A Tribute to the Kremer O-Ring Model, and its Application to Education Economics

The Kremer O-Ring Model

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.

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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’

The Case for Prioritising Female Education

A famous African proverb tells us that “if you educate a man, you educate an individual, but if you educate a woman you educate a nation”. Should we take this claim seriously? There is a lot of evidence to suggest we should, which together forms a case for prioritising female education.

Workforce Emancipation

First, education emancipates women by increasing their chances of entering the workforce. For example, Erten and Keskin (2018) show that women induced to get more education in Turkey by a 1997 reform that increased compulsory schooling from five to eight years were more likely to work outside the home. Grepin and Bharadwaj study a similar reform in Zimbabwe that relaxed constraints on black Zimbabwean’s access to secondary school to find that each additional year of education led to a 3-percentage point increase in the probability of a woman working outside the home. This is good not just for women but for the economy as a whole, as it diversifies the talent pool of its workforce which, in almost all countries, is predominantly male (OECD).

An increase in female labour force participation can also have a positive feedback loop via the effect it has on the aspirations of younger generations. There are numerous studies that show how ‘mould-breakers’ can move social groups out of self-reinforcing low-aspirations traps. For example, in 1993 India passed a law that reserved leadership positions for women in randomly selected village councils. Policy changes like these are gold dust to social science researchers – the randomisation of the intervention creates a nice ‘natural experiment’ whereby we can viably compare ‘treated’ and ‘non-treated’ villages. Beaman et al. (2012) exploit this to show that in villages assigned a female leader, the gender gap in aspirations was closed by 32% and the gender gap in adolescent educational attainment was completely erased. Educating girls today can create leaders tomorrow; the effects of which can echo through generations.

Health Spillovers

While increased education usually increases female labour force participation, in some countries this is not the case. For example, in Malawi, Baird et al. (2016) show that out-of-school females who were prompted to re-enter school by a cash transfer were not more likely to be working two years after the transfers ended.

Even in contexts such as these, a case remains for prioritising female education. Educated mothers know more about nutrition (UNICEF), health and sanitation (Glewwe, 2009) and are more likely to immunise their children (Keats, 2014), leading to substantial health spillovers in the household. These spillovers are likely to be far greater for women than for men for the simple reason that in developing (and developed) countries, women almost always do the lion-share of domestic duties (UN Women).  

A specific example helps illustrate this point. A recent chart published by Our World in Data shows that 3% of global deaths (~1.7 million) are caused by diarrhoea: more than suicide, homicide, conflict and terrorism combined.

Figure 1: Annual Number of Deaths by Cause, 2016

Source: Our World in Data

In a separate study, Datta and Mullainathan (2014) show that 35-50% of Indian mothers surveyed believed that the correct treatment for diarrhoea is to withhold fluids, due to a faulty mental model that associates it with ‘leaking’. This is one of the saddest but simultaneously most hopeful findings I’ve come across. How many of these 1.7 million deaths could have been prevented by extremely basic maternal education? The welfare implications of this are difficult to comprehend.

Cool Heads, Warm Hearts: A Foray into Moral Philosophy

Of course, there is also a moral dimension to this debate that is hard to ignore. Another of the most memorable (but harrowing) statistics in Economics is Amartya Sen’s (1990) calculation that there are 100 million ‘missing’ women in the world: a result of sex-selective abortions, female infanticide and inadequate healthcare and nutrition for female children. This is not just an artefact of the present day: in almost every society that has ever existed, women’s claims to equal rights, freedoms, authority and resources have been systematically violated (Harari, 2015). This is particularly the case in contemporary developing countries, which almost exclusively languish towards the bottom of cross-country gender parity indexes (UNESCO).

              

Faced with a world like this, how should we react? Economics offers little guidance on normative questions like these: we need to venture into the field of moral philosophy. In a world where the returns to male and female education were equal across every dimension, women would still command a greater claim to society’s resources due to both present day inequalities and historic injustices bestowed upon them.[1] It is worth reemphasising that this claim holds even in absence of the ‘instrumental’ arguments I have outlined thus far.

Who is responsible for meeting this claim: the state, the firm or the individual? While all three have the capacity to redistribute resources, the ability of states to move resources and coordinate people en masse is unparalleled – which makes their obligation correspondingly much larger. This does not absolve individuals (particularly men) and firms entirely: both certainly have a role to play in challenging unfair gender norms and practices in the workplace and home. However, this does not change the fact that states are the most suitably placed to fulfil women’s moral claim to a greater share of society’s resources. States can fulfil this claim by – amongst other things – prioritising female access to education and other public goods.

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References

• Baird et al. (2016), ‘When the Money Runs Out: Do Cash Transfers Have Sustained Effects on Human Capital Accumulation?’
• Beaman et al. (2012), ‘Female Leadership Raises Aspirations and Educational Attainment for Girls: A Policy Experiment in India’
• Datta & Mullainathan (2014), ‘Behavioural Design: A New Approach to Development Policy'
• Erten & Keskin (2018), ‘For Better or for Worse?: Education and the Prevalence of Domestic Violence in Turkey.’
• Glewwe (2009), ‘Why Does Mother’s Schooling Raise Child Health in Developing Countries? Evidence from Morocco’
• Grepin & Bharadwaj (2015), ‘Maternal Education and Child Mortality in Zimbabwe’
• Harari (2015), ‘Sapiens’
• Keats (2014), ‘Women’s Schooling, Fertility and Child Health Outcomes: Evidence from Uganda’s Free Primary Education Programme’
• OECD: https://stats.oecd.org/index.aspx?queryid=54741
• Our World in Data: https://ourworldindata.org/what-does-the-world-die-from
• Sen (1990), ‘More than 100 Million Women are Missing’
• UN Women: http://www.unwomen.org/en/what-we-do/economic-empowerment/facts-and-figures
• UNESCO http://uis.unesco.org/en/glossary-term/gender-parity-index-gpi
• UNICEF: https://www.unicef.org/nutrition/burkinafaso_35979.html

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[1] Theories of distributive justice can be roughly split into two camps: ‘time-slice’ theories (a la John Rawls) say that the justice of a distribution depends on present-day inequalities: all that matters is what people get. ‘Historic’ principles of justice (a la Robert Nozick) instead argue that all that matters is how a particularly distribution came about (i.e. did it violate anyone’s rights?). Crucially, the distribution of resources in most countries is unfavourable to women and came about via the violation of their rights. Therefore, women deserve a greater share of society’s resources, regardless of what camp you are in