The Rules of Contagion

One signature feature of a bubble is that it grows rapidly, with the
rate of buying activity increasing over time. Bubbles often feature
what’s known as ‘super-exponential’ growth;[25] not only does the
buying activity accelerate, the acceleration itself accelerates. With
every increase in price, even more investors join in, driving the price
higher. And like an infection, the faster a bubble grows, the faster it
will burn through the population of susceptible people.
Unfortunately, it can be difficult to know how many people out there
are still susceptible. This is a common problem when analysing an
outbreak: during the initial growth phase, it’s hard to work out how far
through we are. For infectious disease outbreaks, a lot depends on
how many infections show up as cases. Suppose most infections go
unreported. This means that for every case we see, there will be a lot
of other new infections out there, reducing the number of people who
are still susceptible. In contrast, if the majority of infections are
reported, there could still be a lot of people at risk of infection. One
way around this problem is to collect and test blood samples from a
population. If most people have already been infected and developed
immunity to the disease, it’s unlikely the outbreak can continue for
much longer. Of course, it’s not always possible to collect a large
number of samples in a short space of time. Even so, we can still say
something about the maximum possible outbreak size. By definition,
it’s impossible to have more infections than there are people in the
population.
Things aren’t so simple for financial bubbles. People can leverage
their trades, borrowing money to cover additional investments. This
makes it much harder to estimate how much susceptibility there is,
and hence what phase of the bubble we’re in. Still, it is sometimes
possible to spot the signals of unsustainable growth. As the dot-com
bubble grew in the late 1990s, a common justification for rising prices
was the claim that internet traffic was doubling every 100 days. This
explained why infrastructure companies were being valued at
hundreds of billions of dollars and investors were pouring money into
internet providers like WorldCom. But the claim was nonsense. In
1998, Andrew Odlyzko, then a researcher at AT&T labs, realised the
internet was growing at a much slower rate, taking about a year to