by Ajay Agrawal
step=3 isuri=1 1003=18#reqid=10 step=3 isuri=1 1003=18. Investment in Intellectual Property Products is from Bureau of Economic Analysis, table 1.5. Investment in Fixed Assets and Consumer Durable Goods, https:// www .bea .gov/ iTable/ iTable .cfm?ReqID=10 step=
1#reqid=10 step=3 isuri=1 1003=96 1004=1950 1005=2016 1006=a 1011=0 1010=x.
336 Jeff rey D. Sachs
3. The dynamics across sectors vary according to the diff erential timing
of automation, with automation spreading from low- skill and predictable
tasks toward higher- skill and less predictable tasks.
4. Automation refl ects the rising intensity of science and technology
throughout the economy, in terms of R&D, IP, and scientifi c expertise in
the labor force.
5. Future technological changes associated with artifi cial intelligence (e.g.,
machine learning) are likely to shift national income from medium- skilled
and high- skilled workers toward owners of business capital (fi xed capital
and intellectual property products).
There are, of course, many unsolved problems of both theory and mea-
surement, but I will now try to lay out some basic concepts in more formal
terms.
13.2 A Basic Model
Consider the goods- producing sector of the economy (agriculture, min-
ing, construction, and manufacturing) the fi rst to automate. Let Q be out-
put. Output is produced by capital and labor. I will distinguish two kinds
of physical capital, buildings ( B) and machines ( M ), and two kinds of non-physical capital, human capital and know- how embodied in machine tech-
nology.
Labor is organized into occupational tasks such as management, pro-
duction, sales, and so forth. In general, these tasks require varying levels
of expertise: unskilled ( U ), intermediate ( I ), and high ( H ), corresponding respectively to levels of education: less than a bachelor’s degree, a bachelor’s
degree, and an advanced degree (masters, professional, or PhD). (Acemoglu
and Autor 2011).
To illustrate, suppose that there are just two tasks for labor: production
( P) and nonproduction ( N ). The production task requires basic skills. The nonproduction task requires intermediate skills. High skills are needed for
three purposes: R&D, professional services such as medicine, and university
education. Tasks requiring basic skills can also be carried out by workers
with intermediate or high skills, and tasks requiring intermediate skills can
also be carried out by workers with high educational attainment.
Machines M can substitute for labor while buildings B are complementary to tasks (see Sachs and Kotlikoff [2012] and Sachs, Benzell, and LaGarda
[2015] for a similar approach). As a simple illustration, suppose that output
Q is a Cobb- Douglas function of P, N, and B:
(1)
Q = PaN bB(1 a b).
Production P is produced either by labor L or machines M (such as P
P
assembly- line robots) assumed to be a perfect substitute, with t measuring
P
the technological sophistication of the machines M :
P
R&D, Structural Transformation, and the Distribution of Income 337
(2)
P = L + t
.
P
P * M P
Similarly, nonproduction tasks can be produced by labor L or ma-
N
chines M :
N
(3)
N = L + t
.
N
N * M N
In the historical evolution of technology, it was easier to devise machines
to carry out basic mechanical tasks (production) rather than intermediate
tasks (nonproduction), so I start with the simplest assumption that t > 0
P
and t = 0. I note again, however, that as machines are getting “smarter,”
N
they are able to fulfi ll more nonproduction tasks.
Workers with basic education can work only in production, while workers
with an intermediate education can work either in production or nonproduc-
tion tasks. Let L equal the number of workers with education U, and L the U
I
number of workers with educational attainment I. Then, with L signifying ij
the number of workers in task i ( N, P) and skill j, full employment requires (4)
L = L
U
PU
L = L + L .
I
NI
PI
The market equilibrium may involve a perfect sorting of tasks by skills
(unskilled workers in production, intermediate- skilled workers in nonpro-
duction, with L = 0), or may involve some intermediate- skilled workers
PI
employed in basic- skill tasks, with L > 0, a situation referred to as down-PI
skilling. In a dynamic context, the latter situation should be temporary, as
workers will not generally invest in additional years of education for jobs
that require a lower educational attainment.
In any period, the capital stock K is determined based on past savings and
is allocated between buildings and machines in production tasks:
(5)
K = B + M .
P
Investors maximize their capital income by allocating K to equate the
marginal products of buildings and machines, or by setting M = 0 at a
P
corner solution (when the marginal product of buildings is higher than that
of machines for B = K and M = 0).
P
In the pure sorting equilibrium, the wages for LU and LI are given as
follows:
(6)
W = a
+ t
)( a 1) Lb S (1 a b)
U
*( LU
P * M P
I
W = b
+ t
) a Lb 1 S (1 a b),
I
*( LU
P * M P
I
and K receives the rate of return r:
(7)
r = (1 a b)* La Lb M ( a+ b).
U
I
P
If t is below a threshold value tT, then the entire capital stock K is allo-P
P
cated to buildings, so that B = K and M = 0. In that case, there is no automa-
338 Jeff rey D. Sachs
tion. If t is above tT, then some capital is allocated to machines, with the p
P
added equilibrium condition
(8)
r = t
.
P * WU
The threshold tT can be found by equating tT
with the marginal
P
P * WU
product of structures when B = K, specifi cally: tT
( a 1) Lb
P * LU
I * K (1 a b) =
1
( a b)* La LbK ( a+ b). With a little algebra, we fi nd that U
I
L
(9)
tT = (1 a b)
U
.
P
* K
The capital share of income KS is given simply as
(10)
KS = ( r * K ).
Q
Suppose now that the economy is operating in the range of automation,
with t > tT and M > 0. The comparative static eff ects of a further rise in P
P
t are as follows:
P
r
(11)
> 0,
>
tP
W
B < 0,
tP
W
I > 0,
tP
M
P > 0,
tP
KS
> 0.
tP
The incremental improvement in machine technology (automation) leads
to a rise in the return to capital (a), a fall in the wage of basic labor (b), a rise
in the wage of intermediate labor (c), a rise in automation (d), and a rise in
the share of capital income (e). This is simply a case of skill- biased technical
change, in the form of technological change that induces the substitution
of less educated workers by machines in the goods- producing sector.
13.3 Investing in Education
So far, we have taken the supplies of L and L as given, a reasonable U
I
assumption at a given moment of time but not in a dynamic context. The rise
in the labor market returns to schooling, [∂( W – W )] / ∂ t > 0, will lead to a I
U
P
rise in investment in schooling, either by household outlays or public outlays.
Remaining in a quasi- static context, suppose we start with initial levels
R&D, Structural Transformation, and the Distribution of Income 339
of K, L , and L denoted by K(0), L (0), and L (0) and assume a given fl ow B
I
B
I
of saving ( SV ) that may be allocated to fi xed business investment F or education E for upgrading basic skills to intermediate skills:
I
(12)
SV = F + E , I
K = K(0)*(1 d) + F,
E
L = L (0) + I ,
I
I
cI
E
L = L (0)
I .
U
U
cI
The parameter c is the unit cost of producing one intermediate- skilled
I
worker from one low- skilled worker, taken here to be fi xed. This cost includes
both the direct education outlays (such as tuition) as well as the opportunity
costs, notably the reduction of a student’s labor market participation and
earnings during the years of study.
Once again, the marginal returns to alternative investments should be set
equal, so that the marginal product of fi xed capital, equal to r, should be
set equal to the returns to education, measured as W – W . In equilibrium, I
U
(13)
r * c = W
W .
I
I
U
How, then, does a rise in t aff ect the investment in education? There are
P
two eff ects. By raising the returns to fi xed investment, r, the investment allocation can be shifted away from human capital to business fi xed capital. On
the other hand, by raising the wage of intermediate- skilled workers relative
to basic- skilled workers, the net return to schooling is raised. In practice, the
second eff ect is likely to dominate, especially if we also recognize that the rise
in the return to capital will also likely increase the overall rate of saving SV.
If the education incentive eff ect indeed dominates, then the techno-
logical improvement increases the fl ow of students into higher education,
thereby reducing the supply of basic- skilled workers and raising the supply
of intermediate- skilled workers. The boost in the supply of skilled labor
moderates the increase in wage inequality following the rise in t . In the
P
extreme case that r remains constant, the wage diff erential would also remain
unchanged by an off setting increase in the skilled workforce suffi
cient to
drive the wage diff erential back to the original level r * c.
13.4 Endogenous
Growth
The model is greatly enriched by allowing the rate of technological
advance to depend on the investments in R&D carried out by highly skilled
scientists and engineers. Let us therefore now introduce a cadre of high-
skilled professional workers in the number L . We will suppose that these
H
340 Jeff rey D. Sachs
workers are generally holders of advanced degrees in science, technology,
engineering, and mathematics (STEM) fi elds.
The highly skilled workers L are employed in four major activities:
H
(a) research and development, L
; (b) higher education, L
; (c) health
R&D
ED
care L (medical doctors, medical equipment engineers, statisticians, etc.);
HL
and (d) professional consultancy services L . Other than health profes-
C
sionals and academic researchers, most workers with advanced degrees
are employed in professional fi rms (engineering, consultancy, architecture,
legal, etc.) that sell their research and consulting services to companies in
other sectors, such as manufacturing:
(14)
L = L
+ L + L + L .
H
R&D
ED
HL
C
High- skilled professionals require an advanced degree, and therefore edu-
cation at the postbachelor’s level, denoted E . Thus, we revise the equations
H
in (11) as follows:
(15)
SV = F + E + E ,
I
H
K = K(0)*(1 d) + F,
E
L = L (0) + H ,
H
H
cH
E
E
L = L (0) + I
H ,
I
I
c
c
I
H
E
L = L (0)
I .
U
U
cI
The benefi t of investing in advanced training depends, of course, on the
productivity of high- skilled workers in their four respective activities: R&D,
education, health care, and consultancy. We need, therefore, to specify pro-
duction functions for these four activities.
One of the main fruits of R&D will be to improve automation, meaning
a rise in t . A plausible relationship might be something like
P
(16)
t ( t + 1) = t ( t)
) + R & D( t),
P
P
*(1 dep tP
so that R&D( t) in turn would be produced with some combination of skilled
labor, smart machines, and buildings in the R&D sector, such as
(17)
R & D( t) = (
* L
) g * B(1 g).
R&D
R&D
R&D
The parameter
signifi es the effi
ciency of research by high- skilled
R&D
workers. A high value of
would signify a fruitful period for scien-
R&D
tifi c research, for example, due to a signifi cant breakthrough in scientifi c
knowledge. The inventions of the transistor and integrated circuit in the
1940s and 1950s, and the design of modern computers around the same
time, meant that the productivity of applied physicists and engineers rose
R&D, Structural Transformation, and the Distribution of Income 341
a golden age for R&D that lasts till today, and that is indeed accelerating.
The parameter t
signifi es the possibility of artifi cial intelligence sub-
R&D
stituting for researchers in new R&D. This is of course already happening
in areas such as drug discovery, where machine learning can scan through
vast libraries of drug candidates for potential research targets. To date,
advanced machines have mostly complemented rather than substituted for
high- skilled researchers, yet it is not hard to envision the day soon when
smart machines excel at research in biochemistry, genomics, code writing,
and machine design. The inventors of ultrasmart machines will eventually
put themselves out of business, or at least drastically lower their own wages
as t
rises signifi cantly.
R&D
The health sector output HL would have a similar production function,
such as
(18)
HL( t) = (
+ t
) g
(1 g ).
HL * LHL
HL * M HL
* SHL
A rise in would increase the supply of health services and the demand
HL
for health workers. But what of the demand for health services? We might
suppose that the demand would also increase with . As health technology
HL
breakthroughs are made, these tend to become part of a minimum basic
package of health services guaranteed by law and backed by public outlays.
Thus, the public outlays on health services would tend to rise with .
HL
13.5 Parameterizing the Model for the US Economy
The practical longer- term goal of this model will be to create a comput-
able general equilibrium (CGE) model of the US economy that can ana-
lyze the past and future eff ects of technological change, especially artifi cial
intelligence and robotics, on the distribution of incomes, wealth, jobs, and
sectors. A primary purpose will be to analyze the likely progress of AI in sub-
stituting for many occupations that currently have high educational require-
ments, such as in health care (remote patient monitoring, advanced imaging,
machine- led diagnostics), education (online education, expert systems for
teacher training and pedagogy), and various areas of research and develop-
ment. This is a work in progress.
At this stage, it will have to suffi
ce to present some early simulation results
of an illustrative model not yet parameterized for US conditions. I will pres-