>           VAX      DAVAX        REF        DDC         FC        FVA         FDC
#>         <num>      <num>      <num>      <num>      <num>      <num>       <num>
#>  1:  8.224093  7.2163401 0.51057032 0.22444602  1.7408905  1.6914093 0.049481197
#>  2:  9.079825  8.0548444 0.48365898 0.26248341  2.2740321  2.2161439 0.057888186
#>  3:  1.018431  0.9626616 0.02921527 0.07339473  0.4789594  0.4625597 0.016399618
#>  4: 10.951482  9.6750702 1.52403152 0.25604243  2.1684441  2.0962209 0.072223200
#>  5:  7.706572  7.1641956 0.62725969 0.21180881  1.7543595  1.6952298 0.059129673
#>  6: 19.072854 18.2515939 0.94879005 1.27603729 10.3023191  9.9457626 0.356556480
#>  7: 11.215869  8.0001479 1.22131820 0.12709119  1.4357220  1.4094133 0.026308772
#>  8:  4.569764  2.9980790 0.57661309 0.11629029  1.5373328  1.5147708 0.022562035
#>  9:  0.575969  0.4840523 0.03128448 0.02894336  0.2638032  0.2574840 0.006319211
#> 10: 18.188155 16.9826710 1.73917503 0.40898052  3.4636892  3.3483259 0.115363232
#> 11: 13.780948 11.7517352 2.96762614 0.42567402  3.5257516  3.4069182 0.118833420
#> 12: 27.019131 25.4916229 2.31637845 1.86963692 15.0948536 14.5724306 0.522422944
#> 13: 15.324513 12.3850073 1.73220028 0.17429648  1.9689902  1.9329096 0.036080601
#> 14: 14.012735 10.0865741 2.41026176 0.37110283  4.9059004  4.8339009 0.071999434
#> 15:  1.033239  0.8449095 0.11379565 0.05467078  0.4982949  0.4863586 0.011936287
#> 16: 24.243961 20.4567369 4.49063336 0.73836447  5.7270416  5.5642624 0.162779264
#> 17: 30.622454 24.9707904 6.60400204 1.02173293  8.8518110  8.6264777 0.225333351
#> 18:  4.152680  3.8422274 0.36529320 0.31651476  2.0655122  1.9947889 0.070723354
#>            GVC       GVCB       GVCF
#>          <num>      <num>      <num>
#>  1:  3.4836599  1.9653365  1.5183234
#>  2:  4.0451556  2.5365155  1.5086400
#>  3:  0.6373384  0.5523541  0.0849843
#>  4:  5.2249298  2.4244865  2.8004433
#>  5:  3.1358044  1.9661683  1.1696361
#>  6: 13.3484061 11.5783564  1.7700497
#>  7:  5.9998521  1.5628132  4.4370389
#>  8:  3.8019210  1.6536231  2.1482979
#>  9:  0.4159477  0.2927465  0.1232012
#> 10:  6.8173290  3.8726697  2.9446593
#> 11:  8.9482648  3.9514256  4.9968392
#> 12: 20.8083771 16.9644905  3.8438866
#> 13:  6.8149927  2.1432867  4.6717060
#> 14: 11.6134259  5.2770032  6.3364227
#> 15:  0.8550905  0.5529657  0.3021248
#> 16: 14.7432631  6.4654061  8.2778570
#> 17: 22.1292096  9.8735439 12.2556656
#> 18:  3.0577726  2.3820270  0.6757457

The bilateral result contains one row per (exporting country-industry, importing country) pair, excluding within-country flows. Country- and sector-level results are additive aggregations of this table.

Corrected KWW (world perspective, 9 terms)

The world/sink perspective implements the Borin-Mancini correction to the biased KWW decomposition. It is only available at the country level.

bm(x, perspective = "world", approach = "sink")
#>    Exporting_Country  GEXP        DC       DVA      VAX       REF       DDC       FC
#>               <fctr> <num>     <num>     <num>    <num>     <num>     <num>    <num>
#> 1:         Argentina  64.3  53.68996  52.81756 46.73209  6.085473 0.8723949 10.61004
#> 2:            Turkey 113.6  92.46175  89.82482 77.34144 12.483373 2.6369363 21.13825
#> 3:           Germany 147.6 111.29058 106.84240 96.71914 10.123261 4.4481800 36.30942
#>          FVA      FDC
#>        <num>    <num>
#> 1:  8.471827 2.138217
#> 2: 18.265189 2.873058
#> 3: 33.128506 3.180911

Comparing to kww() above, FVA increases and DDC decreases accordingly.

WWZ vs. BM (exporter/source): different perimeters

WWZ and BM (exporter/source) both decompose bilateral exports into value-added and double-counting components, but they disagree on what “double-counted” means — and that choice shapes which questions each method can answer.

WWZ uses a bilateral perimeter: an item is double-counted only if it crosses the same s→r border more than once. Compared to BM, this is looser, so some items that BM classifies as double-counted appear as value-added in WWZ. This makes WWZ well-suited to questions about the GDP content of a specific trade flow — tariff incidence, bilateral trade balances — but the tradeoff is that WWZ results do not add up: summing bilateral terms over all importers does not recover a sensible country-level total. WWZ also conflates source-based and sink-based approaches within the same decomposition, so its terms are not on the same accounting footing and GVC indicators such as DAVAX cannot be computed from the output.

BM (exporter/source) uses the exporting country as the perimeter: an item is double-counted the second time it crosses country s’s border, wherever it goes. One approach throughout, so all 13 terms are comparable. Bilateral results sum to sector totals, sector totals to country totals — and DAVAX, GVC-related trade, and backward/forward participation shares all come out of the same calculation. For most country- or sector-level work, BM (exporter/source) is the natural choice; reach for WWZ when the question is specifically about what crosses a particular bilateral border.

Convenience interface

decomp() is a single entry point for all methods, dispatching on method (default "bm") and passing ... on to the decomposition function:

decomp(x, method = "leontief")
#>     Source_Country     Source_Industry Using_Country      Using_Industry        FVAX
#>             <fctr>              <fctr>        <fctr>              <fctr>       <num>
#>  1:      Argentina         Agriculture     Argentina         Agriculture 28.52278143
#>  2:      Argentina         Agriculture     Argentina Textile_and_Leather  2.79395126
#>  3:      Argentina         Agriculture     Argentina Transport_Equipment  0.35606694
#>  4:      Argentina         Agriculture        Turkey         Agriculture  1.81066955
#>  5:      Argentina         Agriculture        Turkey Textile_and_Leather  3.11738415
#>  6:      Argentina         Agriculture        Turkey Transport_Equipment  0.35901126
#>  7:      Argentina         Agriculture       Germany         Agriculture  1.23641723
#>  8:      Argentina         Agriculture       Germany Textile_and_Leather  1.30283802
#>  9:      Argentina         Agriculture       Germany Transport_Equipment  4.12087363
#> 10:      Argentina Textile_and_Leather     Argentina         Agriculture  1.06206936
#> 11:      Argentina Textile_and_Leather     Argentina Textile_and_Leather 19.12053186
#> 12:      Argentina Textile_and_Leather     Argentina Transport_Equipment  0.41813924
#> 13:      Argentina Textile_and_Leather        Turkey         Agriculture  0.48370042
#> 14:      Argentina Textile_and_Leather        Turkey Textile_and_Leather  1.83290239
#> 15:      Argentina Textile_and_Leather        Turkey Transport_Equipment  0.43058635
#> 16:      Argentina Textile_and_Leather       Germany         Agriculture  0.59370415
#> 17:      Argentina Textile_and_Leather       Germany Textile_and_Leather  1.15375958
#> 18:      Argentina Textile_and_Leather       Germany Transport_Equipment  4.74903511
#> 19:      Argentina Transport_Equipment     Argentina         Agriculture  0.21043693
#> 20:      Argentina Transport_Equipment     Argentina Textile_and_Leather  0.14228369
#> 21:      Argentina Transport_Equipment     Argentina Transport_Equipment  1.06369578
#> 22:      Argentina Transport_Equipment        Turkey         Agriculture  0.03329456
#> 23:      Argentina Transport_Equipment        Turkey Textile_and_Leather  0.07905450
#> 24:      Argentina Transport_Equipment        Turkey Transport_Equipment  0.04024626
#> 25:      Argentina Transport_Equipment       Germany         Agriculture  0.02318460
#> 26:      Argentina Transport_Equipment       Germany Textile_and_Leather  0.07482343
#> 27:      Argentina Transport_Equipment       Germany Transport_Equipment  0.19326212
#> 28:         Turkey         Agriculture     Argentina         Agriculture  0.71952151
#> 29:         Turkey         Agriculture     Argentina Textile_and_Leather  1.34237213
#> 30:         Turkey         Agriculture     Argentina Transport_Equipment  0.11504126
#> 31:         Turkey         Agriculture        Turkey         Agriculture 34.92704803
#> 32:         Turkey         Agriculture        Turkey Textile_and_Leather  6.99949698
#> 33:         Turkey         Agriculture        Turkey Transport_Equipment  1.47711579
#> 34:         Turkey         Agriculture       Germany         Agriculture  2.55430885
#> 35:         Turkey         Agriculture       Germany Textile_and_Leather  1.52213499
#> 36:         Turkey         Agriculture       Germany Transport_Equipment  6.18062537
#> 37:         Turkey Textile_and_Leather     Argentina         Agriculture  0.41201175
#> 38:         Turkey Textile_and_Leather     Argentina Textile_and_Leather  1.38523849
#> 39:         Turkey Textile_and_Leather     Argentina Transport_Equipment  0.11764036
#> 40:         Turkey Textile_and_Leather        Turkey         Agriculture  2.69291816
#> 41:         Turkey Textile_and_Leather        Turkey Textile_and_Leather 40.16714096
#> 42:         Turkey Textile_and_Leather        Turkey Transport_Equipment  1.31799873
#> 43:         Turkey Textile_and_Leather       Germany         Agriculture  1.10939926
#> 44:         Turkey Textile_and_Leather       Germany Textile_and_Leather  1.15207241
#> 45:         Turkey Textile_and_Leather       Germany Transport_Equipment  9.50690317
#> 46:         Turkey Transport_Equipment     Argentina         Agriculture  0.03482652
#> 47:         Turkey Transport_Equipment     Argentina Textile_and_Leather  0.08553139
#> 48:         Turkey Transport_Equipment     Argentina Transport_Equipment  0.02667530
#> 49:         Turkey Transport_Equipment        Turkey         Agriculture  0.81210167
#> 50:         Turkey Transport_Equipment        Turkey Textile_and_Leather  0.90751892
#> 51:         Turkey Transport_Equipment        Turkey Transport_Equipment  3.16041392
#> 52:         Turkey Transport_Equipment       Germany         Agriculture  0.11511911
#> 53:         Turkey Transport_Equipment       Germany Textile_and_Leather  0.07448266
#> 54:         Turkey Transport_Equipment       Germany Transport_Equipment  0.64647326
#> 55:        Germany         Agriculture     Argentina         Agriculture  0.92530356
#> 56:        Germany         Agriculture     Argentina Textile_and_Leather  2.25142713
#> 57:        Germany         Agriculture     Argentina Transport_Equipment  0.16222512
#> 58:        Germany         Agriculture        Turkey         Agriculture  2.31122022
#> 59:        Germany         Agriculture        Turkey Textile_and_Leather  2.05958253
#> 60:        Germany         Agriculture        Turkey Transport_Equipment  0.51211484
#> 61:        Germany         Agriculture       Germany         Agriculture 29.87633590
#> 62:        Germany         Agriculture       Germany Textile_and_Leather  5.24719728
#> 63:        Germany         Agriculture       Germany Transport_Equipment  9.60069308
#> 64:        Germany Textile_and_Leather     Argentina         Agriculture  0.64666560
#> 65:        Germany Textile_and_Leather     Argentina Textile_and_Leather  0.72785683
#> 66:        Germany Textile_and_Leather     Argentina Transport_Equipment  0.08244379
#> 67:        Germany Textile_and_Leather        Turkey         Agriculture  1.53837777
#> 68:        Germany Textile_and_Leather        Turkey Textile_and_Leather  2.54889673
#> 69:        Germany Textile_and_Leather        Turkey Transport_Equipment  0.63316614
#> 70:        Germany Textile_and_Leather       Germany         Agriculture  1.45935830
#> 71:        Germany Textile_and_Leather       Germany Textile_and_Leather 18.95868110
#> 72:        Germany Textile_and_Leather       Germany Transport_Equipment  8.15831503
#> 73:        Germany Transport_Equipment     Argentina         Agriculture  0.66638333
#> 74:        Germany Transport_Equipment     Argentina Textile_and_Leather  0.65080723
#> 75:        Germany Transport_Equipment     Argentina Transport_Equipment  0.25807221
#> 76:        Germany Transport_Equipment        Turkey         Agriculture  1.29066963
#> 77:        Germany Transport_Equipment        Turkey Textile_and_Leather  1.48802285
#> 78:        Germany Transport_Equipment        Turkey Transport_Equipment  0.56934671
#> 79:        Germany Transport_Equipment       Germany         Agriculture  1.73217260
#> 80:        Germany Transport_Equipment       Germany Textile_and_Leather  1.51401054
#> 81:        Germany Transport_Equipment       Germany Transport_Equipment 34.74381924
#>     Source_Country     Source_Industry Using_Country      Using_Industry        FVAX
#>             <fctr>              <fctr>        <fctr>              <fctr>       <num>
decomp(x, aggregation = "sector")
#>    Exporting_Country  Exporting_Industry  GEXP        DC       DVA       VAX     DAVAX
#>               <fctr>              <fctr> <num>     <num>     <num>     <num>     <num>
#> 1:         Argentina         Agriculture  33.2 29.795288 29.493900 26.540382 20.385155
#> 2:         Argentina Textile_and_Leather  28.5 22.056767 21.569374 18.582499 13.084653
#> 3:         Argentina Transport_Equipment   2.6  1.837902  1.754288  1.609208  1.328962
#> 4:            Turkey         Agriculture  45.9 38.432068 37.469257 32.468054 27.673077
#> 5:            Turkey Textile_and_Leather  59.2 48.074157 46.789941 39.702280 33.025635
#> 6:            Turkey Transport_Equipment   8.5  5.955528  5.565619  5.171110  4.804889
#> 7:           Germany         Agriculture  38.7 33.067867 32.402844 29.139637 26.657741
#> 8:           Germany Textile_and_Leather  31.0 25.719889 25.082406 21.487520 18.915931
#> 9:           Germany Transport_Equipment  77.9 52.502827 49.357153 46.091985 43.743217
#>          REF        DDC        FC        FVA        FDC       GVC       GVCB      GVCF
#>        <num>      <num>     <num>      <num>      <num>     <num>      <num>     <num>
#> 1: 2.9535185 0.30138767  3.404712  3.3423229 0.06238937 12.814845  3.7060999  9.108745
#> 2: 2.9868748 0.48739312  6.443233  6.3486717 0.09456147 15.415347  6.9306263  8.484721
#> 3: 0.1450801 0.08361414  0.762098  0.7438425 0.01825550  1.271038  0.8457122  0.425326
#> 4: 5.0012037 0.96281049  7.467932  7.2556717 0.21226046 18.226923  8.4307426  9.796180
#> 5: 7.0876610 1.28421633 11.125843 10.8426216 0.28322154 26.174365 12.4100595 13.764306
#> 6: 0.3945085 0.38990949  2.544472  2.4573486 0.08712297  3.695111  2.9343811  0.760730
#> 7: 3.2632066 0.66502295  5.632133  5.4445468 0.18758643 12.042259  6.2971562  5.745103
#> 8: 3.5948858 0.63748284  5.280111  5.1021480 0.17796309 12.084069  5.9175939  6.166475
#> 9: 3.2651685 3.14567421 25.397173 24.5181932 0.87897942 34.156783 28.5428469  5.613936

Given a list of icio objects — typically one ICIO table per year — it runs the decomposition on each and stacks the results, prepending an identifier column:

decomp(list(`2015` = x, `2016` = x), idcol = "Year")
#>      Year Exporting_Country  GEXP        DC       DVA      VAX    DAVAX       REF
#>    <char>            <fctr> <num>     <num>     <num>    <num>    <num>     <num>
#> 1:   2015         Argentina  64.3  53.68996  52.81756 46.73209 34.79877  6.085473
#> 2:   2015            Turkey 113.6  92.46175  89.82482 77.34144 65.50360 12.483373
#> 3:   2015           Germany 147.6 111.29058 106.84240 96.71914 89.31689 10.123261
#> 4:   2016         Argentina  64.3  53.68996  52.81756 46.73209 34.79877  6.085473
#> 5:   2016            Turkey 113.6  92.46175  89.82482 77.34144 65.50360 12.483373
#> 6:   2016           Germany 147.6 111.29058 106.84240 96.71914 89.31689 10.123261
#>          DDC       FC      FVA       FDC      GVC     GVCB     GVCF
#>        <num>    <num>    <num>     <num>    <num>    <num>    <num>
#> 1: 0.8723949 10.61004 10.43484 0.1752063 29.50123 11.48244 18.01879
#> 2: 2.6369363 21.13825 20.55564 0.5826050 48.09640 23.77518 24.32122
#> 3: 4.4481800 36.30942 35.06489 1.2445289 58.28311 40.75760 17.52551
#> 4: 0.8723949 10.61004 10.43484 0.1752063 29.50123 11.48244 18.01879
#> 5: 2.6369363 21.13825 20.55564 0.5826050 48.09640 23.77518 24.32122
#> 6: 4.4481800 36.30942 35.06489 1.2445289 58.28311 40.75760 17.52551

Output format

All decompositions return a data.table, so column selection follows data.table rules: d$GEXP and d[["GEXP"]] work as usual, but d[, "GEXP"] returns a one-column table rather than a vector, and d[c("GEXP", "DVA")] is a join, not a column subset — use d[, .(GEXP, DVA)] or as.data.frame(d) if you want base-R semantics.

References

Borin, A., & Mancini, M. (2019). Measuring what matters in global value chains and value-added trade. World Bank Policy Research Working Paper 8804.

Koopman, R., Wang, Z., & Wei, S.-J. (2014). Tracing value-added and double counting in gross exports. American Economic Review, 104(2), 459–494.

Wang, Z., Wei, S.-J., & Zhu, K. (2013). Quantifying international production sharing at the bilateral and sector levels. NBER Working Paper 19677.

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.

Sebastian Krantz

2026-07-27

The leather dataset

Building an `icio` object

Leontief decomposition

Koopman-Wang-Wei (KWW) decomposition

Wang-Wei-Zhu (WWZ) decomposition

Borin-Mancini (BM) decomposition

Country level (exporter perspective, 13 terms)

Sector level

Bilateral sector level

Corrected KWW (world perspective, 9 terms)

WWZ vs. BM (exporter/source): different perimeters

Convenience interface

Output format

References

Global Value Chain Decomposition with icio

Sebastian Krantz

2026-07-27

The leather dataset

Building an icio object

Leontief decomposition

Koopman-Wang-Wei (KWW) decomposition

Wang-Wei-Zhu (WWZ) decomposition

Borin-Mancini (BM) decomposition

Country level (exporter perspective, 13 terms)

Sector level

Bilateral sector level

Corrected KWW (world perspective, 9 terms)

WWZ vs. BM (exporter/source): different perimeters

Convenience interface

Output format

References

Building an `icio` object