72 Finance & economics The Economist May 7th 2022
GrowingSolow
F
rom thepoint of view of the 1950s, America’s economic pro
gress over the 70 years that followed has been a huge disap
pointment. Futurists foresaw a world of superpills, space farms
and cities encased in glass. Science and technology would engi
neer unending riches and everything consumers could ever want.
Yet the speed of gains achieved during the Space Age, it turned out,
soon ebbed: between 2000 and 2019 America’s real income per
head grew by 1.2% a year on average, down from 2% between 1980
and 1999 and 2.5% in the 1950s. And instead of flying cars, Peter
Thiel, a venture capitalist, once jibed, “we got 140 characters”.
A new paper suggests such disappointment is not warranted—
because it stems from an equally huge misunderstanding of how
economic progress happens. Thomas Philippon, a professor of fi
nance at New York University, argues the postwar experience was
unusual. Looking at American data going back to 1890 and British
data from 1600 to 1914 he finds that, when technological progress
is properly understood, the world has been on broadly the same
path for centuries. In the grand scheme of things, in other words,
there has been no slowdown at all.
Most economists’ starting point for thinking about growth is
Robert Solow’s 1956 paper, “A contribution to the theory of growth”.
Mr Solow’s model for predicting a country’s longterm wealth re
lies on what he dubs the “production function”. It is a mathemat
ical black box: on one side labour and capital go in; out the other
come all the consumer goods and services that contribute to peo
ple’s standard of living. One way of growing is obvious: shove
more labour and capital into the box. But that cannot deliver im
provements for ever. Adding more labour means the output is di
vided between more workers. And capital wears out, so more in
vestment is needed over time just to stay put.
Instead longterm growth can only come from improving the
black box—the way in which labour and capital are combined. The
fancy name economists give to this is total factor productivity
(tfp), though they sometimes refer to it with more intuitive la
bels, such as technology or knowledge. You might think of it as a
recipe. On one side lie labour and capital, the ingredients. On the
other is the finished dish: economic output. tfpis an attempt to
measure how effective the recipe is at combining the ingredients,which in turn depends on factors including the level of education
on offer to the population, the quality of business management
and the depth of scientific knowhow.
Mr Solow assumed that the annual contribution of tfpto gdp
would grow exponentially. This may have been for purely mathe
matical reasons: he wanted his model economy to grow at a fixed
rate, of say 2% a year, which required ever larger gains as gdpgot
bigger to keep the pace of growth constant. Later economists, in
cluding Paul Romer, a Nobel Prizewinner, have tried to work out
the chemistry underpinning tfp’s presumed exponential growth.
Their theories usually contend that some investment goes not in
to capital, but into research and development. And because
knowledge can be freely copied, they observe, this investment has
an increasing marginal product, meaning that each prior bit of re
search makes the next bit of research more effective. Knowledge
thus cascades out, creating more knowledge as it does, akin to
how a virus spreads in the early stage of an epidemic.
The problem, according to Mr Philippon, is that tfpdoes not
actually grow exponentially. Using the most popular data sources
for longterm growth, he compares predictions from two different
models to observed trends in tfp. A linear pattern—which he calls
“additive growth”—consistently fits better with how progress has
actually unfolded. Contrary to existing theories, that suggests pre
vious research does not make the next idea any easier to find. It al
so explains why, as Mr Philippon puts it, some economists keep
predicting some future wave of innovation that just never comes.
This is not a counsel of despair. While the rate of growth in per
centage terms may be slowing, Mr Philippon’s model predicts that
the size of any increment is roughly constant. Societies do get
richer—but just not as fast as generally thought.
Encouragingly, Mr Philippon also finds evidence of moments
when the rate of tfpgrowth does temporarily accelerate and the
annual increment gets higher. His paper plots one such moment
in Britain between 1650 and 1700, and another around 1830, consis
tent with when historians date the first and second Industrial Rev
olutions. He also finds one in America around 1930, which he cred
its to the adoption of electrification. Such moments only seem to
take place about every century or so. But they do help to explain Mr
Solow’s mistake: it would have been easy for him, as he was living
through one of these periods of acceleration, to fall for the illusion
of exponential progress.The ways of growth are inscrutable
Mr Philippon’s statistical analysis does not speak to tfp’s deeper
conceptual problems. One is that capital is hard to value. There is
usually a difference between its historical cost, suitably depreciat
ed, and the discounted value of the profits it will eventually pro
duce. Unlike labour, which can be quantified in hours, there is no
nonmonetary unit with which to value oil rigs and pharmaceuti
cal patents alike. After Mr Solow’s 1956 paper came out, a group of
economists at the University of Cambridge showed that its meth
od for valuing capital was circular, a point Mr Solow’s followers
conceded. But the model is still widely used regardless.
Similar problems bedevil tfpitself. Statistical techniques that
try to measure the concept of “knowledge” typically bundle all the
variation in growth that cannot be explained by changes in the
workforce or investment into the black box. Hence tfp’s other,
less flattering name—the “Solow residual”. Rather than areliable
metric of society’s level of knowledge, tfpso far seems toremain,
in the words of a Solow critic, a “measure of our ignorance”.nFree exchange
A calming explanation for why economic progress often disappoints