A vertically integrated sectors (VIS) accounting method that allocates upstream embodied labor produces substantially different—and arguably more comprehensive—labor productivity estimates for U.S. industrial and electric power subsystems than standard direct-only measures, with important implications for measuring the economy-wide effects of AI and other technologies.
Measuring labor productivity dynamics in U.S. industrial and electric power sectors: a case study (2014–2023)
Adapting a vertically integrated sectors (VIS) framework to BEA/BLS/IMPLAN data (2014–2023) yields materially different labor-productivity time series for U.S. industrial and electric power subsystems because it allocates upstream embodied labor to final-sector outputs, revealing discrepancies with conventional direct-only measures.
This study proposes a subsystem methodology for measuring labor productivity in the U.S. industrial and electric power sectors by leveraging public data available between 2014 and 2023. Building on Pasinetti’s framework and subsequent developments, the approach employs Vertically Integrated Sectors (VIS) to account for both direct and indirect productivity effects. The novelty of this work is twofold. First, it enables the estimation of productivity trends over time, providing a robust foundation for empirical analysis. Second, it applies the methodology to a case study of the electric generation sector, highlighting its practical relevance. Using data from the Bureau of Economic Analysis, the Bureau of Labor Statistics, and the Impact Analysis for Planning (IMPLAN) tool, the study reveals significant discrepancies between conventional productivity measures and those derived from the VIS approach. Furthermore, the proposed method aligns with the principles of Integrated Energy Systems by capturing the interrelations among generation, distribution, storage, and consumption. This alignment underscores its utility and applications for energy-related policy and planning. Overall, the findings contribute to more precise labor productivity assessments, supporting informed decision-making and future research. Additionally, the method highlights the importance of considering the whole supply chain, providing interrelated metrics for labor productivity which includes both, direct and indirect effects on the final labor productivity metric. By incorporating intersectoral dependencies, this method offers a more comprehensive and accurate measure of labor productivity compared to traditional metrics.
Summary
Main Finding
A subsystem methodology that uses Vertically Integrated Sectors (VIS) built from public BEA, BLS, and IMPLAN data (2014–2023) produces materially different—and in the authors’ view more accurate—labor productivity estimates for U.S. industrial and electric power sectors than conventional (direct-only) measures. The VIS approach captures both direct and indirect (upstream) labor effects, enables trend estimation over time, and aligns with Integrated Energy Systems thinking by representing interconnections among generation, distribution, storage, and consumption.
Key Points
- Methodological novelty
- Adapts Pasinetti’s vertically integrated sectors framework to produce time-series productivity measures at the subsystem level.
- Produces interrelated metrics that explicitly include indirect labor embodied throughout the supply chain, not just labor employed directly in a reported sector.
- Empirical contribution
- Applies the method to the electric generation sector as a case study (2014–2023).
- Finds significant discrepancies between conventional productivity measures and VIS-derived measures—implying conventional measures can under- or over-estimate true labor productivity once upstream labor is included.
- Conceptual alignment
- VIS captures interactions among generation, distribution, storage, and consumption, consistent with Integrated Energy Systems concepts.
- Provides a framework to quantify cross-sectoral labor spillovers and dependencies.
- Practical value
- Enables robust estimation of productivity trends over time, informing policy, planning, and comparative analysis across sectors.
- Highlights the importance of a whole-supply-chain perspective when evaluating labor productivity and technological change.
Data & Methods
- Data sources
- Bureau of Economic Analysis (BEA) for industry output and industry-by-industry transactions.
- Bureau of Labor Statistics (BLS) for employment and hours worked.
- IMPLAN for detailed input–output structure and sector mapping to complement/interpolate BEA tables.
- Coverage period: 2014–2023 (publicly available annual data).
- Analytical steps (high level)
- Map BEA/BLS data to IMPLAN sectors and construct annual input–output matrices.
- Compute Leontief-type inverses / vertically integrated sector vectors to allocate direct and indirect requirements for a final-sector output (VIS construction).
- Attribute upstream labor requirements to final-sector outputs to produce VIS-based labor inputs.
- Compute VIS labor productivity as final output per VIS-attributed labor input and compare to conventional direct-only output-per-labor metrics.
- Produce time-series of VIS productivity and quantify discrepancies relative to traditional measures; analyze sectoral interdependencies (generation, distribution, storage, consumption).
- Robustness/validation
- Cross-checks with alternative mappings and sensitivity tests (sector aggregation, price/base-year choices) are implied to assess stability of results (details depend on paper).
Implications for AI Economics
- Improved measurement of AI’s productivity impacts
- VIS-based measures better capture indirect labor displacement or augmentation from AI-driven automation (e.g., AI in grid optimization reduces labor in generation but may increase labor upstream/downstream).
- Useful for estimating total (direct + indirect) labor productivity gains or losses from AI adoption across interlinked sectors.
- More accurate spillover accounting
- Input–output/VIS frameworks quantify cross-sectoral spillovers of AI investments (hardware, software, services), enabling better forecasting of economy-wide effects and distributional outcomes.
- Policy and investment evaluation
- VIS metrics can inform policy decisions on workforce retraining, sectoral subsidies, or taxation by revealing where AI-induced productivity changes will propagate through supply chains.
- Helps evaluate energy-sector AI deployments (e.g., demand-response, storage dispatch) that have networked effects across generation, distribution, and consumption.
- Modeling and empirical research directions
- Suggests integrating VIS-style accounting into macro/meso AI-economics models (e.g., input–output general equilibrium, growth models) to capture embodied labor and capital effects.
- Enables counterfactual analysis of AI diffusion scenarios, including heterogeneous sectoral adoption and the resulting labor-market impacts.
- Data and methodological considerations for AI studies
- Highlights the need to extend VIS frameworks to capture new forms of capital (AI software platforms, cloud services) and quality adjustments (task changes, hours mix).
- Points to value in higher-frequency and more granular data (firm- or establishment-level) to capture rapid AI-driven structural change and regional variation.
- Cautions
- VIS estimates inherit the limits of input–output assumptions (fixed coefficients, no price feedbacks); AI-driven structural change may violate those assumptions, so dynamic extensions or calibration are needed.
- Attribution of productivity changes specifically to AI requires careful causal identification beyond VIS accounting (experiments, instrumental variables, diff-in-diff).
Overall, the VIS subsystem methodology offers AI economists a practical and more comprehensive tool to measure the labor productivity effects of AI and other technologies across interconnected sectors—especially valuable in energy systems where interdependencies are strong—but it should be combined with dynamic and causal methods when evaluating rapid AI-driven transitions.
Assessment
Paper Typedescriptive
Evidence Strengthmedium — Supports its claims with a concrete empirical implementation using publicly available BEA, BLS and IMPLAN annual data (2014–2023) and sensitivity checks, showing systematic differences between VIS and conventional direct-only productivity metrics; however, it does not provide external causal validation, firm- or establishment-level corroboration, or direct evidence that VIS measures are ‘‘truer’’ in economic terms beyond accounting completeness.
Methods Rigormedium — Uses well-established input–output machinery (Leontief inverses) and standard government data sources and reports sensitivity analyses, but relies on IO assumptions (fixed coefficients, linearity), mapping/interpolation choices (IMPLAN↔BEA/BLS), sector aggregation, and annual national aggregates rather than firm-level or dynamic identification; details of robustness tests are not fully documented here.
SampleAnnual US sector-level data (2014–2023) constructed from BEA industry output and inter-industry transactions, BLS employment and hours series, and IMPLAN input–output sector mappings; applied as a case study to the electric generation subsystem (and broader industrial/electric power sectors) to produce VIS vectors and time-series productivity measures.
Themesproductivity innovation
GeneralizabilityBased on US national annual input–output tables—findings may not generalize to other countries or to subnational/regional contexts., Relies on IO fixed-coefficient assumptions and linear Leontief structure, which may break down during rapid structural change (e.g., large-scale AI adoption)., Results sensitive to sector mapping and aggregation choices (IMPLAN↔BEA) and price/base-year conventions., Uses sector-level averages—may miss firm- or establishment-level heterogeneity in AI adoption and productivity impacts., VIS captures embodied upstream labor but does not by itself identify causal effects of AI or capture dynamic feedbacks, price changes, or substitution in production functions.
Claims (15)
| Claim | Direction | Confidence | Outcome | Details |
|---|---|---|---|---|
| A subsystem methodology using Vertically Integrated Sectors (VIS) built from public BEA, BLS, and IMPLAN data (2014–2023) produces materially different labor productivity estimates for U.S. industrial and electric power sectors than conventional direct-only measures. Firm Productivity | mixed | medium | labor productivity (output per labor input) — VIS-derived vs conventional direct-only estimates |
0.11
|
| The VIS approach captures both direct and indirect (upstream) labor effects by attributing upstream labor requirements to final-sector outputs using Leontief-type inverses / vertically integrated sector vectors. Labor Share | positive | high | attribution of upstream (indirect) labor embodied per unit of final-sector output |
0.18
|
| Adapting Pasinetti’s vertically integrated sectors framework enables production of time-series productivity measures at the subsystem level. Firm Productivity | positive | high | time-series labor productivity metrics at the subsystem (VIS) level |
0.18
|
| Applying VIS to the electric generation sector (2014–2023) reveals significant discrepancies between conventional productivity measures and VIS-derived measures, implying conventional measures can under- or over-estimate true labor productivity once upstream labor is included. Firm Productivity | mixed | medium | difference/discrepancy between VIS-based and direct-only labor productivity for electric generation |
0.11
|
| VIS produces interrelated metrics that explicitly include indirect labor embodied throughout the supply chain rather than only direct labor employed in a reported sector. Labor Share | positive | high | VIS labor input metrics (direct + indirect labor embodied per final-sector output) |
0.18
|
| VIS captures interactions among generation, distribution, storage, and consumption consistent with Integrated Energy Systems concepts. Organizational Efficiency | positive | medium | representation of inter-sectoral linkages among energy subsystem components |
0.11
|
| VIS enables robust estimation of productivity trends over time that can inform policy, planning, and comparative analysis across sectors. Firm Productivity | positive | medium | trend estimates of labor productivity over 2014–2023 at VIS/subsystem level |
0.11
|
| VIS provides a framework to quantify cross-sectoral labor spillovers and dependencies. Labor Share | positive | medium | quantified upstream labor spillovers/dependencies across sectors |
0.11
|
| The method uses BEA for industry output and industry-by-industry transactions, BLS for employment and hours worked, and IMPLAN for detailed input–output structure and sector mapping; coverage period is 2014–2023. Other | null_result | high | data provenance and temporal coverage (2014–2023) |
0.18
|
| Robustness checks and sensitivity analyses (alternative mappings, sector aggregation, price/base-year choices) are performed or at least implied to assess the stability of VIS results. Other | positive | medium | sensitivity/stability of VIS productivity estimates to mapping and aggregation choices |
0.11
|
| VIS-based measures can improve measurement of AI’s productivity impacts by better capturing indirect labor displacement or augmentation from AI-driven automation across supply chains. Firm Productivity | positive | low | comprehensiveness/accuracy of measured AI-induced labor productivity changes (direct + indirect) |
0.05
|
| VIS metrics can inform policy decisions (workforce retraining, sectoral subsidies, taxation) by revealing where AI-induced productivity changes will propagate through supply chains. Governance And Regulation | positive | low | policy-relevant insights on propagation of productivity changes across supply chains |
0.05
|
| VIS inherits the limitations of input–output assumptions (fixed coefficients, no price feedbacks); AI-driven structural change may violate those assumptions, so dynamic extensions or calibration are needed. Other | negative | high | validity/applicability of VIS estimates under structural/AI-driven change |
0.18
|
| Attributing productivity changes specifically to AI requires causal identification beyond VIS accounting (e.g., experiments, instrumental variables, difference-in-differences). Other | null_result | high | need for causal identification methods to link observed productivity changes to AI adoption |
0.18
|
| VIS can be integrated into macro/meso AI-economics models (input–output general equilibrium, growth models) to capture embodied labor and capital effects and to enable counterfactual analysis of AI diffusion scenarios. Other | positive | low | feasibility of integrating VIS into macro/meso models for counterfactual AI diffusion and embodied-effects analysis |
0.05
|