Uneven Growth Automation’s Impact on Income and Wealth Inequality Benjamin Moll Lukasz Rachel Pascual Restrepo Oxford, 11 February 2020
Uneven Growth in the United States: Stagnant incomes at bottom, rising incomes at top Source: U.S. Census (2015) 1 Income in thousands (2014 dollars) Recession 220 $206,600 200 180 95th 160 $157,500 $117,800 140 90th 120 100 $93,200 80 50th (median) 60 $44,300 $53,700 40 $10,100 10th 20 $12,300 0 1967 1975 1980 1985 1990 1995 2000 2005 2010 2014
Candidate Cause: Technology inequality & capital inc SYZZ 1 • Huge literature: technology afgects wage inequality • Examples: SBTC and polarization of wages • But what about capital income and wealth?
What We Do = technologies that substitute labor for capital in production 1. macro aggregates 2. factor income distribution: capital vs labor 3. personal income, wealth distribution 2 • Theory that links tech to income & wealth distribn, not just wages • Use it to examine distributional efgects of automation technologies • Tractable framework to study dynamics of • Key modeling difgerence to growth model: perpetual youth ⇒ • nondegenerate wealth distribution • long-run capital supply elasticity < ∞
Our Main Point why now? Analytic version in our theory: 2. Automation may lead to stagnant wages and lackluster investment Paraphrasing these results owning lots of robots rather than “workers” 3 Technology ⇒ returns ⇒ distributional consequences return to wealth = ρ + σ g + premium ( α ) where α = capital share = average automation 1. New mechanism: technology increases inequality via return to wealth • income/wealth distributions have Pareto tail with fatness = α • productivity gains partly accrue to capital owners • α := R × K Y and part of α ↑ shows up in R not K / Y • if “robots” increasingly outperform labor, this benefjts people
How does this square with trends in returns? Just told you that 4 return to wealth = ρ + σ g + premium ( α ) But haven’t treasury rates decreased over time? Panel (a): Returns Panel (b): Returns - σ × g 8 8 return in p.p., rel. to 1980 return in p.p., rel. to 1980 After-tax return business capital After-tax return business capital - σ × g 6 6 After-tax ROIC After-tax ROIC - σ × g HLW estimate of r* HLW estimate of r* - σ × g 4 4 2 2 0 0 -2 -2 1960 1970 1980 1990 2000 2010 1960 1970 1980 1990 2000 2010 1. Treasury rates = return on specifjc asset, ave return on US capital ↑ 2. Model w risky & safe assets: relevant r = ∑ J j = 1 r j × portfolio share j 3. Inequality depends r − ρ − σ g . Even if r ↓ , arguably r − ρ − σ g ↑ .
Model Meets Data 5 • Calibrate incidence of automation using exposure to routine jobs • accounts for changes in wage inequality 1980-2014 • Conservative (i.e. high) value for long-run capital supply elasticity • Examine consequences of automation for • aggregates? Small expansions in I , Y • income, wealth inequality? Sizable increase, uneven growth • wages? Stagnation except for top of distribution • Small shock (3% inc in TFP) can have large distributional efgects
Small productivity gains but large distributional efgects 6 Change in income by percentile of the income distribution 1 60 60 Total income growth in our model 0.9 Total income growth in rep. household model 50 50 0.8 40 40 0.7 percent change 30 0.6 30 0.5 20 20 0.4 10 10 0.3 0 0 0.2 0.1 -10 -10 0 0 20 40 60 80 100 99 99.5 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 income percentile top tail
Literature and Contribution Automation and inequality (Acemoglu-Restrepo, Caselli-Manning, Hémous-Olsen, ...) Technology and wealth distribution (Kaymak-Poschke, Hubmer-Krusell-Smith, Straub ,...) Returns as driver of top wealth inequality (Piketty, Benhabib-Bisin, Jones,...) Tractable theory of macro aggregates, factor and personal income dist Perpetual youth literature (Blanchard) : closed form for wealth distribution 7 • capital income & wealth, not just wages • capital supply elasticity < ∞ very difgerent from = ∞ • new mechanism: technology ⇒ return ⇒ wealth inequality (in addition to: technology ⇒ wage dispersion ⇒ wealth inequality) • tractable form of capital income risk, integrated in macro model • Piketty: r − g ↑ due to lower taxes, lower g . This paper: technology.
Plan 1. Framework and model of automation 2. Steady state 3. Transition dynamics – skip today 4. Model meets data 8
1. Framework: Households and Technology 8
wealth inequality Model has two key building blocks (Benhabib-Bisin, Piketty, Jones, ...) 9 Long-run capital supply elasticity < ∞ (Aiyagari,...) Capital Supply returns ⇒ + Capital Demand • Our paper: model this in very stylized fashion – perpetual youth • cost: some unrealistic implications • payofg: analytic solution for everything incl distributions • Same mechanisms would be present in richer, less tractable models
Framework: Perpetual Youth Households s.t. Households: age s , skills z , solve 0 ∫ ∞ e − ( ϱ + p ) s c z ( s ) 1 − σ max ˙ a z ( s ) = ra z ( s ) + w z − c z ( s ) 1 − σ ds { c z ( s ) , a z ( s ) } s ≥ 0 • w z : wage for skill z , ℓ z households • r : return to wealth • ϱ : discount rate • p : probability of dying ( p = 0 ⇒ rep agent) • ρ = ϱ + p : efgective discount rate Key assumption: “imperfect dynasties” • average wealth of newborn < average wealth of living • stark implementation: eat wealth when die ⇒ no bequests, a z ( 0 )= 0 • other mechanisms: annuities, pop growth, estate taxation • perpetual youth = just tractable stand-in for other sources of churn 10
Framework: Technology (Zeira, Acemoglu-Restrepo) z 3. Capital mobile across sectors, labor immobile Task-based model: machines/software substitute for tasks, not jobs with z z 1. Each skill type z works in difgerent sector that produces Y z First: “reduced form” production side, next slide: where this comes from 11 ∏ ∑ Y γ z Y = A γ z = 1 2. Y z produced using Cobb-Douglas tech with skill-specifjc exponent α z ) α z ( ψ z ℓ z ( k z ) 1 − α z Y z = α z 1 − α z α z = share of tasks technologically automated. Automation: α z ( t ) ↑
Derivation from Task-based Model (Zeira, Acemoglu-Restrepo) Comes out of following task-based model: For simplicity, derivation with only one skill type. Reduced form: 0 12 ) α ( ψ L ( K ) 1 − α Y = ( ∗ ) α 1 − α 1. Final good produced combining unit continuum of tasks u ∫ 1 ln Y ( u ) du ln Y = 2. Tasks produced using capital k ( u ) or labor ℓ ( u ) at prices R and w { ψℓ ( u ) + k ( u ) if u ∈ [ 0 , α ] Y ( u ) = ψℓ ( u ) if u ∈ ( α, 1 ] • α = share of tasks technologically automated. Automation: α ( t ) ↑ • Example: HR manager, tasks = screen CVs, interview applicants,... • Displacement vs productivity efgects
• 1. and 2. with k u Derivation from Task-based Model (Zeira, Acemoglu-Restrepo) 0 imply ( ). 1 L u K L ) For simplicity, derivation with only one skill type. Reduced form: 13 1. Final good produced combining unit continuum of tasks u Comes out of following task-based model: ) α ( ψ L ( K ) 1 − α Y = ( ∗ ) α 1 − α ∫ 1 ln Y = ln Y ( u ) du 2. Assumption 1 (full adoption): w /ψ > R (suffjcient to have L < ¯ { ψℓ ( u ) + k ( u ) if u ∈ [ 0 , α ] Y ( u ) = ψℓ ( u ) if u ∈ ( α, 1 ]
Derivation from Task-based Model (Zeira, Acemoglu-Restrepo) Comes out of following task-based model: L ) 0 For simplicity, derivation with only one skill type. Reduced form: 1. Final good produced combining unit continuum of tasks u 13 ) α ( ψ L ( K ) 1 − α Y = ( ∗ ) α 1 − α ∫ 1 ln Y = ln Y ( u ) du 2. Assumption 1 (full adoption): w /ψ > R (suffjcient to have L < ¯ { k ( u ) if u ∈ [ 0 , α ] Y ( u ) = ψℓ ( u ) if u ∈ ( α, 1 ] • 1. and 2. with k ( u ) = K /α, ℓ ( u ) = L / ( 1 − α ) imply ( ∗ ). □
2. Characterizing Steady State 13
Output, Factor Payments and Capital Demand K R 1 14 z • Aggregate output: z γ z α z ∏ ∑ ( ψ z ℓ z ) γ z ( 1 − α z ) Y = A K α = ∑ z γ z α z : aggregate capital-intensity, A = constant ( α z , γ z ) • Factor payments: w z ℓ z = ( 1 − α z ) γ z Y , RK = α Y , w = ( 1 − α ) Y α z ’s ⇒ relative wages, factor shares. But efgect on levels unclear • Aggregate capital demand α w = ¯ 1 − α • Expositional assumption for presentation: g = 0 , δ = 0 ⇒ R = r
Steady State Capital Supply r dynasties Imperfect pK surviving households Wealth accumulated by r 1 Households’ consumption and saving decisions: r Useful later: relevant state = efgective wealth = assets + human capital 15 r ( ρ − r ) ( ) c z ( s ) = + r a z ( s ) + w z σ ( ) ˙ a z ( s ) = 1 σ ( r − ρ ) a z ( s ) + w z ( ∗ ) x z ( s ) := a z ( s ) + w z Find aggregate capital supply by integrating ( ∗ ) with w := ∑ z w z ℓ z : ( ) 1 − ρ/ r 0 = ˙ K = σ ( r − ρ ) K + w − ⇒ K w = ¯ ρ + p σ − r � �� � ����
Steady-State Equilibrium: Return to Wealth 16
Same diagram as in richer theories (Aiyagari, Benhabib-Bisin,...) 17
18 Automation ⇒ higher r and modest expansion in K
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