Artificial Intelligence and Economic Growth Aghion, B. Jones, and C. Jones October 2017 1 / 43
What are the implications of A.I. for economic growth? • Build some growth models with A.I. ◦ A.I. helps to make goods ◦ A.I. helps to make ideas • Implications ◦ Long-run growth ◦ Share of GDP paid to labor vs capital ◦ Firms and organizations • Singularity? 2 / 43
Two Main Themes • A.I. modeled as a continuation of automation ◦ Automation = replace labor in particular tasks with machines and algorithms ◦ Past: textile looms, steam engines, electric power, computers ◦ Future: driverless cars, paralegals, pathologists, maybe researchers, maybe everyone? • A.I. may be limited by Baumol’s cost disease ◦ Baumol: growth constrained not by what we do well but rather by what is essential and yet hard to improve 3 / 43
Outline • Basic model: automating tasks in production • A.I. and the production of new ideas • Singularity? • Some facts • Organization of firms and wage inequality 4 / 43
The Zeira 1998 Model 5 / 43
Simple Model of Automation (Zeira 1998) • Production uses n tasks/goods: Y = AX α 1 1 X α 2 2 · ... · X α n n , n � where α i = 1 and i = 1 if not automated L it X it = K it if automated • Substituting gives Y t = A t K α t L 1 − α t 6 / 43
Y t = A t K α t L 1 − α t • Comments: ◦ α reflects the fraction of tasks that are automated ◦ Embed in neoclassical growth model ⇒ g A g y = where y t ≡ Y t / L t 1 − α • Automation: ↑ α raises both capital share and LR growth ◦ Hard to reconcile with 20th century ◦ Substantial automation but stable growth and capital shares 7 / 43
Subsequent Work • Acemoglu and Restrepo (2017) ◦ Old tasks are gradually automated as new (labor) tasks are created ◦ Fraction automated can then be steady ◦ Rich framework, with endogenous innovation and automation, all cases worked out in great detail • Peretto and Seater (2013), Hemous and Olson (2016), Agrawal, McHale, and Oettl (2017) 8 / 43
Automation and Baumol’s Cost Disease 9 / 43
Baumol’s Cost Disease and the Kaldor Facts • Baumol: Agriculture and manufacturing have rapid growth and declining shares of GDP ◦ ... but also rising automation • Aggregate capital share could reflect a balance ◦ Rises within agriculture and manufacturing ◦ But falls as these sectors decline • Maybe this is a general feature of the economy! ◦ First agriculture, then manufacturing, then services 10 / 43
Model • Production is CES in tasks, with EofS < 1 (complements) �� 1 � 1 /ρ X ρ Y t = A t it di where ρ < 0 (Baumol) 0 • Let β t = fraction of tasks automated by date t : � ρ � 1 /ρ � ρ � � K t � L Y t = A t β t + ( 1 − β t ) β t 1 − β t Y t = A t (( B t K t ) ρ + ( C t L ) ρ ) 1 /ρ = ⇒ 1 ρ − 1 1 ρ − 1 where B t = β and C t = ( 1 − β t ) t • Note: increased automation ⇒ ↓ B t and ↑ C t since ρ < 0 . (e.g. a given amount of capital is spread over more tasks.) 11 / 43
Factor Shares of Income • Ratio of capital share to labor share: � 1 − ρ � K t � ρ � α K t β t = α L t 1 − β t L t • Two offsetting effects ( ρ < 0 ): ◦ ↑ β t raises the capital share ◦ ↑ K t / L t lowers the capital share If these balance, constant factor shares are possible 12 / 43
Automation and Asymptotic Balanced Growth • Suppose a constant fraction of non-automated tasks become automated each period: ˙ β t = θ ( 1 − β t ) Then β t → 1 and C t grows at a constant rate! • With Y t = F ( B t K t , C t L t ) , balanced growth as t → ∞ : ◦ All tasks eventually become automated ◦ Agr/Mfg shrink as a share of the economy... ◦ Labor still gets 2/3 of GDP! Vanishing share of tasks, but all else is cheap (Baumol) 13 / 43
Simulation: Automation and Asymptotic Balanced Growth GROWTH RATE OF GDP 3% 2% 1% 0% 0 50 100 150 200 250 300 350 400 450 500 YEAR 14 / 43
Simulation: Capital Share and Automation Fraction 1 0.9 Fraction automated, t 0.8 0.7 0.6 0.5 Capital share K 0.4 0.3 (also automated share of GDP) 0.2 0.1 0 0 50 100 150 200 250 300 350 400 450 500 YEAR 15 / 43
Constant Factor Shares? • Consider g A > 0 — technical change beyond just automation • Alternatively, factor shares can be constant if automation follows � − ρ � g β t = ( 1 − β t ) g kt , 1 − ρ • Knife-edge condition... • Surprise: growth rates increase not decrease. Why? Requires g Yt = g A + β t g Kt . • g A = 0 means zero growth. g A > 0 means growth rises 16 / 43
Simulation: Constant Capital Share 0.7 Fraction automated, t 0.6 0.5 0.4 0.3 Capital share K 0.2 0.1 0 0 50 100 150 200 250 300 YEAR 17 / 43
Simulation: Constant Capital Share GROWTH RATE OF GDP 5% 4% 3% 2% 0 50 100 150 200 250 300 YEAR 18 / 43
Simulation: Switching regimes... GROWTH RATE OF GDP 3% 2% 1% 0% 0 50 100 150 200 250 300 YEAR 19 / 43
Simulation: Switching regimes... 1 0.9 Fraction automated, t 0.8 0.7 0.6 0.5 Capital share K 0.4 0.3 0.2 0.1 0 50 100 150 200 250 300 YEAR 20 / 43
A.I. and Ideas 21 / 43
AI in the Ideas Production Function • Let production of goods and services be Y t = A t L t • Let idea production be: �� 1 � 1 /ρ A t = A φ ˙ X ρ it di , ρ < 0 t 0 • Assume fraction β t of tasks are automated by date t . Then: A t = A φ ˙ t F ( B t K t , C t S t ) where 1 − ρ 1 − ρ ρ B t ≡ β ; C t ≡ ( 1 − β t ) ρ t • This is like before... 22 / 43
AI in the Ideas Production Function • Intuition: with ρ < 0 the scarce factor comes to dominate � B t K t � F ( B t K t , C t S t ) = C t S t F , 1 → C t S t C t S t • So, with continuous automation A t → A φ ˙ t C t S t • And asymptotic balanced growth path becomes g A = g C + g S 1 − φ • We get a “boost” from continued automation ( g C ) 23 / 43
Can automation replace population growth? • Maybe! Suppose S is constant, g S = 0 ◦ Intuition: Fixed S is spread among exponentially-declining measure of tasks ◦ So researchers per task is growing exponentially! • However ◦ This setup takes automation as exogenous and at “just the right rate” ◦ What if automation is endogenized? ◦ Is population growth required to drive automation? ◦ Could a smart/growing AI entirely replace humans? 24 / 43
Singularities 25 / 43
Singularities • Now we become more radical and consider what happens when we go “all the way” and allow AI to take over all tasks. • Example 1: Complete automation of goods and services production. Y t = A t K t → Then growth rate can accelerate exponentially g Y = g A + sA t − δ we call this a “Type I” growth explosion 26 / 43
Singularities: Example 2 • Complete automation in ideas production function A t = K t A φ ˙ t • Intuitively, this idea production function acts like A t = A 1 + φ ˙ t • Solution: � 1 /φ � 1 A t = A − φ − φ t 0 • Thus we can have a true singularity for φ > 0 . A t exceeds any finite value before date t ∗ = 1 . φ A φ 0 27 / 43
Singularities: Example 3 – Incomplete Automation • Cobb-Douglas, α and β are fraction automated, S constant ˙ sLA σ t K α K t = ¯ t − δ K t . A t = K β ˙ t S λ A φ t • Standard endogenous growth requires γ = 1 : σ β γ := 1 − α · 1 − φ. • If γ > 1 , then growth explodes! ◦ Can occur without full automation ◦ Example: α = β = φ = 1 / 2 and σ > 1 / 2 . 28 / 43
Objections to singularities 1 Automation limits (no β t → 1 ) 2 Search limits A t = A 1 + φ ˙ t but φ < 0 (e.g., fishing out, burden of knowledge...) 3 Natural Laws �� 1 � 1 /ρ ( a it Y it ) ρ Y t = where ρ < 0 0 now can have a it → ∞ for many tasks but no singularity (cf. Moore’s Law vs. Carnot’s Theorem) ◦ Baumol theme: growth determined not by what we are good at, but by what is essential yet hard to improve 29 / 43
Some Facts 30 / 43
Capital Shares in U.S. Industries 1 Petroleum Mfg. Oil/Gas Extraction 0.8 Utilities 0.6 Agriculture 0.4 Construction 0.2 0 1940 1960 1980 2000 2020 31 / 43
Capital Shares in U.S. Industries 1 Chemicals 0.8 0.6 Motor Vehicles 0.4 Plastics Computers 0.2 Furniture 0 1940 1960 1980 2000 2020 32 / 43
Capital Shares in U.S. Industries 1 0.8 Movies 0.6 Publishing Air Trans. Wholesale 0.4 0.2 Retail 0 1940 1960 1980 2000 2020 33 / 43
Capital Shares in U.S. Industries 1 0.8 Telecommunications 0.6 Federal Govt 0.4 Health (hospitals) 0.2 Education Health (ambulatory) 0 1940 1960 1980 2000 2020 34 / 43
Capital Share of Income: Transportation Equipment CAPITAL SHARE 55 50 U.S. 45 Spain 40 35 Italy 30 Germany 25 20 U.K. France 15 10 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 YEAR 35 / 43
Recommend
More recommend
