O-ring and foolproof sectors


Jason Collins


January 14, 2013

In my last post, I described Kremer’s O-ring theory of economic development. Kremer’s insight was that if production in an economy consists of many discrete tasks and failure in any one of those tasks can ruin the final output, small differences in skills can drive large differences in output between firms. This can lead to high levels of inequality as the high-skilled work together and are disproportionately more productive.

In a new paper in the Journal of Economic Behavior and Organization (although kicking around as a working paper for a few years), Garett Jones tweaks Kremer’s model to capture the observation that measures of worker skill are a stronger predictor of cross-country economic performance than of within-country differences in income.

Jones pictures an economy that comprises two sectors: an O-ring sector of the type described by Kremer; and what Jones calls a foolproof sector. The foolproof sector is not as fragile as the more complex O-ring sector and includes jobs such as cleaning, gardening and other low-skill occupations. The key feature of the foolproof sector is that being of low skill (which Jones suggests relates more to IQ than quantity of education) does not necessarily destroy the final product. It only reduces the efficiency with which it is produced. A couple of low-skill workers can substitute for a high-skill worker in the foolproof sector, but they cannot effectively fill the place of a high-skill O-ring sector worker, no matter how many low-skill workers are supplied.

In this economy, low-skill workers will work in the foolproof sector as these firms will pay them more than an O-ring sector firm. High-skill workers are found in both sectors, with their level of participation in each sector such that high-skill workers are paid the same regardless of which sector they work in (the law of one price).

Thus, within a country, firms will pay high-skill workers more than their low-skill counterparts, but not dramatically so. Their wage differential is determined by the difference in their outputs in the foolproof sector.

Across countries, however, things are considerably different. The highest skill workers in a country provide labour for the O-Ring sector. If they are low skilled relative to the high-skilled in other countries, their output in that fragile sector will be much lower. This occurs even for relatively small skill differences. Their income will reflect their low output, with wages also lower in the foolproof sector as high-skill workers apportion themselves between sectors such that the law of one price holds. The net result is much lower wages for workers in comparison to another country with a higher-skill elite.

This picture does depend on the relative proportions of the low and high skilled in the population. If there are too many low skilled people, the wage differences within a country may be greater as all the high-skilled will work solely in the O-ring sector and wages will not equalise. Some of the low skilled may even engage in a lower output O-ring sector. However, the general picture of a large gap in income between countries remains.

There are a couple of interesting things about this model. First, the low skilled can be productive. An additional low skilled person, such as a low-skill immigrant, does not drag everyone down or necessarily destroy a production process. The productivity of those in the O-ring sector remains unchanged. This is somewhat in line with the traditional economic story that everyone can provide value through their comparative advantage. That picture is, of course, incomplete. As Jones points out in other work, there may be other costs to the unskilled, such as lower cooperation or patience and political costs. But this model suggests is that we should look to the quality of the high skilled in the population, and worry less about whether there are too many at the bottom end.

The other point worth noting about Jones’s paper, as for Kremer’s, is that small differences matter. Large income differences are not evidence of large skill differences (although, obviously, they are also not evidence against). Conversely, small changes in skills can have large consequences for a nation’s wealth.