This paper is concerned with upstreamness and downstreamness of industries and countries in global value chains. Upstreamness and downstreamness measure respectively the average distance of an industrial sector from final consumption and from primary inputs, and they are computed from based on the most used global Input-Output tables databases, e.g., the World Input-Output Database (WIOD). Recently, Antr\`as and Chor reported a puzzling and counter-intuitive finding in data from the period 1995-2011, namely that (at country level) upstreamness appears to be positively correlated with downstreamness, with a correlation slope close to $+1$. This effect is stable over time and across countries, and it has been confirmed and validated by later analyses. We analyze a simple model of random Input/Output tables, and we show that, under minimal and realistic structural assumptions, there is a positive correlation between upstreamness and downstreamness of the same industrial sector, with correlation slope equal to $+1$. This effect is robust against changes in the randomness of the entries of the I/O table and different aggregation protocols. Our results suggest that the empirically observed puzzling correlation may rather be a necessary consequence of the few structural constraints (positive entries, and sub-stochasticity) that Input/Output tables and their surrogates must meet.

翻译：本文关注全球价值链中产业和国家层面的上下游度指标。上下游度分别衡量某产业部门与最终消费和初级投入的平均距离，其计算基于最常用的全球投入产出表数据库，例如世界投入产出数据库(WIOD)。近期，Antràs和Chor报告了1995-2011年数据中一个令人费解且反直觉的发现：在国家层面，上下游度似乎与下游度呈正相关，且相关斜率接近+1。该效应在时间维度和不同国家间保持稳定，并已被后续分析验证。我们构建了一个随机投入产出表的简化模型，并证明在最小化且符合实际的结构假设下，同一产业部门的上下游度与下游度存在正相关关系，相关斜率等于+1。该效应对投入产出表条目随机性的变化以及不同聚合规则均具有稳健性。我们的研究结果表明，实证观察到的反常相关性可能恰是投入产出表及其替代形式必须满足的若干结构约束（非负条目与次随机性）所带来的必然结果。