O-Ring Model

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 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 an 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.

For a 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 for 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.

As famously shown by
the 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 this 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 .9;

this can be interpreted
in different ways

but an easy interpretation
is to think that --

.9 means there's 90% chance
of completing the task perfectly

and a 10% chance of complete failure.

It could also mean, --

there's a 50% chance of
completing the task perfectly --

and a 50% chance of
reducing the value by 20%.

That is, 1/2 times 1
plus 1/2 times .8,

reducing the value of the entire
product by 20% equals .9.

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 multiplied 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, at a 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

for a relatively small drop
in the quality level.

One of the most important
implications of the O-ring model

is that 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 have 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 of tasks times
qh times qh or 2qh quared.

The low quality workers then are
2ql squared for the same reasons.

If we mix, we then have again two firms.

In one firm we get 2 the number
of tasks times 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.

That gives us 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 that 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 0.

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,

is going to be the same as
the effect of quality on wages

this is 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, what 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.

A 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 think of it as an 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 O-ring production, --

what you get is wages,
you get a big right hand tail.

You get 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 an 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
performing the same tasks --

will earn higher wages
in a high-skill firm

than in a low-skill firm.

So, for example,

highest quality secretaries will work
with the highest quality CEO's

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 pay 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 applies
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 take a longer
picture view of this as well; --

is 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.

They, in fact, may not want
to invest in an education,

or in building up their skills

because the skills won't pay very much

when they don't have those people
to work on their team, --

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 worthwhile
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 Itzhak Perlman
with a Stradivarius.

Implication of this --

is that poor countries
will have more workers

in less capital intensive
primary productions,

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 take a closer look at this.

So, what we're showing here
is three jobs scaled

so that you 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,

where you've got to get
even hundreds 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 more 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 in every other sector of
the economy are 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 complementarities,

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,
of rooting around bottlenecks.

If you can import
a fairly high-quality good,

perform just a few tasks in 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 complementarities 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 is complex,

that production often requires that
every member of a team be working

in the same direction like a sports team.

Every member has 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.

The 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.