My favourite model in all of Economics is the Kremer O-Ring Model. Devised in 1993, the model depicts a firms’ production process as a series of sequential tasks that all inter-depend on each other. In order for the firms’ final product to be of any high value, all tasks need to be executed proficiently. Consequently, a single mistake in the chain can ruin the contribution of all the others.
To illustrate this, imagine the production process at
Dominos: a chain of workers all responsible for a different component of the
pizza. If the baker messes up the dough this ruins the value of the whole
pizza, regardless of how expertly the sauce is cooked or the toppings are
arranged.
Until now I have refrained from using a single equation in
my blogs; however, I cannot resist introducing one now to illustrate this
central idea:
Here, y represents a generic term for ‘output’ (e.g. pizzas,
clothes) while q represents the quality of a particular
worker i. For simplicity, assume q is a variable distributed between 0 and 1.
For example, a q of 0.9 means a worker executes her task perfectly 90% of the
time (and fails the other 10%). The large pi symbol is simply a multiplicative
operator: it instructs us to multiply together each q from q(1) to q(n).
A numerical example helps bring this
equation to life. Imagine two 5-person production teams: Team A has four talented
workers (0.9) and one dud (0.1); Team B has five average workers (0.6). Their
respective outputs are as follows:
Team
A: 0.9*0.9*0.9*0.9*0.1 = 0.066
Team
B: 0.6*0.6*0.6*0.6*0.6 = 0.078
Crucially, even though the average worker is more talented in Team
A, Team B still produces more. The dud worker ruins the output of the rest; anyone
who has played 5-aside football without a proper goalkeeper may appreciate this
idea.
The model takes its name from the
Challenger Space Shuttle disaster of 1986, where the shuttle exploded 73
seconds after take-off. Catastrophe was caused by the failure of a single
O-ring: a small rubber gasket (costing a few cents) that was supposed provide a tight seal between metal parts.
This echoes the central message of the model: an enormously complex process can
be destroyed by the failure of any one, seemingly trivial part.
Figure
1: The Challenger Space Shuttle at Take-Off
Source: www.snopes.com
Why do I like this model? I like it because from so little
we can learn so much. The equation I outlined above – less than 2cm of algebra
– generates many testable hypotheses that appear borne out in the real world.
For example, due to the sequential nature of production, the
model predicts that people of similar abilities will seek each other out and
band together to form firms. This reflects the type of assortative matching we
see in the modern labour market, especially amongst highly talented people.
The model also implies that the wages paid to these people will
be disproportionately large, due to the non-linear effects implied by the
multiplicative production function. To see this, plug in a value of 0.9 for
each member of Team A and 0.8 for each member of Team B. This small difference
in skill amplifies into large differences
in output, which itself drives large differentials in wages. This gives rise to
a very skewed income distribution: similar to the one we see today.
The model also explains the positive correlation we observe between firm sizes and wages (Haugen, 2016). The idea is simple: if you are a
large firm with many stages of production, a mistake at a single stage becomes extremely costly. To ensure mistakes are
minimised, firms must hire highly talented people who command higher wages.
A similar idea underlies another prediction of the model: that
more complicated products will be made in richer countries. Again, complicated
products imply extremely costly mistakes; hence firms are better off locating
in environments with an abundance of high-skilled labour. This is why Germany
specialises in automobiles and satellite technology while the Democratic
Republic of Congo specialises in agriculture and mineral extraction.
Application to Education Economics
Fortunately for the theme of this blog, the model also has a lot
to say about education decisions. For example, the model can explain
education-poverty ‘traps’ whereby people in poor countries have no incentive to
invest in education to improve their skills. Consider two people: Amy who is
born in rich country A and Ben who is born in poor country B. Amy and Ben are
of comparable skill (0.3) and both have the chance to invest in education to make them
more productive (0.9). Each is confronted with the following prospective labour
force:
Country A:
0.9*0.9*0.9*0.9
Country B: 0.3*0.3*0.3*0.3
Will both invest in education? Assuming education is costly, Ben
may not invest in education as there are no similarly educated workers for him
to match with in Country B. This is not the case for Amy, who is able to
realise the full benefits of her education by teaming up with other talented
workers who amplify her newly-developed skills.
The model can also explain a ubiquitous phenomenon in developing
countries: brain drain. Suppose Ben does end up investing in education. Does he
have any incentive to remain in country B? He is likely to be far more
productive in country A where he can be matched with other high-quality workers
and command much higher wages.
We see the same phenomena at a local level: imagine Country A is
now UNICEF and Country B is a generic Ministry in a developing country. Faced
with this choice, many talented local staff will eschew civil service work in
favour of working for donors, sapping the capacity of the local public sector. I
am witnessing this type of domestic brain drain first-hand in Zanzibar; it is
an issue both donors and NGOs should be more mindful of to avoid outcomes that
run counter to their objectives.
Word
count: 984 words
References
Thanks to this post goes to Doug Gollin, my Microeconomics
Professor at Oxford who first introduced me to the O-ring model and whose slides this blog draws inspiration from.
- Haugen (2016), ‘Firm Size Wage Premiums Around the World: Evidence from PIAAC’
- Kremer (1993), ‘The O-Ring Theory of Economic Development’
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