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# O-Ring Theory

BIBLIOGRAPHY

Michael Kremer formulated the O-ring theory in 1993. His article, The O-ring Theory of Economic Development, published in the Quarterly Journal of Economics, presents a production function in which production consists of many tasks, all of which must be successfully completed for the product to have full value. Mistakes can be extremely costly reducing the products value. The name O-ring comes from the accident of the space shuttle Challenger that exploded because one of the components, the o-rings, failed.

The production function has two crucial assumptions. The first is that workers must be sufficiently imperfect substitutes for each other; that is, it is not possible to substitute several low-skill workers for one high-skill worker. Skill is defined as the probability of a worker successfully completing a task, q. The second assumption is that there are strong complementarities among inputs; that is, if there are n tasks, output, y, is given by multiplying the q -values of each of the n tasks together. Assuming that firms are risk-neutral, labor is supplied inelastically and labor markets are competitive, production is given by:

where k is capital and B is output per worker with a single unit of capital if all tasks are performed perfectly. Profit maximizing firms choose a level of capital, k, and the skill of each worker, qi, facing a wage schedule w (q) and a rental rate, r. The first-order condition associated with each of the qi is

Thus, the increase in output a firm obtains by replacing one worker with a slightly higher skill worker, leaving everything else constant, must equal the increase in its wage bill necessary to pay the higher skill worker. Thus the wage schedule is a function of worker skill.

As the derivative of the marginal product of skill for the ith worker with respect to the skill of the other

workers is positive, firms with high q workers in the first n 1 tasks place the highest value on having high-skill workers in the n th task, so they bid the most for these workers. As a result workers of the same skill are matched together in firms.

Kremer stressed that this production function is consistent with many stylized facts such as: (1) wage and productivity differentials between rich and poor countries are enormous; (2) firms hire workers of different skill and produce different quality products; (3) there is a positive correlation among the wages of workers in different occupations within firms; (4) firms only offer jobs to some workers rather than paying all workers their estimated marginal product; and (5) income distribution is skewed to the right. Assuming sequential production in which the highest q workers are allocated to the later stages of production it is possible to show that: (1) poor countries have higher shares of primary production in gross national product (GNP); (2) workers are paid more in industries with high value inputs; and (3) the effects of efficiency wages, bottlenecks, and trade restrictions are magnified. When the number of tasks, n, is endogeneized it is possible to show that: (1) rich countries specialize in complicated products; (2) firms are larger in rich countries; and (3) firm size and wages are positively correlated. Finally, when skill is endogeneized as the product of investment in education or effort Kremer showed that there is some level of education subsidy that improves welfare. Although many of these predictions of the model may be due to a variety of causes, together they suggest that O-ring production functions are empirically relevant.

Kremer stressed that if strategic complementarity is sufficiently strong one may have multiple equilibria and each may be inefficient. Therefore, there is room for public policies to move the economy to a preferred equilibrium. According to Michael Todaro and Stephen Smiths 2003 work, one of the limitations of the model is that it falls short on practical policy implications.

The applications of the O-ring theory are wide. In 2006 Charles Jones adapted it to study the role of knowledge in the theory of economic development. Alberto Dalmazzos 2002 work combines the O-ring production function with efficiency wages; the workers employed in a firm with a more complex production process should earn higher wages than identical workers that work on identical tasks in firms with less complex production processes. Tuomas Pekkarinens 2002 estimates for the Finnish metal industry find evidence supporting this hypothesis.

In the O-ring theory productivity is associated with the job rather than with the worker, which raises questions about how workers get access to the higher productivity jobs. Peter Doeringer and Michael Piores 1971 work shows that internal labor market analysis promotions have the role to allow workers to get access to the higher productivity jobs and firms to extract the maximum effort from workers. The economy may be characterized by dual labor markets in which one sector offers high wages, stability, and good working conditions and the other sector offers low wages, high turnover, and poor working conditions, pressing one back to the structuralist analysis.

Kremer acknowledged that his paper combines Sherwin Rosens 1981 analysis of multiplicative quality effects with Gary Beckers 1981 analysis of matching in marriage markets. However, some of Kremers ideas were advanced by the theory of stratification formulated by Kingsley Davis and Wilbert Moore in 1945 and developed by Arthur Stinchcombe in 1963 and Stinchcombe and T. Robert Harris in 1969. According to Davis and Moore, stratification in all societies was viewed as an unconsciously evolved device by which societies assured that the most functionally important positions would be filled by the most capable persons. Stinchcombe, focusing upon organizational rather than social stratification, hypothesized that the more complementary are individual contributions to total production, the greater will be the inequality of rewards. Stinchcombe and Harris anticipated the production function presented by Kremer in which the case of interdependence of activities in production is modeled as the product of the probability that every worker will be working.

SEE ALSO Coordination Failure; Development Economics; Enterprise; Inequality, Income; Labor Market Segmentation; Productivity; Wages

## BIBLIOGRAPHY

Abrahamson, Mark. 1973. Talent Complementarity and Organizational Stratification. Administrative Science Quarterly 18: 186193.

Becker, Gary. 1981. Treatise on the Family. Cambridge, MA: Harvard University Press.

Dalmazzo, Alberto. 2002. Technological Complexity, Wage Differentials and Unemployment. Scandinavian Journal of Economics 104: 515530.

Davis, Kingsley, and Wilbert E. Moore. 1945. Some Principles of Stratification. American Sociological Review 10: 242249.

Doeringer, Peter, and Michael Piore. 1971. Internal Labor Markets and Manpower Analysis. Lexington: DC Heath.

Kremer, Michael. 1993. The O-ring Theory of Economic Development. Quarterly Journal of Economics 108: 551575.

Pekkarinen, Tuomas. 2002. Complexity, Wages, and the O-Ring Production Function: Evidence from Finnish Panel Data. Labour Economics 9: 531546.

Rosen, Sherwin. 1981. The Economics of Superstars. American Economic Review 71: 845858.

Stinchcombe, Arthur L. 1963. Some Empirical Consequences of the Davis-Moore Theory of Stratification. American Sociological Review 28: 805808.

Stinchcombe, Arthur L., and T. Robert Harris. 1969. Interdependence and Inequality: A Specification of the Davis-Moore Theory. Sociometry 32: 1323.

Todaro, Michael P., and Stephen C. Smith. 2003. Economic Development. 8th ed. New York: Addison Wesley.

João Ricardo Faria