## wpiea2025068-print-pdf

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---

### Contributions and relation to existing literature
- Extends task-based frameworks (Zeira (1998); Acemoglu and Autor (2011); Acemoglu and Restrepo (2018); Moll et al. (2022)) to analyze AI, accounting for:
  - Differential incidence of prior routine-biased automation (Felten et al. (2021)).
  - Possibility that AI can be a complement for some workers as well as a substitute (building on Pizzinelli et al. (2023)).
- Demonstrates that complementarity with high-income workers can have “stark implications for the potential inequality implications” of AI.
- Introduces an extended model that endogenizes technology adoption decisions (building on Drozd et al. (2022)) to show how AI’s unique characteristics may amplify adoption and economic impacts relative to prior automation waves.
- Highlights a potential trade-off for policymakers between inequality objectives and productivity gains from adoption.

### Data and measurement of technology exposure
- Exposure indices:
  - Routine Task Index (RTI) constructed similar to Autor and Dorn (2013).
  - AI Occupational Exposure (AIOE) index (Felten et al. (2021)).
  - Complementarity index (Pizzinelli et al. (2023)).
- Household microdata:
  - Wealth and Assets Survey (WAS) for the UK.
  - Waves used: 2016, 2018, and 2020 (covering April 2016-March 2020).
  - Sample restricted to working-age employed individuals (excludes self-employed and entrepreneurs).
  - Final sample: 28,588 workers across 14,780 households.
  - All nominal values deflated to 2019 prices.

### Empirical findings — exposure across the income distribution
- Classification and thresholds:
  - Continuous exposure measures converted to binary by defining “exposed” occupations as top 30 percent of total hours worked (30 percent threshold applied to both automation and AI).
- Key patterns:
  - Automation exposure is broadly decreasing in income:
    - Nearly 50 percent of workers in the lowest income percentiles were exposed to automation (RTI top 30 percent by hours worked).
    - Fewer than 20 percent of high-income workers were exposed to automation.
  - AI exposure concentrated among higher-income workers:
    - Fewer than 20 percent of workers in the bottom income decile are exposed to AI.
    - Over 60 percent of workers in the top income decile are exposed to AI.
- Within-household correlation:
  - High degree of correlation in exposure within households (assortative matching).
- Complementarity by income percentile:
  - Complementarity monotonically increases in income up to the 80th percentile, then levels off.
  - Highest-income workers are both most exposed to AI and more likely to be complementary with AI.

### Empirical findings — income, wealth, and portfolio composition
- Non-labor income and mitigation capacity:
  - Highest-income workers have the largest share of income from non-labor sources.
  - Realized investment income in WAS understates potential benefits because unrealized capital gains are not captured.
- Wealth concentration and risky asset exposure:
  - Total wealth highly concentrated among high-income workers.
  - Share invested in “risky assets” (defined-contribution pensions, equities, corporate bonds) is much higher for high-earners.
- Pension treatment:
  - DC pensions classified as risky assets.
  - DB pensions treated as safe assets (similar to government bonds).

### Structural analysis — approach and channels
- Three channels in quantitative framework:
  - Negative: task displacement lowers real labor income.
  - Positive: productivity gains raise real labor income.
  - Positive: higher returns on capital increase capital income.
- Two-stage modeling strategy:
  - Baseline model: treats technology adoption and capital shares as exogenous (follows Moll et al. (2022)).
  - Extended model: endogenizes firms’ adoption decisions and capital use to capture amplified adoption and distributional impacts from AI cost savings on high-wage tasks.
- Wealth dissipation shock:
  - Finite capital supply elasticity via probability p that assets disappear yields non-degenerate wealth distribution and allows innovation to raise equilibrium return on capital.

### Baseline model specifics and assumptions
- Production and tasks:
  - Final good Y via Cobb-Douglas aggregation of intermediates Yz with weights ηz and ∑ηz = 1.
  - Share αz of tasks in sector z can be performed by capital; task output definitions conditional on u ∈ [0, αz] or u ∈ (αz, 1].
  - In baseline, capital chosen for tasks it can perform; capital share in sector equals αz.
- Households and preferences:
  - Epstein-Zin preferences with parameters ρ (discount components), γ (risk aversion), σ (inverse IES).
  - Fraction χ of households can invest in capital.
- Labor supply and mobility:
  - Inelastic labor supply to assigned sector z; no occupational switching.
- Limitations:
  - Results represent impacts absent retraining/occupational mobility policies.

### Calibration of technology adoption (Section 4.2)
- Automation calibration (1980-2014):
  - Shift-share approach: 1/(1−αz,2014) − 1/(1−αz,1980) = ωRz [1/(1−α2014) − 1/(1−α1980)].
- AI calibration (2014-2048 baseline):
  - Use ωAIOEz from Felten et al. (2021).
  - Baseline assumption: aggregate change in capital share over 2014-2048 matches change from 1980-2014 for automation (magnitude fixed for comparability).
- Complementarity modeled via changes in ηz:
  - For complementarity scenario: ηz,T = ηz,0 (1 + λ) with renormalization.
  - Alternative scenario increases ψz to allow aggregate productivity gains: ψz,T = wzR /1.3*(1 + θz − θmin).

### Calibration of remaining model parameters (UK — Table 1 parameters)
- σ Inverse IES: 2
- γ Risk aversion: 2
- p Dissipation rate: 4.5%
- ρ Discount rate: 1% (target r = 6.5%)
- ξ Share investors: 10% (Target κ2014 = 1.35 and 1/ζ2014 = 0.46)
- ν Capital risk: 6% (Target κ2014 = 1.35 and 1/ζ2014 = 0.46)
- g TFP growth in ψz: 1.5%
- δ Depreciation rate: 5%
- A Productivity term: 0.143 Y/L in 2014
- ηz,0 Sector shares: Match income distribution in 2014
- ψz,0 Relative productivity of labor: - Moll et al. (cost savings of 30%)

### Baseline steady-state results (automation and AI)
- Automation (1980-2014):
  - Wage Gini rose 2.05 p.p.
  - Wealth Gini rose 6.89 p.p.
- AI baseline (no complementarity, 2014-2048):
  - Wage Gini falls 1.73 p.p.
  - Wealth Gini rises 7.18 p.p.
  - Capital income increases for highest-income workers offset wage declines so total income for highest-income workers still rises.

### Accounting for complementarity (AI scenarios)
- Complementarity-only:
  - Wage Gini falls 0.22 p.p.
  - Wealth Gini increases to 7.16 p.p.
- Complementarity plus aggregate productivity gains:
  - ηz,T = ηz,0 (1 + θz) and ψz = wzR /1.3*(1 + θz − θmin).
  - All workers better off in levels; inequality implications unchanged relative to complementarity-only scenario.

### Quantitative scenario table (Table 2 outcomes)
- Scenarios: Auto (baseline) | AI (baseline) | AI (comp. 1) | AI (comp. 2)
  - Wage Gini: 2.05 p.p. | -1.73 p.p. | -0.22 p.p. | -0.22 p.p.
  - Wealth Gini: 6.89 p.p. | 7.18 p.p. | 7.16 p.p. | 7.16 p.p.
  - Capital Share: 5.5 p.p. | 5.5 p.p. | 5.5 p.p. | 5.5 p.p.
  - Output: 9.6% | 10.6% | 10.6% | 12.2%
  - Mean Wages: 0.2% | 0.2% | 0.2% | 1.6%

### Extended model calibration (Section 5.3; Table 3)
- Two-stage calibration: match historical automation (1980–2014) then simulate AI (2014–2048).
- Key calibrated parameters:
  - κ0: Technology scalar — 1
  - λ: Technology efficiency — 3
  - ζ: Task complexity dist. — 1.086
  - βz: Benefits of adoption — ν ωz
  - ν: Exposure scalar — 0.203
  - bauto,1980: Initial adoption cost — 1.3636
  - bauto,2014: Final adoption cost — 0.2 ∗ bauto,1980
  - bai,2014: Initial adoption cost — 0.5727
  - bai,2048: Final adoption cost — 0.2 ∗ bai,2014

### Results of extended model (Section 5.4)
- General comparison:
  - Extended automation results similar to baseline automation (calibration constrained by history).
  - Extended AI predicts substantially higher AI adoption than baseline AI.
- Aggregate impacts (AI extended vs AI baseline):
  - Capital share change: 10.2 p.p. (AI extended) versus 5.5 p.p. (AI baseline).
  - TFP growth: 1.7 percent (AI extended) versus 1.4 percent (AI baseline).
  - Output growth: 20.7 percent (AI extended) versus 10.6 percent (AI baseline).
  - Average wages: almost unchanged in baseline scenarios; mean wages change: 0.2% (AI baseline) vs -0.5% (AI extended).
- Inequality implications (AI extended):
  - Wage Gini falls 3.91 p.p. (AI extended) versus -1.73 p.p. (AI baseline).
  - Wealth Gini increases 13.67 p.p. (AI extended) versus 7.16 p.p. (AI baseline).
- Table 4 summary (Auto baseline | Auto extended | AI baseline | AI extended):
  - Wage Gini: 2.05 p.p. | 2.16 p.p. | -1.73 p.p. | -3.91 p.p.
  - Wealth Gini: 6.89 p.p. | 6.92 p.p. | 7.18 p.p. | 13.67 p.p.
  - Capital Share: 5.5 p.p. | 5.5 p.p. | 5.5 p.p. | 10.2 p.p.
  - Output: 9.6% | 9.6% | 10.6% | 20.7%
  - Mean Wages: 0.2% | 0.1% | 0.2% | -0.5%

### Efficiency–inequality trade-off and policy response (Section 6)
- Trade-off overview:
  - Endogenizing adoption reveals trade-off: reducing adoption can lower wealth inequality but also reduce output by discouraging productive technologies and inducing misallocation.
  - For AI, high adoption may lower wage inequality while increasing wealth inequality.
- Capital tax mechanics:
  - Capital tax τK raises effective cost of capital to (1 + τK) R and alters firm intensive and extensive adoption margins.
  - Capital Share decision rule and margins summarized in model equations (exact functional forms in Table 5 and Appendix A.2).

### Policy simulations (Section 6.2; Table 6)
- Government implements capital tax τK = 15 percent and redistributes revenue as a Universal Basic Income (UBI).
- Revenue implications:
  - Under automation, τK = 15 percent raises tax revenue equal to 4.8 percent of pre-tax GDP.
  - Under AI, τK = 15 percent raises tax revenue equal to 5.6 percent of pre-tax GDP.
- Quantitative impacts (τK: Auto | τK: AI):
  - Wage Gini: -0.34 p.p. | 0.70 p.p.
  - Wage + UBI Gini: -3.83 p.p. | -3.44 p.p.
  - Wealth Gini: -2.12 p.p. | -3.74 p.p.
  - Capital Share: -0.80 p.p. | -1.60 p.p.
  - Output: -15.5% | -26.9%
  - Mean Wages: -8.7% | -11.8%
- Interpretation:
  - Capital tax with UBI reduces post-transfer inequality but entails large output and mean-wage declines, especially under AI.
  - The deadweight loss is large: "the total income lost across all households exceeds the tax revenue raised by more than a factor of two."
  - Pre-transfer wage Gini can rise under AI tax but falls after UBI; lowest-income households can ultimately be better off while average worker is worse off.

### Aggregate and distributional takeaways
- Structural model findings:
  - Baseline occupational-exposure assumption: wage Gini decreases 1.73 p.p.; wealth Gini rises 7.18 p.p.
  - Routine-biased automation comparison: wage Gini rises 2.05 p.p.; wealth Gini rises 6.89 p.p.
  - Complementarity mitigates wage declines for high-income workers and can mute wage-inequality reductions.
- Political economy and implications:
  - Trade-offs between equity and aggregate productivity are pronounced for AI relative to prior automation.
  - Policy instruments (capital taxes, progressive labor taxes, wealth taxes) differ in distortions and distributional focus; a full optimal tax analysis is beyond the paper’s scope.
  - Political-economy feedbacks (regulation or adoption acceleration) could alter adoption patterns and thus efficiency–equity outcomes.

*Source: Section 3–6 and Appendices A–C of wpiea2025068-print-pdf*

### 26.9 percent and average wages by 11.8 percent.  These costs are nearly twice as large as they

### wpiea2025068-print-pdf - 26.9 percent and average wages by 11.8 percent.  These costs are nearly twice as large as they

### Contributions and relation to existing literature
- Extends task-based frameworks (Zeira (1998); Acemoglu and Autor (2011); Acemoglu and Restrepo (2018); Moll et al. (2022)) to analyze AI, accounting for:
  - Differential incidence of prior routine-biased automation (Felten et al. (2021)).
  - Possibility that AI can be a complement for some workers as well as a substitute (building on Pizzinelli et al. (2023)).
- Demonstrates that complementarity with high-income workers can have “stark implications for the potential inequality implications” of AI.
- Complements policy literature emphasizing both productivity gains and distributional risks of AI (Cazzaniga et al. (2024); Brollo et al. (2024)).
- Introduces an extended model that endogenizes technology adoption decisions (building on Drozd et al. (2022)) to show how AI’s unique characteristics may amplify adoption and economic impacts relative to prior automation waves.
- Highlights a potential trade-off for policymakers between inequality objectives and productivity gains from adoption.

### Data and measurement of technology exposure
- Exposure indices:
  - Routine Task Index (RTI) for automation: constructed similar to Autor and Dorn (2013) using O*NET routine-task classification; measures occupations’ relative intensity of routine tasks.
  - AI Occupational Exposure (AIOE) index (Felten et al. (2021)): measures overlap between AI applications and human abilities needed for occupations; agnostic on substitution vs augmentation.
  - Complementarity index (Pizzinelli et al. (2023)): uses social and environmental task contexts in O*NET to identify potential labor-augmenting exposure to AI.
- Household microdata:
  - Wealth and Assets Survey (WAS) for the UK.
  - Waves used: 2016, 2018, and 2020 (covering April 2016-March 2020).
  - Sample restricted to working-age employed individuals (excludes self-employed and entrepreneurs).
  - Final sample: 28,588 workers across 14,780 households.
  - All nominal values deflated to 2019 prices.

### Empirical findings — exposure across the income distribution
- Classification approach:
  - Continuous exposure measures converted to binary variables by sorting occupations and defining “exposed” as occupations comprising the top 30 percent of total hours worked (30 percent threshold applied to both automation and AI for comparability with Moll et al. (2022)).
  - Exposure shares then calculated for each income percentile (total income including labor and non-labor).
- Key patterns:
  - Automation exposure is broadly decreasing in income:
    - Nearly 50 percent of workers in the lowest income percentiles were exposed to automation (as measured by RTI top 30 percent by hours worked).
    - Fewer than 20 percent of high-income workers were exposed to automation.
  - AI exposure is concentrated among higher-income workers:
    - Fewer than 20 percent of workers in the bottom income decile are exposed to AI.
    - Over 60 percent of workers in the top income decile are exposed to AI.
- Within-household correlation:
  - High degree of correlation in exposure within households (consistent with assortative matching), producing “very similar patterns in individual and household exposure.”
- Complementarity by income percentile:
  - Complementarity monotonically increases in income up to the 80th percentile, then levels off.
  - Highest-income workers, while most exposed to AI, are also more likely to be complementary with AI—mitigating potential displacement and implying possible productivity gains for those workers.

### Empirical findings — income, wealth, and portfolio composition
- Non-labor income and mitigation capacity:
  - Highest-income workers have the largest share of income from non-labor sources (capital income, pensions, investment returns), which could help mitigate negative employment consequences from AI exposure.
  - Realized investment income in WAS understates potential benefits because unrealized capital gains are not captured.
- Wealth concentration and risky asset exposure:
  - Total wealth is highly concentrated among high-income workers.
  - Share of workers’ wealth invested in “risky assets” (defined-contribution pensions, equities, corporate bonds) is much higher for high-earners than for low-income workers.
- Pension treatment:
  - Defined contribution (DC) pensions classified as risky assets for potential benefits from higher equity returns.
  - Defined benefit (DB) pensions treated as safe assets (similar to government bonds) since they guarantee fixed payments.

### Structural analysis — approach and channels
- Three channels brought together in a quantitative framework:
  - Negative: task displacement lowers real labor income.
  - Positive: productivity gains raise real labor income.
  - Positive: higher returns on capital increase capital income.
- Two-stage modeling strategy:
  - Baseline model: follows Moll et al. (2022) and treats technology adoption and capital shares as exogenous to isolate direct effects of exposure on labor and capital income.
  - Extended model (Section 5): endogenizes firms’ adoption decisions and capital use to capture amplified adoption and distributional impacts from AI cost savings on high-wage tasks.
- Mapping heterogeneity:
  - Each percentile of the worker income distribution is mapped into a sector z to capture heterogeneity in sector-level changes in the share of tasks performable by capital (αz).
- Capital supply elasticity:
  - Model incorporates finite capital supply elasticity via a “wealth dissipation shock” (probability p that assets disappear), yielding a non-degenerate wealth distribution and allowing technological innovation to raise the equilibrium return on capital.

### Baseline model specifics and assumptions
- Production structure:
  - Final good Y produced via Cobb-Douglas aggregation of intermediates Yz with weights ηz and ∑ηz = 1.
  - Each intermediate good is a continuum of tasks u aggregated via lnYz = ∫0^1 lnYz(u) du.
  - Share αz of tasks in sector z can be performed by capital; task output Yz(u) = ψz lz(u) + kz(u) if u ∈ [0, αz], and Yz(u) = ψz lz(u) if u ∈ (αz, 1].
  - In the baseline, capital is chosen for tasks it can perform as it is assumed cheaper; capital share in a sector equals αz.
- Households and preferences:
  - Households have Epstein-Zin preferences and face a probability p of a wealth dissipation shock.
  - Parameters noted: ρ (discount components), γ (risk aversion), σ (inverse intertemporal elasticity of substitution).
  - Only a fraction χ of households can invest in capital.
- Labor supply and mobility:
  - Households inelastically supply labor to their assigned sector z (no unemployment in model; workers displaced at task level but not from jobs).
  - No occupational switching in response to shocks—results reflect large switching costs or absence of retraining policies.
- Interpretation and limitations:
  - Model captures heterogeneity in exposure and capital holdings across income distribution.
  - Results represent impacts absent policies to promote retraining or occupational mobility; such policies could materially change welfare outcomes.

*Source: wpiea2025068-print-pdf*

### 4.2    Calibration of Technology Adoption

### 4.2    Calibration of Technology Adoption

### Calibration approach for sectoral capital shares and displacement
- Key parameter: sector-level capital shares αz determine displacement induced by automation and AI and must reflect exposure patterns documented in Section 3.
- Method: shift-share approach following Moll et al. (2022):
  - 1/(1−αz,2014) − 1/(1−αz,1980) = ωRz [1/(1−α2014) − 1/(1−α1980)]
  - This apportions the aggregate change in the capital share [1/(1−α2014) − 1/(1−α1980)] into sectoral changes using routine exposure ωRz.
  - Time interval for automation calibration: 1980-2014 (decades with pronounced automation adoption in industrialized economies).
- For AI:
  - Use exposure index ωAIOEz from Felten et al. (2021).
  - Baseline assumption: the change in the aggregate capital share over 2014-2048 in response to AI matches the change from 1980-2014 for automation (holds aggregate shock magnitude fixed to compare inequality impacts).
  - Sensitivity analysis on different aggregate capital share changes reported in Appendix B.

### Modeling sectoral complementarity with AI
- Complementarity modeled as change in sector weight ηz in the Cobb-Douglas production function in response to technology adoption (value-added of sectors with greater complementarity increases).
- Wage equation within a sector (intuitive form):
  - wz = (1−αz) ηz lz Y(K)
- Technological innovation can push wages down via higher αz or up via higher ηz.
- Calibration of ηz:
  - Initial ηz set to match the wage distribution in 2014.
  - For automation and baseline AI scenario: ηz kept fixed after adoption.
  - Complementarity scenario: ηz,T = ηz,0 (1 + λ), where λ captures relative complementarity across occupations.
  - Because ηz are sectoral weights that must sum to one, recalibrated ηz are renormalized—complementarity reallocates relative weights, increasing some sectors’ income at the expense of others.
- Alternative complementarity scenario allowing aggregate productivity gains:
  - In addition to ηz recalibration, set ψz,T = wzR /1.3*(1 + θz − θmin) to increase ψz (relative productivity) and raise aggregate productivity so all sectors can be better off while gains remain unevenly distributed.

### Calibration of remaining model parameters (UK)
- Wealth holdings: only defined contribution pension wealth included in measure of risky assets; defined benefit pensions treated as safe assets.
- Parameters (as described in Table 1):
  - σ Inverse IES: 2 (Standard)
  - γ Risk aversion: 2 (Standard)
  - p Dissipation rate: 4.5% (Moll et al.)
  - ρ Discount rate: 1% (Moll et al.; target r = 6.5%)
  - ξ Share investors: 10% (Target κ2014 = 1.35 and 1/ζ2014 = 0.46)
  - ν Capital risk: 6% (Target κ2014 = 1.35 and 1/ζ2014 = 0.46)
  - g TFP growth in ψz: 1.5% (Standard)
  - δ Depreciation rate: 5% (Standard)
  - A Productivity term: 0.143 Y/L in 2014
  - ηz,0 Sector shares: Match income distribution in 2014
  - ψz,0 Relative productivity of labor: - Moll et al. (cost savings of 30%)

### Baseline steady-state results (automation and AI, model predictions)
- Automation (1980-2014):
  - Task displacement fell predominantly on low-income households, suppressing their wages.
  - High-income households saw substantial increase in capital income, particularly the top 1 percent.
  - Inequality changes due to automation:
    - Wage Gini rose 2.05 p.p.
    - Wealth Gini rose 6.89 p.p.
- AI baseline (no complementarity, 2014-2048):
  - High-income workers most likely to see wage declines from AI displacement; low-income workers see wage gains due to higher aggregate productivity.
  - Wage inequality falls; wage Gini falls 1.73 p.p.
  - Capital income increases for highest-income workers offset wage declines, so total income for highest-income workers still rises.
  - Wealth inequality increases: wealth Gini rises 7.18 p.p.

### Accounting for complementarity (AI scenarios)
- Allowing sectoral complementarity (heterogeneous ηz changes):
  - Middle- and high-income workers have highest expected complementarity; despite displacement pressure they can gain wage increases from higher relative productivity.
  - Low-income workers have low complementarity and receive a lower share of productivity gains, lowering their wages.
  - Inequality outcomes with complementarity:
    - Wage Gini falls only 0.22 p.p. (muted reduction relative to baseline AI)
    - Wealth Gini increases to a similar degree as baseline AI
- Complementarity plus aggregate productivity gains:
  - Recalibrate ηz,T = ηz,0 (1 + θz) and set ψz = wzR /1.3*(1 + θz − θmin) to capture TFP increases conditional on adoption.
  - Under aggregate productivity gains, all workers are better off (higher base levels of all wages).
  - Inequality implications remain unchanged relative to the complementarity-only scenario because the differential effects across the distribution are the same.

### Quantitative scenario table (Table 2: changes in inequality metrics, aggregate productivity and output)
- Scenarios: Auto (baseline) | AI (baseline) | AI (comp. 1) | AI (comp. 2)
- Wage Gini: 2.05 p.p. | -1.73 p.p. | -0.22 p.p. | -0.22 p.p.
- Wealth Gini: 6.89 p.p. | 7.18 p.p. | 7.16 p.p. | 7.16 p.p.
- Capital Share: 5.5 p.p. | 5.5 p.p. | 5.5 p.p. | 5.5 p.p.
- Output: 9.6% | 10.6% | 10.6% | 12.2%
- Mean Wages: 0.2% | 0.2% | 0.2% | 1.6%

### Interpretation and limitations highlighted in the text
- Complementarity reallocates gains across sectors; some sectors and workers gain while others lose relative share.
- Model accounts for productivity gains through complementarity with existing tasks but does not capture creation of entirely new products, services, and occupations (new tasks) that historical technological revolutions produced; estimates therefore consider impacts only on existing occupations and may understate positive labor-market effects of AI.

*Source: wpiea2025068-print-pdf - 4.2    Calibration of Technology Adoption*

### 5.3    Calibration of Extended Model

### 5.3    Calibration of Extended Model

### Calibration approach and steps
- Two-stage calibration:
  - Stage 1: Calibrate economic environment parameters using historical data on automation from 1980 to 2014.
  - Stage 2: Use calibrated parameters to model potential impact of AI adoption from 2014 to 2048.
- Steps and assumptions:
  - Calibrate task complexity distribution parameter λ and Pareto shape parameter ξ to match the observed aggregate capital share in the UK in 1980 (pre-significant automation). These parameters jointly determine the initial distribution of tasks between capital and labor.
  - Model differential impact of automation across sectors using exposure measure ωz based on the Routine Task Index.
  - Benefits of adoption for each sector, βz, are calculated as βz = ν ωz, where ν is an exposure scalar.
  - Assume automation technology existed in 1980 but was not adopted due to high costs; calibrate initial adoption cost bauto,1980 such that there is initially no adoption, with the marginal firm indifferent between adopting and not adopting.
  - Capture evolution of adoption costs by setting final adoption cost bauto,2014 to be 20 percent of the initial cost, reflecting an 80 percent decline in the quality-adjusted price of industrial robots in the UK from 1980 to 2014.
  - Normalize technology scalar κ0 to 1.
  - Calibrate exposure scalar ν to match observed change in aggregate capital share in the UK between 1980 and 2014.

### AI scenario calibration
- Maintain same economic environment parameters (κ0, λ, ζ, and ν) calibrated for the automation scenario, implicitly assuming the economic environment remains unchanged between scenarios except for the existence of a new AI technology.
- Use a different exposure measure ωz based on occupational exposure to AI in Felten et al. (2021), producing a different distribution of adoption benefits βz proportional to this exposure.
- Calibrate initial AI adoption cost bai,2014 to match the observed aggregate capital share in the UK in 2014.
- Assume the same percentage decline in adoption costs for AI as observed for automation: set bai,2048 to be 20 percent of bai,2014.
- All other parameters are calibrated as in the baseline model.
- Robustness: Appendix C shows findings are robust to calibrating the AI scenario to have identical initial conditions to automation (e.g., matching the aggregate capital share and data aggregates for 1980 yields very similar results for inequality and adoption).

### Calibrated parameters (as presented in Table 3)
- κ0: Technology scalar — 1 (Free parameter)
- λ: Technology efficiency — 3 (Drodz et al. (2022))
- ζ: Task complexity dist. — 1.086 (Target capital share in 1980)
- βz: Benefits of adoption — ν ωz (Match exposure to automation and AI)
- ν: Exposure scalar — 0.203 (Target change in aggregate capital share)
- bauto,1980: Initial adoption cost — 1.3636 (Marginal firm indifferent to adoption)
- bauto,2014: Final adoption cost — 0.2 ∗ bauto,1980 (Graetz and Michaels (2018))
- bai,2014: Initial adoption cost — 0.5727 (Marginal firm indifferent to adoption)
- bai,2048: Final adoption cost — 0.2 ∗ bai,2014 (Match automation)

*Source: Table 3 in the content unit.*

---

### 5.4    Results of Extended Model

### General comparison to baseline model
- Automation:
  - Extended model results for automation closely mirror the baseline model.
  - Impacts on wages and total income are almost identical, with slightly less adoption at lower incomes offset by slightly more adoption at higher incomes.
  - Similarity partly by design due to calibration to historical data (1980–2014), constraining aggregate adoption.
- AI:
  - Extended model predicts significantly higher levels of AI adoption compared to both the baseline AI model and automation in the extended model.
  - Mechanism: AI is particularly adept at tasks performed by higher-paid workers, making automation of expensive, high-wage tasks more attractive and increasing adoption.

### Quantitative impacts and channels
- Increased AI adoption in extended model leads to:
  - Much larger change in the capital share for AI adoption: 10.2 p.p. (AI extended) versus 5.5 p.p. (AI baseline and automation scenarios).
  - Larger gains in productivity and output:
    - TFP growth: 1.7 percent (AI extended) versus 1.4 percent (AI baseline).
    - Output growth: 20.7 percent (AI extended) versus 10.6 percent (AI baseline).
  - Aggregate compensation to labor changes very little; average wages are almost unchanged in all scenarios because a lot of higher output accrues to capital.

### Inequality implications
- Wages:
  - Extended AI model predicts low-income workers see larger wage increases due to stronger productivity and output growth; higher-income workers experience larger wage decreases due to greater task displacement.
  - Wage Gini predicted to fall by 3.91 p.p. in the extended AI scenario versus a 1.73 p.p. decrease in the baseline AI model.
- Wealth and capital income:
  - Greater AI adoption raises return on capital and substantially increases capital income for highest-income households.
  - Wealth Gini projected to increase by 13.67 p.p. in the extended AI scenario versus 7.16 p.p. in the baseline AI model.
- Summary trade-off:
  - Extended model shows a pronounced effect: larger reduction in wage inequality (benefiting low-income workers) alongside a dramatic increase in wealth inequality driven by higher returns to capital.
  - Predicts potentially greater labor market implications than previous automation due to cost-savings from displacing expensive high-income workers.

### Key scenario outcomes (from Table 4)
- Scenarios: Auto (baseline) | Auto (extended) | AI (baseline) | AI (extended)
  - Wage Gini: 2.05 p.p. | 2.16 p.p. | -1.73 p.p. | -3.91 p.p.
  - Wealth Gini: 6.89 p.p. | 6.92 p.p. | 7.18 p.p. | 13.67 p.p.
  - Capital Share: 5.5 p.p. | 5.5 p.p. | 5.5 p.p. | 10.2 p.p.
  - Output: 9.6% | 9.6% | 10.6% | 20.7%
  - Mean Wages: 0.2% | 0.1% | 0.2% | -0.5%

---

### 6    Efficiency–Inequality Trade-Off and Policy Response

### Trade-off overview
- Endogenizing capital share and adoption reveals a meaningful policy trade-off between reducing inequality and maximizing efficiency:
  - Policies that reduce adoption (or tax adoption gains) can lower wealth inequality but also reduce output by discouraging adoption of productive technologies and inducing misallocation between labor and capital.
  - For AI, high adoption may lower wage inequality while increasing wealth inequality, complicating policy choices.

### Implementing a capital tax (Section 6.1)
- Motivation: Tax capital income to reduce rising wealth inequality directly (lower capital returns) and indirectly (discourage technology adoption).
- Trade-offs and alternatives:
  - Capital taxes reduce inequality but induce misallocation by distorting firms’ input choices between capital and labor.
  - Progressive labor income taxes could redistribute without distorting capital returns but would not directly address growing disparity in capital returns and could distort labor supply.
  - Wealth taxes target accumulated wealth rather than capital income flows; qualitatively similar to capital taxes in increasing effective cost of capital, but differ in practice and could affect sectors differently given heterogeneous returns.
  - More detailed modeling with heterogeneous assets, returns, and entrepreneurial abilities would be needed to fully capture differences between tax instruments; a full optimal tax analysis is beyond scope.
- Mechanics in the model:
  - A capital tax τK raises the effective cost of capital to (1 + τK) R.
  - Effects (Table 5):
    - Lowers threshold q* below which firms use capital instead of labor, creating misallocation even for non-adopting firms.
    - Reduces intensive margin of technology adoption n* by making capital investment less attractive.
    - Indirectly lowers adoption at the extensive margin by lowering q*.

### Tax impacts on firm decisions (from Table 5)
- Capital Share decision rule (with tax impact):
  - q* = max{ [wz / ((1+τK)R)]^{1/λ}, b^{-βz/λ} [ (wz / ((1+τK)R))^{1+βz/λ} ] }
- Extensive Margin:
  - qmin = κ^{1/βz}0 b (βz^{-1} + 1)^{1/(1+βz)} (exact functional form as in Table 5)
- Intensive Margin:
  - n* = [ 1 / ( b (1+τK) R / κ0 Zz q^{λ} ) ]^{1/(1+βz)}

---

### 6.2    Policy Simulations

### Government implementation details
- Introduce government sector that collects capital tax revenue and redistributes it to households as a Universal Basic Income (UBI).
- Government budget constraint:
  - T = τK R K, where T is total tax revenue and K is aggregate capital stock.
  - Under balanced budget, total government transfers equal T; per-household transfer is T / N.
- Modify household budget constraint to include UBI (lump-sum transfer T/N) and capital income tax.

### Calibration of policy simulations
- Impose τK = 15 percent.
- Revenue implications:
  - Under automation, τK = 15 percent would raise tax revenue equal to 4.8 percent of pre-tax GDP.
  - Under AI, τK = 15 percent would raise tax revenue equal to 5.6 percent of pre-tax GDP.
- Simulate impacts on inequality, capital share, output, and wages relative to final steady states without policy.

### Quantitative policy simulation outcomes (from Table 6)
- Scenario columns: τK: Auto | τK: AI
  - Wage Gini: -0.34 p.p. | 0.70 p.p.
  - Wage + UBI Gini: -3.83 p.p. | -3.44 p.p.
  - Wealth Gini: -2.12 p.p. | -3.74 p.p.
  - Capital Share: -0.80 p.p. | -1.60 p.p.
  - Output: -15.5% | -26.9%
  - Mean Wages: -8.7% | -11.8%

### Interpretation of simulation results
- Automation:
  - Capital tax reduces wage Gini by 0.34 p.p. pre-transfer and by 3.83 p.p. after UBI; wealth Gini falls by 2.12 p.p.
  - These reductions come at substantial output and wage costs: output falls by 15.5% and mean wages fall by 8.7%.
- AI:
  - Capital tax reduces wealth Gini by 3.74 p.p. and capital share by 1.60 p.p., but output falls by 26.9% and mean wages fall by 11.8%.
  - Pre-transfer wage Gini rises by 0.70 p.p., but after UBI wage Gini falls by 3.44 p.p.
- Overall trade-off:
  - Policies that raise effective cost of capital (e.g., capital taxes) can reduce inequality from AI adoption but at large efficiency costs (substantial declines in output and mean wages).
  - The welfare and distributional trade-offs are quantitatively large in these simulations, highlighting the difficult policy choices policymakers face when responding to AI-driven changes in capital returns and adoption.

*Italic line: Source: Section 5.3–6.2 (Calibration of Extended Model; Results; Efficiency–Inequality Trade-Off; Policy Simulations) from the provided content unit.*

### 15.5 percent and mean wages decline by 8.7 percent.  Note that the decline in output is larger

### wpiea2025068-print-pdf - 15.5 percent and mean wages decline by 8.7 percent.  Note that the decline in output is larger

### Aggregate effects of a capital tax on automation and AI adoption
- The capital tax reduces technology adoption and also lowers output of non-adopting firms by inducing misallocation, distorting their input mix away from capital.
- For automation at the discussed tax rate:
  - Aggregate output decline is larger than the increase in output due to automation.
  - Mean wages decline by 8.7 percent.
  - At this tax rate, the economy is "still on the increasing side of the Laffer curve in both scenarios."
- For AI at the discussed tax rate:
  - Output falls by 26.9 percent.
  - Mean wages decline by 11.8 percent.
- The deadweight loss is large: "the total income lost across all households exceeds the tax revenue raised by more than a factor of two."

### Distributional impacts across workers (pre- and post-transfer)
- Automation scenario (Figure 13a):
  - The capital tax reduces pre-transfer wages across the distribution to a largely similar extent.
  - Once accounting for a uniform transfer (UBI), the lowest-income households are ultimately better off.
  - The average post-transfer wage remains lower than the average pre-tax pre-transfer wage.
- AI scenario (Figure 13b):
  - Wealth Gini falls by 3.74 percentage points.
  - Wage inequality increases pre-transfer, rising 0.70 percentage points, because the tax particularly dampens AI adoption in high-wage occupations with largest productivity benefits.
  - UBI reduces post-transfer wage inequality by 3.44 percentage points.
  - Pre-transfer wage effects are most negative for low-income workers, as reduced AI adoption particularly limits productivity gains in their sectors.
  - Although the lowest-income workers ultimately benefit from the UBI, the average worker is substantially worse off due to the large decline in output.

### Structural model quantitative findings
- Under baseline assumption (occupational exposure to AI associated directly with task displacement):
  - Gini coefficient for wage inequality decreases by 1.73 percentage points.
  - Wealth Gini rises 7.18 percentage points.
- Routine-biased automation (for comparison):
  - Wage Gini rises by 2.05 percentage points.
  - Wealth Gini rises by 6.89 percentage points.
- Allowing for complementarity between labor and AI:
  - Mitigates the fall in wages expected for high-income workers, limiting or possibly preventing a decrease in wage inequality.
- An increase in aggregate productivity from AI would partly compensate for task displacement, increasing the share of workers unconditionally better off and further raising capital returns.

### Policy trade-offs, political economy, and implications
- There is an inherent welfare trade-off between equity and aggregate productivity:
  - Capital taxes can reduce wealth inequality and protect lowest-income households through redistribution, but at significant costs to output and average living standards.
  - The costs to output and productivity from redistributive policies appear to be larger for AI than for previous waves of automation.
  - A cited policy simulation: a 15 percent capital tax could substantially reduce post-transfer inequality, but the associated costs to output and productivity would be nearly twice as large for AI as for previous waves of automation.
- Political-economy feedbacks may alter adoption:
  - Labor market disruptions and widening wealth inequality could slow adoption through regulatory restrictions or other interventions.
  - Productivity benefits could create constituencies that accelerate adoption.
  - These feedback loops could produce adoption patterns different from the model’s predictions, affecting both efficiency and equity implications of AI.

### Conclusions emphasized by the authors
- AI may affect inequality through multiple channels: decreasing wage inequality via labor market disruption while increasing wealth inequality via higher capital income for wealthy households.
- High-income workers:
  - Are much more likely to work in occupations exposed to new AI technologies (roughly 60 percent of workers at the 90th income percentile vs. 15 percent at the 10th percentile).
  - Have the lowest share of total income from wages, the largest wealth holdings, and the largest share of their wealth in risky but high-return assets such as equity—positioning them to both insure against labor-market impacts and benefit from higher capital returns.
  - Are more likely to be complementary with AI, possibly reducing their risk of job loss relative to past automation waves.
- The amplified adoption potential of AI intensifies both productivity gains and inequality impacts, presenting a starker policy trade-off than with previous technologies.
- A full optimal policy analysis is left to future work.

*https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025068-print-pdf.pdf*

### References

### References and Appendices (wpiea2025068-print-pdf - References)

### Key citations and thematic literature
- Extensive bibliography on automation, AI, labor markets, and distribution, including:
  - Acemoglu and Autor (2011); Acemoglu et al. (2022); Acemoglu and Restrepo (2018, 2019, 2022).
  - Autor and Dorn (2013); Autor, Katz, and Kearney (2006); Autor, Levy, and Murnane (2003).
  - Moll, Rachel, and Restrepo (2022); Benhabib, Perla, and Tonetti (2021); Korinek and Stiglitz (2017, 2018).
  - Sectoral and country-focused work: Albania, Brazil statistics (Brazil (2019); DataZoom (2023)); OECD (2021, 2023).
  - IMF and NBER working and staff discussion notes on Gen-AI and AI exposure (Cazzaniga et al. (2024); Brynjolfsson et al. (2023); Brollo et al. (2024); Hebous et al. (2024); Eloundou et al. (2023)).
- Empirical and methodological sources on task-based models, occupational exposure datasets, and job ad analyses (Alekseeva et al. (2021); Felten et al. (2021, 2023); Pizzinelli et al. (2023)).

### Appendix A — Model details (endogenizing the capital share)
- Framework summary:
  - Final good Y is a Cobb-Douglas aggregate of intermediate goods Yz with shares ηz and ∑z ηz = 1 (equation (14)).
  - Each intermediate good Yz is a Cobb-Douglas aggregate across a continuum of tasks with complexity q (equation (15)).
  - Capital requirements for tasks are upward sloping in complexity: kz(q) = Zz qλ (equation (16)); labor requirement lz(q) = Zz (equation (17)).
  - Tasks are priced by whether they are performed by capital (for q ∈ [0, q∗]) or labor (for q ∈ (q∗, ∞)) (equation (18)); task prices pz(q) given in (19).
  - Endogenous threshold q∗ solves q∗ = (wz/ψz R)1/λ (equation (20)).
- Distributional assumption:
  - Tasks in each sector follow a Pareto distribution gz(q) = ξ q−ξ−1 with 0 < ξ < λ.
- Factor intensities and capital share:
  - Expressions for kzyz and lzyz as integrals over task space (equations (23)–(26)).
  - Derived production form Yz = (kz)ξ/λ ξ/λ (ψz lz)1−(ξ/λ) 1−ξ/λ (equation (27)).
  - Capital share αz = ξ/λ.
  - Aggregate capital market clearing yields K = α Y / R and Y = A Kα Yz (ψz lz)(1−αz)ηz with normalization and A defined in (31)–(32).
- Endogenous technology adoption (intensive and extensive margins):
  - Adoption reduces capital needs by κ(n); κ(n) = κ0 β−1 n−β with 0 < β < λ − 1, κ0 > 0, κ < 1 (equation (33)).
  - Intensive-margin optimal n∗ = [1 / b κ0 Zz qλ]1/(1+β) (equation (34)).
  - Extensive-margin adoption threshold qmin solves Zz qλmin = κ 1/β 0 b(β−1 + 1)1+β/β (equation (36)).
  - Piecewise expression for q∗ with adoption in (37) and compact form in (38).
  - Task-level prices under adoption are given in (35).
- Production functions with adoption:
  - For non-adopting firms, kzyz and lzyz given by (39)–(42).
  - For adopting firms, kzyz integrates over three regions; lzyz = Z q∗−ξ (equations (43)–(45)).
  - Combined expression for αz in (46) with factor-intensity ratio in (47).
  - General production function holds: Yz = (kz)ξ/λ ξ/λ (ψz lz)1−(ξ/λ) 1−ξ/λ (equation (48)).

### Appendix A.2 — Impact of capital taxes
- Capital income tax specification:
  - Tax rate τK raises effective cost of capital: Rafter−tax = (1 + τK) R.
  - Task assignment threshold becomes q∗ = min ((wz (1 + τK) R)1/λ, b−βz/λ (wz (1 + τK) R)(1+β)z/λ ) (equation (49)).
  - Intensive-margin adoption n∗ = [1 / b(1 + τK) R κ0 Zz qλ]1/(1+β) (equation (50)).
  - Extensive-margin qmin: Zz qλmin = κ1/β0 b(1 + τK) R(β−1z + 1)1+βz/βz (equation (51)).
  - Task-level prices under tax in (52).
  - Resulting factor intensities kzyz and lzyz in (53)–(54).
- Government budget and transfers:
  - Tax revenue funds a Universal Basic Income (UBI). Government budget: T = τK R K (equation (55)).
  - Household budget constraint incorporates capital tax and per-household UBI transfer T / N (equation (56)).
  - Equilibrium sector wage expression provided in (57).
  - Capital market clearing under tax: K = α Y / (1 + τK) R (equation (58)).
  - Aggregate output under the capital tax: Y = A Kα Yz (ψz lz)(1−αz)ηz with A adjusted for tax distortions (equations (59)–(60)).

### Appendix B — Additional results (empirical fit and scenario analysis)
- Empirical results and figures:
  - Figure B.1: Household Exposure to Automation and AI by Income Percentile.
  - Figure B.2: Comparison of Baseline and Extended Model Fit for Wages — both models fit UK wage changes 1980–2014 relatively well but miss the relatively smaller decline for the lowest income workers (National Minimum Wage effect noted).
- Scenario analyses:
  - Displacement vs productivity scenarios: changing aggregate capital share alters the ‘tilt’ of wage impacts; changing aggregate productivity shifts the entire wage-change curve higher with no impact on inequality (Figure B.3).
  - Capital supply elasticity scenarios: lower capital supply elasticity leads to lower wages overall and higher return to capital, boosting total income for highest-income workers (Figure B.4).
  - Figures illustrate predicted impacts of AI on wages and total income over 2014–2048 (Figures B.3 and B.4).

### Appendix C — Calibration robustness
- Robustness check:
  - Calibration of the extended model to 1980 aggregate capital share yields very similar results for inequality and adoption compared to calibration to 2014.
  - Figure C.1: Change in Wages by Income Percentile — baseline AI scenario in red vs extended model calibrated to 1980 in black; percent change in wages by total income percentile shown.

*Source: wpiea2025068-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025068-print-pdf.pdf_