The Race Between Man and Machine: Implications of ... · The Race Between Man and Machine: Implications of Technology for Growth, Factor Shares and Employment Daron Acemoglu and Pascual

The Race Between Man and Machine: Implications ofTechnology for Growth, Factor Shares and Employment

Daron Acemoglu and Pascual Restrepo

MIT

The Life and Work of Gary BeckerOctober 16th 2015.

Acemoglu & Restrepo (MIT) Race Between Man and Machine The Life and Work of Gary Becker

Race Between Machine and Man Introduction

Introduction

Recent concerns about the implications of technology:

The replacement of labor by machines in various tasks has reducedwage growth (Autor, Levy and Murnane, 2013, Acemoglu and Autor,2011) and will create (or has already created) nonemployment (e.g.,Brynjolffson and McAfee, 2012).Technological change, or the associated accumulation of capital, isreducing the share of labor in national income (e.g., Karabarbounis andNeiman, 2014, Piketty and Zucman, 2014, Oberfield and Raval, 2014).

But we lack a conceptual framework that can elucidate howtechnological change, which has always replaced some labor-intensivetasks by capital, has coexisted with steady wage growth, roughlyconstant unemployment and factor shares in the past, and whataspects of new technologies are impacting these economic outcomestoday.



This Paper

A framework to study the joint evolution of technology, factor sharesand employment.

Main new ingredient: in addition to capital simplifying andreplacing tasks previously performed by labor, new more complextasks relying on labor are created.

E.g.:

the replacement of the stagecoach by the railroad, of the sailboat bythe steamboat or of dockworkers by cranes are examples ofcapital-labor substitution, but these went hand-in-hand with thecreation of several entirely new labor-intensive tasks, including a newclass of engineers, new types of managers and financiers, machinists,repairmen, conductors, and so on;today, as computers and machines replace labor, we are also creatingnew design tasks ranging from engineering tasks based on newmachines to programming and apps design.



This Paper (continued)

This new ingredient is embedded in a dynamic model in which twotypes of innovations create different and countervailing forces:

1 Labor-replacing innovations enable capital to replace previouslylabor-intensive tasks.

2 Labor-intensive innovations create new, more complex versions ofexisting tasks (typically replacing previously capital-intensive tasks).

With this structure, growth will take place due to productivityupgrading of a fixed set of tasks as well as from the substitution ofcapital for labor.

This setup is embedded in a dynamic economy with endogenous,directed technological change, which highlights importantself-correcting market forces.



Related Literature

The framework incorporates features from several different types ofmodels:

Models of capital-labor substitution at the task level: Zeira (1998),Acemoglu and Autor (2011), Costinot and Vogel (2012).Directed technological change models: Acemoglu (1998, 2002),Hemous and Olsen (2014).Models of endogenous shape of the aggregate production function:Acemoglu (2003), Jones (2005), Oberfield (2014).


Race Between Machine and Man Outline

Outline

Motivating Evidence

Static Model

Comparative Statics

The Structure of Balanced Growth Path

Dynamic Model with Directed Technological Change

Welfare Analysis

Extensions

Conclusions and Future Work


Race Between Machine and Man Motivating Evidence

Motivating Evidence: Novel jobs.

-200

-150

-100

-50

050

100

150

200

Per

cent

chan

ge

in e

mplo

ymen

t gro

wth

ove

r nex

t 10 y

ears

0 20 40 60 80Share of novel tasks and jobs within occupational group at beginning of decade

From 1980 to 1990 From 1990 to 2000 From 2000 to 2007

Figure: Employment growth and share of novel jobs (from Lin 2011). Theadditional job creation in occupational groups with novel jobs accounts for about50% of total employment growth between 1980 and 2008.


Race Between Machine and Man Static Model

Static Model: Production

There is a unique final good Y produced by combining a continuumof tasks y (i), with i ∈ [N − 1,N].

Y =

(∫ N

N−1y (i)

σ−1σ di

) σσ−1

, σ ∈ (0,∞) : elasticity of substitution.

Set the resulting ideal price index as numeraire.

The range N − 1 to N implies that the set of tasks is constant, butolder tasks might be replaced by new (more complex and moreproductive) versions thereof.

Namely, an increase in N adds a new task at the top whilesimultaneously replacing one at the bottom.



Static Model: Intermediates

Each task is produced by combining capital or labor with anintermediate good q(i) embodying technology.

In preparation for the model with endogenous technology, we assumethat each intermediate is supplied by a monopolist, which canproduce one unit of intermediate at the cost of µψ units of the finalgood (where µ ∈ (0, 1)).

There is also fringe of competitive imitators that can copy thetechnology for each intermediate and produce it at the cost of ψ unitsof the final good.

We assume that µ is such that the unconstrained monopoly price isgreater than ψ.

This implies that in the pricing game between the monopolist and thefringe, there will be a limit price equilibrium, and each unit of everyintermediate will be sold at a constant price ψ.



Static Model: Intermediates (continued)

Tasks with i ≤ I are technologically automated, and can beproduced with labor or capital according to

y (i) = B[

ηq(i)ζ−1

ζ + (1− η) (k(i) + γ(i)l(i))ζ−1

ζ

] ζζ−1

Tasks with i > I are not technologically automated yet, and can onlybe produced with labor:

y (i) = B[ηq(i)

ζ−1ζ + (1− η) (γ(i)l(i))

ζ−1ζ

] ζζ−1

.

We assume γ(i) is strictly increasing, so labor has a comparativeadvantage in more complex tasks (in fact, it is more productive inthese tasks), and normalize B ≡ (1− η)ζ/(1−ζ).



Static Model: Factor Supplies

In the static model, we take capital to be fixed at K and rented at aprice r (determined endogenously).

Total labor used is given by

Ls(W

rK

),

where Ls is a weakly increasing function, and W is the wage rate.

This is a reduced form for many different models of labor supply andquasi-labor supply behavior.It is derived from an efficiency wage model in the Appendix.In Acemoglu and Restrepo (2015), we derive this curve endogenouslyas the equilibrium representation in a search-matching model.



Equilibrium: Task Prices

Let cu (·) be the unit cost of production for a task as a function ofthe price of the relevant factor.Then, equilibrium task prices will be given by

p(i ) =

cu(min

{r ,

W

γ(i )

})≡

[ψ1−ζ + (

1− η

η)ζ min

{r ,

W

γ(i )

}1−ζ] 1

1−ζ

if i ≤ I ,

cu(

W

γ(i )

)≡

[ψ1−ζ + (

1− η

η)ζ

(W

γ(i )

)1−ζ] 1

1−ζ

if i > I ,

(1)

Given factor prices, firms are indifferent between using capital andlabor in task I :

W

r= γ(I ). (2)

Tasks with i ≤ I ∗ ≡ min{I , I } will be automated and produced withcapital, and tasks with i > I ∗ will be produced with labor.



Equilibrium: Task Space



Equilibrium: Market Clearing

Factor demands in capital- and labor-intensive tasks are

k(i) = YBcu(r)ζ−σr−ζ if i ≤ I ∗

and

l(i) = γ(i)ζ−1YBcu(

W

γ(i)

)ζ−σ

W −ζ if i > I ∗.

Thus, factor market clearing conditions can be written as

Y (min{I , I } −N + 1)Bcu(r)ζ−σr−ζdi = K , (3)

and

Y∫ N

min{I ,I}γ(i)ζ−1Bcu

(W

γ(i)

)ζ−σ

W −ζdi = Ls(W

rK

). (4)



Equilibrium in the Static Model

Proposition (Equilibrium in the static model)

For any range of tasks [N − 1,N], automation I ∈ (N − 1,N], and capitalK , there exists a unique equilibrium characterized by factor prices, W andr , and threshold tasks, I and I ∗, such that: (i) I is determined by equation(2) and I ∗ = min{I , I }; (ii) all tasks i ≤ I ∗ are produced using capital andall tasks i > I ∗ are produced using labor; (iii) capital and labor marketclearing conditions, equations (3) and (4), are satisfied; and (iii) factorprices satisfy:

(I ∗ −N + 1)cu(r)1−σ +∫ N

I ∗cu(

W

γ(i)

)1−σ

di = 1. (5)



Diagrammatic Representation

Let ω ≡ WrK

.

Figure: Graphical representation of the equilibrium. Case with I ∗ < I .



Diagrammatic Representation

Figure: Graphical representation of the equilibrium. Case with I ∗ = I .


Race Between Machine and Man Comparative Statics

Comparative Statics

Proposition (Comparative statics if I ∗ = I < I )

We have:d lnω

dI=

d ln(W/r)

dI< 0,

d lnω

dN=

d ln(W/r)

dN> 0

andd lnω

d lnK+ 1 =

d ln(W/r)

d lnK=

1

σSR> 0.

Here, σSR ∈ [0,∞) is the short-run elasticity of substitution betweenlabor and capital, which is a weighted average of σ and ζ.d lnWdI

< 0 if σSR is sufficiently large, and d lnWdI

≥ 0 otherwise.



Comparative Statics (continued)

Proposition (Comparative statics if I ∗ = I < I )

Let ε ≡ d ln γ(I )dI

> 0 be the semi-elasticity of the comparative advantage

schedule, so that dI ∗ = 1ε d ln(W/r). Then:

d lnω

dI=

d ln(W/r)

dI= 0,

d lnω

dN=

d ln(W/r)

dN> 0 and

d lnω

d lnK+ 1 =

d ln(W/r)

d lnK=

1

σMR> 0,

where σMR is the medium-run aggregate elasticity of substitution

σMR = σSR

(1−

1

ε

∂ ln(W/r)

∂I ∗

)> σSR .

Also, d lnWdI

< 0 if σMR is sufficiently large, and d lnWdI

≥ 0 otherwise.



Comparative Statics: Interpretation

New result relative to the standard factor-augmenting technologyframework: technological advances can reduce factor prices (herewages for automation and the rental rate on capital for new tasks).

This is related to Acemoglu and Autor (2011): technologies changethe range of tasks performed by factors, creating “strong priceeffects”.

Note also that when I < I , the elasticity of substitution betweencapital and labor is σMR rather than σSR because of the endogenouschanges in the set of tasks produced by capital (in response tochanges in factor prices).



Special Cases

Two special cases further highlight the workings of the model: η → 0(so intermediates determine the equilibrium allocation of tasks tofactors, but do not get revenue) or ζ → 1 (where their revenuesbecome a constant fraction of total revenue).

In this case,

lnω =

(1

σ− 1

)lnK +

1

σln

(∫ N

I ∗γ(i)σ−1di

I ∗ −N + 1

), and

Y =

[(I ∗ − N + 1)

1σ K

σ−1σ +

(∫ N

I ∗γ(i)σ−1di

) 1σ

Lσ−1

σ

] σσ−1

,

where σ ≡ η + (1− η)σ (and thus when η → 0, σ = σ), highlightingthe role of the two different types of technologies in changing the roleof the two factors in the (derived) aggregate production function.


Race Between Machine and Man Dynamic Economy

Dynamic Model: Preferences and Resource Constraint

We now move to a dynamic model with capital accumulation andendogenous technological change.

A representative household economy with preferences overconsumption ∫

∞

0e−ρt C (t)

1−θ − 1

1− θdt.

and the resource constraint:

K (t) = Y (t)− C (t)− δK (t)− ψµ∫ N

N−1q(i , t)di .

r(t) is the rental rate of capital and depreciation is δ.



The Structure of Balanced Growth Path

We assume the specific form for the comparative advantage schedule:

γ(i) = eAi , with A > 0.

This implies that labor is more productive in new more complex tasksand will build growth through quality improvements.

We start by assuming exogenous technological change, and define

n(t) ≡ N(t)− I (t)



The Structure of Balanced Growth Path (cont)

Assume I ∗ = I (as we will guarantee later).Normalize the variables y (t) ≡ Y (t)/γ(I (t)), k(t) ≡ K (t)/γ(I (t)),c(t) ≡ C (t)/γ(I (t)), and w(t) ≡ W (t)/γ(I (t)).The market clearing conditions become:

y (t)(1− n(t))cu(r(t))ζ−σr(t)−ζ = k(t),

and

y (t)∫ n(t)

0γ(i)ζ−1cu

(w(t)

γ(i)

)ζ−σ

w−ζdi = Ls(

w(t)

r(t)k(t)

).

Additionally, the ideal price index condition becomes

(1− n(t))cu(r(t))1−σdi +∫ n(t)

0cu(w(t)

γ(i)

)1−σ

di = 1.

These uniquely determine the rate of return on capital,r(t) = rE (n(t), k(t)), wages wE (n(t), k(t)), and net output,f E (n(t), k(t)).



The Structure of Balanced Growth Path (cont)

Define a BGP as an equilibrium in which W , K and Y grow at aconstant rate, g , and the interest rate, r , is constant.

Thus, in a BGP the normalized variables converge to fixed values, andnecessarily I = N = ∆, so that n(t) is constant.

Their behavior outside the steady state is determined by the Eulerequation

˙c(t)

c(t)=

1

θ(rE (n(t), k(t))− δ − ρ)− A∆, (6)

and resource constraint

k(t) = f E (k(t), n(t))− c(t)− (δ + A∆)k(t). (7)



Dynamic Equilibrium: Summary

Proposition (Dynamic equilibrium with exogenous technological change)

Suppose technology evolves exogenously, ρ > ρ and lim n(t) > n for allt ≥ T.

1 Asymptotically, I ∗ = I and all automated tasks produce with capital.

2 A balanced growth path exists if and only if asymptoticallyN = I = ∆. In this balanced growth path I ∗ = I . Y ,C ,K and wgrow at a constant rate A∆ and r is constant.

3 Given such a path for technology, the dynamic equilibrium is uniquestarting from any initial condition and converges to the balancedgrowth path.



Dynamic Equilibrium: Diagrammatic Representation

Figure: BGP and dynamics for our model with exogenous technological changeand n(t) → n.



The Productivity Effect

Consider the balanced growth path characterized above withN(t)− I (t) = n and g = A∆. Crucially, in the long runr = ρ + δ + θg .

The long-run effect of technology on wages can now be computedfrom the ideal price index condition:

(I −N − 1)cu(ρ + δ + θg)1−σ +∫ N

Icu(

W

γ(i)

)1−σ

= 1. (8)

This in particular implies:

dW

dI∝

1

σ − 1[cu (r)1−σ − cu

(W

γ(I )

)1−σ

] ≥ 0.

Thus, several of the intuitive results from the static model continueto apply, but because of the productivity effect, automation alsoincreases the wage level in the long run.



The Productivity Effect and Wages

Figure: Evolution of wages following a one-time temporary increase in I


Endogenous Technology

Endogenous Technology: Innovation Possibilities Frontier

We now endogenize technology by assuming that it can be developedby firms using scientists, which are in inelastic supply, S .

SI (t) ≥ 0 of these scientists are hired by monopolists at a competitivewage wS for automation, and SN(t) ≥ 0 of them are hired forcreating new tasks. The market clearing condition for scientists is

SI (t) + SN(t) ≤ S .

Advances in automation and creation of new tasks follow the nexttwo differential equations

I (t) = κISI (t), (9)

andN(t) = κNSN(t), (10)

where κI and κN are positive constants.



Dynamic Model: Profits and Value Functions (continued)

The flow profits from automation, which naturally replaces a taskpreviously performed by labor (i.e., i > I (t)), can be written as

πI (t, i) = (1− µ)

(η

1− η

)ζ

ψ1−ζY (t)cu (r(t))ζ−σ.

Flow profits of producing such task with an intermediate technologythat only allows the use of labor, is given by

πN(t, i) = (1− µ)

(η

1− η

)ζ

ψ1−ζcu(W (t)

γ(i)

)ζ−σ

.



Dynamic Model: Profits and Value Functions (continued)

We assume a patent structure in which new entrants mustcompensate replaced firms by making a take-it-or-leave it offer.

With this patent structure, new firms will compensate existing patentholders by their full continuation value of production.

Therefore, values from automation and new labor-intensive tasksdepend on differences in costs:

VI (t) ∝

∫∞

te−∫ τ

tr(s)ds

Y (τ)

(cu (r(τ))ζ−σ − c

u

(W (τ)

γ(I (t))

)ζ−σ)dτ, (11)

and

VN (t) ∝

∫∞

te−∫ τ

tr(s)ds

Y (τ)

(cu

(W (τ)

γ(N(t))

)ζ−σ

− cu (r(τ))ζ−σ

)dτ. (12)

Observe that these values are positive only when σ > ζ.



Dynamic Model: Equilibrium conditions

A dynamic equilibrium with endogenous technology is determined by:

The evolution of the state variables is given by

k(t) = f E (k(t), n(t))− c(t)− (δ + AκISI (t))k(t)

n(t) = κN (S − SI (t))− κISI (t).

Consumption satisfies the Euler equation

c(t) = c(t)

(1

θ(rE (k(t), n(t))− δ − ρ)− AκISI (t)

).

The allocation of scientists satisfies:

SI (t) =

0 if κIVI (t) < κNVN (t)∈ [0, S ] if κIVI (t) = κNVN (t)

S if κIVI (t) > κNVN(t),

with VN (t) and VI (t) given by equations (11) and (12).A transversality condition for the household holds.



Dynamic Equilibrium: Summary

Proposition (Equilibrium with endogenous technological change)

Suppose that σ > ζ, ρ > ρ and S < S (where S is a suitably definedthreshold). Then:

1 There exists κ such that for κIκN

> κ there is a unique balanced growthpath.

2 Along this path we have I ∗(t) = I (t) and N(t)− I (t) = nD , with nD

determined endogenously from the condition κNVN = κIVI . In thisbalanced growth path, Y ,C ,K and W grow at the constant rateg = A κI κN

κI+κNS, and r , the labor share and employment are constant.

3 The dynamic equilibrium is unique in the neighborhood of thebalanced growth path and is locally (saddle-path) stable. Moreover,when θ → 0, the dynamic equilibrium is globally stable.



Determination of the Balanced Growth Path

Figure: Determination of nD in steady state.



The Race between Machine and Man

Consider an increase in I away from the balance growth path. Thisreduces the labor share and total employment.

But it also reduces the wage per effective unit of labor W/γ(I )relative to interest rates.

Profit-making incentives create forces for self-correction, i.e., for theeconomy to revert back to the same balanced growth path,employment and factor shares.

The role of σ > ζ is important: an increase in I reduces W/γ(I ) andthis increases VN(t) relative to VI (t), providing incentives formonopolists to introduce new more complex (more labor-intensive)tasks, instead of automating tasks in which the production cost withlabor has fallen.

But this effect needs to be stronger than the productivity effect. Ourassumptions ensured that it is.


Endogenous Technology Welfare Analysis

Reducing Automation May Improve Welfare

Is the composition of innovation socially optimal?

In general no, and there is too much automation and too littlecreation of new tasks because of labor’s quasi rents.

Proposition (Excessive automation)

Suppose that ρ > ρ and S < S as in Proposition 5, and that σ > ζ → 1.Moreover, suppose intermediate goods are subsidized and can bepurchased at their marginal cost (or equivalently µ → 1).Consider the decentralized equilibrium path starting from some initial levelof capital, K (0), and endogenous technologies, N(t)− I (t) = nD(t).There exists a feasible allocation satisfying nP(t) ≥ nD(t) withlimt→∞ nP(t) > nD that achieves strictly greater welfare than thedecentralized equilibrium.


Extensions

Extensions I: Automation and Inequality

We include two types of labor, high and low skill, and assume thatnew tasks are at first produced by skilled labor, and then can bestandardized (in a manner similar to Acemoglu, Garcia and Zilibotti,2012) with unskilled labor, before being further standardized to beproduced by capital.

Suppose that for high- and low-skill workers comparative advantage is

γH(i) = eAH i , and

γL(i , t) = eALi+(AH−AL)∆(t−t0(i )),

where AL < AH and t is calendar time and t0(i) the date at whichtask i was introduced.

This implies that there exists a threshold task M such that high-skilllabor performs tasks in (M,N], low-skill labor performs tasks in(I ,M ], and tasks in [N − 1,M ] are performed by capital.


Extensions

Automation and Inequality: Main Result

Proposition (Automation, new tasks and inequality)

Suppose technology evolves exogenously:

1 Then a balanced growth path exists if and only if asymptoticallyN = I = ∆. In this balanced growth path Y ,C ,K and wH ,wL growat a constant rate AH∆ and r is constant. Moreover, the wage ratiobetween high-skilled and low-skilled workers (wH/wL) is constant butdepends on n = N − I

2 Given such a path of technological change, the dynamic equilibrium isunique starting from any initial condition and converges to thebalanced growth path.

3 The immediate effect of increases in both I and N is to increaseWH/WL. But the medium-run impact of an increase in N is toreduce inequality.


Extensions

Extensions II: Creative Destruction of Profits

Another extension is to modify the assumption we have made on thestructural intellectual property rights, reverting to the more standardassumption that new technologies creatively destroy the rents/profitsof existing technologies.

The computation of VN(t) and VI (t) is more involved, but we stillobtain a BGP (and also stability under additional conditions).

Yet, stability requires more stringent assumptions.

This occurs because firms do not take into account the cost ofproduction with other inputs when deciding whether to automate orcreate new tasks.


Extensions Conclusion

Conclusion

Our main contribution is to develop a systematic framework in whichthe force of capital replacing previously labor-intensive tasks ispartially or fully countered by the creation of new labor-intensivetasks.

The framework lends itself to determine the conditions under whichsustained technological progress will be consistent with balancedgrowth.

The framework also shows how different types of technologicalchanges impact factor shares, and in an extension including searchand matching, unemployment.

It also highlights the forces that will self-correct bouts of technologicalchange that greatly distort the factor distribution of income.


Documents

The Race Between Man and Machine: Implications of ... · The Race Between Man and Machine: Implications of Technology for Growth, Factor Shares and Employment Daron Acemoglu and Pascual