Public Descriptive Evidence
and Econometric Motivation

A0Data Sources

A1AI Adoption Trends by Firm-Size Class (BTOS)

Following Bonney et al. (2024 / CES-WP-24-16), I estimate OLS trend regressions of the form \(\text{AdoptRate}_{s,t} = \alpha_s + \beta_s \cdot t + \varepsilon_{s,t}\), separately for each size class. The coefficient \(\beta_s\) is the estimated increase in the adoption rate in percentage points per bi-weekly period.

The adoption growth rate is steepest in the largest size class (β = 0.662 pp per bi-week vs. 0.331 for the smallest). This is the adoption-gradient confound the main paper’s triple-difference must neutralize. The U-shaped level (smallest firms adopt at a higher rate than the 5–99 class) is consistent with micro-entrepreneur adoption; it does not speak to the modularization mechanism.

A1.1 Higher-frequency adoption trends (Ramp AI Index, Bloomberg)

To corroborate the BTOS gradient at monthly frequency over a longer window, I fit the same trend regression \(\text{AdoptRate}_{s,t}=\alpha_s+\beta_s\cdot t+\varepsilon_{s,t}\) to the Ramp AI Index by business size (Jan 2023–May 2026, \(N=41\) months per class), with HAC (Newey–West, 3-lag) standard errors. Ramp tracks AI-tool spend among card-using businesses; its levels run higher than BTOS (different universe), but its size ordering and slope gradient reproduce the BTOS pattern with much greater precision. The Ramp figures are a diffusion index within that business sample, not a population adoption rate: 61.3% is the index value for large card-using firms, not the share of large firms in the economy using AI. Read Ramp for ordering and trend; read BTOS for population levels.

The monthly slope is essentially flat across medium and large and modestly lower for small firms, but the level gradient is large and persistent: large-firm adoption leads small-firm adoption by roughly two-and-a-half years of diffusion at the small-firm trend rate. The adoption-gradient confound is therefore quantitatively first-order, not a formality — it is the single most important reason the main paper's triple-difference conditions on adoption intensity, and why H5 (mediation by \(\hat{m}(f)\)) is load-bearing rather than cosmetic.

A2Expected Employment Change Due to AI, by Firm Size

A3Adoption Gap Over Time

Table A3 now reports the gap from the monthly Ramp AI Index (Bloomberg), which resolves three size classes consistently over Jan 2023–May 2026. The earlier BTOS/SBA gap series (retained in the note below) measured a coarser two-class split on a different universe; both agree that the gap is wide and currently re-expanding.

The gap in levels closed in mid-2025 as small-firm adoption accelerated, then re-widened to 16.9 pp by May 2026 as frontier-firm adoption re-accelerated post-GPT-4o. The ratio compresses toward ~1.3 as both classes mature, but a 16.9-point level gap persists at the latest reading. The pattern is non-monotone but never near closure — consistent with continued frontier-firm acceleration, and sufficient on its own to generate a size gradient in labor outcomes absent any modularization channel.

A4Task-Substitution Gradient by Firm Size

Task substitution is monotonically increasing in firm size. RPA (the hardest-core modularization use case) shows the steepest gradient. Marketing automation reverses: small firms lead — the augmentation-margin signature. This cross-sectional pattern directly supports the modularization-surface prediction.

A5Structural Break Tests: Separations and Entry Unemployment

A5.1 JOLTS layoffs & discharges rate

Estimating \(\text{LayoffRate}_t = \alpha + \beta_1 \cdot \text{Post}_t + \beta_2 \cdot t + \varepsilon_t\) with HC3-robust standard errors (pandemic months excluded, N = 84):

A5.2 Young-worker (recent BA graduate) unemployment

A5.3 Job openings collapse vs. stable separations (JOLTS by industry)

H3 and H4 make a falsifiable claim about the form of the labor response in exposed white-collar work: the margin that moves is vacancy creation, not separation. The non-created job is the distinctive object. JOLTS gross flows by industry (Bloomberg) let us inspect this at sector granularity. Across professional & business services, information, and finance, openings fell sharply from the 2021H2–2022 average to the 2024H2–2026 average while layoffs and discharges rose only modestly off far smaller bases.

The asymmetry is sharper in the vacancy-to-separation ratio, which strips out the differing bases:

A structural-break test on log professional-services openings (Jan 2019–May 2026, pandemic months Mar 2020–Jun 2021 excluded, \(N=73\)) confirms a significant level downshift after ChatGPT:

Substantive reading. Read against the flat layoff rate (A5.1), this resolves the §1 paradox at sector granularity: the white-collar labor market is not shedding incumbents — it is declining to open the next requisition. A separations-only monitor registers almost nothing; the vacancy side has more than halved. This is the macro shadow of hiring suppression (H3), visible because openings are observable even though the counterfactual non-created job is not. It remains motivating, not identifying: JOLTS resolves flows by industry but not by firm size, so the β₁–β₂ interaction is not observed, and the post-2022 rate-hiking cycle, the tech correction, and post-pandemic over-hiring unwind can each compress vacancies independent of AI.

A5.4 Net hiring by sector (ADP) — where the aggregate is carried

JOLTS measures gross flows (openings, separations); ADP measures net employment change by sector and month. The two are complementary: net change = gross hires − separations, so reading them together pins down which margin is moving. Table A5f reports average monthly net change within the consistent post-2022 ADP regime (ADP revised its methodology in 2022; comparisons are kept inside that window).

Two facts stand out. First, net private hiring has narrowed to a near-monopoly of one less-exposed, relational sector: education & health contributed +624k over the trailing year against +567k for all of private payrolls — i.e., more than 100% of net hiring, with the rest of the economy netting roughly zero or negative. Second, the three AI-exposed white-collar service sectors together netted approximately zero per month. Combined with the flat separations of A5.1, near-zero net hiring implies gross hires fell in these sectors — the hiring-suppression signature (H3) in a net-flow series, and the sectoral composition the §10 aggregation logic predicts (stable aggregate, hollow exposed middle).

A5.9Econometric Evidence: Simple Tests Before Identification

This section adds deliberately simple econometric discipline to the descriptive evidence above. The goal is not to identify causal AI effects; the available public and visually digitized data do not support that claim. The goal is narrower: to ask whether the patterns required by H3 are present before moving to firm-level microdata. We proceed from scatterplots to bivariate OLS, controlled OLS, role×seniority fixed-effects panels, and placebo comparisons. The resulting evidence is mixed but informative: the data do not support a uniform white-collar entry-port collapse; they support a narrower claim that entry-port weakness is concentrated in the most automatable and modularizable roles. Each test states whether it supports, weakens, or qualifies H3.

Block 1 — Adoption gradient by firm size

Question: do larger firms adopt AI more? Regressing the 2025 share of firms with AI-related postings on firm-size rank (1 = smallest decile, 8 = top 1%) gives a strong monotone gradient.

Block 2 — AI hiring intensity among adopters

Question: among AI-adopting firms, is AI taking a larger share of hiring? Both the extensive margin (share of firms with any AI posting) and the intensive margin (AI postings as a share of adopters' hiring) trend up, with the intensive series accelerating after the 2022 trough.

Block 3 — Economy-wide junior–senior scissors

Question: did junior postings weaken relative to senior? The Indeed junior/senior ratio (Aug 2024 = 100) falls steadily, and a stacked seniority specification isolates a junior-specific decline.

Block 4 — Revelio role×seniority panel (the core test)

Question: within the same role, did entry/junior postings fall more than experienced? Three nested specifications on the 13-role panel (846–1,833 obs; role and month FE; cluster-robust SE).

Block 5 — Per-role estimates and placebo roles

Question: does the effect concentrate where the tasks are most automatable, and stay absent in in-person placebo roles? The coefficient plot shows the per-role β on Post×EntryJunior with 95% CIs.

Connecting to the separations placebo: where junior postings fall, formal layoffs do not spike (WARN flat, §A5.5; JOLTS layoff rate flat, §A5.1). To the extent any margin moved in exposed roles, it is vacancy suppression rather than separation — the H3 direction.

A6Macro Aggregation (Back-of-Envelope)

Large firms are expected to account for ~84% of the AI-driven aggregate productivity gain despite employing 54% of the labor force, because they carry both higher AI adoption rates and higher measured productivity gains per adopter. The displacement arithmetic implies roughly 92,000 displaced routine workers per year at current adoption rates — large enough to matter at the career-ladder level, but small relative to the payroll total. This reconciles the stable JOLTS rate (Table A5) with the entry-ladder tightening signal (Table A5b).

A7Figures A1–A5

Figures A1–A5

Public Descriptive Evidence — Five Exhibits

A1 (top): AI adoption rate by firm-size class, OLS trend fits to BTOS bi-weekly data. Steeper slope for 250+ confirms the adoption-gradient confound the triple-difference must neutralize. A2 (middle left): Expected employment change due to AI. Monotonic gradient (ρ = ±1.000): small firms expect growth, large firms expect contraction. A3 (middle right): Task-substitution gradient. RPA and overall substitution rise monotonically with size; marketing automation reverses — the augmentation-margin signature. A4 (bottom left): JOLTS layoff rate, Jan 2019–Mar 2026. No large-scale separation event post-ChatGPT; the post-period mean is below the pre-period mean. Supports H4. A5 (bottom right): Back-of-envelope macro attribution. Large firms expected to contribute ~84% of AI-driven aggregate productivity gain despite 54% employment share. Illustrative accounting only. Sources: BTOS (Census Bureau); SBA Spotlight (Press 2025); BLS JOLTS [JTSLDR] via FRED; SUSB 2022; BIS/EIB WP 2026/02; Baslandze et al. 2026.

A8Scope and Limits of the Aggregate Evidence

The public-data tier establishes the motivating facts — adoption gradient, directional employment expectations, task-substitution gradient, flat separations — but cannot close the argument. The firm-size channel (H1), the suppression mechanism (H3), and the modularization mediation (H5) all require microdata that condition on AI exposure and firm structure simultaneously. That is the job of the empirical design in §6 and the Census RDC access in §6.5 of the main paper.

Data sources. BTOS data: census.gov/programs-surveys/btos. JOLTS and CPS series via FRED (series JTSLDR, CGBD2024). SUSB data: census.gov/programs-surveys/susb. SBA Spotlight: advocacy.sba.gov. CES Working Paper CES-WP-24-16: census.gov/hfp/btos/downloads/CES-WP-24-16.pdf.