Welcome everyone.
Today we're going to be talking about O-Ring Theory
Turns out O-Ring Theory has implications for development,
but also has implications for the industrial organization of developed economies.
That is, for how firms and workers are organized
when maximizing the value of production
requires that we work as a team.
O-Ring Theory is also going to have the implications for
our understanding of inequality.
Let's take a look.
The O-Ring Theory of Development
is primarily due to a very creative economist called Michael Kremer.
Now we're going to call O-Ring production, or O-ring production function
if the production task has the following attributes:
It's going to depend upon completing a series of tasks.
Moreover, failure at any one of these tasks
is going to reduce the value of the entire product, perhaps to zero
So this is the weakest link problem.
One weak link in a chain destroys the entire value of the chain.
It's also going to be the case with an O-Ring production function
that we can't substitute quantity for quality.
I'll come back to that in a minute.
Let me give you some examples. Take microchips.
A single spec of dust on a microchip run, ruins all of those microchips.
Or think about a souffle.
To make a souffle, you've got to get the ingredients right,
you've got to get the temperature right,
you've got to take the souffle out of the oven at just the right time.
Mess up on any one of these tasks
and the souffle will collapse.
What about a musical?
To make a great musical, you're going to require an excellent lyricist,
a wonderful composer,
a great director,
superb performers.
You need an entire team
and the talents of that team must all come together
at the right time, at the right place.
Notice what we mean here by you can't substitute quantity for quality.
Two mediocre chefs are
not going to be better at making a
wonderful souffle than one great chef.
Pre-musical, if you don't have
Stephen Sondheim then you can't
replace him by saying "We'll add three
or four or five or more mediocre
composers" to make up to the fact
that we don't have one great composer.
It doesn't work that way.
Now why do we call this O-Ring production?
Well as you probably know this is
due to the destruction, the explosion of
the challenger space shuttle.
It's famously shown by a physicist
Richard Feynman.
The mayor cause of that explosion was the
failure of a very simple product.
A failure of the O-ring to expand
because it was too cold.
So this cheap really inconsequential product,
it was only worth you know ten dollars
or something like that because it
didn't expand at the right time.
Because there's one piece of the puzzle
didn't work right the entire
spacecraft along with seven people
was lost. So that's O-ring production.
Let's formalize this model a little bit.
Assume that there are N tasks,
one worker per task.
Doesn't have to be that way but simplifies things.
We're going to let "qi" be the
quality level of worker "i" or
task "i". So "qi" equal to point nine
This is going to be interpreted
in different ways but an easy
interpretation is to think that point nine
means there's ninety percent
chance of completing the task
perfectly and a ten percent
chance of complete failure.
It could also mean, there's s
fifty percent chance of completing
the task perfectly and a fifty
percent chance of reducing the value
by twenty percent.
That is one-half times one plus one-half times point eight,
reducing the value of the entire
product by twenty percent
equals point nine.
So there are different ways of interpreting
these quality levels.
Output is going to equal the number
of tasks times the quality level
in each task, all multipied together.
So this is really the key to the model.
To multiply these quality
levels in each task altogether.
So for example, if there are ten tasks and
the quality level of every worker is point
.99, then output will be equal to 10 times .99 to the power of 10 or 9.04.
So notice that if each worker
were perfect, an equality level
of 1 then the output would be 10
because each worker has a 1% chance of
messing up, the output of the expected output is 9.
If the quality level of the workers went down
to .95, notice that the output would fall to 6.
So just a small decrease
in the quality level, decreases the output by a lot.
If the quality level went down to .9, again not that big a drop,
the output level goes down to 3.5.
An awfully big drop in output
by a relatively small drop in the quality level.
One of the most important implications of the O-Ring model is we'll have
quality matching.
That is "output will be higher if we put
all the high quality workers together and
all the low quality workers together,
compared with if we mixed the workers up."
Let's do a simple example.
Suppose we two high quality workers and two low quality workers.
If we put the high quality workers together in one firm,
then the output we get is 2 the number
tasks times qh times qh or 2qh quared.
The low quality workers
then are 2l squared for the same reasons.
If we mix we then have again
two firms, in one we get 2 the number
of tasks time qh times ql and
same thing for the second firm.
Okay, which one of these is bigger?
Well we can get rid of the 2s.
Like if it's qh squared plus ql squared
compared with getting rid of the 2s here we still have 2qhql.
Which one of those is bigger?
Let's just put into numbers.
So suppose qh is 1 and ql is 1/2.
Therefore, for the match group we get
1 squared plus 1/2 squared and for the
mix group we get 2 times 1 times 1/2.
Let's see. Well that's a quarter, one and
a quarter for the match group and
just one the mix group.
Therefore you won a match. What about other examples.
Okay let's do a general proof.
If qh is bigger than ql, then notice that
qh minus ql squared is certainly bigger than zero.
Well just using FOIL multiplying these out,
we get qh squared plus ql squared minus 2qhql.
Let's put the 2qhql on the other side,
we get qh squared plus ql squared is bigger than 2qhql.
But notice that this is just exactly our statement here
for comparing the match output with the mix output.
So this tells us that for any qh and any ql,
the match output is bigger than the mix output.
Now it's not too hard to show
that in a competitive economy
with quality matching, higher output
is going to mean higher wages.
So remember now that the effect
of quality on output which we now know
it's going to be the same as the
effect of quality on wages is
as highly non-linear.
So, if all the out-workers have a
quality level of 1, then output is going to be 10 up here.
Notice that if quality falls just a little bit to .9,
output falls a huge amount to less than 4.
So you get a big drop in quality, big drop in output with a fairly small drop in quality.
Indeed notice that if quality falls in half,
output is basically going to zero.
You can't even see in this graph how
small output is with a drop in quality of a half.
So this says is that, if there are differences
in quality levels across countries then
one country may have much much
smaller GDP per capita than the other
country even though the quality
levels are not that different.
Fairly small decrease in the quality levels
of the workers creates a big decrease in wages.
We can also this at a national level.
There's slightly different way.
Suppose the talent
distribution is something like this
on the left hand side, that is most
of the workers have a talent level of
1, this is an arbitrary number here.
I don't think of it as all being perfect, just of it as arbitrary scale.
But suppose most of the workers have this
talent distribution somewhere around here, okay.
When you map that into the
wage distribution, taking into account
the fact we have over in production,
what you get is wages, you got a big right hand tail.
You got wages are much more unequal than talent.
So a fairly equal distribution of talent when
you map that into the O-Ring model,
turns into unequal distribution of wages.
So in particular, notice that
over here, there's hardly anybody
who has a talent level of 2 or greater.
Very very few people in this economy
have a talent level of 2 or greater and
yet wages, a large fraction of the wages
are going to go to people who have
a talent level of 2 or more.
So this shows you how an O-Ring model
magnifies the distribution of talent turning it
into a much more unequal distribution of wages.
Here's another implication of the model.
In an O-Ring model, workers
perform in the same tasks will earn
higher wages in a high-skill firm than in a low-skill firm.
For example, highest quality secretaries will work with the highest quality CEOs.
Simply because
a mistake by one of those secretaries
is going to be so much more damaging
when she works for a high quality
CEO than for a low quality CEO.
Apple. They'll hire the best programmers
and the best designers.
They'll also want to hire the best janitors
and they'll them the most, at least to the
extent that the output of those
janitors contributes to the output
of the entire product.
The same idea with the economy as a whole.
High quality workers will be paid more
when there are more high
quality workers to work with.
Talent likes to work with other talent.
There's a multiplier effect here.
The more high talented, high quality
workers you're surrounded with,
the more your earnings are going to be.
That's one reason I like to work with Tyler.
It's not just, we have to have a
longer picture view of this as well.
If when there's a lot of high quality
workers around, it pays you to invest
in being a high quality worker.
Similarly, if there's just a lot of low-
skill workers around, it doesn't pay
you to be a high quality worker.
So if we think about a very smart person
in a poor country surrounded by
low quality workers, that person
isn't going to earn a lot.
Nor in fact may not want to invest in
an education, or in building up their
skills because these skills won't
pay very much when they don't have
when they can't combine with other
high quality people, when they can't get
that high pay-off which comes with
multiplying high quality by high quality.
This indicates that in this model
there's a potential for multiple equilibrium.
You can have a high quality
equilibrium where everyone wants
to be high-skilled but you could also
have for the exact the same people,
for exactly the same people you might also
end up in a low quality equilibria
where no one is getting high-skilled
and no one thinks it's worth while
to become a high-skilled worker.
In an O-Ring model, capital wants to
work with high quality workers
for exactly the same reasons that
high quality workers want to work with each other.
In particular, note that more capital in these models
doesn't substitute for lower-skilled workers.
So if you give me a Stradivarius, I'm not going to be a better violin player.
You don't want to do something like this,
therefore, you don't want to have
Homer Simpson running the nuclear power plant.
This a failure of quality matching.
Don't do that. Instead what you
want to do is you want to match
the best workers with the most expensive machines.
So what you want is a Perlman with a Stradivarius.
Implication of this is that
poor countries will have more
workers in less capital intensive
primary production.
So for example agriculture, this force
magnifies all the other forces we're talking about earlier.
So in particular, capital
is going to flow away from countries
which have low-skilled workers could
want to go to countries which have
high-skilled workers.
This means that you're going to have lower income and wages
in countries with low-skilled workers.
This magnifies all the effects
we're talking about earlier.
Similarly, poor countries will have
more workers in production tasks
or production jobs that are simpler.
That require fewer tasks.
Let's takea closer look at this.
What we're showing here is three jobs
scaled to get the 100% of
output when the workers are
perfectly high quality.
Job 1 requires the workers to get 5 tasks right.
Job 2, that they get 10 tasks and
Job 3 that they get 40 tasks right.
Now here's point, if you take workers of
reasonably high skilled level .9
but you assign them to a job
which requires that they get 40 things right.
Where getting 1 thing wrong,
one of those tasks wrong
can reduce the value of the entire
product, then your chances of getting
full output are virtually nil.
On the other hand, if you take those same
workers and you assign them to
a job which requires that they just
get 5 things right, then your chances
of getting full output are much higher.
So think about this as being
bicycle production, car production
and space shuttle production.
What it says is that countries with
lower-skilled work forces, they're
going to specialize in things like
bicycle production which tend to
be lower paid. The value of the entire
product tends to be lower when
the number of tasks required is lower.
What this also says is that, if you
have a job requiring a lot of tasks,
like a space shuttle, you've got to get
even hundred of tasks right in order
to get the full value of the product,
then you really want to be working
with workers of the very highest
skill level to have any chance of
producing that high quality product.
We can apply many of these ideas
at the level of the economy as whole.
In which case it becomes a theory of
bottlenecks, linkages and complementarities.
So let's think about N
industries each performing a single task.
In following Kremer, let's
suppose the quality falls by half
in just of these tasks or industries.
So for example, the electricity
production becomes more spotty and
subject to blackouts.
Corruption increases at the licence bureau
requiring us to spend a lot to get a licence.
Well even though, quality has
fallen in just 2 of the many tasks,
which we need to complete, output
is going to fall immediately by 75%.
Moreover there are going to be knock on effects.
Wages on every other sector
of the economy are all also going to fall
because the total value of the product has fallen.
And this fall in wages is
going to greatly reduce the incentive to
invest in quality in all those other
sectors and that reduces output
further in the long run.
So you could have a bottleneck and a bottleneck
affects not just that sector of the
economy but every other sector of the economy.
Because you have complimentarities,
when one sector goes down,
the other sectors also go down as well.
This shows by the way the
importance of trade as a method of
avoiding those bottlenecks,
a rooting around bottlenecks.
If you can import at fairly high quality
good perform in just a few tasks
in the country and then export that good,
then you can root around the bottleneck
and get some development even when not
every sector in your economy is working well.
If instead you've got to produce
everything in house, everything in the
country, then you need every sector in
that economy to be working well.
When you're working with O-ring
production because you have all
these complimentarities across industries.
Okay let's give some final
thoughts about O-ring production.
First, not every industry is an O-ring
industry but perhaps in our modern
world more industries are moving in this direction.
That tells us something
about the sources of growing inequality.
O-ring production also reminds us
that production's complex. That production
often requires that every member of a
team be working in the same direction like a sports team.
Every member's got to be
performing at their highest
level of ability in order to get those wins.
This tells us that organizational capital,
the ability to bring together
high-skilled workers with expensive
capital and to get all those workers
into that capital working together
in a team at the highest level of skill.
That ability to do that is
incredibly important and the more
complex production grows, the more
tasks that are required to achieve
maximum production, the more
valuable organizational capital,
the ability to bring these workers
and capital together, the more valuable
those skills are going to become.
In an O-ring model, you can get virtuous and vicious cycles.
When one industry in a O-ring model
increases its ability, that increases the
incentive of every other industry to
perform at its highest level of ability.
But the same thing is also true in reverse.
When one team member
or when one industry is performing
at a low level, that reduces the incentive
of all the other industries to perform at a high level.
Hence you can get
growth miracles and growth disasters.
Now what does it take to coordinate a
team? To coordinate an economy
on a high-skilled equilibrium where
everyone is working at their
maximum level? Well this is an
incredibly hard problem.
This is all about what culture is about.
It's an incredibly hard problem
but also an incredibly important
problem, something important to think about.
Thanks very much.