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.