I do love a good piece of applied theory. I think of applied theory as the following. Gather some set of stylized facts about the world. Make zero attempt whatsoever to identify causal arguments from the data itself; no IV estimation, no discontinuity design, no random assignment, no natural experiments, etc. Rather, write a model of economic behavior which can simultaneously generate all of the above facts. To the extent that the model also implies some other facts about the world, don’t worry about it; the model is a metaphor, as I’ve discussed on this site in the past. I don’t mean to imply that a model is good iff it can explain some limited sphere we care about, as Friedman argued. I mean a model is good if it can provide a plausible guide to our thinking about an inherently messy social science problem: that is what is meant by “metaphor.”

I can’t help but see the following problem in other empirical literature (whether pure reduced form, or filled with fancy econometrics), particular that in the non-econ social sciences, since applied theory of the type described above is very uncommon outside our field: without a model, I don’t know how to evaluate counterfactuals. I don’t know how to give advice to future policymakers when some fact changes vis-a-vis the period examined in the paper. I have to worry too much about data quality, and social science data is uniformly terrible. Most importantly, I am often limited to examining questions of a very specific type, a problem particularly common in the natural experiment crowd. This is because the amount of economic theory that I can include in an exclusion restriction, for example, is much less than I could include in a full model. This isn’t to say that papers can’t do nice modeling *and* nice theory: the best do both! Ben Handel’s health insurance paper, or Todd and Wolpin’s PROGRESA paper, certainly do both. I am also aware that the vast majority of empirical economists do not agree with all (or even any!) of the above: I’m going to post Imbens’ counterargument to the benefits of applied theory here soon.

In any case, in The Burden of Knowledge, Ben Jones uses Hall’s patent database to establish the following stylized facts. Teamwork increases over time and is higher in fields requiring more base knowledge. Specialization, measured in the (inverse of the) probability of an inventor switching fields from one patent to the next, is increasing over time and is lower in fields requiring more base knowledge. Age of inventors when they get their first patent is increasing over time, but does not appear to vary based on the base level of knowledge in the inventor’s field. Base knowledge is measured in an interesting way. A field requires more base knowledge if patents in the “tree” of patents cited by a patent. That is, my patent cites 6 other patents, which each cite 6 more, which each cite 6 more, and all of the rest are patents from before 1975 (and thus not in the data), then my patent’s tree has 216 cites. A quick glance at summary statistics suggests that this measure is correlated with what intuitively seem like “more advanced” fields.

At this point, no attempt whatsoever is made to establish a causal relationship using the data. Instead, Jones writes down a macroecon-style general equilibrium model. Every individual chooses to invent in a given field, or else to be a production worker. Inventors are paid rents equal their marginal productivity, and workers are paid via a no-profit function on firms. Each field is represented as a cylinder, with the height representing the difficulty of reaching the frontier in that field, and the outside of the circle representing various specializations within the field. An inventor “buys” a field, and a breadth within that field represented as an arc on the base of the cylinder, paying an amount that is a function of the area of that slice of the cylinder.

Over time, ideas arrive at each inventor at a rate which varies across fields. Buying more breadth gives you a higher arrival rate for ideas. Having more inventors near you lowers the arrival rate (you duplicate inventions, basically). A higher level of societal productivity can either increase the arrival rate, as in Romer, or decrease it, as in the “easy inventions are being fished-out” hypothesis. In order to implement an invention, the “circle must be covered”: the inventor must pay other inventors in his field such that their combined breadth covers the circle.

Now just solve the model in equilibrium, along a balanced growth path, meaning societal productivity growth is constant (letting population grow at some exogenous rate). The model gives that, at any time, spending on education is proportional to lifetime income for the inventor. This proportionality holds regardless of the difficulty of the field. Since education is just a portion of a cylinder, this immediately gives that breadth is higher in fields where the state-of-the-art difficulty is lower. Since inventions are implemented only when the circle is covered, teamwork must increase in more difficult, more specialized fields. I find the cylinder model of innovation quite elegant. On the other hand, I don’t know why 20 pages of algebra and explanation should be required to explain the last two paragraphs of results: would that economics journal editors edited more strictly for length!

The interesting empirical extension, I think, is this: some inventions are “stepping stones”, in that in order to discover C, I must first learn A and B, and even after C is discovered, I can only know C if I know A and B. For instance, let A be arithmetic, B be algebra and C be calculus. Other inventions are all-encompassing: once I know C, I know everything relevant to the world in A and B and no longer really need them. Once you know modern control and dynamic programming, you can solve any problem you would have solved with calculus of variations, plus more: for applied work, CoV doesn’t need to be learned at all anymore. Inventions of the second type are much more socially beneficial than the first type. Which type is becoming more common over time, though?

http://www.kellogg.northwestern.edu/faculty/jones-ben/htm/burdenofknowledge.pdf (Final WP – final version in ReStud 2009)

I thing the sequence was arithmetic (book-keeping), then geometry (star gazing, construction et al.), then algebra, which added abstraction. Algebra was useful in using geometry to create calculus.