Co-authoring is not about comparative advantage

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Comparative advantage is one of our field’s defining insights and “an essential part of every economist’s intellectual toolkit“. The principle is both true and non-obvious, so understanding it separates those who have taken an economics class from those who have not. While economists are rightfully proud of comparative advantage, there is at least one circumstance in which I think economists overuse it.

If you chat with economists about their co-authored research, you’ll often hear them casually attribute the division of labor within their research team to comparative advantage. I’m sure I’ve said this a number of times myself. But co-authoring is not about comparative advantage.

Suppose producing a paper involves two tasks: solving a model and estimating it. If you are better at both tasks than your co-author, then you ought to do both yourself and break up with your co-author. My advice seems contrary to David Ricardo’s famous insight that there are still gains from specialization and trade when one party has absolute advantage in both tasks. But the optimal assignment of tasks does not always depend on comparative advantage.

The Ricardian production function

The principle of comparative advantage is tied to a particular production function. In the Ricardian model, production functions are linear. Thus, individuals’ marginal products are constant. This fact allows us to describe individuals’ choices in terms of relative productivities and relative prices.

In a Ricardian world, the ordering of task assignments depends only on relative productivities: at any relative price, an individual has comparative advantage in the task in which her relative productivity is higher. Absolute productivities show up in a market-clearing condition that determines the relative prices necessary for supply of each task to equal its demand.

Does this sound like co-authorship? Some of the institutional details are wrong. Co-authors don’t usually pay each other for their output. Adding more people may pay off because each of n co-authors can receive more than 1/n credit. But beyond the unusual features of “selling” your output to academia, the Ricardian model’s description of the production process as a research team just doesn’t fit.

Producing research as a team

As Michael Sattinger (1993) explains, not all assignment models are models of comparative advantage:

Some economists may believe that comparative advantage is the only production principle underlying the assignment of workers to jobs, but this is incorrect. As a counterexample, consider an economy in which a job is associated with the use of a particular machine that can be used by only one person at a time…
The reason comparative advantage does not indicate the optimal assignment in this case is that earnings from a job are no longer proportional to physical output at the job. With cooperating factors of production (either explicit in the form of a machine or implicit via a scarcity in the jobs available), an opportunity cost for the cooperating factor must be subtracted from the value of output to yield the earnings.

In the Ricardian model, absolute disadvantage is not a problem, because quantity can make up for quality. If the laborers assigned to a task have low productivity, more labor can be employed in that task to produce more output. But in many situations, quantity cannot substitute for quality. This is most obvious in sports, where rules constrain team size: a hockey team can only have one goaltender. When jobs are scarce, comparative advantage does not determine the optimal assignment.

In a famous applied theory paper, Michael Kremer explored the consequences of producing in a team in which the number of tasks is fixed, each task may be performed by only one person, and a mistake in any one task diminishes the entire project’s value. The latter feature makes this the “O-Ring Theory of Development”, as the space shuttle Challenger blew up due to the failure of only one of its thousands of components.

This production function sounds more like the economics research process. A paper is a discrete unit of output, and it is likely only as persuasive as its weakest link. Poor writing can totally obfuscate good theory. Rarely can a beautiful theory salvage garbage empirics. And it is hard to believe that input quantity can substitute for input quality: “this paper was written by mediocre theorists, but there were so many of them working on it!”

In Kremer’s O-Ring model, the efficient assignment is that workers of similar skill work together in teams. A great theorist pairs with a great empiricist. As a first pass, this seems a reasonable description of the co-authorships we actually observe.

Co-authoring is not about comparative advantage

Of course, production is more complicated than that. How do we explain the valuable contributions of research assistants to projects when their supervisors (would like to claim that they) have absolute advantage across all tasks? One needs a model of hierarchical or sequential production in which research assistants handle easier problems and then pass on unsolved problems to their supervisors. Luis Garicano, Esteban Rossi-Hansberg, and co-authors have studied these knowledge-based hieararchies in environments ranging from law firms to exporters.

In short, the optimal assignment depends on the nature of the production function. Despite economists’ frequent invocation of our beloved insight, co-authoring is not about comparative advantage.

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