Archive for the ‘Comparative advantage’ Category

Co-authoring is not about comparative advantage

16 October 2017

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.


“Ricardian Productivity Differences and the Gains from Trade”

18 November 2013

You’ll recall that Ralph Ossa emphasized sectoral heterogeneity in trade elasticities as one reason the ACR formula might understate the gains from trade. I haven’t read it yet, but this new NBER WP by Andrei Levchenko and Jing Zhang also emphasizes the importance of sectoral heterogeneity in thinking about this topic:

[T]he simpler formulas that do not use information on sectoral trade volumes understate the true gains from trade dramatically, often by more than two-thirds. The error in the formulas across countries is strongly negatively correlated to the strength of Ricardian comparative advantage: the one-sector formula-implied gains understate the true gains from trade by more in countries with greater dispersion in sectoral productivity. The model-based exercise thus reinforces the main result of the paper that accounting for sectoral heterogeneity in productivity is essential for a reliable assessment of the gains from trade.

Eaton & Kortum – “Putting Ricardo to Work”

9 March 2012

This forthcoming Journal of Economic Perspectives article by Jonathan Eaton and Sam Kortum on the Ricardian model of trade is fantastic. It walks the reader from Ricardo (1818) to Mill (1844) to Dornbusch, Fischer, and Samuelson (1977) to Eaton and Kortum (2002) to the modern frontier. Put it on your syllabi.

Whither Ricardian comparative advantage?

8 June 2011

In his Nobel lecture, Paul Krugman suggested the new trade theory’s relevance might be fading in some dimensions, as trade between countries with vastly different incomes and capacities rose rapidly in recent decades:

And nobody doubts that trade between the United States and Mexico, where wages are only 13 percent of the U.S. level, or China, where they are only about 4 percent, reflects comparative advantage rather than arbitrary, scale-based specialization. The old trade theory has regained relevance.

But a couple of recent pieces of evidence supposedly point towards the decline of traditional Ricardian forces for trade. In a recent NBER working paper, Andrei Levchenko and Jing Zhang calibrate a multi-sector Eaton-Kortum model along the lines of Costinot, Donaldson, and Komunjer and claim:

First, we find strong evidence that comparative advantage has become weaker. Controlling for the average productivity growth of all sectors in a country, sectors that were at the greater initial comparative disadvantage grew systematically faster. This effect is present in all time periods, and is similar in magnitude in both developed and developing countries. The speed of convergence in sectoral productivities implied by the estimates is about 25% per decade.

This morning, Dani Rodrik posted a graph that shows convergence in labor productivity in manufacturing industries since the 1980s. I believe Rodrik’s graph comes from directly estimating labor productivity using UNIDO data, rather than a model-derived measure of productivity. (Rodrik blogged the results without mentioning the underlying/forthcoming paper from which they’re excerpted, so not all the details are clear.)

So two different measures of cross-country productivity differences suggest that Ricardian comparative advantage may be declining as a force for international trade volumes. It’ll be interesting to see how, both theoretically and empirically, we can resolve the contrasting claims of Krugman and Levchenko, Zhang, and Rodrik.

Further: A commenter suggests looking to Heckscher-Ohlin-Vanek rather than Ricardo. Indeed, some of Krugman’s Nobel lecture comments are referring to factor-driven comparative advantage rather than Ricardian comparative advantage. That resolution gives one interesting answer to the question I posed in the post’s title.