# O-ring theory of economic development

The O-ring theory of economic development is a model of economic development put forward by Michael Kremer in 1993, which proposes that tasks of production must be executed proficiently together in order for any of them to be of high value. The key feature of this model is positive assortative matching, whereby people with similar skill levels work together.
The model argues that the O-ring development theory explains why rich countries produce more complicated products, have larger firms and much higher worker productivity than poor countries.
The name is a reference to the 1986 Challenger shuttle disaster, a catastrophe caused by the failure of O-rings.

## Model

The model assumes that firms are risk-neutral, labor markets are competitive, workers supply labor inelastically, workers are imperfect substitutes for one another, and there is a sufficient complementarity of tasks.
Production is broken down into $n$ tasks. Laborers can use a multitude of techniques of varying efficiency to carry out these tasks depending on their skill. Skill is denoted by $q$, where $0\leq q\leq 1$. The concept of $q$ differs depending on interpretation. It could represent the probability of a worker successfully completing a task, the quality of task completion expressed as a percentage, or the quality of task completion with the condition of a margin of error that could reduce quality. Output then equals the product of the $q$ values of each of the $n$ tasks together and scaling it by a firm specific constant, $B$. This scalar is positively correlated with the number of tasks. The production function is:
    F(q$_i$, q$_j$) = Bq$_i$q$_j$
The important implication of this production function is positive assortative matching. This can be seen in a hypothetical four-person economy with two low skill workers (q$_L$) and two high skill workers (q$_H$). This equation dictates the productive efficiency of skill matching:
    q$_H$$^2$ + q$_L$$^2$ ≥ 2q$_H$q$_L$
By this equation total product is maximized by pairing those with similar skill levels.

## Conclusions

There are several implications that can be derived from the model:
* Workers performing the same task earn higher wages in a high-skill firm than in a low-skill firm;
* Wages will be more than proportionately higher in developed countries than would be assumed by measurements of skill levels;
* Workers will consider human capital investments in light of similar investments by those around them;
* The effects of local bottlenecks are magnified which also reduces the expected returns to skill;
* O-ring effects across firms can create national low-production traps.
This model helps explain brain drain and international economic disparity. As Kremer puts it, "If strategic complementarity is sufficiently strong, microeconomically identical nations or groups within nations could settle into equilibria with different levels of human capital".

## Extensions

Garett Jones (2013) builds upon Kremer's O-ring theory to explain why differences in worker skills are associated with "massive" differences in international productivity levels despite causing only modest differences in wages within a country. For this purpose, he distinguishes between O-ring jobs—jobs featuring high strategic complementarities in terms of skill—and foolproof jobs—jobs characterized by diminishing returns to labor—and assumes both production technologies to be available to all countries. He then goes on to show that small international variations in average worker skill per country result in both large international and small intra-national income inequality.