Where has all the excludability gone?

My previous post, which answered the question, “Why has growth has been speeding up?” made no use of the concept of excludability. So why did I make such a big deal about partial excludability in my 1990 paper?

At least since Marshall handed down his Principles of Economics (arguably since Adam Smith told the story of the pin factory), economists have fretted about how to reconcile the increasing returns associated with what Smith called increases in “the extent of the market” with the obvious fact that in real economies, lots of firms of all sizes compete with each other. One of most important things about growth theory that I learned from Chad Jones is that this question is separable from the question about why the growth rate has been speeding up.

Speeding up follows from the two key properties of production possibilities that I emphasized in that post–combinatorial explosion and nonrivaly. These are facts about the physical world that nature gives to us, provided we recognize that part of what nature gave us was the amazing capacity to humans was the ability to codify things we learn in words that other humans understand.

What Chad pointed out in an aside that I will never forget is that that to understand speeding up, it is enough to take a specification of the production possibilities, attach an objective function, and just solve a social planner’s problem. All the reasonable proposals for decentralizing an equilibrium have a path for growth that is qualitatively similar to the path that solves the planner’s problem. If your production possibilities give you a solution to the planner’s problem with a growth rate that speeds up, you will be able to come up with a decentralized version that does so too.


It is easy to add complexity to some existing analysis. What is rare is seeing how to simplify one; how to strip it down even further, to its bare essentials. In my attempts at understanding speeding-up, I doubt that I would ever have thought simplify my 1990 model by setting aside the question about decentralization.

I could see the glaring problems with the model from my thesis and I was determined to fix those in the 1990 paper. But I could have kept going by following the approach that Tufte recommends in the visual presentation of data. You are not done when you can say, “yes, this answers the question I posed, and does so precisely.” You must also ask, “Is there a way to do it more simply?” Or as Tufte would say: Now, can you redo it using “less non-data ink?”


It does not matter for speeding up, but the question of how to reconcile the presence of many competing firms with the nonconvexities signaled by the type of scale effects that show up via increases in Smith’s “extent of the market” is if of more than academic interest. Some of those firms will be in different countries. Understanding how different firms capture some of the benefit generated by codified knowledge is ultimately the key to understanding how codified knowledge diffuses from leading to following nations.

When I was working on my 1990 paper, I was already thinking ahead to this question about diffusion, which lies at the heart of “missed opportunities.” There is a glaring weaknesses in any models based on Marshallian “external increasing returns to scale” including the one in my 1983 thesis, which became my 1986 JPE paper, and then in the model in Lucas’s 1988 paper, which used the same modeling strategy. These models cannot explain the extent of the external or spillover effects that they simply assume. Do they stop at a border? If so, why do they stop more at some borders than others? Or do they stop at the edge of a city? Or are the confined to a hallway where people bump into each other? What is the range of some radio transmitter operated by a homunculus with access to the human capital stored in a person’s neurons? Models in the Marshallian tradition just make up answers like this.

Shouldn’t diffusion, every bit as much as innovation, depend on real things that real people do? Can’t economists come up with a theory of diffusion that does not have to invoke some mysterious form of action at a distance implied by these transmissions through the aether?  And shouldn’t prices and incentives be part of the story? Don’t they encourage real people to do more or less of the real things that real people do? Isn’t this what economics is all about, explaining behavior with incentives not assumptions?

So it could be separated from the analysis of speeding up, but decentralization was an issue that growth theorists were going to have to take seriously, at least if their approach to science involves Feynmann-integrity:

It’s a kind of scientific integrity, a principle of scientific thought that corresponds to a kind of utter honesty. … If you make a theory, for example, and advertise it, or put it out, then you must also put down all the facts that disagree with it, as well as those that agree with it.

Richard Feynman from a commencement address.

But perhaps not if their approach to science is based on Stigler-conviction:

[N]ew economic theories are introduced by the technique of the huckster …  a one-sided man. He is utterly persuaded of the significance and correctness of his ideas and he subordinates all other truths because they seem to him less important than the general acceptance of his truth. He is more a warrior against ignorance than a scholar among ideas.

George Stigler, 1955, “The Nature and Role of Originality in Scientific Progress,” Economica, New Series, Vol. 22, No. 88, p. 296.


Previous posts in this series of posts inspired by the 25th anniversary of the publication of my 1990 JPE paper:

#6: Speeding Up: Theory

#5: Speeding Up and Missed Opportunities: Evidence

#4: Economic Growth

#3: Clear Writing Produces Clearer Thoughts

#2: Human Capital and Knowledge

#1: Nonrival Goods After 25 Years

Thanks to Joshua Gans for spurring this series with his post here.