Economic Growth in the Long Run: Artificial Intelligence Explosion or an Empty Planet?

so welcome to our webinar on the
governance and economics of ai
i'm glad that so many of you from all
corners
of the earth are joining us today i'm
anton kornick i'm an economist
at the university of virginia and the
topic of our webinar today
is economic growth in the long run will
there be an
artificial intelligence explosion or an
empty planet
and we have two eminent speakers ben
jones and judge jones
as well as two distinguished discussants
rachel nye and phil drama i will
introduce each one of them
more fully when they are taking the
stage we are excited
to have this discussion today because
the field of economic growth theory
has gone through a really interesting
resurgence in recent years
so at the risk of oversimplifying
a lot of growth theory in the past has
focused on describing
or explaining the steady-state growth
experience
that much of the advanced world has
experienced in the post-war period
that was captured in what economists
call the calder facts
but in recent years a chorus of
technologists
especially in the field of ai have
emphasized
that there is no natural law that growth
in the future
has to continue on the same trajectory
as it has in the past
and they have spoken of the possibility
of an
artificial intelligence explosion or
even a singularity
in economic growth our two speakers
ben jones and chad jones have been at
the forefront of this literature
in a paper that is published in an nvr
volume on the economics of ai
and ben will tell us a bit about this
today
and since an explosion in economic
growth is by no means guaranteed
chad will then remind us that the range
of possible outcomes for economic growth
is indeed vast and we cannot rule out
that growth may in fact go in the other
direction
our webinar today is co-organized
by the center for the governance of ai
at oxford's future of humanity institute
and by the university of virginia's
human and machine intelligence group
both of which i'm glad to be a member of
it is also sponsored
by uva's darden school of business
and uh before i yield to our speakers
let me thank everyone
who has worked hard to put this event
together
alan daffo marcus anderjung and leroux
at the center for the governance of ai
and paul humphries
at the uv machine human machine
intelligence group
as well as ask me yousef at darden
so let me now introduce ben
jones uh more formally
ben is the gordon enduro grand family
professor of entrepreneurship
at the kellogg school of management at
northwestern
he studies the sources of economic
growth in advanced economies
with an emphasis on innovation
entrepreneurship
and scientific progress he also studies
global economic development including
the roles of education
climate and national leadership in
explaining the wealth and poverty
of nations and his research has appeared
in many of the top journals of the field
and has been profiled
in media outlets like the wall street
journal the economist
and the new yorker then the
virtual floor is yours
okay thank you very much uh anton uh for
that introduction and let me share my
screen here
uh it's great to be with you uh to talk
about these these issues and thanks
again to anton and the organizers for
putting this together and for inviting
me to participate
um so the first paper the one i'm gonna
talk about is actually joint with chad
your second speaker
uh he's gonna appear in both uh and this
is also with philippe aguion
and the idea in this paper uh was rather
than sort of a typical
economics paper where you go super deep
into one model and
you know do all the details this was
really to kind of step back
and look at the kind of breadth of
growth models that we have
and then say you know well how would you
insert artificial intelligence into this
search more standard understandings of
growth and where would that lead us
and so we actually have a series of sort
of toy models here
uh and they can of course you know
exploring you know the variety of
directions this can lead us
and seeing what you kind of have to
believe in order for those various
outcomes to
to occur so that's kind of the the idea
behind this paper
um and you know i'm to do this in an
almost extremely non-mathematical way
not a completely math free way but i
know that this is a
this is a seminar with a a group of
people with diverse
uh disciplinary backgrounds so i don't
want to presume people are steeped in
endogenous growth models
uh so i'm gonna try to really emphasize
the intuition as i go uh to the best
that i can
i will have to show a little bit of math
a couple times but not too much okay so
so the idea in this paper is okay how
would we think about ai and you might
think that ai
you know helps us make you know goods
and services and you know things things
that go into gdp
and that we consume uh it also
you know might help us be more creative
okay so we're gonna distinguish between
ai
entering kind of the ordinary production
function for goods and services in the
economy
but also that it might go into the
so-called knowledge production function
into r
d and it might help us you know succeed
better in in
revealing new insights and and uh and
breakthroughs
uh uh about uh the world and the economy
and then the kind of implications we
want to look at just two very high level
implications you know what what will
happen to long run growth under various
assumptions what do you have to believe
to get different
outcomes in terms of the rate at which
standards of living are improving
but also inequality what share like the
gdp might go up gdp per capita
might go up but what share of that is
going to go to
labor particular workers is obviously a
lot of fear that ai would displace
workers
uh and that may be more and more of the
fruits of of income will go to the
owners of the capital say the owners of
the ai
and then of course there's this other
idea almost more from science fiction it
seems but you know taken seriously by
some in the
and certainly the computer science
community that we might actually
experience
radical accelerations in growth even to
the point of some
singularity anton reference to growth
has been very steady according to sort
of
you know since the industrial revolution
uh and
and but maybe we're going to see an
actual structural break where things
will really
really take off and of course i think
chad's paper hill show later is
maybe going the other way uh potentially
we'll explore that as well
um all together okay so how are we gonna
think about ai and
you might think ai is this radically new
thing and in some ways it is but
you know one way to think about it is
that we are we are
you know furthering automation right
what are we doing we're taking a task
that is performed by labor
maybe reading a radiology you know
result in a medical setting
and then we're going to have a machine
or algorithm do that for us right
um and we're going to be you know image
search on google i used to have to
categorize which is a
cat and now google can just have an ai
that tells us which which image is a cat
um but if you think about it in
automationdirect it can be very useful
because then we can sort of think about
ai
in more standard terms that we're used
to to some extent
in economics so if you think in the past
you know the industrial revolution was
largely about
replacing labor with certain kinds of
capital equipment
maybe that was textile looms and steam
engines for power
you know ai is sort of a continuation of
that process in this view and it's
things like you know driverless cars and
and pathology and other another
applications so that's one main theme in
the work and how we want to introduce ai
into our thinking of growth and see
where it takes us
the the second main theme that really
comes out in this paper we developed
writing it
is that we want to be very careful to
think about not just what we get good at
but what we're not so good at and the
idea that growth might be determined
more by bottlenecks the growth may be
you know constrained not by what we get
really good at but what is actually
really important what is essential
and yet it's hard to improve and i'll
make a lot of sense of that as we go
intuitively but just
so what are we saying so i have a
picture that these guys are sugar beet
farmers you know pulling sugar
beets out of the ground by hand
harvesting them and that was done this
is a
kind of combine harvester harvester type
machine that's you know automating that
and pulling sugar beets out of the
ground
uh with a machine so that's kind of like
20th century automation
and then a lower graph lower picture i'm
trying to think about you know
automation as
as ai uh and on the left if you've seen
the movie hidden figures
these are the computers i always think
it's very interesting so computer was
actually a job description
these women were computers at nasa
involved in space flight
and they were actually doing
computational calculations by hand
and then on the right i have one of
nasa's supercomputers who have basically
replaced
that job description entirely so we see
a lot of laborers being replaced by
capital
raising productivity but also displacing
workers and so how do we think about
those forces
okay so one way to think about this
model is to start with azir's model
which is the following so imagine
there's just n different things we do
in the economy and different tasks and
each task
represents the same constant share of
gdp of total output
and to an economist here that would
sound let's call it douglas right so we
that's a
douglas model but if you're not
economist ignore that we just imagine
the tasks
you know every task is an equivalent
share of gdp for simplicity
and when we think about automation what
we're saying is that a task you know was
done by
labor but now it might be done by
capital equipment instead ai would be a
computer an
algorithm a combine harvester would be a
piece of farming equipment
automation and so if you think that a
fraction of the tasks beta
so there's you know of all the tasks one
for beta percent are automated
then the capital share of total gdp is
beta so that means labor gets one minus
beta
and then the expenditure on the capital
equipment is a beta share of gdp
okay so that would seem that's a very
simple model
it's very elegant in a way and it would
say that if we keep automating if you
increase
beta we keep taking tax that were done
by labor and replacing them with
machines
or ai what will happen well the capital
share of income will increase and the
labor share of income will decrease so
that sounds like it will be
you know inequality in a create
inequality in the sense that labor
will get less less income that might
sound very natural maybe think it's
what's happening today we have seen the
capital share it seems to be going up
right in a lot of countries and advanced
economies and like in the u.s
um it seems like there's a lot of
automation going on from robots to these
new ai type things
those are of course just two trends
though so maybe they just happen to be
correlated we think that the ai
is causing causing that rise in the
capital chair well this would be a model
in which that could be true
the problem with that model though is if
you look backwards we've seen tons of
automation like sugar beads or so many
other things robots and auto
manufacturing automobile manufacturing
uh
that you know we didn't see the capital
chair go up in the 20th century it was
very very steady
so that suggests that if you know this
wouldn't really fit kind of our
normal understanding of automation and
so it's not clear that this seems like
quite the right model
so how can we repair it a simple way to
repair it uh it was what really did one
idea that we developed in the paper
is to introduce so-called baumel's cost
disease which is that the better you get
at a task the less you spend on it
so as you automate more tasks maybe the
capital share wants to go up
but something else also happens right so
if i automate a task like collecting
sugar beats
what can i do i can start throwing a lot
more capital at that task i can keep
getting more and more machines and doing
sugar beats
right and moreover the capital i put at
the task the capital equipment
might get better and better i first used
a pretty rudimentary type of capital and
eventually
these very fancy fancy machines or i
introduced computers but then computers
get faster
if you throw more capital or better
capital at it what's going to happen
well you're going to get more productive
at getting sugar beats or doing
computation at nasa
and so the cost of doing the task is
going to drop but if the cost drops and
things are kind of competitive in the
market
the price should drop right the price
will also drop
so what's going on you can do more of it
a greater quantity
but the price of the task you're
performing will fall
so what's the share in gdp well the
quantity is going up but the price is
falling
if the price is falling fast enough then
actually the share in gdp
will go down even though you do more of
it so you get more sugar beats but the
price sugar beats plummets
and so sugar beats as a share of gdp is
actually declining
and then what happens is that the
non-automated sort of bottleneck tasks
the ones you're not very good at
actually come to dominate even more and
more okay so if you think backwards in
you know 20th century history are
done by the industrial revolution we see
that agriculture
and manufacturing have had rapid
productivity growth and lots of apparent
automation like sugar beets
yet agriculture and manufacturing
agriculture surely having
dwindling and dwindling share of gdp and
manufacturing gdp shares also seem to be
going down so it's like what you get
good at and what you automate actually
interestingly
becomes less important with time it
starts to disappear in the overall
economy
we're left with things like health
services education services government
services
this is bumble's cost disease point
things that we find hard to improve the
hard stuff
actually comes to take on a larger and
larger share of gdp and if we can't
improve that
then our chances for growth because it
matters so much to gdp
dwindle okay so in this view the ira
capital share is the balance between
automating more tasks which tends to
make the capital share go up
but the expenditure share in each task
declines and that tends to make it go
down
so what a model we offer in this paper
is what we can call
more of the same maybe that's what ai is
maybe ai is just more balanced growth
and we keep automating more and more
tasks but then they keep becoming a
dwindling share of the economy
and we never automate everything and you
can actually show as we do in the paper
a model
where even though i think this is all
the set of tasks and a greater and
greater share being done by
capital equipment and artificial
intelligence and a tinier and tinier
share being done by labor
even though labor gets stuck in a very
very small share it still actually gets
say two-thirds of gdp it still gets the
same historical number
and again why is that is because this
stuff all the labor
all the capital stuff is doing more
tasks but it's prices plummeting because
we're so good at it
and you're left with just a small set of
tasks being done by labor but paying
enormously for them
okay and that may be what's going on in
the economy maybe that's what's been
going on in the 20th century certainly
consistent with what's been going on in
20th century to you know first order
without overstating that case
but it's it's broadly consistent with
the stylized facts of growth
but that would suggest ai is again just
more of the same we just keep automating
it so here's a simulation from our paper
this is steady state growth you look on
the x-axis we're looking over you know
five centuries
you get steady state growth even as
what's happening with automation here's
the green line
the green line you're ultimately
automating almost everything you're just
sort of slowly automating everything
you never quite get to the end and you
just get constant growth and you get you
can get a constant capital share
okay not a we're not a rising capital
ship and so actually this is an idea
that i've been
developing a new paper which is almost
done that's sort of seeing how we how
much we how far we can go along this
this line um okay but let's go a
different pack because a lot of people
who observe
artificial intelligence are excited by
the possibility that maybe it will
accelerate growth
and you know many futurists make these
claims that we could even get some
massive accel
acceleration something like a
singularity so we explore that in this
paper as well
and so what would you have to believe
for this to happen um
so we considered we kind of consider two
different typologies of a growth
explosion
what we call a type one growth explosion
where the growth rates we're going to
depart from this
steady state 20th century 20 early 21st
century experience
and we're going to see a slow
acceleration growth maybe to very very
high levels
we'll call that a type 1 growth
explosion uh and the other would be a
type 2 where we mean a literal
in a mathematical sense singularity
where you go to infinity in productivity
and income
uh in some finite point in time in the
future you actually literally have a
singularity
where you go to you go to infinity so
and you can actually surprisingly
using sort of standard growth reasoning
and automation you can get either of
those outcomes all right so the first
one a simple example and they're more
but one example of the first one
is when you do achieve complete
automation so not just you kind of keep
automating at a rate and never quite
finished
now we're going to fully automate here's
my first equation y
gdp k capital
that's the automation capital that's all
the combat harvesters and the
super computers and the ai and then a is
the kind of the quality of the capital
the productivity of one unit of capital
all right if you so this is fully
automating in other words there's no
labor there there's no l
the labor is now irrelevant to
production of gdp we can do the whole
thing just with machines that's what
that's saying
it just depends on k and the quality of
decay which we call
a if you look at that what's the growth
rate in y it's going to be the growth
rate and y is the growth rate in a so
for gdp the growth in gdp is the growth
rate in a
the technology level plus the growth
rating capital now but the thing about
capital which is really interesting and
different from labor which i think is
where chad's going to be going in his
paper
is that you know with with capital you
can keep making more and more of it
right because you make how do you make
capital well you invest in it you build
it
and that comes out of gdp so think about
this equation if i push up capital
i get more output and then without more
output i can invest more
okay and then more importantly if i push
up the level of technology
i get more and more for every unit of
capital that increases gdp i can invest
more and keep building more capital
okay so the growth rate actually turns
out to be what's below i'm ignoring
depreciation
but basically you can see that as long
as you keep pushing up a
if you can keep pushing up the level of
technology so you keep improving the ai
you keep improving computers uh the
growth rate's going to track with a and
it's going to keep going up and up and
up and up and this is a type 1 growth
explosion so called y it's an ak model
it's a standard model in endogenous and
early standard model and endogenous
growth theory
if we can automate everything that
suggests in fact
that we could have a very sharp effect
on the growth rate that's a very
uh strong view of one view of what ai
might do
interestingly another place to put ai as
i
alluded to in the very beginning is you
could put it into creativity and
innovation itself
and if you do that things can really
take off all right so this is a
knowledge production function a dot
is the rate of change of the level of
technology the quality of the capital
and if i fully automate how we produce
that again there's no labor in this
equation it just depends on capital
and then the state of technology itself
a and that's going to act a lot like the
second equation
which is that the growth in a is going
to depend on the level of a to some
parameter phi
and that's like positive feedback i push
up a growth goes up in a
which causes growth and y to go up i
push up both you know and then a goes up
and then you go like this okay
and that actually will produce if you
solve the differential symbol
differential equation it does produce a
true mathematical singularity it'll be
some point in time t
star which is definable at which we will
achieve infinite productivity all right
now maybe that sounds like a fantasy and
it would be a fantasy
if if so because there may be certain
obstacles to that happening and then
i'll just go very quickly through a
couple one obstacle
is that you just simply can't automate
everything right so both of those models
assume
you can get to a lot of automation right
but maybe automation is very it's
actually very hard
maybe though it's easy to automate sugar
beats but there are just certain
cognitive tasks for example with regard
to ai
that are going to be very very hard to
automate if we never get to full
automation we can still get growth to go
up
but we're never going to get these kind
of singularities in these models
okay in the simplest form so if you
think that there are some
kind of bottleneck tasks that we can't
automate uh then we're gonna get again
we're not we're not gonna get these
labor-free
full automation singularities you have
to believe that you know to some extent
that we can truly automate all these
things and of course that's an open
question with ai
but how far it can go in goods and
services production and sort of creative
innovative activity
a second a second constraint kind of the
latter two constraints on substances
come from the universe itself which is
this differential equation at the top if
that parameter phi is greater than zero
it will give you a singularity you will
get one
okay you fully automate idea production
and you will get one in finite time
but the question then is really whether
we believe that parameter phi is
actually larger than zero
what that what is that saying it's
saying that if it's greater than zero
then when i increase a i increase the
level of technology in the economy i
make future growth faster
right but if phi is less than zero what
happens when i when i raise the level of
existing technology and phi is less than
zero i make future growth
slower it takes away that positive
feedback loop okay
and then you don't get a singularity and
there are good reasons to think that phi
might be less than zero we don't know
but there are reasons to think it
because let's say that like there's only
so many good ideas in the universe and
we came up with calculus and we came up
with the good ones early
and the remaining ones are hard to
discover or just there aren't that many
good ones left and so if you think we're
kind of fishing out the pond
right think of ai as like changing the
fisherman we get better fishermen on the
edge of the pond
but if the pond itself is running out of
fish big fish for us of new ideas
it doesn't matter what your fishermen
are there's nothing left in the pawn to
catch
uh and then there's some other i have an
other version that called the burden of
knowledge but
regardless there are some ideas of
in in the existing economic growth
literature about science and innovation
that suggests find well maybe less than
zero and that's just going to turn off
that
singularity and then the third one which
is somewhat related
is that there just might be bottleneck
tasks and this kind of comes back to
that bomball cost disease reasoning but
more at a task level
so for example you know let's say that
gdp here is actually
you know it's a combination of our
output and all these tasks in the most
simple form let's say it's the minimum
so this is a very real bottleneck
you're only as good as your weakest link
it's one version of a simple version of
abominable cost disease
so if it's the min function it doesn't
matter how good you get at every task
the only thing that matters is how good
you are at your worst test right
so in other words we might be really
really good at agriculture but at the
end of the day we're really bad at
something else and so that's what's
holding us back
um and you know i think actually this is
actually quite instructive because
think about moore's law people get so
excited about moore's law in computing
and a lot of people who believe in
singularities
are staring at the moore's law curve and
it's this incredibly dramatic
exponential
rapid rapid rapid increase in
productivity which is
mind-boggling in a way at the same time
this has been going on for a long time
that moore's law and if you look at
economic growth we don't see an
acceleration
right if anything we probably see it
slow down right and that suggests that
no matter how good you get at computers
there are other things
holding us back like it still takes as
long to get from
you know one point on a map to another
based on the
available transportation technologies
that's not really changing um
so you know as going back to the bomb
theme if things are really depend on
what we're sort of
what is essential but hard to improve we
can actually take our computing
productivity to infinity literally and
it just doesn't matter
it won't it'll help it'll make us richer
it's good but it won't fundamentally
change
our growth prospects unless we can go
after the hard problems that are the
hard ones to solve
so to conclude you know this these are a
whole series of models obviously we do
this at much greater length in the paper
if you'd like to read it
um you can put ai in the production of
goods and services
you know if you can't fully automate but
just kind of slowly automate you kind of
looks like more of the same it's sort of
a natural way to go
but if you can get to full automation
where you don't need labor anymore you
can get a rapid acceleration and growth
through this so-called
what we call a type 1 singularity when
you put a ai in the
product ideas production function in the
creation of new knowledge
you can get even stronger growth effects
and that in fact could even lead to one
of these true mathematical singularities
sort of in science fiction
but there are a bunch of reasons in both
cases to think that
we might be limited because of other
automation limits because their search
limits and that creative process really
with regard to the knowledge production
function
or more generally in either setting with
natural laws like you know i didn't say
it a lot but like the second
law of thermodynamics seems like a big
constraint on energy efficiency
that we're actually pretty close to uh
in current technology and if energy
matters then you know
that's going to be a bottleneck even if
we can get other things to sort of
skyrocket in terms of productivity and
so i think a theme that you know chad
and i certainly came to
writing this paper was the kind of
interesting idea that you know
ultimately growth seems determined
potentially not by what you are good at
but by what is essential yet hard to
improve and and that
that is kind of a important force to
keep in mind when we all get excited
about
where we are advancing quickly and then
we go back to the aggregate numbers and
we don't see much progress
this is just like a pretty useful way
potentially to frame that and begin to
think about it maybe we should be
putting a lot of our effort into
thinking about what we're bad at
improving
and why that is if we really want to
understand future
growth and standards of living um okay
so i i went pretty quickly but hopefully
i would use my time
i didn't spill over too much beyond my
time and uh look forward to the
discussions
from thanks rachel and phil in advance
and look forward to chad's comments as
well
thank you thank you ben the timing was
perfect
and to all our participants let me
invite you
to submit questions through the q a
field at the bottom of the screen
after all the presentations we will
continue the event with the discussions
of the points that you are raising and
incidentally to the speakers
if there are some questions
clarification question for example
where you can type a quick response feel
free
to respond to a q a in the q and a box
directly
so let me now turn over to chad chad
jones is the stanco 25 professor of
economics
at the stanford graduate school of
business he is noted for his research on
long-term
economic growth and in particular he has
examined the fundamental sources of
growth in income
over time and the reason underlying the
enormous differences in standards of
living across countries
in recent years he has used his
expertise
in macroeconomic methods to study the
economic
causes behind the rise in health
spending
and top income inequality and he's the
author of one of the most popular
textbooks
in macroeconomics as well as very well
published
in the top journals in economics chad
the floor is yours
wonderful thanks very much anton it's
really a pleasure to to be here
um i think antoine did a great job of
introducing this session in in pairing
these
these two papers together um as he said
you know a lot of growth theory
historically has looked back and tried
to understand how can constant
exponential growth be possible for 100
years
and the first paper that ben presented
kind of looked at you know
automation artificial intelligence and
possibilities for growth rates to
to rise and even explode this paper is
going to look at the opposite
possibility
and you know ask could there be
uh you know the end of economic growth
and i think
all these all these ideas are worth
exploring and i guess my general
perspective is you know part of the role
of economic theory
is to you know zoom in on particular
forces and study them closely
and then at the end of the day we can
come back and ask well how do these
different forces play against each other
so that's kind of the spirit of this
paper
okay so um a large number of growth
models work this way basically people
produce ideas
and those ideas are the engine of
economic growth so
you know the original papers by paul
romer and egg young and howard and
grossman and helmand work this way
these sort of semi-endogenous growth
models that i've worked on and sam
gordom
and paul sneakerstrom uh basically all
idea driven growth models work this way
people produce ideas and ideas drive
growth
now these models typically assume that
population
is either constant or growing
exponentially
and for historical purposes that seems
like a good assumption
an interesting question to think about
though is what does the future hold
um from this perspective i would say
before i started this paper
my view of the future of global
population which i think of as kind of
the conventional view
is that it was likely to stabilize at 8
or ten billion people
you know 100 years from now or something
um
interestingly there was a paper a book
published last year by bricker and
ibbitson called empty planet
and this book made a point that after
you see it is
you know very compelling and interesting
they claim that maybe the future
is actually not one where world
population stabilizes
maybe the future is one where world
population declines maybe the future is
negative population growth
and the evidence for that is remarkably
strong i would say
in that high income countries already
have fertility rates that are below
replacement
so the total fertility rate is sort of a
measure in the cross section
of how many kids are women having on
average
and you know obviously two is a special
number here if women are having more
than two kids
on average then population is going to
tend to rise if women are having fewer
than two kids
on average then population will decline
and maybe it's 2.1 to take into account
mortality but but you get the idea
the interesting fact you know
highlighted by bricker and evanson and
well known to demographers
is that fertility rates in many many
countries especially advanced countries
are already below replacement so the
fertility rate in the u.s is about 1.8
in high income countries as a whole 1.7
china 1.7 germany 1.6 japan
italy and spain even lowered 1.3 or 1.4
so in many advanced countries fertility
rates are already well below replacement
and then if we look historically you
know again we kind of all know this
graph
qualitatively fertility rates have been
declining so take
india for example in the 1950s and 60s
the total fertility rate in india was
something like six women had six kids on
average
and then it fell to five then to four
and then to three
and the latest numbers in india i think
are 2.5 or 2.4
but the perspective you get from this
kind of graph is
well if we wait another decade or two
even india may have fertility below
replacement rates fertility rates have
been falling all over
the world and
maybe they're going to end up below too
so the question in this paper is
what happens to economic growth if the
future of population growth
is that it's negative rather than zero
or positive
right and the way the paper structures
it considers this possibility from two
perspectives
first let's just feed in exogenous
population growth let's just assume
population growth is negative half a
percent per year forever
feed that into the standard models and
then see what happens
and the really surprising thing that
happens is you get a result that i call
in honor of the book
the the empty planet result and that is
that
not only does the population vanish with
negative population growth
you know the global population is
disappearing
but while that happens living standards
stagnate
so this is you know quite a negative
result living standards stagnate
for a vanishing number of people and it
contrasts with the standard
you know growth model result that you
know all these growth models that i
that i mentioned earlier have which i
i'm now going to call an expanding
cosmos result
but it's it's basically a result that
you you get exponential growth in living
standards so living standards grow
exponentially
at the same time the population grows
exponentially so on the one hand you
have this sort of traditional expanding
cosmos view of the world
and what this paper identifies is hey if
these
patterns in fertility continue we may
have a completely different kind of
result
where instead of living standards
growing for a population that itself is
growing
maybe living standards stagnate for a
population that disappears
okay then the second half of the paper
and i'll only have a chance to allude to
how this works
says well what if you endogenize the
rate of fertility what if you endogenize
the population growth
do you learn anything else and
you can get an equilibrium that features
negative population growth that's good
we can get something that looks like the
world
and the surprising result that comes out
of that model
is that even a social planner if you ask
what's the best you can do in this world
let you know
choose the allocation that maximizes the
utility of
everyone in the economy and you know
with population growth the question of
who is everyone is is an interesting
question
um but the the result here is that a
planner who prefers this expanding
cosmos result
can actually get trapped by the empty
planet outcome
and that's a surprising kind of result
it might seem like it doesn't make any
sense at all but i'll try to highlight
how it can happen
okay i'm going to skip the literature
view in the interest of time
i've already kind of told you how i'm
going to proceed
basically what i want to do is look at
this negative population growth
in the sort of classic roma framework
and then in a semi endogenous growth
framework and then go to the uh
fertility results okay so let me start
off by illustrating
this empty planet result in a set of
traditional models so
make one change in traditional models
you know instead of having
positive population growth or zero
population growth have negative
population growth and see what happens
that's that's the name of the game for
the first half of the paper
okay to to to do that let me just remind
you what the traditional results
are in a really simplified version of
the romer the roamer model
um and you know i'm sure you all know
but this this this
the model this is based on and this
paper by romer won the nobel prize in
economics a couple of years ago so this
is a
a very well respected uh important
modeling in the growth literature
so the insight that got romer the nobel
prize
was the notion that ideas are not rival
ideas uh don't suffer the same kind of
inherent scarcity as good so um if
if there's an apple on the table you can
eat it or i can eat it apples are scarce
bottles of of olive oil are scarce um
you know coal is scarce uh you know a
surgeon's time is scarce
everything in economics that we're
traditionally studying
is a scarce factor of production and
economics is the study of how you
allocate those scarce factors
but ideas are different if we've also
got the fundamental theorem of calculus
one person can use it a million people
can use it a billion people can use it
and you don't run out of the fundamental
theorem of calculus the same way you'd
run out of
apples or computers and so
that means that production is
characterized by increasing returns to
scale there's constant returns to
objects here just people
and increasing returns to objects and
ideas taken together this parameter
sigma
being positive measures the degree of
increasing returns to scale
then where do ideas come from in the
roma model there's a basic assumption
that says that you know each person can
produce
a constant proportional improvement in
productivity so the growth rate of
knowledge
is proportional to the number of people
and then the roma model just assumed
that population
was constant i'll come this is the
assumption i'm going to come back and
relax in just a second
um so if you if you solve this model
income per person lower case y is just
you know gdp divided by the number of
people that's just proportional to the
number of ideas
right the amount of knowledge each
improvement in knowledge raises
everyone's income because the
non-rivalry that's the the deep roamer
point
and then the growth rate of income per
person
depends on the growth rate of knowledge
which is proportional to population
right so this is a model where you can
get constant exponential growth
in living standards with a constant
population
and if you look at this equation you
realize well if there's population
growth in this model
that gives us exploding growth in living
standards
um we don't see exploding growth and
living standards historically
and we do see population growth so
there's some tension there and that's
what the semi-endogenous growth models
are designed to fix that i'll come back
to in a second
okay in the meantime what i want to do
is change this assumption that
population is constant
and replace it with an assumption that
the population itself is declining at a
constant exponential rate
so let ada denote this rate of
population decline
so think of eight as one percent per
year half a percent per year the
population's falling
at half a percent per year and then what
happens in this model
well if you combine the second and third
equations you get this this law of
motion for knowledge and
this differential equation is easy to
integrate right it says the growth rate
of knowledge
is itself falling at a constant
exponential rate
and not surprisingly if the growth rate
is falling exponentially
then the level is bounded that's what
happens when you integrate this
differential equation
you get the result that the stock of
knowledge
converges to some finite upper bound a
star
and since knowledge converges to some
finite upper bound
income per person does as well and you
can calculate these as functions of the
parameter values and it's interesting to
do that and i do a little bit of that
in the paper but let me let me leave it
for now by just saying
what we did is just by by changing this
assumption that population was constant
making it you know population growth
negative
you get this empty planet result you get
that living standards
asymptote they stagnate at some value y
star
as the population vanishes that's the
empty planet result
now we're going to look at this other
class of models the simian dodgers
growth class of models
and what was interesting about these
models is that
in the original framework the
the sort of roamer style models in the
simian dodgers growth models
led to very different results in the
presence of positive population growth
these models yield
very different outcomes and what's kind
of interesting is that with negative
population growth they yield very
similar outcomes
okay so again let me go through the same
kind of order as before
let me present the traditional result
with positive population growth
and then change that assumption and show
you what happens when population growth
is negative
so same goods production function we're
taking advantage of roamer's non-rivalry
here
and i'm making basically one change if
you want set lambda equal to one that
doesn't really matter
i'm introducing what ben described in
in the earlier paper as as you know this
sort of ideas are getting harder to find
force
right the fishing out force right and
beta kind of measures the rate at which
ideas are getting harder to find it says
the growth rate of knowledge is
proportional to the population
but the more ideas you discover the
harder it is
to to find the next one right and beta
measures the degree to which it's
getting harder
so beta to think of beta some positive
number
and then let's put in population growth
at some positive rate
n that's exogenous okay same equation
income per person is proportional to the
stock of ideas raised to some power
the stock of ideas is itself
proportional to the number of
people and that's an interesting finding
here which is
the more people you have the more ideas
you produce
and the more total stock of knowledge
you have and therefore the richer the
economy is
right people correspond to the economy
being rich in the long run by having
lots of ideas
not to the economy growing rapidly
that's what what happens
uh versus the earlier models and then if
you take this equation
and you know take logs and derivatives
of it it says that the growth rate of
income per person
depends on the growth rate of knowledge
which in turn depends on the growth rate
of people
the growth rate of income per person is
proportional to the rate of population
growth
where the factor of proportionality is
the degree of increasing returns to
scale in the economy essentially
okay and so this model you can have
positive population growth
being consistent with constant
exponential growth in living standards
so this is the expanding cosmos result
right we get exponential growth in
living standards
for a population that itself grows
exponentially maybe it fills the earth
maybe it fills the solar system maybe it
fills the cosmos right that's the kind
of take it to the
implausible extreme maybe a result of
this model
okay now let's do the same thing suppose
we change that assumption that
population growth is positive
to one of population growth being
negative again that kind of
remarkably i would say looks like the
future of the of the world that we live
in
right uh based on the evidence that i
presented earlier
okay so once again we've got this
differential equation you substitute
from the the
negative population growth equation in
and you see that
you know not only does the growth rate
of knowledge decline exponentially
because of this term but it falls even
faster so the growth rate of knowledge
falls even faster than exponentially
so of course the stock of knowledge is
still going to be bounded this is
another differential equation that's
really easy to integrate
and you get that once again the stock of
knowledge
is bounded right and you can play around
with the parameter values and
do some calculations um in the interest
of time
uh let me not do that let me instead say
what you know what we see let me just
sort of summarize
um is so first as a historical statement
fertility's been trending downward we
went from five kids to four kids to
three kids to two kids and now even less
in rich countries and an interesting
thing about that
is from the microeconomic perspective
from the perspective of the individual
family
there's nothing at all special about
having more than two kids or fewer than
two kids it's an individual family's
decision and some families decide on
three some families excited two
one zero whatever but there's nothing
magic
about above two versus below two from an
individual family's perspective
but the macroeconomics of the problem
makes this distinction absolutely
critical
because obviously if on average women
choose to have slightly more than two
kids
we get positive population growth
whereas if women decide to have slightly
fewer than two kids
we get negative population growth and
what i've shown you on the previous
you know four or five slides is that
that
difference makes all the difference in
the world to how we think about
growth and living standards in the
future if there's negative population
growth
that could condemn us to this empty
planet result
where living standards stagnate as the
population disappears
instead of this world we thought we
lived in where living standards were
going to keep growing exponentially
along with the population and so this
this relatively small difference
matters enormously when you project
growth forward
and the the sort of fascinating thing
about it is it seems like as an
empirical matter
we're much closer to the below two view
of the world
than we are to the above to view the
world so maybe this empty planet result
is something we should take seriously
that's i would say that
the most important finding in the paper
okay let me go to the second half of the
paper just very briefly and i won't go
through the model in detail it's
admittedly subtle and complicated and
took me a long time to understand fully
but i do want to give you the intuition
for what's going on so i write down a
model
where people choose how many kids to
have
right and in the equilibrium of this
model
um the idea part of kids is an
externality so we have kids because we
love them
and in my simple model people ignore the
fact
that their kids might you know be the
next you know
einstein and marie curry or jennifer
dude i guess
um you know with the nobel prize for
christopher
um and that they might create ideas that
benefit everyone in the world
right the individual families ignore the
fact that their kids might be isaac
newton
and so the planner is going to recognize
that you know social welfare recognizes
that having kids creates ideas and so
the planner wants you to have more kids
than you and i want to have there's an
externality in the simple model along
those lines
and admittedly this is a modeling choice
you can you know people are writing down
these kind of fertility models for a
while and
there are lots of other forces and you
can get different results i don't want
to claim this is a general result
rather i see it as illustrating an
important possibility
okay um okay
so so how do as i mentioned the key
insight that you get out of studying
this this endogenous fertility model
is that the social planner can get
trapped in the empty planet even a
social planner who wants this expanding
cosmos
if they're not careful and i'll try to
say what i mean by if they're not
careful
they can get trapped in the empty planet
so how do i understand that
so in this model population growth
depends on a state variable x which you
can think of as
knowledge per person it's a to some
power divided by n to some power let me
just call it knowledge per person
and we can parameterize the model so
that the equilibrium
women have fewer than two kids and so
population growth is negative
and if population growth is negative
look at what happens to x
i've already told you that a converges
to some constant
and n is declining and so x is going off
to infinity
so in the equilibrium x is rising
forever
what about in in the optimal allocation
the allocation that maximizes some
social welfare function
well the planner's going to want us to
have kids not only because we love them
but because they produce ideas that
raise everyone's income
the key subtlety here is suppose we
start out in the equilibrium allocation
where x is rising and population growth
is negative and ask
when do we adopt the good policies that
raise fertility the planner wants you to
have more kids
do we do we adopt the the policies that
raise fertility immediately
do we wait a decade do we wait 50 years
do we wait 100 years
that's the if you're not sufficiently
careful the point is
if society waits too long to switch to
the optimal rate of fertility
well then x is going to keep rising
and the idea value of kids gets small
as x rises because remember x is
knowledge per person
as x rises we have tons of knowledge for
every person in the economy
so the marginal benefit of another piece
of knowledge is getting smaller and
smaller
so the idea value of kids is getting
smaller and smaller
and because we've already said the
loving your kids force still leads to
negative population growth
well even if you add a positive you know
idea value of kids
the planner might still want negative
population growth if you wait too long
if you wait for the idea value of kids
to shrink sufficiently low
then even the planner who ex-ante
preferred the expanding cosmos
gets trapped by the empty planet so what
this says is that
it's not enough to worry about fertility
policy we have to worry about it sooner
rather than later
and um here's just a diagram i think i'm
almost out of time let me just conclude
so what i take away from this paper is
that fertility considerations
are likely to be much more important
than we thought this distinction between
slightly above two and slightly below
two that from an individual family
standpoint
you know just barely seems to matter
from an aggregate standpoint from a
macroeconomic standpoint
is is a big deal it's the difference
between the expanding cosmos
and the empty planet um as i mentioned
when i started this is not a prediction
it's a study of one force but i think
it's it's much more likely than i would
have thought
you know before before i started this
project and
uh there are other possibilities of
course we've we've talked about one with
ai producing ideas so that people aren't
necessary
important in my production function is
that people are a necessary input
you don't get ideas without having
people and maybe id
maybe ai can change that that's
something we should discuss in the
in the open period um there are other
forces technology may affect fertility
and mortality
maybe we end up reducing the mortality
rate to zero so that even having one
kid per person is enough to keep
population growing for example
um maybe evolutionary forces favor
groups that
you know have high fertility for for for
some reason maybe it selects for those
genes and so maybe
this this you know below replacement
world we look like we're living in maybe
that's not going to happen in the long
run
but anyway i think i'm out of time let
me go ahead and stop there
thank you very much chad and um
let me remind everybody of the q and a
again
our first discussion of these ideas is
rachel
nay rachel is a professor of economics
at the london school of economics and
the research associate at the center for
economic performance
as well as a research affiliate at the
center for economic policy research
her interests include macroeconomic
topics
such as growth and development
structural transformation
as well as labor markets and housing
markets
rachel the floor is yours thank you
anton
um thank you very much for having me
discuss this
two very interesting paper there's a lot
of interesting contents in both paper
but because of time what i will focus on
is the aspect related to the future of
economic growth
and and the role played by artificial
intelligence
declining population growth now when we
talk about artificial intelligence there
are many aspects of it
there were political as a bad
philosophical aspect which
i will not have time to talk about so
today i will purely focus on
their implication for future of economic
growth
okay so economic growth is about the
improvement in the living standard
when we think about the fundamental
source of growth as both ben
and chad point out is about technology
progress
technology progress can happen through
ind
or experience which is like we will be
doing something and we get better
than in doing something but the key
thing for technological progress
is that it require brain input so far
for the last 2000 years or so the main
brain input is the human brain
so here are some examples we already
heard mentioning that how their research
outputs
have improved the living standard for
for mankind over the last
two thousand years now chuck's paper
is very interesting and it is bringing
on some something that is really
important
so here is the figure that basically
repeat what chad has shown us
he's from the united nations about the
total
the life worker woman how many child
women have as you've seen in high income
country
has already fallen below the replacement
ratio which is about two
for the world as a whole is also falling
and in fact united nations predict that
but
in 80 years the population growth will
be stagnant
so there will be zero population growth
and that means going forward will
receive negative population growth
what chad has convincingly showed is
that when that is happening we might get
the empty planet result
which is the results that living
standard will be stagnant
and human race will start to disappear
now this is really an alarming result
and the reason for this is because the
private incentive of having children
we love children do not take into
account that
the children are producing ideas that
are useful for technology
technological progress so clearly
there's a role for
policy here and which chat mentioned
earlier as well
so we could try to you know introduce
some policy that help
to exterminate people to have more
children and the problem is
if wait too long then the empty panel
results
will not be able cannot be avoided so
that is something really really
worrying then it goes to ben's paper
which gives you the alternative scenario
which to say what if we have the
following situation
okay suppose we think of human brain or
man is
basically like machine so artificial
intelligence
can replicate human brain in fact in
chinese
we say the computer we translate as in
the
electrical brain so it's really saying
its electrical brain really can
replacing
human brain if it can
then what we will obtain is that we can
avoid stagnation
which is the empty planet itself and
even more
we might be able to move through to a
technology technology singularity
where the artificial intelligence can
self-improve
and the growth can explode now i think
we are all kind of convinced by then the
singularity results
seems quite impossible because one
simple thing
one can say is that many essential
activity
that cannot be done by ai and because of
that
which is sometimes we call the bonus
effect because of that you will not get
the situation where growth explode
so let me focus on the situation whether
ai
can solve the problem that chad
mentioned
which is the stagnation result so
how possible is it really that we can
have ai
completely replace human in generating
technological progress
meaning in that d production function
we do not need human anymore we can just
have
ai in it how is that possible
so here's a brief timeline of the
development of artificial intelligence
which
is quite remarkable which started in
1950
so over the last 70 years a lot of
progress has been made
okay there's lots of great discovery
but is it enough and what do we look for
into the future
so there's a report by the stanford
university called
the artificial intelligence index report
what this shows a few points i want to
highlight
one is that human brain itself
is actually still needed in improving
ai so for the last 20 years
since uh 2010 for the last 10 years
2010 to 2019 what we've seen is
published paper about artificial
intelligence
has increased by 300 percent
and the paper online before they were
published
has increased by two thousand percent so
there's a huge
increase in how researchers are trying
to improve
ai and at the same time i we also see a
lot of students choose to go to
university to study ai so it looks like
we still need quite a lot of human brain
to pour into make the artificial
intelligence
to replace the human brain so that
progress being made in many areas but
there is a lot of you know
question here ai is good for searching
pattern
using the observed observed data okay so
that is basically how artificial
intelligence work
with big data but can it really work
like human brains
on intuition and imagination now on the
right hand side
here i took one example from this annual
report
which is to show a video to the machine
and ask the machine to recognize what is
going on in that video
when you show the video of some high
activity link
for example like zumba dancing the
precision rate is very high
the machine really pick up the activity
very easily
but if you look at these hot uh other
activities for example here it showed
the hardest activity is drinking coffee
so presumably when people enjoy their
coffee they do not do much
special movement and there's no special
characteristic
for the machine to pick up very easily
so the precision rate is less than 10
and it has been very little progress
over the last 10 years
so my take from this is that it's still
quite a long time for the artificial
intelligence
to completely replace the human brain
and
it really matters a lot to see
if the world is going to have stagnant
population in 80 years
do we have enough time to make the
artificial
intelligence replace human growth so
when you think about the future of
growth
here's the question which is less costly
and more likely
producing human brain or producing human
brain like artificial intelligence
can we human with the help of artificial
intelligence
actually create an einstein-like
artificial intelligence
it to me i don't know it seems quite
difficult
but on the other hand if we go back to
check jones paper
we say that we need policy we need
policy to
increase fertility but it's not an easy
task on its own
agitated women today face a trade-off
between
career concern and having children so
just by giving child care subsidy on
maternity leave these are costly policy
and most of the time it might not work
so when we think about fertility of
course there's lots of theory about
volatility here i'm just going to focus
on a few things
what what is behind this so if you look
at historically
how can we have very high fertility in
the past which is like five children
per woman so because
there is a big role played by family
farm so family farm on the right hand
side here is some data from the iro
which shows you how the fraction of
women working on family farm has been
declining over time
now family plum is very special it
creates demand for children
good children can help on the farm and
they also allow women to combine
home production and work but
the process of urbanization and
structural transformation
have come along with the disappearance
of family farm
modern day when a woman have to go to
work it really means
leaving home so making it incompatible
to combine home production
and work so if you look at home
production here i show you a picture
of the home production time per day and
market production time per day
for women and for men so the first bar
is the woman the second bar is men
and these two bars represent the world
what we see here is something
really striking women's hotel home hour
and child care time is triple of mad
men's
so for every one hour man that's for
home production women have to do three
hours
now that itself this kind of picture
might give
young women especially of course when
choosing whether to get married
and to have children while we see that
women's education
is rising and there is rising concern
for gender equality
so let me just conclude with this on the
future fertility
so i i hope uh you know i solo convinced
myself
you know the artificial intelligence
will take some time but if we don't
change anything in 80 years
population growth will go negative so we
need to really think about how we can do
something about fertility
child care subsidy and maternity leave
will not be enough
one possibility maybe it will help women
to
choose to have more children is that if
there's more possibility of outsourcing
home production to the market
but that really rely on the development
of the service economy
now of course their social norm is
important as well
the social norm around the role of a
mother can play a crucial role for a
woman's decision to become a mother
but social norms itself are changing
over time
and they will change and it will respond
to technology and policy
so some hope there is if these things
are all working
perhaps we can revert the trend of
fertility
to bring it up above the replacement
level
before or you know together with the
artificial intelligence
and that will be the future of growth
hope thank you very much
thank you very much rachel our next
discussant is philip trammell phil is an
economist
at the global priorities institute at
the university of oxford
his research interests lie at the
intersection of
economic theory and moral philosophy
with specific focus on the long term
and as part of this focus he is also an
expert on long and growth
issues and incidentally he has also
written a recent paper on growth and a
transformative ai
together with me in which we synthesize
the literature
related to the theme of today's webinar
feel the floor is yours
uh phil we cannot hear you
is there perhaps a microphone that you
may have to plug in
um can you hear me now
yes all right sorry about that
um right so thank you chad ben and
rachel
and thank you anton for um giving me
this chance to
see if i can keep up with the joneses
some of what i uh say will overlap with
what's already been said but
yeah hopefully i have something you to
say
as anton said at the beginning when
thinking about growth
economists are typically content to
observe as
cal d'or first famously did that
growth has been roughly exponential at
two to three percent a year since the
industrial revolution
and so they'll assume that this will
continue
at least over the time scales that they
care about
sometimes they do this bluntly by just
stipulating an exogenous growth process
going on in the background and then
you know studying something else but
even when constructing endogenous or
semi-endogenous growth models
that is ones that model the inputs to
growth explicitly research and so on
a primary concern of these models is
usually to match
this stylized description of growth over
the past few centuries
for example the agion jones and jones
paper that ben presented
is unusually sympathetic to the
possibility of a growth regime shift
and acceleration but even so
it focuses less on scenarios in which
capital becomes highly substitutable for
labor
and tech production ones that you know
overcome that
balmol effect on the ground that
as long as that phi parameter been
mentioned is positive
which i think the authors believed at
the time
then capital accumulation is enough to
generate explosive growth
which is not what we've historically
observed and restrictions along these
lines
appear throughout the growth literature
as a result alternate growth regimes
currently seem to just be off most
people's radar
for example environmental economists
think have to think about longer time
scales than most economists
but they typically just assume
exponential growth
or a growth rate that falls to zero over
the next few centuries
a recent survey of economists and
environmental scientists
just asked when will growth end um
as if that you know roughly
characterized the the uncertainty
and of those with an opinion about half
said within this century
and about half said never
no one seems to have filled in a comment
saying they thought it would accelerate
or
anything like that plus when asked why
it might end
insufficient fertility wasn't explicitly
listed as
a reason and no one seems to have
commented on its absence
but on a longer time frame accelerating
growth wouldn't be a historical
the growth rate was far lower before the
industrial revolution
and before the agricultural revolution
it was lower still
so some forecasts on the basis of these
longer run trends
have predicted continual acceleration to
grow sometimes in the near future
if it multiplied by a factor of 20 again
you know it might be
we might see 40 growth a year or
something
um furthermore radically faster growth
doesn't seem
deeply theoretically impossible i don't
think you know lots of systems do
grow very quickly if you put mold in a
petri dish
it'll multiply a lot faster than two
percent a year right
so more formally the ben paper
finds that you can get permanent
acceleration
under this innocent seeming pair of
conditions
first you need capital that can start
doing research without human input
or can substitute well enough to
overcome that palm oil effect
and second you need phi at least zero
the fish fishing out effect uh not
not too strong um
yeah just to just to recap what here's
what phi elite zero means
when you have advanced tech on the one
hand
it gets easier to advance further
because you have the aid of
all the tech you've already developed
and on the other hand it gets harder
because you've already picked all the
low hanging fruit
phi less than zero means the second
effect wins out
okay so as you can see these two
conditions are basically a way of
formalizing the idea
of recursively self-improving ai
leading to a singularity and then
translating that into the language of
economics
that's a that's a great you know
contribution and formalization
in its own right but a really nice thing
about it
is that it lets us test these
requirements for the singularitarian
scenario
so as ben noted a recent paper estimates
phi to be substantially negative
or using chad's notation beta to be
positive implying that um
even reproducing and self-improving
robot researchers
couldn't bring about a real singularity
like a you know type one or type two
but they could still bring about a
one-time growth rate increase
as long as yeah they can perform all the
tasks involved in research
in any event um this is just one model
there
there are plenty others andrew sandberg
here put together a
summary of these back in 2013 uh of you
know
what what people had come up with at the
time
and uh anton and i did the same more
recently
to cover the past decade of economist
engagement with ai
but i i think the most significant
contribution on on this
front is just the paper that ben
presented
um it solidifies my own belief for
whatever little it's worth
that an ai growth the growth explosion
of one kind or another
even just a you know a growth rate
increase rather than a singularity
is not inevitable but not implausible
and it's at least a scenario we should
have on our radar
um so
yeah this is all very valuable for those
of us
interested in thinking about the range
of possibilities for
long-run growth
for those of us also interested in
trying to shape how the long-run future
might go though
what we especially want to keep an eye
out for are
opportunities for very long run path
dependence
right not just forecasting
in fact um i think almost a general
principle for those
interested in maximizing their long-term
impact would be to
look for systems with multiple stable
equilibria
which have very different social
welfares in them
and we're not yet locked into one and
then to look for opportunities to
steer toward a good a good stable
equilibrium
so we have to ask ourselves does the
development of ai
um offer us any opportunities like this
um if so i don't think the economics
literature has yet identified and
identified them actually
as ben garfinkel here has pointed out a
philanthropist who saw electric power
coming decades in advance
might not have found that insight to be
decision relevant
it just doesn't really help you do good
there could be long-term consequences of
the social disruption ai could weak or
of who first develops ai and like takes
over the world or something
um and most dramatically if we do
something to prevent ai from
wiping out the human species that would
certainly be a case
of avoiding a very bad and very stable
equilibrium
but scenarios like these aren't really
represented in the economics literature
on ai
by contrast path dependency is
a really clear implication of chad's
paper
um we may have this once in forever
opportunity to
steer civilization from the empty planet
equilibrium
to the um expanding
cosmos equilibrium by lobbying for
policies that maintain positive
population growth and thus maintain a
positive incentive
to uh to fund research and fertility
to my mind this is a really important
and
novel insight and it would be worth a
lot more papers to trace out
more fully under what conditions it
holds
but um i think it's pretty robust so
the key ingredient is just that if
there's too much tech per person
um the social planner can stop finding
it worthwhile to pay for further
research
for the reasons chad explained fertility
has proportional consumption costs right
you have to
to bring about a proportional population
increase people have to
give up a certain fraction of their time
um
to have the children but it would no
longer be producing proportional
research increases
because there's this mountain of ideas
you can hardly add much to in
proportional terms
so as long as this dynamic holds
you'll get that pair of equilibrium
so for example in the model people's
utility takes this quirky form you see
here
where c is average consumption of the
time
and n is how many descendants people
have alive at a time
but you might wonder you know what if
people are
more utilitarian what if they're perhaps
number dampened
time separable utilitarians like this
well uh if their utility function takes
this form as
chad points out in in the paper actually
we get the same results
and the utility functions are basically
just monotonic
transformations of one another so they
represent the same preference ordering
as how you can see that
anyway likewise in yeah in the model
people generate innovation just by
living
this is equivalent to exogenously
stipulating that
a constant fraction of the population
has to work
as researchers full time
but what if research has to be funded by
the social planner
at the cost of having fewer people
working in final good output
and thus lower consumption well
then at least if my own scratch work is
right
we still have our two stable equilibria
and in fact in this case the bad one
stagnates even more fully
um research can zero out even though
it's not like
everyone has died off because it's just
not worth allocating any of the
population to research as opposed to
final good production
um finally
sort of like rachel is saying i think
there's an important interaction between
the models
if we're headed for the empty planet
equilibrium the technology level
plateaus
but the plateau level can depend on
policy decisions at the margin
right like research funding or just a
little bit more fertility even if it
doesn't break us out of the equilibrium
and the empty planet result doesn't hold
if capital can accumulate
costlessly and do the research for us
so maybe all that matters is
well maybe it could happen that all that
ends up mattering is just making sure we
make it over the ai threshold
and letting the ai take it from there
all right well to wrap up if we care
about the long run
we should consider a wider spectrum of
ways long-run
growth might unfold not just those
matching the caldorf acts the last few
centuries
if we care about influencing the long
run we should also look for those rare
pivotal opportunities to change which
scenario plays out to
simplify a lot the bend paper helps us
with
the former showing how
a growth singularity via ai may or may
not
be compatible with reasonable economic
modeling
and the chad paper helps us with the
latter showing a counter-intuitive
channel through which
we could get locked into a low growth
equilibrium
sort of ironically via excessive tech
per person
and a policy channel that could avert it
he focuses on fertility subsidies
destroying technological ideas would do
the trick too because it would you know
shrink the number of ideas per person
but hopefully the future of civilization
doesn't
ultimately depend on long-termists
taking to book burning
and yeah hopefully all this paves the
way for future research on
how we can reach an expanding cosmos so
thank you
thank you phil and thank you all for
your contributions
and to everyone who has posted so many
interesting
questions in our q a now
luckily many of them have already been
answered in writing
because we are at the end of our
allocated time
so let me perhaps just uh
let both of our speakers have 30 seconds
to give us a quick reaction to the
discussion
uh then would you like to go first sure
iowa thanks everyone for all the great
questions in the q and a thanks rachel
and phil for very interesting uh
discussions i use very interesting to
pair these papers and i think
you know the distinction of whether you
know can you automate the ideas
production function
or not i mean that you know that's kind
of where what do we believe about that
um uh in terms of which which very
different trajectory do we end up on i
think it's a super interesting question
for a search
i guess you know just last comment you
know i think the singularity type people
you know they tell a story something
like you get a computer one algorithm
that's as good or better than a human
and because you can then
have huge increasing returns to scale
from that invention of that algorithm
that ai you then can just keep repeating
it over and over again as
instantiations on computing equipment
then you kind of can get to sort of
infinite input into the or very high
input growth into the
idea production function and i mean
that's where people get that's where you
get this
really get really strong externality i
think in a more micro statement of
what's going on
but i think the point that you know chad
and i are making that first paper with
philippe you know
another way to think about it is
actually you're not just going to repeat
the human
we're going to what we're going to do
it's sort of like we had a slide rule
and then we had a computer
and we have centrifuges we're gonna
we're gonna you know we have
automated pipetting we're gonna you know
it's again research just like production
is a whole set of different tasks
and probably what's gonna happen is
we're gonna slowly continue to automate
uh
some of those tasks and and you know the
more you automate you know the more you
leverage the
people who are left and can throw
capital at those automated tasks and i
think that is the way
that still away doesn't get you to
single areas necessarily but it's the
way potentially past uh the point chat's
making
uh and it's very who knows uh to me but
but i think it's really interesting i
think i think
again i think this work collectively
helps us really think about
where the where the rubber hits the road
in terms of what we have to believe and
where the action will be
in terms of the long run the long run uh
outcomes
think you've been chad yeah so let me uh
thank uh phil and rachel for excellent
discussions those were really
informative
and um i i think the one thing i took
away from your discussion and from
pairing these two papers together
is the point that you you both
identified so i'll just repeat it i
think it's important
you know an interesting question is does
the
ai revolution come soon enough to avoid
the empty planet and i think that's
really when you put these papers
together
the thing that jumps out of you the most
and as phil kind of mentioned in
ben was just referring to you know small
improvements
can help you get there and so maybe it's
possible to leverage our way into that
but
it's by no means obvious as it's been
pointed out if you've got this you know
fixed pool of ideas
then the ai improves the the fissures
but doesn't change the pool and so
you know i think a lot of these
questions deserve a lot more research
and so i think
anton thanks for putting this session
together i think it was really great and
very helpful
thank you everyone for joining us today
and i hope to see you again soon
at one of our future webinars on the
governance and economics of ai
bye
you


Stuart Armstrong: Is AI an existential threat? We don't know, and we should work on it

welcome this is an expanded version of
our talk that i gave for
york university in toronto the question
for debate there was is a.i an
existential threat
i contributed to the debate on the side
of
yes it is also on the side of
no it isn't well
probably but um
despite all that it's still worth
working on this
issue right why did i have such a clear
and definite answer
well let's look into this the first
main reason is that we suck
as a race humanity does at predicting
ai this is the original dartmouth
conference in 1956
which were basically predicting ai or ai
equivalent over a summer's work
i've actually read their proposal and
it's a very good one
it's done they know what they do they
see where there might be some
difficulties they sketch out
realistic plans and it was all written
by the
best computer scientists of the time and
the people had the most experience
in practical getting machines
to do what they wanted to and it was
disastrously wrong
and nine years later dreyfus in an
otherwise
excellent uh article seemed to suggest
that we're basically
reaching the limit of what algorithms
could do
i think it's safe to say that neither of
these predictions have been fully borne
out in practice
and a lot of predictions on ai are like
that
here we have sketched out various
predictions made at various
times about when we might have ai
it's not easy to figure out because
what a i means varies from
person to person but this is a rough
estimate
here is turing's original prediction
here you can distinguish the ai winter
where everyone was pretending
that they didn't work on ai anymore
and there is some pattern uh a bit of an
accumulation in 2030
but not really much the only the
strongest pattern
that we found in this graph is that
there's a certain tendency to predict ai
15 to 25 years in the future
but that's about it there's no
convergence of estimates
nor in fact should we expect that
because the quality of human decisions
and the quality of human experts
doesn't depend all that much on the
experts
themselves depends much more on what
they're trying to do
tasks that have the features on the left
tend to have very good human experts and
tasks that have the features on the
right
tend to have pretty poor human experts
to pick two examples which are very
close
socially and professionally
anesthesiologists
tend to be real experts and doctors who
interpret mammogram scanners
don't even though they're very
comparable in education and skill levels
the main reason is that
anesthesiologists tend to get
the immediate feedback their patient is
either
not unconscious or dead both of which
become clear pretty quickly
whereas interpreting a mammogram you may
never know if you were correct
and if you do it'll be months later
the most important ones are as i said
the feedback
being available other important ones are
expert agreements
and whether the problem is decomposable
or not
for predicting ai the sort of general
uh intelligence ai um that's where
people were talking about in the 80s
were kind of stuck in these areas
so we mostly should expect poor
performance on ai predictions
which is what we see
this is an old xkcd
comic where various fields are competing
on grounds of purity it's also
a sense how they compete on grounds of
predictability
different subjects have different levels
of quality
in their predictions if a physicist
gives you an estimate you asked what's
the fifth significant figure
if a sociologist says something well
it's
kind of maybe true the reason
for this is because these different
experts
have access to different methods
mathematicians are lucky enough to be
able to use deductive methods
physicists can use the hard version of
the scientific methods
all the way down to poor historians who
are limited
to using past examples
and in this little space here most
future predictions
rely on expert opinion which is even
worse than past examples
now nor does the great uncertainty make
the experts more modest or tentative
about their predictions
just to pick on economists for one
example
here is paul krugman a waxing lyrical
about the chicago school of economics
and here is john cochran from that
school
responding in a sikh and an equally
generous spirit
now econo economics is a field where
the average quarterly gdps get adjusted
by
about 1.7 points on average what that
means is when you say
the economy grew or shrunk by blah
points this quarter that number
gets adjusted typically later on by
about 1.7 points
which is often more than enough to flip
a recession
to growth or vice versa
so this is not a hard field by any means
but its practitioners seem very firm in
their convictions
most now what about
ai would cause us to suspect that it is
safe
or that it is an existential threat most
of the arguments for safety
involve treating the ai as a typical
technology
in this tech tree from civilization
artificial
intelligence is an end tech but so is
space
colonization and nanotech and a few
other things if you treat ai as a
typical technology
you generally conclude that there's no
reason to be overly worried
the arguments that
argue that ai is dangerous tend to focus
specifically on the features of ai the
unique features of ai
some might recognize this as the outside
view
looking at ai as another technology
amongst others versus the inside view
zooming in on that technology
so let's start with the outside view
why might we suspect that
ai will not turn out to be an
existential risk
well the first reason is that humans
have a very poor track record for
revolutionary predictions
in all fields in economics and social
systems
uh people were predicting various
triumphs of various systems of
various times and most of them have
turned out to be wrong
or correct just by chance
there if we restrict ourselves to more
technological predictions
before the second world war people were
predicting the bomber will always get
through
and thus that warfare would be something
completely
unimaginably different from before and
there is no point in building anything
but bombers
fortunately the uk did not fully listen
to this belief or else they would have
lost the battle of britain for example
even if we go back in time we have queen
elizabeth the first
turning down a patent for a
primitive knitting machine on the
grounds of this could cause
mass unemployment so the predictions of
mass unemployment
were already there quite a long time ago
there has been technological peace
theories floating around for some time
and that is not really ever been borne
out
fully though there is some evidence for
it
nowadays but it's still not
a revolutionary impact and finally
imagine that you went back in time say
20 years
and talked with your younger self about
this wonderful smartphone
that you have what you could do with it
you could access all the world's
knowledge for example play games have
videos
communicate with all your friends across
the world
and imagine what your past self would
have thought
and how those would not necessarily come
to pass
if they focused on all the world's
knowledge
well they must may be thinking wow so
that means that disagreements and
arguments must be a thing of the past
which they're definitely not so they
underestimated
the well it you wouldn't have
underestimated the social impact but you
would have thought the social impact
went in a different direction
uh then maybe it has gone so predictions
based on revolutionary ideas which
an existential threat is an extreme
example of
tend to have a poor track record
secondly humans do act
in ways that derail predictions of
doom like the millennium bug the
millennium bug
was overhyped in retrospect not
because it was wrong but because people
acted to prevent it from happening so
if the ai is an existential threat maybe
we're going to act to solve that problem
in his uh song two's lex
uh tom lear was thinking about nuclear
proliferation
and how it would inevitably spread
across the world and er ending with the
immortal line
will all stay serene and calm when
alabama gets the bomb
and yet the nuclear nonproliferation
treaty
that was from the 70s derailed this
and other trends as well and instead of
having the
25 nations 15-25 nations that were
expected we've
kind of plateaued around 10 at the
moment even though there are
many more countries than this who could
get nuclear weapons
if they felt like it
another reason for predictions getting
derailed
that are not dependent on human
intervention
is that the threats typically start with
the easiest
and most vulnerable parts of the system
to use
a timely example a pandemic
spreads easily initially and then
afterwards the survivors are more immune
and has great difficulties
continuing to spread so any
any danger tends to drive adaptation and
resistances
to it and finally
a lot of predictions are based upon
apocalyptic or utopian
ways of thinking and these tend
to have a spectacularly bad track record
ai is both the sort of super
intelligence general intelligence
being either an extreme risk or an
extreme
solution so it tends to drive some very
poor
thinking now this doesn't mean
that we can figure out when we might
have ai or what features it might have
just by thinking of human psychology
but it does mean that we should look at
these arguments
with more of a grain of salt than we
might otherwise
so this is a rough look at all the
counter arguments for ai
being an existential risk by comparing
it with other
hopefully similar risks
and now let's look at the other side why
might we suspect that ai
might be an existential risk
well let's look at the power of
intelligence itself
here's a chimp brain and a human brain
they're not
all that difference in size and
definitely not an organization
yet chimps have a population of 200 000
roughly and use basic wooden tools uh
us humans have heavy industry nuclear
weapons and we've spread
across the entire surface of a planet
for
a large mammal we are undoubtedly
the winners of the race of population
and the chimps that remain in the worlds
tend to remain on human sufferance
the ones uh the populations they get
killed off get killed off by
humans the ones that are protected are
protected by humans
so they small difference in brain power
has made an absolutely massive
difference in power
since we've extended our brains with
computers we've
walked on the moon developed hydrogen
weapons and
had extreme and unprecedented economic
growth
so if we continue in this analogy what
would happen
if we went to the next step
of intelligence had an intelligence even
superior to this
here we would expect completely
transformative effects
which may entail existential risks just
due to the difference
in potential power
another argument focuses on what you
could do with
human level intelligence
if you have a human level intelligence
in software
form so general intelligence in software
form we could imagine that we would then
take
the ai equivalents of edison einstein
jk rowling margaret thatcher oprah
confucius
goebbels steve jobs and bernie madoff
all of these are humans who are
cognitively brilliant
in their domain of expertise we
take copies of the ai equivalents
we give them vast amount of data and we
run them at thousands and thousands of
times human speed
so that this super committee has
say three weeks uh the subjective time
for each of its answers for this
kind of entity the internet
and the human race itself will be more a
useful resource
for its goal rather than an obstacle or
a competitor
or an equal similarly the
power of copying should not be
underestimated
if we have this super committee or even
just a human level
ai we can create corporations with it
corporations are mainly dependent on
capital
and on their human capital
um and logistics resources and other
stuff
to do with their human capital like
offices
but if we have
the ai we can create
the human capital just as easily as we
can imagine just by copying it
again and again and again and this would
have
a this would be unified in a way that
humans just
aren't and therefore we can create
some of the most powerful entities in
existence today
in five minutes or in one minute by
copying from an ai
they're currently certain number of
billions of computers this number
keeps on changing so i'll call it a
smaller mega billion computers if we had
ais
that could run on that how many could we
make well probably quite a lot
and with this much human capital
how many computers could we then create
and how many ai's could we run on that
well much more as well so
basically there is the potential for
many many many more ais in the world
than humans have ever existed and these
ais
could be superior to humanity in the
super committee sense
and coordinate with each other in ways
that humans can't
so that's a brief overview of some of
the arguments that ai
will not be an existential risk and that
ai would be an existential risk
the correct response
to uncertainty is to be uncertain
don't be like those economists
who are very sure that they're right and
that the others are wrong
in a field uh with poor measurements
so on the probability range we have zero
and a hundred percent
certain and impossible these are kind of
things that never really happen you're
never really 100 sure of something but
you can get pretty close
there's the 99.99 etc and
it's converse
so things that are very close to 100 are
things like basic mathematical fact
and laws of physics
the fact that you won't win the lottery
is up there in the 99.9
conversely the opposite of these things
can be found on the other end of the
scale
and then we have the mid-range
roughly from 65 to 35
where we put things that are uncertain
and things can inhabit this range for a
variety
of different reasons maybe we have no
evidence
what would be the gender of the first
leader of mars
we don't really know this uh we have no
idea
no real idea who the first leader of
mars might be we don't know if there'll
still be two mainly two genders by that
time
then there's things where we have very
weak evidence like what is the gender
of the 2037 us president
it's pretty sure that this
this person is already involved in
politics at some level
so the sample that we have is not
infinite but we really don't know
and then there's things where balanced
evidence such as the gender
of the next u.s presidents the one after
biden
because biden has a female vice
president
this is uniquely more
likely than it is it has been in
previous years
but where it comes to predicting whether
agi artificial general intelligence us
the new name for what we used to call ai
whether that has an existential risk
we're between no
evidence and weak evidence and
i put the probability that it's an
existential risk
roughly in the thirty
percent to five percent range depending
on how the problem is phrased
now you might think this is safely low i
definitely don't i would not go into a
plane that i was told
had only a five percent chance of
crashing on the trip
i would definitely not go one that had a
30 chance of crashing on the trip
and since if ai turns out to be an
existential risk which is defined as
by nick bostrom as something that can
threaten
humanity's survival or permanently
curtail its potential
um when the planet crashes oops doesn't
begin to cover it
so this is why even though i think
is more likely to not be an existential
risk
mainly due to human efforts to ensure it
isn't
i still think it is very important for
people to work
on it and that's why i'm working on it
myself
as a brief aside towards the end
i just want to over uh put forward some
of my work
if that's okay the ai risk
thesis could be phrased roughly as a.i
could be effective at unbounded
unfriendly goals unfriendly goals means
well
bad stuff for humans potentially
unbounded means it just does not
stop and effective is
well powerful and effective and there
are ways
at fighting this sentence at
all of the key words and i have worked
on a variety
of different ones here and i put out
various papers which
i encourage you to look at if you're
interested
that's the end of the aside in
conclusion
expert predictions on ai aren't worth
much
if we see ai's a typical technology then
it's likely not an existential threat
the unique features of ai its
intelligence
its goal potential goal direction things
like that
make it seem dangerous in ways that
other
revolutionary technologies are not
uncertainty will always push towards the
middle
if you don't know about something you
can't conclude
it's definitely safe or definitely
dangerous with any certainty despite
human tendency to do so
and finally despite all this it is still
worth
working on ai safety just because the
expected impact
is so huge thanks for listening there
and have a good day