by Ajay Agrawal
9.7 Conclusion
In this chapter, we discussed potential implications of AI for the growth
process. We began by introducing AI in the production function of goods
and services and tried to reconcile evolving automation with the observed
stability in the capital share and per capita GDP growth over the last cen-
tury. Our model, which introduces Baumol’s “cost disease” insight into
Zeira’s model of automation, generates a rich set of possible outcomes. We
thus derived suffi
cient conditions under which one can get overall balanced
growth with a constant capital share that stays well below 100 percent, even
with nearly complete automation. Essentially, Baumol’s cost disease leads
to a decline in the share of GDP associated with manufacturing or agricul-
ture (once they are automated), but this is balanced by the increasing frac-
tion of the economy that is automated over time. The labor share remains
substantial because of Baumol’s insight: growth is determined not by what
we are good at but rather by what is essential and yet hard to improve. We
also saw how this model can generate a prolonged period with high capital
share and relatively low aggregate economic growth while automation keeps
pushing ahead.
Next, we speculated on the eff ects of introducing AI in the production
technology for new ideas. Artifi cial intelligence can potentially increase
growth, either temporarily or permanently, depending on precisely how it
is introduced. It is possible that ongoing automation can obviate the role
of population growth in generating exponential growth as AI increasingly
replaces people in generating ideas. Notably, in this chapter, we have taken
automation to be exogenous and the incentives for introducing AI in various
Artifi cial Intelligence and Economic Growth 275
places clearly can have fi rst- order eff ects. Exploring the details of endog-
enous automation and AI in this setup is a crucial direction for further
research.
We then discussed the (theoretical) possibility that AI could generate
some form of a singularity, perhaps even leading the economy to achieve
infi nite income in fi nite time. If the elasticity of substitution in combining
tasks is less than one, this seems to require that all tasks be automated.
But with Cobb- Douglas production, a singularity could occur even with
less than full automation because the nonrivalry of knowledge gives rise to
increasing returns. Nevertheless, here too the Baumol theme remains rele-
vant: even if many tasks are automated, growth may remain limited due to
areas that remain essential yet are hard to improve. Thus in the appendix
we show that if some steps in the innovation process require human R&D,
then super AI may end up slowing or even ending growth by exacerbating
business- stealing, which in turn discourages human investments in inno-
vation. Such possibilities, as well as other implications of “super- AI” (for ex-
ample for cross- country convergence and property right protection), remain
promising directions for future research.
The chapter next considered how fi rms may infl uence, and be infl uenced
by, the advance of artifi cial intelligence, with further implications for under-
standing macroeconomic outcomes. We considered diverse issues of market
structure, sectoral reallocations, and fi rms’ organizational structure. Among
the insights here we see that AI may in part discourage future innovation
by speeding up imitation; similarly, rapid creative destruction, by limiting
the returns to an innovation, may impose its own limit on the growth pro-
cess. From an organizational perspective, we also conjectured that while AI
should be skill- biased for the economy as a whole, more AI- intensive fi rms
are likely to: (a) outsource a higher fraction of low- occupation tasks to
other fi rms, and (b) pay a higher premium to the low- occupation workers
they keep inside the fi rm.
Finally, we examined sectoral- level evidence regarding the evolution of
capital shares in tandem with automation. Consistent with increases in
the aggregate capital share, the capital share also appears to be rising in
many sectors (especially outside services), which is broadly consistent with
an automation story. At the same time, evidence linking these patterns to
specifi c measures of automation at the sectoral level appears weak, and
overall there are many economic forces at work in the capital share trends.
Developing sharper measures of automation and investigating the role of
automation in the capital share dynamics are additional, important avenues
for further research.
276 Philippe Aghion, Benjamin F. Jones, and Charles I. Jones Appendix
Artifi cial Intelligence in a Schumpeterian
Model with Creative Destruction
In this appendix we describe and model a situation in which superin-
telligence (or “super- AI”) may kill growth because it exacerbates creative
destruction and thereby discourages any human investment into R&D. We
fi rst lay out a basic version of the Schumpeterian growth model. We then
extend the model to introduce AI in the innovation technology.
Basics
Time is continuous and individuals are infi nitely lived, there is a mass L of
individuals who can decide between working in research or in production.
Final output is produced according to
y = Ax ,
where x is the fl ow of intermediate input and A is a productivity parameter measuring the quality of intermediate input x. Each innovation results in
a new technology for producing fi nal output and a new intermediate good
to implement the new technology. It augments current productivity by the
multiplicative factor > 1: A = A . Innovations in turn are the (random) t+1
t
outcome of research, and are assumed to arrive discretely with Poisson rate
. n where n is the current fl ow of research.
In a steady state the allocation of labor between research and manu-
facturing remains constant over time, and is determined by the arbitrage
equation
(9A.1)
=
v,
where the LHS of (A) is the productivity- adjusted wage rate = ( w/ A) which a worker earns by working in the manufacturing sector and v is
the expected reward from investing one unit fl ow of labor in research. The
productivity- adjusted value v of an innovation is determined by the Bell-
man equation
rv = ( )
nv,
where ( ) denotes the productivity- adjusted fl ow of monopoly profi ts
accruing to a successful innovator and where the term (– nv) corresponds
to the capital loss involved in being replaced by a subsequent innovator.
The above arbitrage equation, which can be reexpressed as
(9A.2)
=
( ) ,
r + n
together with the labor market- clearing equation
Artifi cial Intelligence and Economic Growth 277
(9A.3)
x( ) + n = L,
where x( ) is the manufacturing demand for labor, jointly determine
the steady- state amount of research n as a function of the parameters
,, L, r,.
The average growth rate is equal to the size of each step, ln, times the
average number of innovations per unit of time, l n that is, g = n ln.
A Schumpeterian Model with Artifi cial Intelligence
As before, there are L workers who can engage either in production of
existing intermediate goods or in research aimed at discovering new inter-
mediate goods. Each intermediate good is linked to a particular GPT. We
follow Helpman and Trajtenberg (1994) in supposing that before any of the
intermediate goods associated with GPT can be used profi tably in the fi nal
goods sector, some minimal number of them must be available. We lose noth-
ing essential by supposing that this minimal number is one. Once the good
has been invented, its discoverer profi ts from a patent on its exclusive use in
production, exactly as in the basic Schumpeterian model reviewed earlier.
Thus the diff erence between this model and the above basic model is that
now the discovery of a new generation of intermediate goods comes in two
stages. First a new GPT must come, and then the intermediate good must be
invented that implements that GPT. Neither can come before the other. You
need to see the GPT before knowing what sort of good will implement it,
and people need to see the previous GPT in action before anyone can think
of a new one. For simplicity we assume that no one directs R&D toward
the discovery of a GPT. Instead, the discovery arrives as a serendipitous
by-product of the collective experience of using the previous one.
Thus the economy will pass through a sequence of cycles, each having two
phases; GPT arrives at time T. At that time the economy enters phase 1 of i
i
the i th cycle. During phase 1, the amount n of labor is devoted to research.
Phase 2 begins at time T + when this research discovers an intermediate
i
i
good to implement GPT. During Phase 2 all labor is allocated to manufac-
i
turing until GPT arrives, at which time the next cycle begins.
i+1
A steady- state equilibrium is one in which people choose to do the same
amount of research each time the economy is in Phase 1, that is, where n is
constant from one GPT to the next. As before, we can solve for the equi-
librium value of n using a research- arbitrage equation and a labor market-
equilibrium curve. Let be the wage, and v the expected present value of
j
j
the incumbent intermediate monopolist’s future profi ts, when the economy
is in phase j, each divided by the productivity parameter A of the GPT
currently in use. In a steady state these productivity- adjusted variables will
all be independent of which GPT is currently in use.
Because research is conducted in Phase 1 but pays off when the economy
enters into Phase 2 with a productivity parameter raised by the factor , the
278 Philippe Aghion, Benjamin F. Jones, and Charles I. Jones usual arbitrage condition must hold in order for there to be a positive level
of research in the economy
=
v .
1
2
Suppose that once we are in Phase 2, the new GPT is delivered by a Pois-
son process with a constant arrival rate equal to m. Then the value of v is
2
determined by the Bellman equation
rv = ( ) + μ v v
(
).
2
2
1
2
By analogous reasoning, we have
rv = ( )
nv .
1
1
1
Combining the above equations yields the research- arbitrage equation
μ ( )
=
( ) +
1
/ r + μ .
1
2
r + n
Because no one does research in Phase 2, we know that the value of is
2
determined independently of research, by the market- clearing condition
L = x( ) Thus we can take this value as given and regard the last equation 2
as determining as a function of n The value of n is determined, as usual, 1
by this equation together with the labor- market equation
L
n = x( ).
1
The average growth rate will be the frequency of innovations times the
size lng, for exactly the same reason as in the basic model. The frequency,
however, is determined a little diff erently than before because the economy
must pass through two phases. An innovation is implemented each time a
full cycle is completed. The frequency with which this happens is the inverse
of the expected length of a complete cycle. This in turn is just the expected
length of Phase 1 plus the expected length of Phase 2:
1 / n + 1 / μ = μ + n .
μ n
Thus we have the growth equation
μ n
g = ln
,
μ + n
where n satisfi es
μ f ( L n)
(
)
f ( L
n) =
f ( L) +
/ r + μ
r + n
with
f (.) = x 1(.)
as a decreasing function of its argument.
Artifi cial Intelligence and Economic Growth 279
We are interested in the eff ect of on g and in particular by what happens
when → ∞ as a result of AI in the production of ideas. Obviously, n → 0
when → ∞ Thus E = 1/ n + 1/ → ∞ and therefore
1
g = ln .
0.
E
In other words, we have described and modeled a situation where superin-
telligence exacerbates creative destruction to a point that all human invest-
ments in to R&D are being deterred and as a result growth tapers off . How-
ever, two remarks can be made at this stage:
Remark 1: Here, we have assumed that the second innovation stage
requires human research only. If instead AI allowed that stage to also be
performed by machines, then AI will no longer taper off and can again
become explosive as in our core analysis.
Remark 2: We took automation to be completely exogenous and costless.
But suppose instead that it costs money to make increase to infi nity: then,
if creative destruction grows without limit as in our analysis above, the incen-
tive to pay for increasing will go down to zero since the complementary
human R&D for the stage- two innovation is also going to zero. But this
goes against having → ∞ and therefore against having AI kill the growth
process.19
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