4 measurement.

A number of studies have laid the groundwork in understanding and quantifying production sharing and trade in value added following such “macro-approach”. Key contributions include Hummels et al. (2001), Johnson and Noguera (2012), Koopman et al. (2014), and Borin and Mancini (2015). These have been instrumental in conceptualizing this field and in developing sound measurement methodologies, that are now accepted as standard in the literature. In particular, Hummels et al. (2001) introduced a fundamental idea, suggesting that a minimal condition for trade to be considered GVC-related, is that it must cross at least two country borders.<sup>1</sup> Early measures have tended to concentrate on specific aspects of the trade-GVC relationship, providing foundational estimates of participation, which have been refined in later research for greater comprehensiveness, accuracy and statistical rigor. The ’vertical specialization’ index by Hummels et al. (2001), which gauges the import content of a country’s exports, was widely popular. However, as noted by the authors, it measures participation only partially, accounting for backward but not forward linkages. Koopman et al. (2014) introduced an accounting method to decompose a country’s gross exports by the source and final destination of their embedded value added. This approach, which is highly used in the literature, quantifies the extent of a country’s production included in other nations’ exports. It however does not trace whether exports undergo further processing in the importing or downstream countries, nor it aligns fully with theory (see Section S2 in the supplementary online appendix for further details). Another notable contribution is Johnson and Noguera (2012), which defined the value-added exports to gross exports ratio (VAX). The complement of this measure (1 _− V AX_ ) has been interpreted in some cases as a measure of the share of trade involved in GVCs. While changes in this indicator align closely with variations in international production fragmentation, especially globally (Johnson and Noguera, 2017), the indicator in levels tends to underestimate the significance of GVCs in trade, a point elaborated in Antr`as and Chor (2022).<sup>2</sup> Building on the definition by Hummels et al. (2001), Borin and Mancini (2015) showed how to calculate GVC-related trade using global input-output tables in a way that aligns with the original concept established by Hummels and co-authors in 2001. The accounting framework proposed by Borin and Mancini was the first to provide a quantitative assessment of trade crossing at least two borders. The method ensured that the measure of GVC-trade corresponds to the sum of two established metrics of cross-border GVC linkages: forward GVC participation (producing and exporting inputs for further re-export by the trading partner) and backward GVC participation (utilizing imported inputs for goods exported abroad). More recently, Borin and Mancini (2023) proposed a comprehensive methodology for value-added accounting of trade flows at the aggregate, bilateral, and sectoral levels, aligning different accounting perspectives to the economic questions they address best.

All the above-mentioned concepts and measures are now commonly accepted in academic

> 1In theory, value-added generated in the final stages of an internationally fragmented production process should be regarded as related to Global Value Chains (GVC), even if it only crosses one border. However, in practical terms, this segment cannot be distinguished from conventional trade using standard inter-country input-output (ICIO) tables. Due to this empirical constraint, the study Hummels et al. (2001) and all other macro-level measures (that is, at the country-sector level) of GVC-related trade in the wider literature concentrate on the “minimal” criterion for GVC trade, namely, crossing at least two borders.

> 2This comes from the fact that only a sub-portion of **VAX** is not GVC-related - see Section S2 in the supplementary online appendix for further details.