GlobalValueChains.jl

Fast value-added and Global Value Chain (GVC) decompositions following the Borin & Mancini (2019) framework implemented by the Stata icio command (Belotti, Borin & Mancini, Stata Journal 2021).

The package precomputes the expensive shared matrices (notably the global Leontief inverse) once per table and then computes country-, sector-, and bilateral-sector-level decompositions vectorised across all exporters, sectors and destination pairs. Where the Stata workflow re-derives the Leontief inverse on every icio call — tens of thousands of calls for a full bilateral-sector run — GlobalValueChains.jl does the full bilateral-sector decomposition of a 245-country × 18-sector table (≈1.08 million rows) in well under a second after the one-off setup.

Installation

using Pkg
Pkg.develop(path = "/path/to/GlobalValueChains.jl")   # not yet registered

Quick start

using GlobalValueChains

# (a) from the icio CSV format: a headerless [T | FD] matrix + a country-list file
m = read_icio_csv("EM_2015.csv", "EM_countrylist.csv"; sectors = ["AFF","MIN", ...])

# (b) or directly from matrices (e.g. the VA / FD / T objects of an MRIO)
#     VA: length GN vector (or `nothing` to use the icio residual X .- colSums(T))
#     FD: GN×G final demand   T: GN×GN intermediate transactions
m = load_icio(VA, FD, T; regions = iso3, sectors = sector_codes)

# Country / sector / bilateral level — exporter perspective, source approach, 13 terms (default)
decompose(m)                                            # = decompose(m; level = :country)
decompose(m; level = :sector)
decompose(m; level = :bilateral)

# Country level — corrected KWW / Borin-Mancini (world perspective), sink or source approach
decompose(m; perspective = :world, approach = :sink)    # 9 terms
decompose(m; perspective = :world, approach = :source)

# Sink allocation (adds VAXIM at the bilateral level), self perimeter, and imports
decompose(m; level = :bilateral, approach = :sink)      # 10 terms
decompose(m; level = :bilateral, perspective = :self)   # sectoral-bilateral perimeter, 9 terms
decompose(m; flow = :imports)                           # importer-perspective imports

Convenience wrappers decompose_country(m), decompose_sector(m), decompose_bilateral(m), and decompose_imports(m) are also exported.

Multiple years

Pass a Dict (label ⇒ model) to run a decomposition for several tables and stack the results with a :year column — the Julia equivalent of the foreach y in $years loop in a Stata .do:

clist = "EM_countrylist.csv"
years = Dict(y => read_icio_csv("EM_$(y).csv", clist) for y in (2015, 2018, 2021, 2023))
decompose(years; level = :bilateral)

The decompositions

GlobalValueChains.jl covers the full set of icio perspectives and approaches via the flow, level, perspective and approach keywords:

flow	level	perspective / approach	rows	terms
:exports	:country	:exporter / :source (default)	one per exporter	13
:exports	:country	:world / :source | :sink	one per exporter	9
:exports	:sector	:exporter / :source	one per exporter-sector	13
:exports	:sector	:exporter / :sink	one per exporter-sector	9
:exports	:sector	:self	one per exporter-sector	9
:exports	:bilateral	:exporter / :source	one per exporter-sector × importer	13
:exports	:bilateral	:exporter / :sink	one per exporter-sector × importer	10
:exports	:bilateral	:self	one per exporter-sector × importer	9
:imports	:country	:importer	one per importer	3
:imports	:bilateral	:importer	one per (importer, VA origin)	2

:source records value added the first time it leaves the exporter's border (production-linkage view); :sink the last time (final-demand view; adds vaxim at the bilateral level); the two coincide at the country level. :self draws the perimeter at the flow itself (broader Johnson 2018 / Los et al. 2016 value added). :world is country-level only.

Output is a tidy DataFrame of absolute values (same units as the table); compute shares yourself. Identifier columns are country (country level) or from_region, from_sector (and to_region for bilateral); imports use importer (and origin). The export term columns:

• 9 terms: gexp dc dva vax ref ddc fc fva fdc
• 13 terms (exporter/source): the above plus davax gvc gvcb gvcf
• 10 terms (bilateral/sink): the 9 plus vaxim
• 9 terms (self): gexp dc dva vax ref ddc fc fva fdc
• imports: gimp va dc (country) or va dc (by origin)

with the accounting identities gexp = dc + fc, dc = dva + ddc, fc = fva + fdc, dva = vax + ref, gvc = gvcb + gvcf = gexp − davax, gvcb = fc + ddc, and gimp = va + dc.

term	meaning
gexp	gross exports
dc / fc	domestic / foreign content
dva / fva	domestic / foreign value added
ddc / fdc	domestic / foreign double counting
vax	domestic VA absorbed abroad (Johnson-Noguera)
ref	reflection (domestic VA returning home)
davax	domestic VA directly absorbed by the importer (source approach)
vaxim	domestic VA absorbed by the importer, incl. re-processing (sink; davax ⊆ vaxim ⊆ vax)
gvc	GVC-related trade (crosses > 1 border)
gvcb / gvcf	backward / forward GVC participation
gimp	gross imports (= va + dc)
va / dc	value added / double counting in imports (by VA origin at the bilateral level)

Validation

Every decomposition has been diffed directly against Stata icio on the EMERGING 245×18 tables and agrees to ≈1e-6 relative — i.e. to Stata's CSV output precision (~7 significant figures): world/sink and world/source at the country level, exporter/source and exporter/sink at the sector and bilateral levels (including vaxim), the self (sectexp/sectbil) perimeter — all nine terms, including the vax/ref abroad/home split of the broad self DVA★ — and the importer-perspective imports (gimp/va/dc). The decompositions are also exactly additive (bilateral → sector → country) and satisfy the Borin-Mancini cross-engine identities to machine precision (summed over importers the sink DVA/FVA/VAX/REF equal the source country totals; world/source and world/sink FVA share the same world total; davax ⊆ vaxim ⊆ vax; imports va + dc = gross imports). Run Pkg.test("GlobalValueChains") for the identity/anchor checks on a synthetic table; misc/ICIO_decomp_variants.{jl,do} regenerate the Stata references, and misc/compare_variants_stata.jl performs the head-to-head diff (read-only — it writes nothing).

Method & references

Algorithmically, the source/exporter split avoids forming a separate modified Leontief inverse per exporter: with Mₛ = Σ_{j≠s} A_{sj} B_{js} (an N×N matrix) the foreign-VA-once coefficients are VBfor·(I + Mₛ)⁻¹, so the whole job is one GN×GN inversion plus G tiny N×N inversions and block sums. The sink, self-perimeter and importer variants need modified Leontief inverses (B^{∤s}, B^{sr,n}, B̃^r), but each is a low-rank change of the cached B, so they reuse it via Woodbury/block updates rather than re-inverting. The world/source and world/sink foreign VA follow Borin & Mancini (2019) eqs. (52) and (54).

• Borin, A. & Mancini, M. (2019). Measuring What Matters in Global Value Chains and Value-Added Trade. World Bank Policy Research WP 8804 (WDR 2020 background paper).
• Belotti, F., Borin, A. & Mancini, M. (2021). icio: Economic analysis with intercountry input–output tables. The Stata Journal 21(3).
• Koopman, R., Wang, Z. & Wei, S.-J. (2014). Tracing value-added and double counting in gross exports. American Economic Review 104(2).

Design influenced by the R package decompr (Quast, Wang, Stolzenburg & Krantz).