Solow After the Machine II

Executive synthesis

The second pass through the machine

The first Solow After the Machine essay began with a theoretical warning: do not confuse tokens with factors, capital deepening with technical change, or task acceleration with system productivity. This sequel begins where that warning becomes testable. It takes a workbook built from the 1997–2024 integrated BEA–BLS production account, reconstructs its calculations across 63 industries, and asks whether the empirical headline survives contact with growth accounting.^[1]

At first glance, the verdict is spectacular. Across 61 market industries from 2021 to 2024, the workbook’s value-added-weighted digital-capital proxy—software, research and development, and IT equipment—grew by 7.83% a year. Integrated total factor productivity grew by 0.57%. The subtraction yields a 7.26 percentage-point “accumulation gap.”

The arithmetic is correct. The economics is not. Capital quantity growth and TFP growth are not rival claims on the same unit of output. Capital enters growth accounting after multiplication by its income share. TFP is already the residual contribution left after measured inputs have been removed. Once the units are made comparable, the gap contracts from 7.26 points to 0.03.

That is the thesis of Part II. The puzzle has moved from accumulation to translation. AI makes a cognitive intermediate cheaper: code, text, forecasts, candidate molecules, decisions waiting to be checked. Firms sell something else—verified, integrated, compliant, shipped, and demanded output. Once generation becomes abundant, the shadow price migrates to the organization around it.

Growth accounting starts from a simple decomposition. Output growth equals the contribution of capital growth, the contribution of labor growth, and growth in total factor productivity. The contribution is the input’s growth rate multiplied by its share in income. TFP already occupies the contribution side of the account.

The workbook’s 7.83% is a quantity growth rate. Its 0.57% is growth in an integrated TFP index. Subtracting one from the other is like comparing the speed of a conveyor belt with the share of factory output not explained by measured inputs. Both are rates. They are not the same economic object.

The official BEA–BLS contribution account supplies the comparable exercise. Between 2021 and 2024, IT equipment, R&D, and software together contributed about 0.63 percentage points to annual value-added growth. TFP contributed 0.60 points. The difference is 0.03 points—not 7.26.^[2]

The correction does not prove an AI productivity boom. Equality between the two contributions is not a theoretical benchmark, and the digital bundle contains conventional software and non-AI R&D while missing AI purchased as cloud and business services. It does something more basic and more valuable: it prevents a category error from becoming a theory of economic failure.

A separate approximation reinforces the scale. Applying adjacent-period compensation shares to the industry asset growth rates yields a digital-capital contribution proxy of about 0.68 points. That is close to the official 0.63, though the methods are not interchangeable. Read as: the capital wave matters, but it matters through shares and services—not through raw quantity growth alone.

Normalize 2017 to 100 and the visual divergence is immediate. By 2024, digital capital reaches 181.7. Labor productivity reaches 113.3. Integrated TFP reaches 105.3. From 2017 to 2024, those paths imply annualized growth of 8.91%, 1.80%, and 0.75%, respectively.

The pattern is consistent with delayed productivity effects. It does not identify a productivity J-curve. The formal J-curve is a claim about complementary intangible investment: firms divert resources into process redesign, data, training, and organizational capital; measured productivity can fall while an unmeasured stock accumulates, then rise when the stock begins to produce.^[3] A widening line chart shows accumulation and timing. It does not observe the complementary stock, the adjustment cost, or the later harvest.

The disciplined conclusion is therefore narrower than either camp wants. The United States is accumulating the substrate of an AI economy faster than it is demonstrating a durable efficiency dividend. That can be the first half of a J-curve. It can also be capital deepening, pandemic-era utilization, a measurement problem, or a mix of all three. A visual lag is a hypothesis generator, not a causal design.

The newest official evidence increases the need for caution. BLS estimates private nonfarm business TFP growth of 0.8% in 2025, down from 1.5% in 2024.^[5] Boyle, Fernald, and Li estimate that higher utilization explains much of the recent output-per-hour surge and may account for essentially all measured TFP growth since early 2024 in their framework.^[6]Running existing people and capital harder is not the same thing as moving the production frontier.

If fast digital-capital accumulation were already translating reliably into measured technical change, industries with more digital-capital growth should show systematically higher TFP growth. They do not. Across 61 market industries, the Pearson correlation is -0.18, with p = 0.18. The rank correlation is 0.02. The 2024 value-added-weighted correlation is 0.14, and the weighted regression explains only 0.02 of the variance.

An absent slope does not prove an absent effect. Adoption is selected, the window is short, inputs and outputs are measured with error, and industries face different shocks. But it does reject the simplest translation story. The workbook does not contain a stable one-for-one—or even reliably positive—cross-sectional relationship waiting to be named “AI productivity.”

The regime map reveals why co-movement and a weak slope can coexist. Industries with digital-capital growth of at least 3% and positive TFP account for 55.7% of market value added. The “capital race”—fast digital capital with negative TFP—accounts for 35.6%. The remaining 8.8% sits in slower-capital regimes. Large industries can dominate the positive-positive quadrant while variation within and across the other quadrants destroys a stable linear relationship.

Chemical products sit in the positive-positive quadrant. From 2021 to 2024, the workbook reports digital-capital growth of 5.22%, TFP growth of 0.62%, labor-productivity growth of 1.39%, gross-output growth of 2.43%, and hours growth of 1.02%. The Törnqvist sensitivity measure for digital capital is nearly identical at 5.21%.

This is constructive co-movement, not AI attribution. Chemical production combines process automation, scientific R&D, enterprise software, capacity utilization, energy shocks, product-mix changes, regulation, and long validation cycles. A quadrant cannot identify which mechanism did the work. It can identify the next research design: follow model suggestions into experiments, validated results, process changes, plant throughput, quality, energy use, and saleable output.

The sector also demonstrates why organizational complements become physical. A model can generate a molecule or operating recommendation quickly. Wet-lab capacity, safety review, regulatory acceptance, shutdown windows, control-system integration, and customer qualification remain slow. The machine makes one stage abundant and reveals the scarcity of the rest.

Software development makes the attenuation visible because its production stages are unusually observable. A 2026 study of more than 100,000 developers estimates that successive generations of AI coding tools increased commits cumulatively by 180%. The gain fell to 50% for projects and 30% for releases, with no detectable increase in total app usage.^[9] The output did not vanish. It queued at review, integration, testing, release, product judgment, and demand. The estimates describe observed adopters and production stages; they should not be generalized to every developer, firm, or workflow without accounting for selection into tool use.

Firm evidence shows the same wedge in a different account. A 2026 survey of nearly 750 corporate executives finds that AI-investing firms report labor-productivity gains 2.4 percentage points higher than non-investors in 2025, while the gain implied by revenue and employment is only 1.0 point higher.^[8] The difference may contain expected quality, future revenue, intermediate-input changes, markups, accounting timing, and attribution bias—not organizational friction alone. It is evidence that experienced capability and measured output are not the same object.

Industrial microdata add the mechanism. Census-linked research presented at the 2026 AEA meeting finds causal J-curves in manufacturing: short-run productivity and profit losses followed by longer-run gains, with worse initial outcomes among older establishments. Growth-oriented strategy and within-firm spillovers mitigate the losses; abandoning structured production-management practices explains a meaningful share of the short-run damage among older plants.^[10]

The next AI dashboard should stop asking whether “AI productivity” has arrived as one number. It should follow the translation chain. At each stage, measure one outcome and one queue. The outcome shows what moved. The queue shows where the bottleneck migrated.

Capital requires share-weighted contributions and full service cost, not licence counts alone. Complements require redesigned-workflow coverage and the training or data backlog. Operational flow requires end-to-end cycle time and review wait. Shipped output requires quality-adjusted revenue, releases, experiments, or operational completion. A frontier shift requires utilization adjustment, persistence, and survival through model migration.

The scorecard deliberately refuses to compress five weakly measured stages into one attractive percentage. A measured capital input beside anecdotal workflow evidence is not “60% ready.” It is a specific diagnosis: the organization knows what it bought and does not yet know what changed. The next investment should follow that diagnosis.

In software, trace prompt to code, code to pull request, pull request to release, and release to usage. In chemicals, trace suggestion to experiment, experiment to validated result, result to process change, process change to throughput, and throughput to saleable output. At every transition, record machine cost, human effort, rejection, rework, delay, error severity, and final acceptance. A local gain that disappears downstream is not a null. It has identified the weak link.

Reproducibility · variables · downloads

How the analysis was constructed

The reconstruction reads cached values from the integrated BEA–BLS workbook, calculates 2021–2024 industry CAGRs, excludes two government industries from market aggregates, and uses 2024 value added as a transparent fixed weight. The digital bundle combines software, R&D, and IT. A Törnqvist-style sensitivity index replaces endpoint shares with adjacent-period average shares. Official contribution data are kept in a separate panel and never spliced into the fixed-weight industry index.

1. 1

   Reconstruct

   Load 63 industry series for capital quantities, compensation, output, hours, value added, and productivity.

2. 2

   Transform

   Compute CAGRs, endpoint-weighted and Törnqvist digital indexes, contribution proxies, and 2024 weights.

3. 3

   Stress-test

   Change pre-periods, compare weighting methods, separate official aggregates, and keep government selectable.

4. 4

   Associate

   Estimate Pearson, rank, weighted correlation, and weighted regression without causal interpretation.

5. 5

   Diagnose

   Map regimes and trace the chemical-products row without turning quadrant membership into attribution.

6. 6

   Publish

   Validate row counts and representative values, hash sources, and generate typed JSON plus downloadable tables.