Modeling Automation†

AEA Papers and Proceedings 2018, 108: 48–53 https://doi.org/10.1257/pandp.20181020

By Daron Acemoglu and Pascual Restrepo*

Computer-assisted machines, robotics, and of substitution between capital and labor—an artificial intelligence AI have already spread object that plays a different role and governs in many industries and( automated) several parts how factor prices affect the use of capital and of the production process. However, we are far labor. from a consensus on how automation should be In contrast, in a task-based framework, auto- conceptualized and modeled. mation, conceptualized as the expansion of the Most economic models formalize technolog- set of tasks that can be produced by machines, ical change as factor augmenting meaning that has very different effects. It always reduces the technological progress acts as if it( increased the labor share and it reduces labor demand and the effective units of one of the factors of production equilibrium wage unless the productivity gains or as Hicks neutral which leads to a proportion)- from automation are sufficiently large. ate increase in the( output obtained from any A task-based approach to modeling automa- input combination . Several authors, including tion also brings new ideas to the table. First, it Sachs and Kotlikoff) 2012 , Graetz and Michaels clarifies that the technologies most threatening to 2015 , and Nordhaus( 2015) , also model auto- labor are not those that are major breakthroughs (mation) as capital-augmenting( ) technological increasing productivity greatly, but those that change, which assumes that automation should are “so-so”—good enough to be adopted but be thought of as embodied in more productive not so good that they increase productivity by or cheaper capital, which will then substitute much. Second, it highlights the important role for( labor in) a process governed by the elastic- of new tasks in which labor has a comparative ity of substitution. Bessen 2017 , on the other advantage in counterbalancing the effects of hand, argues that automation( mostly) increases automation. Third, it enables a discussion of the productivity of labor and models automation the implications of deepening of automation, as labor-augmenting technological change. meaning an improvement in the productivity of We argue that these approaches miss a distinc- machines in tasks that have already been auto- tive feature of automation: the use of machines mated. Fourth, it clarifies that the role of capital to substitute for human labor in a widening range accumulation is distinct from the effects of auto- of tasks Acemoglu and Restrepo, forthcom- mation on the labor share and implies that capi- ing, 2018—henceforth,( AR . Partly as a result, tal accumulation dampens the negative effects of factor-augmenting technologies) have a limited automation on wages if there are such negative scope to reduce the demand for labor this never effects and the labor (share if the elasticity of happens with capital-augmenting technologies,( substitution) is less than one . (Finally, this frame- and can only happen with labor-augmenting work can be generalized to) study the implica- technologies for unrealistic parameter values . tions of shortages of different types of skills and In addition, these approaches relate the impact) the conditions under which there may be exces- of technology on the labor share to the elasticity sive automation.

I. Factor-Augmenting Technologies * Acemoglu: Massachusetts Institute of Technology email: [email protected] ; Restrepo: Boston University Suppose aggregate output is given by (email: [email protected] ). We gratefully acknowledge finan- ( ) cial support from Google, Microsoft, the Sloan Foundation, Y F A K, A L , and the Toulouse Network on Information Technology. = ( K L ) † Go to https://doi.org/10.1257/pandp.20181020 to visit the article page for additional materials and author disclo- where K denotes capital, L is labor, and sure statement s . A and A denote capital-augmenting and ( ) K L 48 VOL. 108 MODELING AUTOMATION 49

labor-augmenting technology, respectively. We Mathematically, this result follows because assume throughout that F is continuously differ- of constant returns to scale. Economically, entiable, concave, and exhibits constant returns constant returns to scale imposes that capital to scale. Let FK and FL denote the derivatives of and labor are q-complements, and anything that F with respect to capital and labor. increases the productivity of capital or makes We focus on competitive labor markets, which capital effectively more abundant increases the implies that the equilibrium wages are equal to marginal product of labor. the marginal product of labor, The effect of capital-augmenting technological change on the labor share is in turn given by W A F A K, A L . = L L ( K L ) _d ln sL _1 sK 1 , The labor share in national income is given by d ln AK = (εKL − ) which is negative if and only if 1 .2 Thus, s _WL , KL L = Y capital-augmenting technologyε reduces> the labor share only if the elasticity of substitution and because of constant returns to scale, the cap- between capital and labor is greater than one. ital share is sK 1 sL. There is a debate on whether we should view = − the elasticity of substitution between capital and A. Capital-Augmenting Technological Change labor as less than or greater than one. Recent estimates that exploit cross-country differences Suppose first that we model automation as put it to be greater than one Karabarbounis capital-augmenting technological change. The and Neiman 2014 , while the bulk( of the evi- impact of this type of technological change on dence in the literature) places it to be between the equilibrium wage is given by 0.5 and 1 see Oberfield and Raval 2014 and the references( therein . If we follow this broad ) _d ln W _sK consensus in the literature, capital-augmenting 1 0, ( ) d ln AK = εKL > technological progress increases the labor share. In summary, if automation were to be con- where ceptualized as capital-augmenting technological change, it would never reduce labor demand or ______d ln K L the equilibrium wage, and it would increase the 2 KL ( / ) 0 ( ) ε = − d ln FK FL > labor share—two predictions that are neither ( / ) intuitively appealing nor always consistent with is the elasticity of substitution between cap- the evidence see, e.g., AR 2017, for evidence ital and labor.1 Thus, capital-augmenting that robots have( a negative impact on local technology always increases labor demand and employment and wages . the equilibrium wage. ) B. Labor-Augmenting Technological Change

Let us next turn to the implications of 1 Let us rewrite 2 as labor-augmenting technologies, AL . We have ( ) d ln F d ln F d ln A K d ln A L . εKL ( K − L ) = −[ ( K ) − ( L )] _d ln W _sK 3 1 , Then using the facts that d ln R d ln FK d ln AK; ( ) d ln AL = − KL d ln W d ln F d ln A ; d ln K d ln= L 0 because+ of ε = L + L = = ( inelastic supplies ; and d ln AL 0 because technological change is capital augmenting) , we= obtain( ) d ln W d ln R 1 d ln A . εKL ( − ) = ( − εKL ) K Also, because F exhibits constant returns to scale, we have 2 Y RK WL. Log differentiating this equation, we obtain Since labor is supplied inelastically, we d ln s = + have _ L _ d ln W _ d ln Y . The result is obtained s d ln A s d ln R s d ln W. d ln A d ln A d ln A K K = K + L K = K − K _d ln Y Combining these two equations yields 1 . by observing that = sK and combining this with 1 . ( ) d ln AK ( ) 50 AEA PAPERS AND PROCEEDINGS MAY 2018

3 which is positive provided that KL sK . ensures that the measure of tasks is normalized Thus, labor-augmenting technologicalε change> to 1, simplifying the discussion. increases the equilibrium wage unless the elas- Suppose that tasks i I are technologically ticity of substitution between capital and labor non-automated and have> to be produced by labor is very low. If we take the consensus range with the production function for the elasticity of substitution between 0.5 and 1, and a capital share in the range 0.3–0.4, 5 y i i l i , labor-augmenting technology increases labor ( ) ( ) = γ ( ) ( ) demand and the equilibrium wage. where i denotes the productivity of labor in The effect of labor-augmenting technology on task i. γIn ( )contrast, tasks i I are technologi- the labor share is in turn given by cally automated and can be≤ produced by either labor or capital, that is, _d ln sL _1 sK 1 , d ln A = ( − KL ) 6 y i i k i i l i , L ε ( ) ( ) = η( ) ( ) + γ ( ) ( ) which is negative if and only if KL 1 . where i is the productivity of capital in task i. In summary, labor-augmentingε

_ machines can substitute for labor. σ N _1 1 The following results are established in AR 4 Y y i σ− di σ− , ( ) = ( N 1 ( ) σ ) forthcoming . ∫ − ( ) where is the elasticity of substitution between i Aggregate output is given by a CES aggre- tasks andσ the integration between N 1 and N gate( ) of capital and labor, − _1 I 1 1 σ _ 3 7 Y i σ− di K σ− The derivation is similar to the one in foot- (( N 1 ) σ ( ) = − η( ) note 1. Differentiating Y RK WL , we obtain ∫ _ = + σ sL d ln AL sK d ln R sL d ln W. Combining this with _1 1 = + N 1 σ− d ln W d ln R 1 d ln A , which again fol- 1 σ _ εKL ( − ) = (εKL − ) L i σ− di L σ− , lows from 2 , yields 3 . ( I ) σ ) ( ) ( ) + ∫ γ( ) VOL. 108 MODELING AUTOMATION 51 where the elasticity of substitution between cap- effect can dominate it suffices to return to ital and labor is given by . 8 and note that it becomes very small when σ ( )I I W R. This condition in turn holds ii Under Assumption A1, automation whenγ ( ) / η(the) capital-output≃ / ratio, K Y , is close to ( ) 4 / increases productivity and aggregate output per the threshold ̅ Y . worker. In particular, κ v Automation increases the demand for cap- 1 1 ital( and) the equilibrium rental rate; that is, 8 ____d ln Y ____ 1 ___W −σ ___R −σ 0. dI 1 I I ( ) = − σ [( ) − ( ) ]> γ( ) η( ) 1 I σ− _d ln R _ 1 _d ln Y _1 ______η( ) 0. Intuitively, Assumption A1 implies that it is dI = dI + I 1 > σ σ i σ− di cheaper to produce tasks in the neighborhood of 0 η( ) I with capital rather than labor. Thus an expan- ∫ sion of the set of tasks that can be produced with It is also useful to note that this approach capital raises productivity. further provides a micro-foundation for several models that consider technological changes that iii Automation changes the share parameters directly alter the exponents of capital and labor of (the) CES in equation 7 . As a consequence, in a Cobb-Douglas production function e.g., automation does not map( )to a combination of Zuleta 2008, and Peretto and Seater 2013( . In factor-augmenting technological improvements, particular, consider the special case of our model) and always makes production less labor inten- where N 1 and 1 . Then,5 sive and reduces the labor share. Namely, the = σ = labor share in this case is I 1 I Y B _K _L − . = ( I ) (1 I) − s ______1 , L _1 = I 1 It is also useful to return to Assumption 1 σ _ i σ− di K σ− A1. If in contrast to this assumption we had ( N 1 ) σ 1 ______− η( ) ∫ _1 I I W R , then tasks near I would not + N 1 γ ( ) /η( ) > / 1 σ _ be produced with machines, because the effec- i σ− di L σ− (∫I γ( ) ) σ tive cost of doing so would be greater than pro- ducing them with labor. In this case, all tasks in which is strictly decreasing in I regardless of the 0, I ̃ for some I ̃ I would be produced with value of the elasticity of substitution between [capital,] and all remaining< tasks with labor. In capital and labor. Thus the effect of automation this case, an increase in I would not affect the on the labor share, when modeled in this fash- allocation of tasks to factors. In addition, other ion, is entirely distinct from the effect of capital changes, for example, an increase in the function accumulation whose impact on the labor share i , would impact the threshold task I ,̃ though depends on the elasticity of substitution. η(this) endogenous change in the set of tasks produced with capital would have different implica- iv Automation can reduce the equilibrium tions than an increase in I under Assumption A1. ( ) wage, even though it increases productivity. The For example, a rise in I ̃ triggered by an increase impact of automation on the wage is given by in i would only have a second-order effect on η(aggregate) output, and the equilibrium wage 1 I σ− _d ln W _ 1 _d ln Y _1 ______γ( ) . dI = dI − N 1 σ σ i σ− di 4 I γ( ) It is easy to construct examples for which the dis- ∫ placement effect dominates the productivity effect. If we The first term is the productivity effect, which take 0.7 the midpoint of most estimates , and set i σ =i (0.2 for all i 0, 1 , we obtain) that the results from the increase in aggregate out- thresholdγ ( ) = η( ) = is 2 , and the displacement∈ [ ] effect dominates put from automation; it is given by 8 and is κ̅Y ( ) when the capital to output ratio satisfies K Y 2, 6.5 . positive. The second term is the displacement This interval comfortably includes the US capital-output / ∈ ( ) effect, which is always negative. To see that ratio which is approximately 3. I 1 for realistic parameter values the displacement 5 Here B exp ln i di ln i di . = (∫0 γ ( ) + ∫I η( ) ) 52 AEA PAPERS AND PROCEEDINGS MAY 2018 would strictly increase because of the direct Automation and Capital Accumulation.— effect of higher i . This discussion explains Because automation increases the demand for why we conceptualizedη( ) automation as a tech- capital and the rental rate, it encourages capital nological change expanding the set of tasks that accumulation. It is thus possible to have periods can be productively performed by capital. of fast automation during which the labor share ( ) declines and capital accumulation accelerates even if the elasticity of substitution between III. New Ideas from the Task-Based Approach capital and labor is less than one. This perspec- tive also implies that rather than being the cause We conclude by emphasizing several ideas of the decline in the labor share as argued by that are highlighted by our task-based approach. Piketty 2014 , capital accumulation( may be a response to automation) and lessen its negative The Productivity Effect.—Our analysis impact on the labor share when the elasticity of stressed the central role of the productivity substitution is less than one( . effect. Whether automation increases or reduces ) the equilibrium wage depends on how power- The Role of Skills.—A version of this frame- ful the productivity effect is. This observation work with workers with heterogeneous skills implies that, in contrast to some popular dis- specializing in different types of tasks can be cussions, the automation technologies that are used to study the implications of automation on more likely to reduce the demand for labor are wage inequality as well as the role of a shortage not those that are “brilliant” and highly produc- of certain types of skills in shaping the impact of tive, but those that are “so-so”—just productive automation on productivity gains and inequality enough to be adopted but not much more pro- see AR forthcoming, 2018 . ductive or cost-saving than the production tech- ( ) niques that they are replacing see AR 2018 . Excessive Automation.—It is difficult to ana- ( ) lyze the issue of excessive automation with New Tasks.—This approach highlights the factor-augmenting technologies. Modeling role of the creation of new tasks in which labor automation as the substitution of machines for has a comparative advantage—as captured by tasks previously performed by labor, on the an increase in N in our model. Under natural other hand, shows that there may be excessive assumptions, new tasks increase productiv- automation because of subsidies to capital or a ity, the demand for labor, and the labor share. divergence between the equilibrium wage rate Our framework clarifies that a balanced growth and the social opportunity cost of labor AR process where the labor share remains constant forthcoming, 2018 . ( depends on the simultaneous expansion of auto- ) mated and new tasks see AR forthcoming . REFERENCES ( ) Deepening of Automation.—In our model, we Acemoglu, Daron, and David Autor. 2011. “Skills, can think of increases in I as capturing “auto- Tasks and Technologies: Implications for mation at the extensive margin”—meaning Employment and Earnings.” In Handbook of extending the set of tasks that can be produced Labor Economics, Vol. 4, edited by David Card by capital. The alternative is “automation at the and Orley Ashenfelter, 1043–171. Amsterdam: intensive margin” or “deepening of automa- Elsevier. tion”—meaning increasing the productivity of Acemoglu, Daron, and Pascual Restrepo. 2017. machines in tasks that are already automated, “Robots and Jobs: Evidence from US Labor which corresponds to an increase in i in Markets.” National Bureau of Economic tasks i I. The deepening of automationη( ) is Research Working Paper 23285. equivalent≤ to capital-augmenting technologi- Acemoglu, Daron, and Pascual Restrepo. 2018. cal change; it always increases the demand for “Artificial Intelligence, Automation and Work.” labor, though its impact on the share of labor, for National Bureau of Economic Research Work- the same reasons as we have emphasized so far, ing Paper 24196. depends on the elasticity of substitution between Acemoglu, Daron, and Pascual Restrepo. Forth- capital and labor. coming. “The Race between Machine and VOL. 108 MODELING AUTOMATION 53

Man: Implications of Technology for Growth, Research Working Paper 21547. Factor Shares and Employment.” American Oberfield, Ezra, and Devesh Raval. 2014. “Micro Economic Review. Data and Macro Technology.” National Acemoglu, Daron, and Fabrizio Zilibotti. 2001. Bureau of Economic Research Working Paper “Productivity Differences.” Quarterly Journal 20452. of Economics 116 2 : 563–606. Peretto, Pietro F., and John J. Seater. 2013. “Fac- Bessen, James E. 2017.( ) “Automation and Jobs: tor-Eliminating Technical Change.” Journal of When Technology Boost Employment.” Bos- Monetary Economics 60 4 : 459–73. ton University Law and Economics Research Piketty, Thomas. 2014. “Capital( ) in the Twen- Paper 17–09. ty-First Century.” Cambridge, MA: Belknap Graetz, Georg, and Guy Michaels. 2015. “Robots Press. at Work.” Centre for Economic Performance Sachs, Jeffrey D., and Laurence J. Kotlikoff. 2012. Discussion Papers 1335. “Smart Machines and Long-Term Misery.” Karabarbounis, Loukas, and Brent Neiman. 2014. National Bureau of Economic Research Work- “The Global Decline of the Labor Share.” ing Paper 18629. Quarterly Journal of Economics 129 1 : Zeira, Joseph. 1998. “Workers, Machines, and 61–103. ( ) Economic Growth.” Quarterly Journal of Eco- Nordhaus, William D. 2015. “Are We Approach- nomics 113 4 : 1091–1117. ing an Economic Singularity? Information Zuleta, Hernando.( ) 2008. “Factor Saving Innova- Technology and the Future of Economic tions and Factor Income Shares.” Review of Growth.” National Bureau of Economic Economic Dynamics 11 4 : 836–51. ( )