“Hierarchies and the Organization of Knowledge in Production,” L. Garicano (2000)

The organization of firms, principally but not always in a hierarchy, is related to incentive constraint problems. But this is not all. Informational problems, particularly the transmission of relevant information across the firm to specific individuals who need it, and the collection of knowledge at specific areas in the firm, are also important. Focusing only on that issue, and ignoring incentives, what shape does the firm take?

Garicano considers the following model. Let a firm hire a group of homogenous workers. There is a continuum of “problems” which workers will need to solve. If a worker knows the answer, he solves the problem himself, else he asks someone else for the answer. Workers, after hiring but before production starts, are trained at cost to solve certain problems at a cost linear in the measure of solutions learned. When a solution is not evident and must be asked for, the receiver of the question bears a cost, even if she does not know the answer to that question; time spent answering queries is time not spent producing output. A given worker only has a unit interval of time to spend working or answering questions. Problems arrive at the firm every period according to a known distribution F(Z), where Z is reordered such that the most common problems occur on the left side of the distribution.

In this simple model, one homogenous group of production workers is trained to solve only the easiest problems, and other groups of workers are trained in successively harder problems. Production workers first try to solve the problem themselves, then ask the first level of non production workers for a solution to problems they can’t solve, then ask the second level, etc. This can be proven in four parts; there is nothing tricky. Essentially, divide all the workers into classes where a class specifies what knowledge is learned and what order other classes are asked about problems. First, show that only one class ever produces: if two groups produce output, and the output they produce is not the same, then workers in the less productive group specialize in knowledge to support the more productive group’s production. Second, knowledge never overlaps across classes. since overlapping knowledge is costly and never used. Third, production workers solve the easiest problems, the first level of management solves the slightly harder problems, and so on, with production workers asking levels of management in order until they learn the answer to a problem. If this weren’t true, we could swap an interval of the knowledge held by any two levels, keeping learning costs constant, but now letting easier questions be answered “earlier”, hence reducing communication costs. Fourth, the organization is a hierarchy with fewer workers at higher levels. That final result essentially comes from the fact that only really uncommon problems are solved by workers at the top, hence not many of them are needed.

Making assumptions about the distribution of problem difficult, Garicano also solves for a number of comparative statics when learning costs and communication costs change, or when the production process becomes less predictable in the sense that the distribution of problems shifts rightward. The exact results here rely partly on strong assumptions about the size of the organization, so I omit them here (essentially, everything is proven conditional on a very large firm and exponentially distributed problem difficulty, though the intution behind most of the results probably wouldn’t change were these assumptions to be loosened).

Three final thoughts, related to my current research: is getting knowledge to production workers really the most salient informational issue in firms? This seems backward. One might think that, to the extent firms are organized for knowledge aggregation and transmission reasons, the most important decisions are the ones faced by the boss/president/lead prosecutor, and it is she who uses information held by others in the firm in order to inform her decision. Second, is not contingency-related decisionmaking a relevant concern? That is, often, firms do not even know what problems will arise. Generally, managers specialize in making decisions under those circumstances, solving problems who existence is probably unknown when the firm begins operation. Third, is intrafirm training, particularly at the manager level, that important in real firms? Again, one might imagine that potential workers arrive at the firm endowed with certain knowledge, and then are placed into a role in the firm conditional on that knowledge. This isn’t the say that training doesn’t happen, but surely training paid for by the firm is not always the most common way relevant knowledge is acquired.

http://www2.wiwi.hu-berlin.de/institute/organisation/Lehre/WS_2004_05/Adv_Topic_04-05/material/gar_00.pdf (Final JPE version)

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