In recent years, the decline in labour’s share of national income in advanced economies has drawn attention from many economists and policymakers, leading to intense debates and research into its causes and implications. A 2022 Vox column by Oberfield and Grossman provided an excellent overview of the literature.
One leading explanation of the declining labour share is that capital and labour are substitutes (elasticity of substitution greater than one), and the falling price of capital goods drove down the labour share (Karabarbounis and Neiman 2013). This explanation is consistent with the observed co-movement of the aggregate labour share and capital goods prices over time. However, it conflicts with many micro-level studies finding that capital (equipment, to be specific) and labour are complements (elasticity of substitution less than one) (e.g. Raval, 2019, Oberfield and Raval 2021, among many others).
In our recent study (Aum and Shin 2024), we address this ‘elasticity discord’ by separating capital into equipment and software, hypothesising that these two types of capital interact with labour in fundamentally different ways. Software is part of intangible capital, which is typically not measured well in micro data. We use the micro data from Korea, where firms report their software investment separately from other types of intangibles more prone to measurement problems. We start with two empirical patterns in the Korean data that support the case for investigating software separately from equipment:
- Firm-level panel regressions show that firms’ software intensity predicts a decrease in their labour share. In contrast, firms’ equipment intensity makes no meaningful prediction in either direction.
- In a cross-section of regions, software expenditure shares and local wages are positively related, but equipment expenditure shares and local wages are unrelated.
We go beyond these correlations and estimate the elasticity of substitution across software, equipment, and labour both at the micro and the macro levels, utilising two different data sets (a cross-section of manufacturing plants and a firm panel) and two different instrumental variable strategies (service-sector employment shares and minimum wages).
Our key finding is that, while equipment and labour are indeed complements (micro-level elasticity of 0.6), consistent with the micro-level estimates in the literature, software and labour are substitutes (micro-level elasticity of 1.6), a novel finding. Remarkably, the two different data sets and the two different instrumental variable strategies yield very similar results. The result that software and labour are substitutes is crucial for understanding the dynamics of labour share:
- As the quality of software improves and its price falls, labour shares within firms decrease due to factor substitution and rising markups within firms.
- Production shifts towards software-intensive firms, which in our data tend to have higher markups and lower labour shares. These firms become disproportionately more productive when software becomes better (or cheaper) and capture larger market shares, further decreasing the aggregate labour share.
The figures below show the impact of the falling prices of software (left panel) and equipment (right panel) on the aggregate labour share. The left panel shows that the fall in software prices reduces the aggregate labour share through factor substitution within firms and markup increases. In contrast, the impact of the fall in equipment prices on the aggregate labour share is negligible, because countervailing forces cancel one another. The complementarity (elasticity less than one) between equipment and labour pushes up the labour share within firms, but this effect is offset by reallocation towards firms with high markups and low labour shares. Overall, the rise of software accounts for two-thirds of the 4.4 percentage point decline in the labour share in Korea between 1990 and 2018. The factor substitution and the markup channels contribute almost equally to this decline. This implies that focusing solely on the rising software income share in accounting terms, as in Koh et al. (2020), would significantly underestimate the role of software in the decline of labour share, by failing to capture the role of software in the rise of markups.
Figure 1 Effects of capital-embodied technological change on the labour share
Our findings have important implications for the ongoing debates about technological change, market power, and income distribution. The rise of software is a key driver of the well-documented reallocation toward large (‘super star’) firms with high markups and low labour shares. This pattern has been documented by several studies, including Autor et al. (2020) and Kehrig and Vincent (2021) for the US. The substitutability between software and labour can also explain the pattern of labour share changes across industries and occupations. In the US, the steeper decline in the labour share since 2000 is more pronounced in industries and occupations that are software-intensive (Aum and Shin 2020). In addition, the impacts of software and equipment on labour demand will vary across workers of different skill levels. Our preliminary analysis of the US data shows that software substitutes for both high-skill and low-skill workers, while equipment complements both groups of workers. However, for both software and equipment, the elasticity of substitution with labour is smaller for high-skill workers than for low-skill workers. These findings have a direct implication for the skills premium and wage inequality, a promising avenue for further research.
Our sample period ends in 2018 and thus predates ‘upheaval’ brought on by ChatGPT and Generative Artificial Intelligence (GenAI) in general. Thinking of GenAI as a class of very powerful software, we predict that our finding of labour-software substitutability will endure. In fact, Eisfeldt et al. (2023) provide preliminary evidence that GenAI is on net a substitute for labour.
As software continues to ‘eat the world’, understanding its unique economic impacts becomes increasingly crucial. Our findings highlight the need for a more granular approach to measuring and analysing capital in economic research and policy discussions. The traditional dichotomy between labour and capital may be insufficient in a world where intangible assets, particularly software, are increasingly important for firm productivity, competitiveness, and market power.
To conclude, we offer a fresh perspective on the declining labour share by highlighting the role of software. By distinguishing between software and equipment capital, we reconcile the discord between macro and micro evidence on the elasticity of substitution between capital and labour. This reconciliation advances our understanding of recent trends in the labour income share and markups, potentially leading to more informed policy debates.
References
Autor, D, D Dorn, L F Katz, C Patterson and J Van Reenen (2020), “The Fall of the Labor Share and the Rise of Superstar Firms”, The Quarterly Journal of Economics 135(2): 645-709.
Aum, S and Y Shin (2020), “Why is the Labor Share Declining?”, FRB St. Louis Review 102(4): 413-428.
Aum, S and Y Shin (2024), “Is Software Eating the World?”, NBER Working Paper No. 32591.
Eisfeldt, A L, G Schubert, B Taska and M B Zhang (2023), “Generative AI and firm values”, manuscript.
Karabarbounis, L and B Neiman (2013), “The Global Decline of the Labor Share”, The Quarterly Journal of Economics 129(1): 61-103.
Kehrig, M and N Vincent (2021), “The Micro-Level Anatomy of the Labor Share Decline”, The Quarterly Journal of Economics 136(2): 1031-1087.
Koh, D, R Santaeulàlia-Llopis and Y Zheng (2020), “Labor Share Decline and Intellectual Property Products Capital”, Econometrica 88(6): 2609-2628.
Oberfield, E and G M Grossman (2022), “Trying to Account for the Decline in the Labour Share”, VoxEU.org, 13 January.
Oberfield, E and D Raval (2021), “Micro Data and Macro Technology”, Econometrica 89(2): 703-732.
Raval, D R (2019), “The Micro Elasticity of Substitution and Non-Neutral Technology”, The RAND Journal of Economics 50(1): 147-167.
