Category Archives: Diffusion

On the economics of the Neolithic Revolution

The Industrial and Neolithic Revolutions are surely the two fundamental transitions in the economic history of mankind. The Neolithic involved permanent settlement of previously nomadic, or at best partially foraging, small bands. At least seven independent times, bands somewhere in the world adopted settled agriculture. The new settlements tended to see an increase in inequality, the beginning of privately held property, a number of new customs and social structures, and, most importantly, an absolute decrease in welfare as measured in terms of average height and an absolute increase in the length and toil of working life. Of course, in the long run, settlement led to cities which led to the great inventions that eventually pushed mankind past the Malthusian bounds into our wealthy present, but surely no nomad of ten thousand years ago could have projected that outcome.

Now this must sound strange to any economist, as we can’t help but think in terms of rational choice. Why would any band choose to settle when, as far as we can tell, settling made them worse off? There are only three types of answers compatible with rational choice: either the environment changed such that the nomads who adopted settlement would have been even worse off had they remained nomadic, settlement was a Pareto-dominated equilibrium, or our assumption that the nomads were maximizing something correlated with height is wrong. All might be possible: early 20th century scholars ascribed the initial move to settlement to humans being forced onto oases in the drying post-Ice Age Middle East, evolutionary game theorists are well aware that fitness competitions can generate inefficient Prisoner’s Dilemmas, and humans surely care about reproductive success more than they care about food intake per se.

So how can we separate these potential explanations, or provide greater clarity as to the underlying Neolithic transition mechanism? Two relatively new papers, Andrea Matranga’s “Climate-Driven Technical Change“, and Kim Sterelny’s Optimizing Engines: Rational Choice in the Neolithic”, discuss intriguing theories about what may have happened in the Neolithic.

Matranga writes a simple Malthusian model. The benefit of being nomadic is that you can move to places with better food supply. The benefit of being sedentary is that you use storage technology to insure yourself against lean times, even if that insurance comes at the cost of lower food intake overall. Nomadism, then, is better than settling when there are lots of nearby areas with uncorrelated food availability shocks (since otherwise why bother to move?) or when the potential shocks you might face across the whole area you travel are not that severe (in which case why bother to store food?). If fertility depends on constant access to food, then for Malthusian reasons the settled populations who store food will grow until everyone is just at subsistence, whereas the nomadic populations will eat a surplus during times when food is abundant.

It turns out that global “seasonality” – or the difference across the year in terms of temperature and rainfall – was extraordinarily high right around the time agriculture first popped up in the Fertile Crescent. Matranga uses some standard climatic datasets to show that six of the seven independent inventions of agriculture appear to have happened soon after increases in seasonality in their respective regions. This is driven by an increase in seasonality and not just an increase in rainfall or heat: agriculture appears in the cold Andes and in the hot Mideast and in the moderate Chinese heartland. Further, adoption of settlement once your neighbors are farming is most common when you live on relatively flat ground, with little opportunity to change elevation to pursue food sources as seasonality increases. Biological evidence (using something called “Harris lines” on your bones) appears to support to idea that nomads were both better fed yet more subject to seasonal shocks than settled peoples.

What’s nice is that Matranga’s hypothesis is consistent with agriculture appearing many times independently. Any thesis that relies on unique features of the immediate post-Ice Age – such as the decline in megafauna like the Woolly Mammoth due to increasing population, or the oasis theory – will have a tough time explaining the adoption of agriculture in regions like the Andes or China thousands of years after it appeared in the Fertile Crescent. Alain Testart and colleagues in the anthropology literature have made similar claims about the intersection of storage technology and seasonality being important for the gradual shift from nomadism to partial foraging to agriculture, but the Malthusian model and the empirical identification in Matranga will be much more comfortable for an economist reader.

Sterelny, writing in the journal Philosophy of Science, argues that rational choice is a useful framework to explain not only why backbreaking, calorie-reducing agriculture was adopted, but also why settled societies appeared willing to tolerate inequality which was much less common in nomadic bands, and why settled societies exerted so much effort building monuments like Gobekli Tepe, holding feasts, and participating in other seemingly wasteful activity.

Why might inequality have arisen? Settlements need to be defended from thieves, as they contain stored food. Hence settlement sizes may be larger than the size of nomadic bands. Standard repeated games with imperfect monitoring tell us that when repeated interactions become less common, cooperation norms become hard to sustain. Hence collective action can only be sustained through mechanisms other than dyadic future punishment; this is especially true if farmers have more private information about effort and productivity than a band of nomadic hunters. The rise of enforceable property rights, as Bowles and his coauthors have argued, is just such a mechanism.

What of wasteful monuments like Gobekli Tepe? Game theoretic deliberate choice provides two explanations for such seeming wastefulness. First, just as animals consume energy in ostentatious displays in order to signal their fitness (as the starving animal has no energy to generate such a display), societies may construct totems and temples in order to signal to potential thieves that they are strong and not worth trifling with. In the case of Gobekli Tepe, this doesn’t appear to be the case, as there isn’t much archaeological evidence of particular violence around the monument. A second game theoretic rationale, then, is commitment by members of a society. As Sterelny puts it, the reason a gang makes a member get a face tattoo is that, even if the member leaves the gang, the tattoo still puts that member at risk of being killed by the gang’s enemies. Hence the tattoo commits the member not to defect. Settlements around Gobekli Tepe may have contributed to its building in order to commit their members to a set of norms that the monument embodied, and hence permit trade and knowledge transfer within this in-group. I would much prefer to see a model of this hypothesis, but the general point doesn’t seem impossible. At least, Sterelny and Matranga together provide a reasonably complete possible explanation, based on rational behavior and nothing more, of the seemingly-strange transition away from nomadism that made our modern life possible.

Kim Sterelny, Optimizing Engines: Rational Choice in the Neolithic?, 2013 working paper. Final version published in the July 2015 issue of Philosophy of Science. Andrea Matranga, “Climate-driven Technical Change: Seasonality and the Invention of Agriculture”, February 2015 working paper, as yet unpublished. No RePEc IDEAS page is available for either paper.

Labor Unions and the Rust Belt

I’ve got two nice papers for you today, both exploring a really vexing question: why is it that union-heavy regions of the US have fared so disastrously over the past few decades? In principle, it shouldn’t matter: absent any frictions, a rational union and a profit-maximizing employer ought both desire to take whatever actions generate the most total surplus for the firm, with union power simply affecting how those rents are shared between management, labor and owners. Nonetheless, we notice empirically a couple of particularly odd facts. First, especially in the US, union-dominated firms tend to limit adoption of new, productivity-enhancing technology; the late adoption of the radial tire among U.S. firms is a nice example. Second, unions often negotiate not only about wages but about “work rules”, insisting upon conditions like inflexible employee roles. A great example here is a California longshoremen contract which insisted upon a crew whose sole job was to stand and watch while another crew did the job. Note that preference for leisure can’t explain this, since surely taking that leisure at home rather than standing around the worksite would be preferable for the employees!

What, then, might drive unions to push so hard for seemingly “irrational” contract terms, and how might union bargaining power under various informational frictions or limited commitment affect the dynamic productivity of firms? “Competition, Work Rules and Productivity” by the BEA’s Benjamin Bridgman discusses the first issue, and a new NBER working paper, “Competitive Pressure and the Decline of the Rust Belt: A Macroeconomic Analysis” by Alder, Lagakos and Ohanian covers the second; let’s examine these in turn.

First, work rules. Let a union care first about keeping all members employed, and about keeping wage as high as possible given full employment. Assume that the union cannot negotiate the price at which products are sold. Abstractly, work rules are most like a fixed cost that is a complete waste: no matter how much we produce, we have to incur some bureaucratic cost of guys standing around and the like. Firms will set marginal revenue equal to marginal cost when deciding how much to produce, and at what price that production should be sold. Why would the union like these wasteful costs?

Let firm output given n workers just be n-F, where n is the number of employees, and F is how many of them are essentially doing nothing because of work rules. The firm chooses price p and the number of employees n given demand D(p) and wage w to maximize p*D(p)-w*n, subject to total production being feasible D(p)=n-F. Note that, as long as total firm profits under optimal pricing exceed F, the firm stays in business and its pricing decision, letting marginal revenue equal marginal cost, is unaffected by F. That is, the optimal production quantity does not depend on F. However, the total amount of employment does depend on F, since to produce quantity D(p) you need to employ n-F workers. Hence there is a tradeoff if the union only negotiates wages: to employ more people, you need a lower wage, but using wasteful work rules, employment can be kept high even when wages are raised. Note also that F is limited by the total rents earned by the firm, since if work rules are particularly onerous, firms that are barely breaking even without work rules will simply shut down. Hence in more competitive industries (formally, when demand is less elastic), work rules are less likely to imposed by unions. Bridgman also notes that if firms can choose technology (output is An-F, where A is the level of technology), then unions will resist new technology unless they can impose more onerous work rules, since more productive technology lowers the number of employees needed to produce a given amount of output.

This is a nice result. Note that the work rule requirements have nothing to do with employees not wanting to work hard, since work rules in the above model are a pure waste and generate no additional leisure time for workers. Of course, this result really hinges on limiting what unions can bargain over: if they can select the level of output, or can impose the level of employment directly, or can permit lump-sum transfers from management to labor, then unionized firms will produce at the same productivity at non-unionized firms. Information frictions, among other worries, might be a reason why we don’t see these types of contracts at some unionized firms. With this caveat in mind, let’s turn to the experience of the Rust Belt.

The U.S. Rust Belt, roughly made up of states surrounding the Great Lakes, saw a precipitous decline from the 1950s to today. Alder et al present the following stylized facts: the share of manufacturing employment in the U.S. located in the Rust Belt fell from the 1950s to the mid-1980s, there was a large wage gap between Rust Belt and other U.S. manufacturing workers during this period, Rust Belt firms were less likely to adopt new innovations, and labor productivity growth in Rust Belt states was lower than the U.S. average. After the mid-1980s, Rust Belt manufacturing firms begin to look a lot more like manufacturing firms in the rest of the U.S.: the wage gap is essentially gone, the employment share stabilizes, strikes become much less common, and productivity growth is similar. What happened?

In a nice little model, the authors point out that output competition (do I have lots of market power?) and labor market bargaining power (are my workers powerful enough to extract a lot of my rents?) interact in an interesting way when firms invest in productivity-increasing technology and when unions cannot commit to avoid a hold-up problem by striking for a better deal after the technology investment cost is sunk. Without commitment, stronger unions will optimally bargain away some of the additional rents created by adopting an innovation, hence unions function as a type of tax on innovation. With sustained market power, firms have an ambiguous incentive to adopt new technology – on the one hand, they already have a lot of market power and hence better technology will not accrue too many more sales, but on the other hand, having market power in the future makes investments today more valuable. Calibrating the model with reasonable parameters for market power, union strength, and various elasticities, the authors find that roughly 2/3 of the decline in the Rust Belt’s manufacturing share can be explained by strong unions and little output market competition decreasing the incentive to invest in upgrading technology. After the 1980s, declining union power and more foreign competition limited both disincentives and the Rust Belt saw little further decline.

Note again that unions and firms rationally took actions that lowered the total surplus generated in their industry, and that if the union could have committed not to hold up the firm after an innovation was adopted, optimal technology adoption would have been restored. Alder et al cite some interesting quotes from union heads suggesting that the confrontational nature of U.S. management-union relations led to a belief that management figures out profits, and unions figure out to secure part of that profit for their members. Both papers discussed here show that this type of division, by limiting the nature of bargains which can be struck, can have calamitous effects for both workers and firms.

Bridgman’s latest working paper version is here (RePEc IDEAS page); the latest version of Adler, Lagakos and Ohanian is here (RePEc IDEAS). David Lagakos in particular has a very nice set of recent papers about why services and agriculture tend to have such low productivity, particularly in the developing world; despite his macro background, I think he might be a closet microeconomist!

“Immigration and the Diffusion of Technology: The Huguenot Diaspora in Prussia,” E. Hornung (2014)

Is immigration good for natives of the recipient country? This is a tough question to answer, particularly once we think about the short versus long run. Large-scale immigration might have bad short-run effects simply because more L plus fixed K means lower average incomes in essentially any economic specification, but even given that fact, immigrants bring with them tacit knowledge of techniques, ideas, and plans which might be relatively uncommon in the recipient country. Indeed, world history is filled with wise leaders who imported foreigners, occasionally by force, in order to access their knowledge. As that knowledge spreads among the domestic population, productivity increases and immigrants are in the long-run a net positive for native incomes.

How substantial can those long-run benefits be? History provides a nice experiment, described by Erik Hornung in a just-published paper. The Huguenots, French protestants, were largely expelled from France after the Edict of Nantes was revoked by the Sun King, Louis XIV. The Huguenots were generally in the skilled trades, and their expulsion to the UK, the Netherlands and modern Germany (primarily) led to a great deal of tacit technology transfer. And, no surprise, in the late 17th century, there was very little knowledge transfer aside from face-to-face contact.

In particular, Frederick William, Grand Elector of Brandenburg, offered his estates as refuge for the fleeing Huguenots. Much of his land had been depopulated in the plagues that followed the Thirty Years’ War. The centralized textile production facilities sponsored by nobles and run by Huguenots soon after the Huguenots arrived tended to fail quickly – there simply wasn’t enough demand in a place as poor as Prussia. Nonetheless, a contemporary mentions 46 professions brought to Prussia by the Huguenots, as well as new techniques in silk production, dyeing fabrics and cotton printing. When the initial factories failed, knowledge among the apprentices hired and purchased capital remained. Technology transfer to natives became more common as later generations integrated more tightly with natives, moving out of Huguenot settlements and intermarrying.

What’s particularly interesting with this history is that the quantitative importance of such technology transfer can be measured. In 1802, incredibly, the Prussians had a census of manufactories, or factories producing stock for a wide region, including capital and worker input data. Also, all immigrants were required to register yearly, and include their profession, in 18th century censuses. Further, Huguenots did not simply move to places with existing textile industries where their skills were most needed; indeed, they tended to be placed by the Prussians in areas which had suffered large population losses following the Thirty Years’ War. These population losses were highly localized (and don’t worry, before using population loss as an IV, Hornung makes sure that population loss from plague is not simply tracing out existing transportation highways). Using input data to estimate a Cobb-Douglas textile production function, an additional percentage point of the population with Huguenot origins in 1700 is associated with a 1.5 percentage point increase in textile productivity in 1800. This result is robust in the IV regression using wartime population loss to proxy for the percentage of Huguenot immigrants, as well as many other robustness checks. 1.5% is huge given the slow rate of growth in this era.

An interesting historical case. It is not obvious to me how relevant this estimation to modern immigration debates; clearly it must depend on the extent to which knowledge can be written down or communicated at distance. I would posit that the strong complementarity of factors of production (including VC funding, etc.) are much more important that tacit knowledge spread in modern agglomeration economies of scale, but that is surely a very difficult claim to investigate empirically using modern data.

2011 Working Paper (IDEAS version). Final paper published in the January 2014 AER.

“The ‘Industrial Revolution’ in the Home: Household Technology and Social Change in the 20th Century,” R. S. Cowan (1976)

The really fascinating thing about the “Second Industrial Revolution” (roughly 1870 until World War I) is how much of its effect is seen first for consumers and only later for production. Electricity is the famous example here; most energy-heavy industries were purposefully located near low-cost energy sources like fast-flowing water. Energy produced via transmitted electricity simply wasn’t that competitive until well into the 20th century in these industries.

Ruth Cowan, a historian, investigated how household production was affected by the introduction of electricity, which in the non-rural US roughly means between 1918 and the Great Depression; electrification rose from 25 percent to 80 percent during this period. Huge amounts of drudgery, once left to housewives and domestic workers, was reduced. Consider the task of ironing. Before electricity (barring gas irons, which were not widespread), ironing involved heating a heavy flatiron on a stove, carrying it to the ironing board and quickly knocking out wrinkles before the heat dissipated, bringing in back to stove, and so on. The replacement of the coal stove by central heating similarly limited tedious work, including constant cleaning of coal dust. Cowan traces diffusion of these technologies in part by examining advertisements in magazines like the Ladies’ Home Journal.

The interesting aspect of this consumer revolution, however, was that it did not in fact reduce the amount of work done by housewives. By the end of the 1920s, urban women, most affected by these technological changes, were still doing more housework per week than rural women. It appears the standard story of how Industrial Revolution technologies affected industry – more specialization, more importance of managerial talent, disappearing emotional content of work – was not true of household production. Instead, upper middle class women no longer employed specialized domestic help (and the implied importance of managerial talent on the part of the housewife), and advertisements for new consumer goods frequently emphasized the emotional content of, e.g., the improved cleanliness of modern appliances with respect to children’s health. Indeed, technological progress tended to significantly increase the number of tasks women were expected to perform within the house. There’s not much reason in economic theory for TFP improvements to lead to reductions or increases in worker skill or autonomy, so perhaps it’s no surprise that the household sector saw a different pattern from certain industrial sectors.

Final version in Technology & Culture Jan 1976. If you’re not familiar with the term “Second Industrial Revolution”, Joel Mokyr has a nice summary of this period of frequent important macro/GPT inventions. Essentially, the big inventions of the late 19th century were much more reliant on scientific knowledge, and much more connected to network effects and increasing returns to scale, than those of the late 18th and early 19th century.

“Does Knowledge Accumulation Increase the Returns to Collaboration?,” A. Agrawal, A. Goldfarb & F. Teodoridis (2012)

The size of academic research “teams” has been increasing, inexorably, in essentially every field over the past few decades. This may be because of bad incentives for researchers (as Stan Liebowitz has argued), or because more expensive capital is required for research as in particle physics, or because communication technology has decreased the cost of collaboration. A much more worrying explanation is, simply, that reaching the research frontier is getting harder. This argument is most closely associated with my adviser Ben Jones, who has noticed that while team size has increased, the average age star researchers do their best work has increased, co-inventors on inventions has increased, and the number of researchers doing work across fields has decreased. If the knowledge frontier is becoming more expensive to reach, theory suggests a role for greater subsidization of early-career researchers and of potential development traps due to the complementary nature of specialized fields.

Agrawal et al use a clever device to investigate whether the frontier is indeed becoming more burdensome. Note that the fact that science advances does not mean, ipso facto, that reaching the frontier is harder: new capital like computers or Google Scholar may make it easier to investigate questions or get up to date in related fields, and certain developments completely subsume previous developments (think of, say, how a user of dynamic programming essentially does not need to bother learning the calculus of variations; the easier but more powerful technique makes the harder but less powerful technique unnecessary). Agrawal et al’s trick is to look at publication trends in mathematics. During the Soviet era, mathematics within the Soviet Union was highly advanced, particularly in certain areas of functional analysis, but Soviet researchers had little ability to interact with non-Soviets and they generally published only in Russian. After the fall of the Soviet Union, there was a “shock” to the knowledge frontier in mathematics as these top Soviet researchers began interacting with other mathematicians. A paper by Borjas and Doran in the QJE last year showed that Soviet mathematics were great in some areas and pretty limited in others. This allows for a diff-in-diff strategy: look at the change in team size following 1990 in fields where Soviets were particularly strong versus fields where the Soviets were weak.

Dropping papers with a Russian-named coauthor, classifying papers by fields using data from the AMS, the authors find that papers in Soviet-heavy fields had the number of coauthors increase from 1.34 to 1.78, whereas Soviet-weak fields teams grew only from 1.26 to 1.55. This difference appears quite robust, and is derived from hundreds of thousands of publications. To check that Soviet-rich fields actually had influence, they note that papers in Soviet-rich subfields cited Soviet-era publications at a greater rate after 1990 than Soviet-poor subfields, and that the increase in coauthoring tended to be driven by papers with a young coauthor. The story here is, roughly, that Soviet emigres would have tooled up young researchers in Soviet-rich fields, and then those young coauthors would have a lot of complementary skills which might drive collaboration with other researchers.

So it appears that the increasing burden of the knowledge frontier does drive some of the increase in team size. The relative importance of this factor, however, is something tough to tease out without some sort of structural model. Getting around the burden of knowledge by making it easier to reach the frontier is also worthy of investigation – a coauthor and I have a pretty cool new paper (still too early to make public) on exactly this topic, showing an intervention that has a social payoff an order of magnitude higher than funding new research.

Oct 2012 working paper (no IDEAS version). As a sidenote, the completely bizarre “copyright notice” on the first page is about the most ridiculous thing I have seen on a working paper recently: besides the fact that authors hold the copyright automatically without such a notice, the paper itself is literally about the social benefits of free knowledge flows! I can only hope that the copyright notice is the result of some misguided university policy.

“Path Dependence,” S. Page (2006)

When we talk about strategic equilibrium, we can talk in a very formal sense, as many refinements with their well-known epistemic conditions have been proposed, the nature of uncertainty in such equilibria has been completely described, the problems of sequential decisionmaking are properly handled, etc. So when we do analyze history, we have a useful tool to describe how changes in parameters altered the equilibrium incentives of various agents. Path dependence, the idea that past realizations of history matter (perhaps through small events, as in Brian Arthur’s work) is widespread. A typical explanation given is increasing returns. If I buy a car in 1900, I make you more likely to buy a car in 1901 by, at the margin, lowering the production cost due to increasing returns to scale or lowering the operating cost by increasing incentives for gas station operators to operate.

This is quite informal, though; worse, the explanation of increasing returns is neither necessary nor sufficient for history-dependence. How can this be? First, consider that “history-dependence” may mean (at least) six different things. History can effect either the path of history, or its long-run outcome. For example, any historical process satisfying the assumptions of the ergodic theorem can be history-dependent along a path, yet still converge to the same state (in the network diffusion paper discussed here last week, a simple property of the network structure tells me whether an epidemic will diffuse entirely in the long-run, but the exact path of that eventual diffusion clearly depends on something much more complicated). We may believe, for instance, that the early pattern of railroads affected the path of settlement of the West without believing that this pattern had much consequence for the 2010 distribution of population in California. Next, history-dependence in the long-run or short-run can depend either on a state variable (from a pre-defined set of states), the ordered set of past realizations, or the unordered set of past realizations (the latter called path and phat dependence, respectively, since phat dependence does not depend on order). History matters in elections due to incumbent bias, but that history-dependence can basically be summed up by a single variable denoting who is the current incumbent, omitting the rest of history’s outcomes. Phat dependence is likely in simple technology diffusion: I adopt a technology as a function of which of my contacts has adopted it, regardless of the order in which they adopted. Path dependence comes up, for example, in models of learning following Aumann and Geanakoplos/Polemarchakis, consensus among a group can be broken if agents do not observe the time at which messages were sent between third parties.

Now consider increasing returns. For which types of increasing returns is this necessary or sufficient? It turns out the answer is, for none of them! Take again the car example, but assume there are three types of cars in 1900, steam, electric and gasoline. For the same reasons that gas-powered cars had increasing returns, steam and electric cars do as well. But the relative strength of the network effect for gas-powered cars is stronger. Page thinks of this as a biased Polya process. I begin with five balls, 3 G, 1 S and 1 E, in an urn. I draw one at random. If I get an S or an E, I return it to the urn with another ball of the same type (thus making future draws of that type more common, hence increasing returns). If I draw a G, I return it to the urn along with 2t more G balls, where t is the time which increments by 1 after each draw. This process converges to having arbitrarily close to all balls of type G, even though S and E balls also exhibit increasing returns.

Why about the necessary condition? Surely, increasing returns are necessary for any type of history-dependence? Well, not really. All I need is some reason for past events to increase the likelihood of future actions of some type, in any convoluted way I choose. One simple mechanism is complementarities. If A and B are complements (adopting A makes B more valuable, and vice versa), while C and D are also complements, then we can have the following situation. An early adoption of A makes B more valuable, increasing the probability of adopting B the next period which itself makes future A more valuable, increasing the probability of adopting A the following period, and so on. Such reasoning is often implicit in the rhetoric linking market-based middle class to a democratic political process: some event causes a private sector to emerge, which increases pressure for democratic politics, which increases protection of capitalist firms, and so on. As another example, consider the famous QWERTY keyboard, the best-known example of path dependence we have. Increasing returns – that is, the fact that owning a QWERTY keyboard makes this keyboard more valuable for both myself and others due to standardization – is not sufficient for killing the Dvorak or other keyboards. This is simple to see: the fact that QWERTY has increasing returns doesn’t mean that the diffusion of something like DVD players is history-dependent. Rather, it is the combination of increasing returns for QWERTY and a negative externality on Dvorak that leads to history-dependence for Dvorak. If preferences among QWERTY and Dvorak are Leontief, and valuations for both have increasing returns, then I merely buy the keyboard I value highest – this means that purchases of QWERTY by others lead to QWERTY lock-in by lowering the demand curve for Dvorak, not merely by raising the demand curve for QWERTY. (And yes, if you are like me and were once told to never refer to effects mediated by the market as “externalities”, you should quibble with the vocabulary here, but the point remains the same.)

All in all interesting, and sufficient evidence that we need a better formal theory and taxonomy of history dependence than we are using now.

Final version in the QJPS (No IDEAS version). The essay is written in a very qualitative/verbal manner, but more because of the audience than the author. Page graduated here at MEDS, initially teaching at Caltech, and his CV lists quite an all-star cast of theorist advisers: Myerson, Matt Jackson, Satterthwaite and Stanley Reiter!

“Threshold Conditions for Arbitrary Cascade Models on Arbitrary Networks,” B.A. Prakash et al (2011)

No need to separate economics from the rest of the social sciences, and no need to separate social science from the rest of science: we often learn quite a bit from our compatriot fields. Here’s a great example. Consider any epidemic diffusion, where a population (of nodes) is connected to each other (along, in this case, unweighted edges, equal to 1 if and only if there is a link between the nodes). Consider the case where nodes can become “infected” – in economics, we may think of nodes as people or cities adopting a new technology, or purchasing a new product. Does a given seeding on the network lead to an “infection” that spreads across the network, or is the network fairly impervious to infections?

This seems like it must be a tricky question, for nodes can be connected to other nodes in an arbitrary fashion. Let’s make it even more challenging for the analyst: allow there to be m “susceptible” states, an “exposed” state, an “infected” state, and N “vaccinated” states, who cannot be infected. Only exposed or infected agents can propagate an infection, and do so to each of their neighbors in any given period according to probabilities a and b, independently across neighbors. Parameters tell me the probability each agent transitions from susceptible or vaccinated states to other such states.

You may know the simple SIR model – susceptible, infected, recovered. In these models, all agents begin as susceptible pr infected. If my neighbor is infected and I am susceptible, he gives me the disease with probability a. If I am infected, I recover with probability c. This system spreads across the population if the first eigenvalue of the adjacency matrix (which equals 1 if two people are connected, and 0 otherwise) is greater than a/c. (Incredibly, I believe this proof dates back to Kermack and McKendrick in 1927). That is, the only way the network topology matters is in a single-valued summary statistic, the first eigenvalue. Pretty incredible.

The authors of the present paper show that this is a general property. For any epidemic model in which disease spreads over a network such that, first, transmissions are independent across neighbors, and second, one can only enter the exposed or infected state from an exposed or infected neighbor, the general property is the same: the disease spreads through the population if the first eigenvalue of the adjacency matrix is larger than a constant which depends only on model parameters and not on the topology of the network (and, in fact, these parameters are easy to characterize). It is a particularly nice proof. First we compute the probabilities of transitioning from each state to any other. This gives us a discrete-time nonlinear dynamic system. Such systems are asymptotically stable if all real eigenvalues of the nonlinear dynamic are less than one in absolute value. If there are no infections at all, the steady state is just the steady state of a Markov chain: only infected or exposed people can infect me, so the graph structure doesn’t matter if we assume no infections, and transition between the susceptible and vaccinated states are just Markov by assumption. We then note that the Jacobian has a nice block structure which limits the eigenvalues to being one of two types, show that the first type of eigenvalues are always less than one in absolute value, then show that the second types are less than one if and only if a property depending on model parameters only are satisfied; this property has nothing to do with the network topology.

The result tells you some interesting things as well. For example, say you wish to stop the spread of an epidemic. Should you immunize people with many friends? No – you should immunize the person who lowers the first eigenvalue of the adjacency matrix the most. This result is independent of the actual network topology or the properties of the disease (how long it incubates, how fast it transmits, how long people stay sick, how likely they are to develop natural immunity, etc.). Likewise, in the opposite problem, if you wish an innovation to diffuse through a society, how should you organize conferences or otherwise create a network? Create links between people or locations such that the first eigenvalue of the adjacency matrix increases by the highest amount. Again, this is independent of the current network topology or the properties of the particular invention you wish to diffuse. Nice.

Final conference paper from ICDM2011. (No IDEAS version).

“What Determines Productivity,” C. Syverson (2011)

Chad Syverson, along with Nick Bloom, John van Reenen, Pete Klenow and many others, has been at the forefront of a really interesting new strand of the economics literature: persistent differences in productivity. Syverson looked at productivity differences within 4-digit SIC industries in the US (quite narrow industries like “Greeting Cards” or “Industrial Sealants”) a number of years back, and found that in the average industry, the 90-10 ratio of total factor productivity plants was almost 2. That is, the top decile plant in the average industry produced twice as much output as the bottom decline plant, using exactly the same inputs! Hsieh and Klenow did a similar exercise in China and India and found even starker productivity differences, largely due a big left-tail of very low productivity firms. This basic result is robust to different measures of productivity, and to different techniques for identifying differences; you can make assumptions which let you recover a Solow residual directly, or run a regression (adjusting for differences in labor and capital quality, or not), or look at deviations like firms having higher marginal productivity of labor than the wage rate, etc. In the paper discussed in the post, Syverson summarizes the theoretical and empirical literature on persistent productivity differences.

Why aren’t low productivity firms swept from the market? We know from theory that if entry is allowed, potentially infinite and instantaneous, then no firm can remain which is less productive than the entrants. This suggests that persistence of inefficient firms must result from either limits on entry, limits on expansion by efficient firms, or non-immediate efficiency because of learning-by-doing or similar (a famous study by Benkard of a Lockwood airplane showed that a plant could produce a plane with half the labor hours after producing 30, and half again after producing 100). Why don’t inefficient firms already in the market adopt best practices? This is related to the long literature on diffusion, which Syverson doesn’t cover in much detail, but essentially it is not obvious to a firm whether a “good” management practice at another firm is actually good or not. Everett Rogers, in his famous “Diffusion of Innovations” book, refers to a great example of this from Peru in the 1950s. A public health consultant was sent for two years to a small village, and tried to convince the locals to boil their water before drinking it. The water was terribly polluted and the health consequences of not boiling were incredible. After two years, only five percent of the town adopted the “innovation” of boiling. Some didn’t adopt because it was too hard, many didn’t adopt because of a local belief system that suggested only the already-sick ought drink boiled water, some didn’t adopt because they didn’t trust the experience of the advisor, et cetera. Diffusion is difficult.

Ok, so given that we have inefficient firms, what is the source of the inefficiency? It is difficult to decompose all of the effects. Learning-by-doing is absolutely relevant in many industries – we have plenty of evidence on this count. Nick Bloom and coauthors seem to suggest that management practices play a huge role. They have shown clear correlation between “best practice” management and high TFP across firms, and a recent randomized field experiment in India (discussed before on this site) showed massive impacts on productivity from management improvements. Regulation and labor/capital distortions also appear to play quite a big role. On this topic, James Schmitz wrote a very interesting paper, published in 2005 in the JPE, on iron ore producers. TFP in Great Lakes ore had been more or less constant for many decades, with very little entry or foreign competition until the 1980s. Once Brazil began exporting ore to the US, labor productivity doubled within a handful of years, and capital and total factor productivity also soared. A main driver of the change was more flexible workplace rules.

Final version in 2011 JEP (IDEAS version). Syverson was at Kellogg recently presenting a new paper of his, with an all-star cast of coauthors, on the medical market. It’s well worth reading. Medical productivity is similarly heterogeneous, and since the medical sector is coming up on 20% of GDP, the sources of inefficiency in medicine are particularly important!

“Recruiting for Ideas: How Firms Exploit the Prior Inventions of New Hires,” J. Singh & A. Agrawal (2011)

Firms poach engineers and researchers from each other all the time. One important reason to do so is to gain access to the individual’s knowledge. A strain of theory going back to Becker, however, suggests that if, after the poaching, the knowledge remains embodied solely in the new employer, it will be difficult for the firm to profit: surely the new employee will have an enormous amount of bargaining power over wages if she actually possesses unique and valuable information. (As part of my own current research project, I learned recently that Charles Martin Hall, co-inventor of the Hall-Heroult process for aluminum smelting, was able to gather a fortune of around $300 million after he brought his idea to the company that would become Alcoa.)

In a resource-based view of the firm, then, you may hope to not only access a new employer’s knowledge, but also spread it to other employees at your firm. By doing this, you limit the wage bargaining power of the new hire, and hence can scrape off some rents. Singh and Agrawal break open the patent database to investigate this. First, use name and industry data to try to match patentees who have an individual patent with one firm at time t, and then another patent at a separate firm some time later; such an employee has “moved”. We can’t simply check whether the receiving firm cites this new employee’s old patents more often, as there is an obvious endogeneity problem. First, firms may recruit good scientists more aggressively. Second, they may recruit more aggressively in technology fields where they are already planning to do work in the future. This suggests that matching plus diff-in-diff may work. Match every patent to another patent held by an inventor who never switches firms, attempting to find a second patent with very similar citation behavior, inventor age, inventor experience, technology class, etc. Using our matched sample, check how much the propensity to cite the mover’s patent changes compares to the propensity to the cite the stayer’s patent. That is, let Joe move to General Electric. Joe had a patent while working at Intel. GE researchers were citing that Intel patent once per year before Joe moved. They were citing a “matched” patent 1 times per year. After the move, they cite the Intel patent 2 times per year, and the “matched” patent 1.1 times per year. The diff-in-diff then suggests that moving increases the propensity to cite the Intel patent at GE by (2-1)-(1.1-1)=.9 citations per year, where the first difference helps account for the first type of endogeneity we discussed above, and the second difference for the second type of endogeneity.

What do we find? It is true that, after a move, the average patent held by a mover is cited more often at the receiving firm, especially in the first couple years after a move. Unfortunately, about half of new patents which cite the new employee’s old patent after she moves are made by the new employee herself, and another fifteen percent or so are made by previous patent collaborators of the poached employee. What’s worse, if you examine these citations by year, even five years after the move, citations to the pre-move patent are still highly likely to come from the poached employee. That is, to the extent that the poached employee had some special knowledge, the firm appears to have simply bought that knowledge embodied in the new employee, rather than gained access to useful techniques that quickly spread through the firm.

Three quick comments. First, applied econometrician friends: is there any reason these days to do diff-in-diff linearly rather than using the nonparametric “changes-in-changes” of Athey and Imbens 2006, which allows recovery of the entire distribution of effects of treatment on the treated? Second, we learn from this paper that the mean poached research employee doesn’t see her knowledge spread through the new firm, which immediately suggests the question of whether there are certain circumstances in which such knowledge spreads. Third, this same exercise could be done using all patents held by the moving employee’s old firm – I may be buying access to general techniques owned by the employee’s old firm rather than the specific knowledge represented in that employee’s own pre-move patents. I wonder if there’s any difference.

Final Management Science version (IDEAS version). Big thumbs up to Jasjit Singh for putting final published versions of his papers up on his site.

“Diffusing New Technology Without Dissipating Rents: Some Historical Case Studies of Knowledge Sharing,” J. Bessen & A. Nuvolari (2012)

The most fundamental fact in the economic history of the world is that, from the dawn on mankind until the middle of the 19th century in a small corner of Europe, the material living standards of the average human varied within a very small range: perhaps the wealthiest places, ever, were five times richer than regions on the edge of subsistence. The end of this Malthusian world is generally credited to changes following the Industrial Revolution. The Industrial Revolution is sometimes credited to changes in the nature of invention in England and Holland in the 1700s. If you believe those claims, then understanding what spurred invention from that point to the present is of singular importance.

A traditional story, going back to North and others, is that property rights were very important here. England had patents. England had well-enforced contracts for labor and capital. But, at least as far as patents are concerned, recent evidence suggests they couldn’t have been too critical. Moser showed that only 10% or so of important inventions in the mid-1800s were ever patented in the UK. Bob Allen, who we’ve met before on this site, has inspired a large literature on collective invention, or periods of open-source style sharing of information among industry leaders during critical phases of tinkering with new techniques.

Why would you share, though? Doesn’t this simply dissipate your rents? If you publicize knowledge of a productive process for which you are earning some rent, imitators can just come in and replicate that technology, competing away your profit. And yet, and yet, this doesn’t appear to happen in many historical circumstances. Bessen (he of Bessen and Maskin 2009, one of my favorite recent theoretical papers on innovation) and Nuvolari examine three nineteenth century industries, American steel, Cornish steam engines and New England power weavers. They show that periods of open sharing on invention, free transfer of technology to rivals, industry newsletters detailing new techniques, etc. can predominate for periods a decade and longer. In all three cases, patents are unimportant in this initial stage, though (at least outside of Cornwall) quite frequently used later in the development of the industry. Further, many of the important cost reducing microinventions in these industries came precisely during the period of collective invention.

The paper has no model, but very simply, here is what is going on. Consider a fast growing industry where some factors important for entry are in fixed supply; for example, the engineer Alexander Holley personally helped design eight of the first nine American mills using Bessemer’s technology. Assume all inventions are cost reducing. Holding sales price and demand constant, cost reductions increase industry profit. Sharing your invention ensures that you will not be frozen out of sharing by others. Trying to rely only on your own inventions to gain a cost advantage is not as useful as in standard Bertrand, since the fixed factors for entry in a new industry mean you can’t expand fast enough to meet market demand even if you had the cost advantage. There is little worry about free riding since the inventions are natural by-products of day-to-day problem solving rather than the result of concentrated effort: early product improvement is often an engineering problem, not a scientific one. Why would I assume sales price is roughly constant? Imagine an industry where the new technology is replacing something already being produced by a competitive industry (link steel rail ties replaced iron ties). The early Bessemer-produced ties in America were exactly this story, initially being a tiny fraction of the rail tie market, so the market price for ties was being determined by the older vintage of technology.

Open source invention is nothing unusual, nor is it something new. It has long coexisted with the type of invention for which patents may (only may!) be more suitable vectors for development. Policies that gunk up these periods of collective invention can be really damaging. I will discuss some new research in coming weeks about a common policy that appears to provide exactly this sort of gunk: the strict enforcement of non-compete agreements in certain states.

2012 Working Paper (IDEAS version)

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