by Ajay Agrawal
demand.3 Baumol (1967) showed that the greater rate of technical change
2. Other papers empirically analyzing the sector shifts include Dennis and Iscan (2009), Buera and Kaboski (2009), Kollmeyer (2009), Nickell, Redding, and Swaffi
eld (2008), and Rowthorn
and Ramaswamy (1999).
3. Acemoglu and Guerrieri (2008) also propose an explanation based on diff erences in capital deepening.
294 James Bessen
Fig. 10.2 Manufacturing share of the labor force
Sources: US Bureau of the Census 1975; BLS Current Employment Situation.
Note: Labor force includes agricultural laborers.
in manufacturing industries relative to services leads to a declining share of
manufacturing employment under some conditions (see also Lawrence and
Edwards 2013; Ngai and Pissarides 2007; Matsuyama 2009).
But diff erences in productivity growth rates do not seem to explain the
initial rise in employment. For example, during the nineteenth century, the
share of employment in agriculture fell while employment in manufacturing
industries such as textiles and steel soared both in absolute and relative
terms. But labor productivity in these manufacturing industries grew faster
than labor productivity in agricultural. Parker and Klein (1966) fi nd that
labor productivity in corn, oats, and wheat grew 2.4 percent, 2.3 percent,
and 2.6 percent per annum from 1840– 1860 to 1900– 10. In contrast, labor
productivity in cotton textiles grew 3 percent per year from 1820 to 1900 and
labor productivity in steel grew 3 percent from 1860 to 1900.4 Nevertheless,
employment in cotton textiles, and in primary iron and steel manufacturing,
grew rapidly then.
The growth of manufacturing relative to agriculture surely involves some
general equilibrium considerations, perhaps involving surplus labor in the
agricultural sector (Lewis 1954). But at the industry level, rapid labor pro-
ductivity growth along with job growth must mean a rapid growth in the
4. My estimates, data described below.
Artifi cial Intelligence and Jobs: The Role of Demand 295
equilibrium level of demand—the amount consumed must increase suffi
-
ciently to off set the labor- saving eff ect of technology. For example, although
labor productivity in cotton textiles increased nearly thirtyfold during the
nineteenth century, consumption of cotton cloth increased one hundred-
fold. The inverted- U thus seems to involve an interaction between produc-
tivity growth and demand.
A long- standing literature sees sectoral shifts arising from diff erences in
the income elasticity of demand. Clark (1940), building on earlier statis-
tical fi ndings by Engel (1857) and others, argued that necessities such as
food, clothing, and housing have income elasticities that are less than one
(see also Boppart 2014; Comin, Lashkari, and Mestieri 2015; Kongsamut,
Rebelo, and Xie 2001; and Matsuyama 1992 for more general treatments
of non homothetic preferences). The notion behind “Engel’s Law” is that
demand for necessities becomes satiated as consumers can aff ord more, so
that wealthier consumers spend a smaller share of their budgets on neces-
sities. Similarly, this tendency is seen playing out dynamically. As nations
develop and their incomes grow, the relative demand for agricultural and
manufactured goods falls and, with labor productivity growth, relative
employment in these sectors falls even faster.
This explanation is also incomplete, however. While a low- income elastic-
ity of demand might explain late twentieth century deindustrialization, it
does not easily explain the rising demand for some of the same goods during
the nineteenth century. By this account, cotton textiles are a necessity with
an income elasticity of demand less than one. Yet, during the nineteenth
century, the demand for cotton cloth grew dramatically as incomes rose.
That is, cotton cloth must have been a “luxury” good then. Nothing in the
theory explains why the supposedly innate characteristics of preferences for
cloth changed.
It would seem that the nature of demand changed over time. Matsuyama
(2002) introduced a model where the income elasticity of demand changes
as incomes grow (see also Foellmi and Zweimüller 2008). In this model, con-
sumers have hierarchical preferences for diff erent products. As their incomes
grow, consumer demand for existing products saturates and they progres-
sively buy new products further down the hierarchy. Given heterogeneous
incomes that grow over time, this model can explain the inverted- U pattern.
It also corresponds, in a highly stylized way, to the sequence of growth across
industries seen in fi gure 10.1.
Yet, there are two reasons that this model might not fi t the evidence very
well for individual industries. First, the timing of the growth of these indus-
tries seems to have much more to do with particular innovations that began
eras of accelerated productivity growth than with the progressive saturation
of other markets. Cotton textile consumption soared following the introduc-
tion of the power loom to US textile manufacture in 1814; steel consump-
tion grew following the US adoption of the Bessemer steelmaking process
296 James Bessen
in 1856, and Henry Ford’s assembly line in 1913 initiated rapid growth in
motor vehicles.
Second, there is the general problem of looking at the income elasticity
of demand as the main driver of structural change: the data suggests that
prices were often far more consequential for consumers than income. From
1810 to 2011, real gross domestic product (GDP) per capita rose thirtyfold,
but output per hour in cotton textiles rose over eight hundredfold; infl ation-
adjusted prices correspondingly fell by three orders of magnitude. Similarly,
from 1860 to 2011, real GDP per capita rose seventeenfold, but output per
hour in steel production rose over 100 times and prices fell by a similar
proportion. The literature on structural change has focused on the income
elasticity of demand, often ignoring price changes. Yet these magnitudes
suggest that low prices might substantially contribute to any satiation of
demand. I develop a model that includes both income and price eff ects on
demand, allowing both to have changing elasticities over time.
The inverted- U pattern in industry employment can be explained by a
declining price elasticity of demand. If we assume that rapid productivity
growth generated rapid price declines in competitive product markets, then
these price declines would be a major source of demand growth. During the
rising phase of employment, equilibrium demand had to increase propor-
tionally faster than the fall in prices in response to productivity gains. During
the deindustrialization phase, demand must have increased proportionally
less than prices. Below I obtain estimates that show the price elasticity of
demand falling in just this manner.
To understand why this may have happened, it is helpful to return to the
origins of the notion of a demand curve. Dupuit (1844) recognized that
consumers placed diff erent values on goods use
d for diff erent purposes. A
decrease in the price of stone would benefi t the existing users of stone, but
consumers would also buy stone at the lower price for new uses such as
replacing brick or wood in construction or for paving roads. In this way,
Dupuit showed how the distribution of uses at diff erent values gives rise to
what we now call a demand curve, allowing for a calculation of consumer
surplus.
This chapter proposes a parsimonious explanation for the rise and fall of
industry employment based on a simple model where consumer preferences
follow such a distribution function. The basic intuition is that when most
consumers are priced out of the market (the upper tail of the distribution),
demand elasticity will tend to be high for many common distribution func-
tions. When, thanks to technical change, price falls or income rises to the
point where most consumer needs are met (the lower tail), then the price
and income elasticities of demand will be small. The elasticity of demand
thus changes as technology brings lower prices to the aff ected industries and
higher income to consumers generally.
Artifi cial Intelligence and Jobs: The Role of Demand 297
10.2 Model
10.2.1 Simple Model of the Inverted- U
Consider production and consumption of two goods—cloth and a
general composite good—in autarky. The model will focus on the impact
of technology on employment in the textile industry under the assumption
that the output and employment in the textile industry are only a small part
of the total economy.
Production
Let the output of cloth be q = A · L, where L is textile labor and A is a measure of technical effi
ciency. Changes in A represent labor- augmenting
technical change. Note that this is distinct from those cases where automa-
tion completely replaces human labor. Bessen (2016) shows that such cases
are rare, and that the main impact of automation consists of technology
augmenting human labor.
I initially assume that product and labor markets are competitive so that
the price of cloth is
(1)
p = w/ A,
where w is the wage. Below, I will test whether this assumption holds in the
cotton and steel industries.
Then, given a demand function, D( p), equating demand with output implies D( p) = q = A L
or
(2)
L = D( p) / A.
We seek to understand whether an increase in A, representing technical
improvement, results in a decrease or increase in employment L. That
depends on the price elasticity of demand, , assuming income is constant.
Taking the partial derivative of the log of equation (2) with respect to the
log of A,
ln L
ln p
ln D( p)
= ln D( p)
1 =
1,
.
ln A
ln p
ln A
ln p
If the demand is elastic ( > 1), technical change will increase employment;
if demand is inelastic ( < 1), jobs will be lost. In addition to this price eff ect, changing income might also aff ect demand as I develop below.
Consumption
Now, consider a consumer’s demand for cloth. Suppose that the con-
sumer places diff erent values on diff erent uses of cloth. The consumer’s fi rst
298 James Bessen
set of clothing might be very valuable and the consumer might be willing
to purchase even if the price is quite high. But cloth draperies might be a
luxury that the consumer would not be willing to purchase unless the price
is modest. Following Dupuit (1844) and the derivation of consumer surplus
used in industrial organization theory, these diff erent values can be repre-
sented by a distribution function. Suppose that the consumer has a number
of uses for cloth that each give her value v, no more, no less. The total yards of cloth that these uses require can be represented as f ( v). That is, when the uses are ordered by increasing value, f ( v) is a scaled density function giving the yards of cloth for value v. If we suppose that our consumer will purchase cloth for all uses where the value received exceeds the price of cloth, v > p, then for price p, her demand is
p
D( p) = f ( z) dz = 1 F( p), F( p) f ( z) dz,
p
0
where I have normalized demand so that maximum demand is 1. With this
normalization, f is the density function and F is the cumulative distribution function. I assume that these functions are continuous, with continuous
derivatives for p > 0.
The total value she receives from these purchases is then the sum of the
values of all uses purchased,
U ( p) = z f ( z) dz.
p
This quantity measures the gross consumer surplus and can be related to the
standard measure of net consumer surplus used in industrial organization
theory (Tirole 1988, 8) after integrating by parts:
U ( p) = z f ( z) dz = – z D ( z) dz = p D( p) + D( z) dz.
p
p
p
In words, gross consumer surplus equals the consumer’s expenditure plus
net consumer surplus. I interpret U as the utility that the consumer derives
from cloth.5
The consumer also derives utility from consumption of the general good,
x, and from leisure time. Let the portion of time the consumer works be l so that leisure time is 1 – l. Assume that the utility from these goods is additively separable from the utility of cloth so that total utility is
5. Note that in order to use this model of preferences to analyze demand over time, one of two assumptions must hold. Either there are no signifi cant close substitutes for cloth or the prices of these close substitutes change relatively little. Otherwise, consumers would have to take the changing price of the potential substitute into account before deciding which to purchase.
If there is a close substitute with a relatively static price, the value v can be reinterpreted as the value relative to the alternative. Below I look specifi cally at the role of close substitutes for cotton cloth, steel, and motor vehicles.
Artifi cial Intelligence and Jobs: The Role of Demand 299
U ( v) + G( x,1 l),
where G is a concave diff erentiable function. The consumer will select v, x, and l to maximize total utility subject to the budget constraint
wl
x + pD( v),
where the price of the composite good is taken as numeraire. The consumer’s
Lagrangean can be written
L( v, x, l) = U( v) + G( x,1 l) + ( wl x p D( v)).
Taking the fi rst order conditions, and recalling that under competitive mar-
kets, p = w / A, we get
p
G
ˆ
v = G
= Gl , G
;
l w
A
l
l
G represents the marginal value of leisure time and the second equality
l
results from applying assumption (1). In eff ect, the consumer will purchase
cloth for uses that are at least as valuable as the real cost of cloth valued
relative to leisure time. Note that if G is constant, the eff ect of prices and the l
eff ect of income are inversely related. This means that the price elasticity of
demand will equal the income elasticity of demand. However, the mar
ginal
value of leisure time might very well increase or decrease with income; for
example, if the labor supply is backward bending, greater income might
decrease equilibrium G so that leisure time increases. To capture that notion, l
I parameterize G = w so that
l
(3)
ˆ
v = w / A = w 1 p, D( ˆ v) = 1 F( ˆ v).
10.2.2 Elasticities
Using equation (3), the price elasticity of demand holding wages constant
solves to
ln ˆ
v
=
ln D = ln D( ˆ v)
= pf ( ˆ v) w 1,
ln p
ln ˆ
v
ln p
1
F ( ˆ
v)
and the income (wage) elasticity of demand holding price constant is
ln ˆ
v
= ln D = ln D( ˆ v)
= 1
(
) .
ln w
ln ˆ
v
ln w
These elasticities change with prices and wages or alternatively with
changes in labor productivity, A. The changes can create an inverted- U in
employment. Specifi cally, if the price elasticity of demand, ε, is greater than
1 at high prices and lower than 1 at low prices, then employment will trace an
inverted- U as prices decline with productivity growth. At high prices relative
to income, productivity improvements will create suffi
cient demand to off set
job losses; at low prices relative to income, they will not.
300 James Bessen
A preference distribution function with this property can generate a kind
of industry life cycle as technology continually improves labor productiv-
ity over a long period of time. An early stage industry will have high prices
and large unmet demand, so that price decreases result in sharp increases in
demand; a mature industry will have satiated demand so further price drops
only produce an anemic increase in demand.
A necessary condition for this pattern is that the price elasticity of demand
must increase with price over some signifi cant domain, so that it is smaller
than 1 at low prices but larger than 1 at high prices. It turns out that many
distribution functions have this property. This can be seen from the following
propositions (proofs in the appendix):