How We Create and Destroy Growth: A Nobel for Romer and Nordhaus

Occasionally, the Nobel Committee gives a prize which is unexpected, surprising, yet deft in how it points out underappreciated research. This year, they did no such thing. Both William Nordhaus and Paul Romer have been running favorites for years in my Nobel betting pool with friends at the Federal Reserve. The surprise, if anything, is that the prize went to both men together: Nordhaus is best known for his environmental economics, and Romer for his theory of “endogenous” growth.

On reflection, the connection between their work is obvious. But it is the connection that makes clear how inaccurate many of today’s headlines – “an economic prize for climate change” – really is. Because it is not the climate that both winners build on, but rather a more fundamental economic question: economic growth. Why are some places and times rich and others poor? And what is the impact of these differences? Adam Smith’s “The Wealth of Nations” is formally titled “An Inquiry into the Nature and Causes of the Wealth of Nations”, so these are certainly not new questions in economics. Yet the Classical economists did not have the same conception of economic growth that we have; they largely lived in a world of cycles, of ebbs and flows, with income per capita facing the constraint of agricultural land. Schumpeter, who certainly cared about growth, notes that Smith’s discussion of the “different progress of opulence in different nations” is “dry and uninspired”, perhaps only a “starting point of a sort of economic sociology that was never written.”

As each generation became richer than the one before it – at least in a handful of Western countries and Japan – economists began to search more deeply for the reason. Marx saw capital accumulation as the driver. Schumpeter certainly saw innovation (though not invention, as he always made clear) as important, though he had no formal theory. It was two models that appear during and soon after World War II – that of Harrod-Domar, and Solow-Swan-Tinbergen – which began to make real progress. In Harrod-Domar, economic output is a function of capital Y=f(K), nothing is produced without capital f(0)=0, the economy is constant returns to scale in capital df/dK=c, and the change in capital over time depends on what is saved from output minus what depreciates dK/dt=sY-zK, where z is the rate of depreciation. Put those assumptions together and you will see that growth, dY/dt=sc-z. Since c and z are fixed, the only way to grow is to crank up the savings rate, Soviet style. And no doubt, capital deepening has worked in many places.

Solow-type models push further. They let the economy be a function of “technology” A(t), the capital stock K(t), and labor L(t), where output Y(t)=K^a*(A(t)L(t))^(1-a) – that is, that production is constant returns to scale in capital and labor. Solow assumes capital depends on savings and depreciation as in Harrod-Domar, that labor grows at a constant rate n, and that “technology” grows at constant rate g. Solving this model gets you that the economy grows such that dY/dt=sy-k(n+z+g), and that output is exactly proportional to capital. You can therefore just run a regression: we observe the amount of labor and capital, and Solow shows that there is not enough growth in those factors to explain U.S. growth. Instead, growth seems to be largely driven by change in A(t), what Abramovitz called “the measure of our ignorance” but which we often call “technology” or “total factor productivity”.

Well, who can see that fact, as well as the massive corporate R&D facilities of the post-war era throwing out inventions like the transistor, and not think: surely the factors that drive A(t) are endogenous, meaning “from within”, to the profit-maximizing choices of firms? If firms produce technology, what stops other firms from replicating these ideas, a classic positive externality which would lead the rate of technology in a free market to be too low? And who can see the low level of convergence of poor country incomes to rich, and not think: there must be some barrier to the spread of A(t) around the world, since otherwise the return to capital must be extraordinary in places with access to great technology, really cheap labor, and little existing capital to combine with it. And another question: if technology – productivity itself! – is endogenous, then ought we consider not just the positive externality that spills over to other firms, but also the negative externality of pollution, especially climate change, that new technologies both induce and help fix? Finally, if we know how to incentivize new technology, and how growth harms the environment, what is the best way to mitigate the great environmental problem of our day, climate change, without stopping the wondrous increase in living standards growth keeps providing? It is precisely for helping answer these questions that Romer and Nordhaus won the Nobel.

Romer and Endogenous Growth

Let us start with Paul Romer. You know you have knocked your Ph.D. thesis out of the park when the great economics journalist David Warsh writes an entire book hailing your work as solving the oldest puzzle in economics. The two early Romer papers, published in 1986 and 1990, have each been cited more than 25,000 times, which is an absolutely extraordinary number by the standards of economics.

Romer’s achievement was writing a model where inventors spend money to produce inventions with increasing returns to scale, other firms use those inventions to produce goods, and a competitive Arrow-Debreu equilibrium still exists. If we had such a model, we could investigate what policies a government might wish to pursue if it wanted to induce firms to produce growth-enhancing inventions.

Let’s be more specific. First, innovation is increasing returns to scale because ideas are nonrival. If I double the amount of labor and capital, holding technology fixed, I double output, but if I double technology, labor, and capital, I more than double output. That is, give one person a hammer, and they can build, say, one staircase a day. Give two people two hammers, and they can build two staircases by just performing exactly the same tasks. But give two people two hammers, and teach them a more efficient way to combine nail and wood, and they will be able to build more than two staircases. Second, if capital and labor are constant returns to scale and are paid their marginal product in a competitive equilibrium, then there is no output left to pay inventors anything for their ideas. That is, it is not tough to model in partial equilibrium the idea of nonrival ideas, and indeed the realization that a single invention improves productivity for all is also an old one: as Thomas Jefferson wrote in 1813, “[h]e who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me.” The difficulty is figuring out how to get these positive spillovers yet still have “prices” or some sort of rent for the invention. Otherwise, why would anyone pursue costly invention?

We also need to ensure that growth is not too fast. There is a stock of existing technology in the world. I use that technology to create new innovations which grow the economy. With more people over time and more innovations over time, you may expect the growth rate to be higher in bigger and more technologically advanced societies. It is in part, as Michael Kremer points out in his One Million B.C. paper. Nonetheless, the rate of growth is not asymptotically increasing by any stretch (see, e.g., Ben Jones on this point). Indeed, growth is nearly constant, abstracting from the business cycle, in the United States, despite a big growth in population and the stock of existing technology.

Romer’s first attempt at endogenous growth was based on his thesis and published in the JPE in 1986. Here, he adds “learning by doing” to Solow: technology is a function of the capital stock A(t)=bK(t). As each firm uses capital, they generate learning which spills over to other firms. Even if population is constant, with appropriate assumptions on production functions and capital depreciation, capital, output, and technology grow over time. There is a problem here, however, and one that is common to any model based on learning-by-doing which partially spills over to other firms. As Dasgupta and Stiglitz point out, if there is learning-by-doing which only partially spills over, the industry is a natural monopoly. And even if it starts competitively, as I learn more than you, dynamically I can produce more efficiently, lower my prices, and take market share from you. A decentralized competitive equilibrium with endogenous technological growth is unsustainable!

Back to the drawing board, then. We want firms to intentionally produce technology in a competitive market as they would other goods. We want technology to be nonrival. And we want technology production to lead to growth. Learning-by-doing allows technology to spill over, but would simply lead to a monopoly producer. Pure constant-returns-to-scale competitive production, where technology is just an input like capital produced with a “nonconvexity” – only the initial inventor pays the fixed cost of invention – means that there is no output left to pay for invention once other factors get their marginal product. A natural idea, well known to Arrow 1962 and others, emerges: we need some source of market power for inventors.

Romer’s insight is that inventions are nonrival, yes, but they are also partially excludable, via secrecy, patents, or other means. In his blockbuster 1990 JPE Endogenous Technological Change, he lets inventions be given an infinite patent, but also be partially substitutable by other inventions, constraining price (this is just a Spence-style monopolistic competition model). The more inventions there are, the more efficiently final goods can be made. Future researchers can use present technology as an input to their invention for free. Invention is thus partially excludable in the sense that my exact invention is “protected” from competition, but also spills over to other researchers by making it easier for them to invent other things. Inventions are therefore neither public nor private goods, and also not “club goods” (nonrival but excludable) since inventors cannot exclude future inventors from using their good idea to motivate more invention. Since there is free entry into invention, the infinite stream of monopoly rents from inventions is exactly equal to their opportunity cost.

From the perspective of final goods producers, there are just technologies I can license as inputs, which I then use in a constant returns to scale way to produce goods, as in Solow. Every factor is paid its marginal product, but inventions are sold for more than their marginal cost due to monopolistic excludability from secrecy or patents. The model is general equilibrium, and gives a ton of insight about policy: for instance, if you subsidize capital goods, do you get more or less growth? In Romer (1986), where all growth is learning-by-doing, cheaper capital means more learning means more growth. In Romer (1990), capital subsidies can be counterproductive!

There are some issues to be worked out: the Romer models still have “scale effects” where growth is not constant, roughly true in the modern world, despite changes in population and the stock of technology (see Chad Jones’ 1995 and 1999 papers). The neo-Schumpeterian models of Aghion-Howitt and Grossman-Helpman add the important idea that new inventions don’t just add to the stock of knowledge, but also make old inventions less valuable. And really critically, the idea that institutions and not just economic fundamentals affect growth – meaning laws, culture, and so on – is a massive field of research at present. But it was Romer who first cracked the nut of how to model invention in general equilibrium, and I am unaware of any later model which solves this problem in a more satisfying way.

Nordhaus and the Economic Solution to Pollution

So we have, with Romer, a general equilibrium model for thinking about why people produce new technology. The connection with Nordhaus comes in a problem that is both caused by, and potentially solved by, growth. In 2018, even an ignoramus knows the terms “climate change” and “global warming”. This was not at all the case when William Nordhaus began thinking about how the economy and the environment interrelate in the early 1970s.

Growth as a policy goal was fairly unobjectionable as a policy goal in 1960: indeed, a greater capability of making goods, and of making war, seemed a necessity for both the Free and Soviet worlds. But by the early 1970s, environmental concerns arose. The Club of Rome warned that we were going to run out of resources if we continued to use them so unsustainably: resources are of course finite, and there are therefore “limits to growth”. Beyond just running out of resources, growth could also be harmful because of negative externalities on the environment, particularly the newfangled idea of global warming an MIT report warned about in 1970.

Nordhaus treated those ideas both seriously and skeptically. In a 1974 AER P&P, he notes that technological progress or adequate factor substitution allow us to avoid “limits to growth”. To put it simply, whales are limited in supply, and hence whale oil is as well, yet we light many more rooms than we did in 1870 due to new technologies and substitutes for whale oil. Despite this skepticism, Nordhaus does show concern for the externalities of growth on global warming, giving a back-of-the-envelope calculation that along a projected Solow-type growth path, the amount of carbon in the atmosphere will reach a dangerous 487ppm by 2030, surprisingly close to our current estimates. In a contemporaneous essay with Tobin, and in a review of an environmentalist’s “system dynamics” predictions of future economic collapse, Nordhaus reaches a similar conclusion: substitutable factors mean that running out of resources is not a huge concern, but rather the exact opposite, that we will have access to and use too many polluting resources, should worry us. That is tremendous foresight for someone writing in 1974!

Before turning back to climate change, can we celebrate again the success of economics against the Club of Rome ridiculousness? There were widespread predictions, from very serious people, that growth would not just slow but reverse by the end of the 1980s due to “unsustainable” resource use. Instead, GDP per capita has nearly doubled since 1990, with the most critical change coming for the very poorest. There would have been no greater disaster for the twentieth century than had we attempted to slow the progress and diffusion of technology, in agriculture, manufacturing and services alike, in order to follow the nonsense economics being promulgated by prominent biologists and environmental scientists.

Now, being wrong once is no guarantee of being wrong again, and the environmentalists appear quite right about climate change. So it is again a feather in the cap of Nordhaus to both be skeptical of economic nonsense, and also sound the alarm about true environmental problems where economics has something to contribute. As Nordhaus writes, “to dismiss today’s ecological concerns out of hand would be reckless. Because boys have mistakenly cried “wolf’ in the past does not mean that the woods are safe.”

Just as we can refute Club of Rome worries with serious economics, so too can we study climate change. The economy affects the climate, and the climate effects the economy. What we need an integrated model to assess how economic activity, including growth, affects CO2 production and therefore climate change, allowing us to back out the appropriate Pigouvian carbon tax. This is precisely what Nordhaus did with his two celebrated “Integrated Assessment Models”, which built on his earlier simplified models (e.g., 1975’s Can We Control Carbon Dioxide?). These models have Solow-type endogenous savings, and make precise the tradeoffs of lower economic growth against lower climate change, as well as making clear the critical importance of the social discount rate and the micro-estimates of the cost of adjustment to climate change.

The latter goes well beyond the science of climate change holding the world constant: the Netherlands, in a climate sense, should be underwater, but they use dikes to restraint the ocean. Likewise, the cost of adjusting to an increase in temperature is something to be estimated empirically. Nordhaus takes climate change very seriously, but he is much less concerned about the need for immediate action than the famous Stern report, which takes fairly extreme positions about the discount rate (1000 generations in the future are weighed the same as us, in Stern) and the costs of adjustment.

Consider the following “optimal path” for carbon from Nordhaus’ most recent run of the model, where the blue line is his optimum.

Note that he permits much more carbon than Stern or a policy which mandates temperatures stay below a 2.5 C rise forever. The reason is the costs to growth in the short term are high: the world is still very poor in many places! There was a vitriolic debate following the Stern report about who was correct: whether the appropriate social discount rate is zero or something higher is a quasi-philosophical debate going back to Ramsey (1928). But you can see here how important the calibration is.

There are other minor points of disagreement between Nordhaus and Stern, and my sense is that there has been some, though not full, convergence if their beliefs about optimal policy. But there is no disagreement whatsoever between the economic and environmental community that the appropriate way to estimate the optimal response to climate change is via an explicit model incorporating some sort of endogeneity of economic reaction to climate policy. The power of the model is that we can be extremely clear about what points of disagreement remain, and we can examine the sensitivity of optimal policy to factors like climate “tipping points”.

There is one other issue: in Nordhaus’ IAMs, and in Stern, you limit climate change by imposing cap and trade or carbon taxes. But carbon harms cross borders. How do you stop free riding? Nordhaus, in a 2015 AER, shows theoretically that there is no way to generate optimal climate abatement without sanctions for non-participants, but that relatively small trade penalties work quite well. This is precisely what Emmanuel Macron is currently proposing!

Let’s wrap up by linking Nordhaus even more tightly back to Romer. It should be noted that Nordhaus was very interested in the idea of pure endogenous growth, as distinct from any environmental concerns, from the very start of his career. His thesis was on the topic (leading to a proto-endogenous growth paper in the AER P&P in 1969), and he wrote a skeptical piece in the QJE in 1973 about the then-leading theories of what factors induce certain types of innovation (objections which I think have been fixed by Acemoglu 2002). Like Romer, Nordhaus has long worried that inventors do not receive enough of the return to their invention, and that we measure innovation poorly – see his classic NBER chapter on inventions in lighting, and his attempt to estimate how much of how much of society’s output goes to innovators.

The connection between the very frontier of endogenous growth models, and environmental IAMs, has not gone unnoticed by other scholars. Nordhaus IAMs tend to have limited incorporation of endogenous innovation in dirty or clean sectors. But a fantastic paper by Acemoglu, Aghion, Bursztyn, and Hemous combines endogenous technical change with Nordhaus-type climate modeling to suggest a middle ground between Stern and Nordhaus: use subsidies to get green energy close to the technological frontier, then use taxes once their distortion is relatively limited because a good green substitute exists. Indeed, since this paper first started floating around 8 or so years ago, massive subsidies to green energy sources like solar by many countries have indeed made the “cost” of stopping climate change much lower than if we’d relied solely on taxes, since now production of very low cost solar, and mass market electric cars, is in fact economically viable.

It may indeed be possible to solve climate change – what Stern called “the greatest market failure” man has ever seen – by changing the incentives for green innovation, rather than just by making economic growth more expensive by taxing carbon. Going beyond just solving the problem of climate change, to solving it in a way that minimizes economic harm, is a hell of an accomplishment, and more than worthy of the Nobel prizes Romer and Nordhaus won for showing us this path!

Some Further Reading

In my PhD class on innovation, the handout I give on the very first day introduces Romer’s work and why non-mathematical models of endogenous innovation mislead. Paul Romer himself has a nice essay on climate optimism, and the extent to which endogenous invention matters for how we stop global warming. On why anyone signs climate change abatement agreements, instead of just free riding, see the clever incomplete contracts insight of Battaglini and Harstad. Romer has also been greatly interested in the policy of “high-growth” places, pushing the idea of Charter Cities. Charter Cities involve Hong Kong like exclaves of a developing country where the institutions and legal systems are farmed out to a more stable nation. Totally reasonable, but in fact quite controversial: a charter city proposal in Madagascar led to a coup, and I can easily imagine that the Charter City controversy delayed Romer’s well-deserved Nobel laurel. The New York Times points out that Nordhaus’ brother helped write the Clean Air Act of 1970. Finally, as is always true with the Nobel, the official scientific summary is lucid and deep in its exploration of the two winners’ work.

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“Eliminating Uncertainty in Market Access: The Impact of New Bridges in Rural Nicaragua,” W. Brooks & K. Donovan (2018)

It’s NBER Summer Institute season, when every bar and restaurant in East Cambridge, from Helmand to Lord Hobo, is filled with our tribe. The air hums with discussions of Lagrangians and HANKs and robust estimators. And the number of great papers presented, discussed, or otherwise floating around inspires.

The paper we’re discussing today, by Wyatt Brooks at Notre Dame and Kevin Donovan at Yale SOM, uses a great combination of dynamic general equilibrium theory and a totally insane quasi-randomized experiment to help answer an old question: how beneficial is it for villages to be connected to the broader economy? The fundamental insight requires two ideas that are second nature for economists, but are incredibly controversial outside our profession.

First, going back to Nobel winner Arthur Lewis if not much earlier, economists have argued that “structural transformation”, the shift out of low-productivity agriculture to urban areas and non-ag sectors, is fundamental to economic growth. Recent work by Hicks et al is a bit more measured – the individuals who benefit from leaving agriculture generally already have, so Lenin-type forced industrialization is a bad idea! – but nonetheless barriers to that movement are still harmful to growth, even when those barriers are largely cultural as in the forthcoming JPE by Melanie Morton and the well-named Gharad Bryan. What’s so bad about the ag sector? In the developing world, it tends to be small-plot, quite-inefficient, staple-crop production, unlike the growth-generating positive-externality-filled, increasing-returns-type sectors (on this point, Romer 1990). There are zero examples of countries becoming rich without their labor force shifting dramatically out of agriculture. The intuition of many in the public, that Gandhi was right about the village economy and that structural transformation just means dreadful slums, is the intuition of people who lack respect for individual agency. The slums may be bad, but look how they fill up everywhere they exist! Ergo, how bad must the alternative be?

The second related misunderstanding of the public is that credit is unimportant. For folks near subsistence, the danger of economic shocks pushing you near that dangerous cutpoint is so fundamental that it leads to all sorts of otherwise odd behavior. Consider the response of my ancestors (and presumably the author of today’s paper’s ancestors, given that he is a Prof. Donovan) when potato blight hit. Potatoes are an input to growing more potatoes tomorrow, but near subsistence, you have no choice but to eat your “savings” away after bad shocks. This obviously causes problems in the future, prolonging the famine. But even worse, to avoid getting in a situation where you eat all your savings, you save more and invest less than you otherwise would. Empirically, Karlan et al QJE 2014 show large demand for savings instruments in Ghana, and Cynthia Kinnan shows why insurance markets in the developing world are incomplete despite large welfare gains. Indeed, many countries, including India, make it illegal to insure oneself against certain types of negative shocks, as Mobarak and Rosenzweig show. The need to save for low probability, really negative, shocks may even lead people to invest in assets with highly negative annual returns; on this, see the wonderfully-titled Continued Existence of Cows Disproves Central Tenets of Capitalism? This is all to say: the rise of credit and insurance markets unlocks much more productive activity, especially in the developing world, and it is not merely the den of exploitative lenders.

Ok, so insurance against bad shocks matters, and getting out of low-productivity agriculture may matter as well. Let’s imagine you live in a tiny village which is often separated from bigger towns, geographically. What would happen if you somehow lowered the cost of reaching those towns? Well, we’d expect goods-trade to radically change – see the earlier post on Dave Donaldson’s work, or the nice paper on Brazilian roads by Morten and Oliveria. But the benefits of reducing isolation go well beyond just getting better prices for goods.

Why? In the developing world, most people have multiple jobs. They farm during the season, work in the market on occasion, do construction, work as a migrant, and so on. Imagine that in the village, most jobs are just farmwork, and outside, there is always the change for day work at a fixed wage. In autarky, I just work on the farm, perhaps my own. I need to keep a bunch of savings because sometimes farms get a bunch of bad shocks: a fire burns my crops, or an elephant stomps on them. Running out of savings risks death, and there is no crop insurance, so I save precautionarily. Saving means I don’t have as much to spend on fertilizer or pesticide, so my yields are lower.

If I can access the outside world, then when my farm gets bad shocks and my savings runs low, I leave the village and take day work to build them back up. Since I know I will have that option, I don’t need to save as much, and hence I can buy more fertilizer. Now, the wage for farmers in the village (including the implicit wage that would keep me on my own farm) needs to be higher since some of these ex-farmers will go work in town, shifting village labor supply left. This higher wage pushes the amount of fertilizer I will buy down, since high wages reduce the marginal productivity of farm improvements. Whether fertilizer use goes up or down is therefore an empirical question, but at least we can say that those who use more fertilizer, those who react more to bad shocks by working outside the village, and those whose savings drops the most should be the same farmers. Either way, the village winds up richer both for the direct reason of having an outside option, and for the indirect reason of being able to reduce precautionary savings. That is, the harm is coming both from the first moment, the average shock to agricultural productivity, but also the second moment, its variance.

How much does this matter is practice? Brooks and Donovan worked with a NGO that physically builds bridges in remote areas. In Nicaragua, floods during the harvest season are common, isolating villages for days at a time when the riverbed along the path to market turns into a raging torrent. In this area, bridges are unnecessary when the riverbed is dry: the land is fairly flat, and the bridge barely reduces travel time when the riverbed isn’t flooded. These floods generally occur exactly during the growing season, after fertilizer is bought, but before crops are harvested, so the goods market in both inputs and outputs is essentially unaffected. And there is nice quasirandom variation: of 15 villages which the NGO selected as needing a bridge, 9 were ruled out after a visit by a technical advisor found the soil and topography unsuitable for the NGO’s relatively inexpensive bridge.

The authors survey villages the year before and the two years after the bridges are built, as well as surveying a subset of villagers with cell phones every two weeks in a particular year. Although N=15 seems worrying for power, the within-village differences in labor market behavior are sufficient that properly bootstrapped estimates can still infer interesting effects. And what do you find? Villages with bridges have many men shift from working in the village to outside in a given week, the percentage of women working outside nearly doubles with most of the women entering the labor force in order to work, the wages inside the village rise while wages outside the village do not, the use of fertilizer rises, village farm profits rise 76%, and the effect of all this is most pronounced on poorer households physically close to the bridge.

All this is exactly in line with the dynamic general equilibrium model sketched out above. If you assumed that bridges were just about market access for goods, you would have missed all of this. If you assumed the only benefit was additional wages outside the village, you would miss a full 1/3 of the benefit: the general equilibrium effect of shifting out workers who are particularly capable working outside the village causes wages to rise for the farm workers who remain at home. These particular bridges show an internal rate of return of nearly 20% even though they do nothing to improve market access for either inputs and outputs! And there are, of course, further utility benefits from reducing risk, even when that risk reduction does not show up in income through the channel of increased investment.

November 2017 working paper, currently R&R at Econometrica (RePEc IDEAS version. Both authors have a number of other really interesting drafts, of which I’ll mention two. Brooks, in a working paper with Joseph Kaposki and Yao Li, identify a really interesting harm of industrial clusters, but one that Adam Smith would have surely identified: they make collusion easier. Put all the firms in an industry in the same place, and establish regular opportunities for their managers to meet, and you wind up getting much less variance in markups than firms which are induced to locate in these clusters! Donovan, in a recent RED with my friend Chris Herrington, calibrates a model to explain why both college attendance and the relative cognitive ability of college grads rose during the 20th century. It’s not as simple as you might think: a decrease in costs, through student loans of otherwise, only affects marginal students, who are cognitively worse than the average existing college student. It turns out you also need a rising college premium and more precise signals of high schoolers’ academic abilities to get both patterns. Models doing work to extract insight from data – as always, this is the fundamental reason why economics is the queen of the social sciences.

“The Development Effects of the Extractive Colonial Economy,” M. Dell & B. Olken (2017)

A good rule of thumb is that you will want to read any working paper Melissa Dell puts out. Her main interest is the long-run path-dependent effect of historical institutions, with rigorous quantitative investigation of the subtle conditionality of the past. For instance, in her earlier work on Peru (Econometrica, 2010), mine slavery in the colonial era led to fewer hacienda style plantations at the end of the era, which led to less political power without those large landholders in the early democratic era, which led to fewer public goods throughout the 20th century, which led to less education and income today in eras that used to have mine slavery. One way to read this is that local inequality is the past may, through political institutions, be a good thing today! History is not as simple as “inequality is the past causes bad outcomes today” or “extractive institutions in the past cause bad outcomes today” or “colonial economic distortions cause bad outcomes today”. But, contra the branch of historians that don’t like to assign causality to any single factor in any given situation, we don’t need to entirely punt on the effects of specific policies in specific places if we apply careful statistical and theoretical analysis.

Dell’s new paper looks at the cultuurstelsel, a policy the Dutch imposed on Java in the mid-19th century. Essentially, the Netherlands was broke and Java was suitable for sugar, so the Dutch required villages in certain regions to use huge portions of their arable land, and labor effort, to produce sugar for export. They built roads and some rail, as well as sugar factories (now generally long gone), as part of this effort, and the land used for sugar production generally became public village land controlled at the behest of local leaders. This was back in the mid-1800s, so surely it shouldn’t affect anything of substance today?

But it did! Take a look at villages near the old sugar plantations, or that were forced to plant sugar, and you’ll find higher incomes, higher education levels, high school attendance rates even back in the late colonial era, higher population densities, and more workers today in retail and manufacturing. Dell and Olken did some wild data matching using a great database of geographic names collected by the US government to match the historic villages where these sugar plants, and these labor requirements, were located with modern village and town locations. They then constructed “placebo” factories – locations along coastal rivers in sugar growing regions with appropriate topography where a plant could have been located but wasn’t. In particular, as in the famous Salop circle, you won’t locate a factory too close to an existing one, but there are many counterfactual equilibria where we just shift all the factories one way or the other. By comparing the predicted effect of distance from the real factory on outcomes today with the predicted effect of distance from the huge number of hypothetical factories, you can isolate the historic local influence of the real factory from other local features which can’t be controlled for.

Consumption right next to old, long-destroyed factories is 14% higher than even five kilometers away, education is 1.25 years longer on average, electrification, road, and rail density are all substantially higher, and industrial production upstream and downstream from sugar (e.g., farm machinery upstream, and processed foods downstream) are also much more likely to be located in villages with historic factories even if there is no sugar production anymore in that region!

It’s not just the factory and Dutch investments that matter, however. Consider the villages, up to 10 kilometers away, which were forced to grow the raw cane. Their elites took private land for this purpose, and land inequality remains higher in villages that were forced to grow cane compared to villages right next door that were outside the Dutch-imposed boundary. But this public land permitted surplus extraction in an agricultural society which could be used for public goods, like schooling, which would later become important! These villages were much more likely to have schools especially before the 1970s, when public schooling in Indonesia was limited, and today are higher density, richer, more educated, and less agricultural than villages nearby which weren’t forced to grow cane. This all has shades of the long debate on “forward linkages” in agricultural societies, where it is hypothesized that agricultural surplus benefits industrialization by providing the surplus necessary for education and capital to be purchased; see this nice paper by Sam Marden showing linkages of this sort in post-Mao China.

Are you surprised by these results? They fascinate me, honestly. Think through the logic: forced labor (in the surrounding villages) and extractive capital (rail and factories built solely to export a crop in little use domestically) both have positive long-run local effects! They do so by affecting institutions – whether villages have the ability to produce public goods like education – and by affecting incentives – the production of capital used up- and downstream. One can easily imagine cases where forced labor and extractive capital have negative long-run effects, and we have great papers by Daron Acemoglu, Nathan Nunn, Sara Lowes and others on precisely this point. But it is also very easy for societies to get trapped in bad path dependent equilibria, for which outside intervention, even ethically shameful ones, can (perhaps inadvertently) cause useful shifts in incentives and institutions! I recall a visit to Babeldaob, the main island in Palau. During the Japanese colonial period, the island was heavily industrialized as part of Japan’s war machine. These factories were destroyed by the Allies in World War 2. Yet despite their extractive history, a local told me many on the island believe that the industrial development of the region was permanently harmed when those factories were damaged. It seems a bit crazy to mourn the loss of polluting, extractive plants whose whole purpose was to serve a colonial master, but the Palauan may have had some wisdom after all!

2017 Working Paper is here (no RePEc IDEAS version). For more on sugar and institutions, I highly recommend Christian Dippel, Avner Greif and Dan Trefler’s recent paper on Caribbean sugar. The price of sugar fell enormously in the late 19th century, yet wages on islands which lost the ability to productively export sugar rose. Why? Planters in places like Barbados had so much money from their sugar exports that they could manipulate local governance and the police, while planters in places like the Virgin Islands became too poor to do the same. This decreased labor coercion, permitting workers on sugar plantations to work small plots or move to other industries, raising wages in the end. I continue to await Suresh Naidu’s book on labor coercion – it is astounding the extent to which labor markets were distorted historically (see, e.g., Eric Foner on Reconstruction), and in some cases still today, by legal and extralegal restrictions on how workers could move on up.

“Firm Dynamics, Persistent Effects of Entry Conditions, and Business Cycles,” S. Moreira (2016)

Business cycle fluctuations have long run effects on a number of economic variables. For instance, if you enter the labor force during a recession, your wages are harmed for many years afterward. Many other economic parameters revert to trend, leaving a past recession just a blip on the horizon. Sara Moreira, a job candidate from the University of Chicago, investigates in her job market paper whether entrepreneurship changes induced by recessions persist in the long run.

New firm formation is procyclical: entrepreneurship fell roughly 20 percent during the recent recession. Looking back at the universe of private firms since the late 1970s, Moreira shows that this procyclicality is common, and that the firms that do form during recessions tend to be smaller than those which form during booms. Incredibly, this size gap persists for at least a decade after the firms are founded! At first glance, this is crazy: if my firm is founded during the 2001 recession, surely any effects from my founding days should have worn off after a decade of introducing new products, hiring new staff, finding new funding sources, etc. And yet Moreira finds this effect no matter how you slice the data, using overall recessions, industry-specific shocks, shocks based on tradable versus nontradable commodities, and so on, and it remains even when accounting for the autocorrelation of the business cycle. The effect is not small: the average firm born during a year with above trend growth is roughly 2 percent larger 10 years later than the average firm born during below trend growth years.

This gap is double surprising if you think about how firms are founded. Imagine we are in middle of a recession, and I am thinking of forming a new construction company. Bank loans are probably tough to get, I am unlikely to be flush with cash to start a new spinoff, I may worry about running out of liquidity before demand picks up, and so on. Because of these negative effects, you might reasonably believe that only very high quality ideas will lead to new firms during recessions, and hence the average firms born during recessions will be the very high quality, fast growing, firms of the future, whereas the average firms born during booms will be dry cleaners and sole proprietorships and local restaurants. And indeed this is the case! Moreira finds that firms born during recessions have high productivity, are more likely to be in high innovation sectors, and and less likely to be (low-productivity) sole proprietorships. We have a real mystery, then: how can firms born during a recession both be high quality and find it tough to grow?

Moreira considers two stories. It may be that adjustment costs matter, and firms born small because the environment is recessionary find it too costly to ramp up in size when the economy improves. Moreira finds no support for this idea: capital-intensive industries show the same patterns as industries using little capital.

Alternatively, customers need to be acquired, and this acquisition process may generate persistence in firm size. Naturally, firms start small because it takes time to teach people about products and for demand to grow: a restaurant chain does not introduce 1000 restaurants in one go. If you start really small because of difficulty in getting funded, low demand, or any other reason, then in year 2 you have fewer existing customers and less knowledge about what consumers want. This causes you to grow slower in year 2, and hence in year 3, you remain smaller than firms that initially were large, and the effect persists every year thereafter. Moreira finds support for this effect: among other checks, industries whose products are more differentiated are the ones most likely to see persistence of size differences.

Taking this intuition to a Hopenhayn-style calibrated model, the data tells us the following. First, it is not guaranteed that recessions lead to smaller firms initially, since the selection of only high productivity ideas into entrepreneurship during recessions, and the problem of low demand, operate in opposite directions, but empirically the latter seems to dominate. Second, if the productivity distribution of new firms were identical during booms and recessions, the initial size difference between firms born during booms and recessions would be double what we actually observe, so the selection story does in fact moderate the effect of the business cycle on new firm size. Third, the average size gap does not close even though the effect of the initial demand shock, hence fewer customers in the first couple years and slower growth thereafter, begins to fade as many years go by. The reason is that idiosyncratic productivity is mean reverting, so the average (relatively low quality at birth) firm born during booms that doesn’t go out of business becomes more like an average overall firm, and the average (relatively high productivity at birth) firm born during recessions sees its relative productivity get worse. Therefore, the advantage recession-born firms get from being born with high quality firms fades, countering the fading harm of the size of these firms from the persistent demand channel. Fourth, the fact that high productivity firms born during recessions grow slowly due to the historic persistence of customer acquisition means that temporary recessions will still affect the job market many years later: the Great Recession, in Moreira’s calibration, will a decade later still be chewing up 600,000 jobs that firms from the 2008-2009 cohort would have employed. Really enjoyed this paper: it’s a great combination of forensic digging through the data, as well as theoretically well-founded rationalization of the patterns observed.

January 2016 working paper. Moreira also has interesting slides showing how to link the skilled wage premium to underlying industry-level elasticities in skilled and unskilled labor. She notes that as services become more important, where labor substitutability is more difficult, the effect of technological change on the wage premium will become more severe.

“Forced Coexistence and Economic Development: Evidence from Native American Reservations,” C. Dippel (2014)

I promised one more paper from Christian Dippel, and it is another quite interesting one. There is lots of evidence, folk and otherwise, that combining different ethnic or linguistic groups artificially, as in much of the ex-colonial world, leads to bad economic and governance outcomes. But that’s weird, right? After all, ethnic boundaries are themselves artificial, and there are tons of examples – Italy and France being the most famous – of linguistic diversity quickly fading away once a state is developed. Economic theory (e.g., a couple recent papers by Joyee Deb) suggests an alternative explanation: groups that have traditionally not worked with each other need time to coordinate on all of the Pareto-improving norms you want in a society. That is, it’s not some kind of intractable ethnic hate, but merely a lack of trust that is the problem.

Dippel uses the history of American Indian reservations to examine the issue. It turns out that reservations occasionally included different subtribal bands even though they almost always were made up of members of a single tribe with a shared language and ethnic identity. For example, “the notion of tribe in Apachean cultures is very weakly developed. Essentially it was only a recognition
that one owed a modicum of hospitality to those of the same speech, dress, and customs.” Ethnographers have conveniently constructed measures of how integrated governance was in each tribe prior to the era of reservations; some tribes had very centralized governance, whereas others were like the Apache. In a straight OLS regression with the natural covariates, incomes are substantially lower on reservations made up of multiple bands that had no pre-reservation history of centralized governance.

Why? First, let’s deal with identification (more on what that means in a second). You might naturally think that, hey, tribes with centralized governance in the 1800s were probably quite socioeconomically advanced already: think Cherokee. So are we just picking up that high SES in the 1800s leads to high incomes today? Well, in regions with lots of mining potential, bands tended to be grouped onto one reservation more frequently, which suggests that resource prevalence on ancestral homelands outside of the modern reservation boundaries can instrument for the propensity for bands to be placed together. Instrumented estimates of the effect of “forced coexistence” is just as strong as the OLS estimate. Further, including tribe fixed effects for cases where single tribes have a number of reservations, a surprisingly common outcome, also generates similar estimates of the effect of forced coexistence.

I am very impressed with how clear Dippel is about what exactly is being identified with each of these techniques. A lot of modern applied econometrics is about “identification”, and generally only identifies a local average treatment effect, or LATE. But we need to be clear about LATE – much more important than “what is your identification strategy” is an answer to “what are you identifying anyway?” Since LATE identifies causal effects that are local conditional on covariates, and the proper interpretation of that term tends to be really non-obvious to the reader, it should go without saying that authors using IVs and similar techniques ought be very precise in what exactly they are claiming to identify. Lots of quasi-random variation generates that variation along a local margin that is of little economic importance!

Even better than the estimates is an investigation of the mechanism. If you look by decade, you only really see the effect of forced coexistence begin in the 1990s. But why? After all, the “forced coexistence” is longstanding, right? Think of Nunn’s famous long-run effect of slavery paper, though: the negative effects of slavery are mediated during the colonial era, but are very important once local government has real power and historically-based factionalism has some way to bind on outcomes. It turns out that until the 1980s, Indian reservations had very little local power and were largely run as government offices. Legal changes mean that local power over the economy, including the courts in commercial disputes, is now quite strong, and anecdotal evidence suggests lots of factionalism which is often based on longstanding intertribal divisions. Dippel also shows that newspaper mentions of conflict and corruption at the reservation level are correlated with forced coexistence.

How should we interpret these results? Since moving to Canada, I’ve quickly learned that Canadians generally do not subscribe to the melting pot theory; largely because of the “forced coexistence” of francophone and anglophone populations – including two completely separate legal traditions! – more recent immigrants are given great latitude to maintain their pre-immigration culture. This heterogeneous culture means that there are a lot of actively implemented norms and policies to help reduce cultural division on issues that matter to the success of the country. You might think of the problems on reservations and in Nunn’s post-slavery states as a problem of too little effort to deal with factionalism rather than the existence of the factionalism itself.

Final working paper, forthcoming in Econometrica. No RePEc IDEAS version. Related to post-colonial divisions, I also very much enjoyed Mobilizing the Masses for Genocide by Thorsten Rogall, a job market candidate from IIES. When civilians slaughter other civilians, is it merely a “reflection of ancient ethnic hatred” or is it actively guided by authority? In Rwanda, Rogall finds that almost all of the killing is caused directly or indirectly by the 50,000-strong centralized armed groups who fanned out across villages. In villages that were easier to reach (because the roads were not terribly washed out that year), more armed militiamen were able to arrive, and the more of them that arrived, the more deaths resulted. This in-person provoking appears much more important than the radio propaganda which Yanigazawa-Drott discusses in his recent QJE; one implication is that post-WW2 restrictions on free speech in Europe related to Nazism may be completely misdiagnosing the problem. Three things I especially liked about Rogall’s paper: the choice of identification strategy is guided by a precise policy question which can be answered along the local margin identified (could a foreign force stopping these centralized actors a la Romeo Dallaire have prevented the genocide?), a theoretical model allows much more in-depth interpretation of certain coefficients (for instance, he can show that most villages do not appear to have been made up of active resistors), and he discusses external cases like the Lithuanian killings of Jews during World War II, where a similar mechanism appears to be at play. I’ll have many more posts on cool job market papers coming shortly!

“International Trade and Institutional Change: Medieval Venice’s Response to Globalization,” D. Puga & D. Trefler

(Before discussing the paper today, I should forward a couple great remembrances of Stanley Reiter, who passed away this summer, by Michael Chwe (whose interests at the intersection of theory and history are close to my heart) and Rakesh Vohra. After leaving Stanford – Chwe mentions this was partly due to a nasty letter written by Reiter’s advisor Milton Friedman! – Reiter established an incredible theory group at Purdue which included Afriat, Vernon Smith and PhD students like Sonnenschein and Ledyard. He then moved to Northwestern where he helped build up the great group in MEDS which is too long to list, but which includes one Nobel winner already in Myerson and, by my reckoning, two more which are favorites to win the prize next Monday.

I wonder if we may be at the end of an era for topic-diverse theory departments. Business schools are all a bit worried about “Peak MBA”, and theorists are surely the first ones out the door when enrollment falls. Economic departments, journals and funders seem to have shifted, in the large, toward more empirical work, for better or worse. Our knowledge both of how economic and social interactions operate in their most platonic form, and our ability to interpret empirical results when considering novel or counterfactual policies, have greatly benefited by the theoretical developments following Samuelson and Hicks’ mathematization of primitives in the 1930s and 40s, and the development of modern game theory and mechanism design in the 1970s and 80s. Would that a new Cowles and a 21st century Reiter appear to help create a critical mass of theorists again!)

On to today’s paper, a really interesting theory-driven piece of economic history. Venice was one of the most important centers of Europe’s “commercial revolution” between the 10th and 15th century; anyone who read Marco Polo as a schoolkid knows of Venice’s prowess in long-distance trade. Among historians, Venice is also well-known for the inclusive political institutions that developed in the 12th century, and the rise of oligarchy following the “Serrata” at the end of the 13th century. The Serrata was followed by a gradual decrease in Venice’s power in long-distance trade and a shift toward manufacturing, including the Murano glass it is still famous for today. This is a fairly worrying history from our vantage point today: as the middle class grew wealthier, democratic forms of government and free markets did not follow. Indeed, quite the opposite: the oligarchs seized political power, and within a few decades of the serrata restricted access to the types of trade that previously drove wealth mobility. Explaining what happened here is both a challenge due to limited data, and of great importance given the public prominence of worries about the intersection of growing inequality and corruption of the levers of democracy.

Dan Trefler, an economic historian here at U. Toronto, and Diego Puga, an economist at CEMFI who has done some great work in economic geography, provide a great explanation of this history. Here’s the model. Venice begins with lots of low-wealth individuals, a small middle and upper class, and political power granted to anyone in the upper class. Parents in each dynasty can choose to follow a risky project – becoming a merchant in a long-distance trading mission a la Niccolo and Maffeo Polo – or work locally in a job with lower expected pay. Some of these low and middle class families will succeed on their trade mission and become middle and upper class in the next generation. Those with wealth can sponsor ships via the colleganza, a type of early joint-stock company with limited liability, and potentially join the upper class. Since long-distance trade is high variance, there is a lot of churn across classes. Those with political power also gather rents from their political office. As the number of wealthy rise in the 11th and 12th century, the returns to sponsoring ships falls due to competition across sponsors in the labor and export markets. At any point, the upper class can vote to restrict future entry into the political class by making political power hereditary. They need to include sufficiently many powerful people in this hereditary class or there will be a revolt. As the number of wealthy increase, eventually the wealthy find it worthwhile to restrict political power so they can keep political rents within their dynasty forever. Though political power is restricted, the economy is still free, and the number of wealthy without power continue to grow, lowering the return to wealth for those with political power due to competition in factor and product markets. At some point, the return is so low that it is worth risking revolt from the lower classes by restricting entry of non-nobles into lucrative industries. To prevent revolt, a portion of the middle classes are brought in to the hereditary political regime, such that the regime is powerful enough to halt a revolt. Under these new restrictions, lower classes stop engaging in long-distance trade and instead work in local industry. These outcomes can all be generated with a reasonable looking model of dynastic occupation choice.

What historical data would be consistent with this theoretical mechanism? We should expect lots of turnover in political power and wealth in the 10th through 13th centuries. We should find examples in the literature of families beginning as long-distance traders and rising to voyage sponsors and political agents. We should see a period of political autocracy develop, followed later by the expansion of hereditary political power and restrictions on lucrative industry entry to those with such power. Economic success based on being able to activate large amounts of capital from within the nobility class will make the importance of inter-family connections more important in the 14th and 15th centuries than before. Political power and participation in lucrative economic ventures will be limited to a smaller number of families after this political and economic closure than before. Those left out of the hereditary regime will shift to local agriculture and small-scale manufacturing.

Indeed, we see all of these outcomes in Venetian history. Trefler and Puga use some nice techniques to get around limited data availability. Since we don’t have data on family incomes, they use the correlation in eigenvector centrality within family marriage networks as a measure of the stability of the upper classes. They code colleganza records – a non-trivial task involving searching thousands of scanned documents for particular Latin phrases – to investigate how often new families appear in these records, and how concentration in the funding of long-distance trade changes over time. They show that all of the families with high eigenvector centrality in the noble marriage market after political closure – a measure of economic importance, remember – were families that were in the top quartile of seat-share in the pre-closure Venetian legislature, and that those families which had lots of political power pre-closure but little commercial success thereafter tended to be unsuccessful in marrying into lucrative alliances.

There is a lot more historical detail in the paper, but as a matter of theory useful to the present day, the Venetian experience ought throw cold water on the idea that political inclusiveness and economic development always form a virtuous circle. Institutions are endogenous, and changes in the nature of inequality within a society following economic development alter the potential for political and economic crackdowns to survive popular revolt.

Final published version in QJE 2014 (RePEc IDEAS). A big thumbs up to Diego for having the single best research website I have come across in five years of discussing papers in this blog. Every paper has an abstract, well-organized replication data, and a link to a locally-hosted version of the final published paper. You may know his paper with Nathan Nunn on how rugged terrain in Africa is associated with good economic outcomes today because slave traders like the infamous Tippu Tip couldn’t easily exploit mountainous areas, but it’s also worth checking out his really clever theoretical disambiguation of why firms in cities are more productive, as well as his crazy yet canonical satellite-based investigation of the causes of sprawl. There is a really cool graphic on the growth of U.S. sprawl at that last link!

“Aggregation in Production Functions: What Applied Economists Should Know,” J. Felipe & F. Fisher (2003)

Consider a firm that takes heterogeneous labor and capital inputs L1, L2… and K1, K2…, using these to produce some output Y. Define a firm production function Y=F(K1, K2…, L1, L2…) as the maximal output that can be produced using the given vector of outputs – and note the implicit optimization condition in that definition, which means that production functions are not simply technical relationships. What conditions are required to construct an aggregated production function Y=F(K,L), or more broadly to aggregate across firms an economy-wide production function Y=F(K,L)? Note that the question is not about the definition of capital per se, since defining “labor” is equally problematic when man-hours are clearly heterogeneous, and this question is also not about the more general capital controversy worries, like reswitching (see Samuelson’s champagne example) or the dependence of the return to capital on the distribution of income which, itself, depends on the return to capital.

(A brief aside: on that last worry, why the Cambridge UK types and their modern day followers are so worried about the circularity of the definition of the interest rate, yet so unconcerned about the exact same property of the object we call “wage”, is quite strange to me, since surely if wages equal marginal product, and marginal product in dollars is a function of aggregate demand, and aggregate demand is a function of the budget constraint determined by wages, we are in an identical philosophical situation. I think it’s pretty clear that the focus on “r” rather than “w” is because of the moral implications of capitalists “earning their marginal product” which are less than desirable for people of a certain political persuasion. But I digress; let’s return to more technical concerns.)

It turns out, and this should be fairly well-known, that the conditions under which factors can be aggregated are ridiculously stringent. If we literally want to add up K or L when firms use different production functions, the condition (due to Leontief) is that the marginal rate of substitution between different types of factors in one aggregation, e.g. capital, does not depend on the level of factors not in that aggregation, e.g. labor. Surely this is a condition that rarely holds: how much I want to use, in an example due to Solow, different types of trucks will depend on how much labor I have at hand. A follow-up by Nataf in the 1940s is even more discouraging. Assume every firm uses homogenous labor, every firm uses capital which though homogenous within each firms differs across firms, and every firm has identical constant returns to scale production technology. When can I now write an aggregate production function Y=F(K,L) summing up the capital in each firm K1, K2…? That aggregate function exists if and only if every firm’s production function is additively separable in capital and labor (in which case, the aggregation function is pretty obvious)! Pretty stringent, indeed.

Fisher helps things just a bit in a pair of papers from the 1960s. Essentially, he points out that we don’t want to aggregate for all vectors K and L, but rather we need to remember that production functions measure the maximum output possible when all inputs are used most efficiently. Competitive factor markets guarantee that this assumption will hold in equilibrium. That said, even assuming only one type of labor, efficient factor markets, and a constant returns to scale production function, aggregation is possible if and only if every firm has the same production function Y=F(b(v)K(v),L), where v denotes a given firm and b(v) is a measure of how efficiently capital is employed in that firm. That is, aside from capital efficiency, every firm’s production function must be identical if we want to construct an aggregate production function. This is somewhat better than Nataf’s result, but still seems highly unlikely across a sector (to say nothing of an economy!).

Why, then, do empirical exercises using, say, aggregate Cobb-Douglas seem to give such reasonable parameters, even though the above theoretical results suggest that parameters like “aggregate elasticity of substitution between labor and capital” don’t even exist? That is, when we estimate elasticities or total factor productivities from Y=AK^a*L^b, using some measure of aggregated capital, what are we even estimating? Two things. First, Nelson and Winter in their seminal book generate aggregate date which can almost perfectly be fitted using Cobb-Douglas even though their model is completely evolutionary and does not even involve maximizing behavior by firms, so the existence of a “good fit” alone is, and this should go without saying, not great evidence in support of a model. Second, since ex-post production Y must equal the wage bill plus the capital payments plus profits, Felipe notes that this identity can be algebraically manipulated to Y=AF(K,L) where the form of F depends on the nature of the factor shares. That is, the good fit of Cobb-Douglas or CES can simply reflect an accounting identity even when nothing is known about micro-level elasticities or similar.

So what to do? I am not totally convinced we should throw out aggregate production functions – it surely isn’t a coincidence that Solow residuals for TFP match are estimated to be high in places where our intuition says technological change has been rapid. Because of results like this, it doesn’t strike me that aggregate production functions are measuring arbitrary things. However, if we are using parameters from these functions to do counterfactual analysis, we really ought know better exactly what approximations or assumptions are being baked into the cake, and it doesn’t seem that we are quite there yet. Until we are, a great deal of care should be taken in assigning interpretations to estimates based on aggregate production models. I’d be grateful for any pointers in the comments to recent work on this problem.

Final published version (RePEc IDEAS. The “F. Fisher” on this paper is the former Clark Medal winner and well-known IO economist Franklin Fisher; rare is it to find a nice discussion of capital issues written by someone who is firmly part of the economics mainstream and completely aware of the major theoretical results from “both Cambridges”. Tip of the cap to Cosma Shalizi for pointing out this paper.

“Agricultural Productivity and Structural Change: Evidence from Brazil,” P. Bustos et al (2014)

It’s been a while – a month of exploration in the hinterlands of the former Soviet Union, a move up to Canada, and a visit down to the NBER Summer Institute really put a cramp on my posting schedule. That said, I have a ridiculously long backlog of posts to get up, so they will be coming rapidly over the next few weeks. I saw today’s paper presented a couple days ago at the Summer Institute. (An aside: it’s a bit strange that there isn’t really any media at SI – the paper selection process results in a much better set of presentations than at the AEA or the Econometric Society, which simply have too long of a lag from the application date to the conference, and too many half-baked papers.)

Bustos and her coauthors ask, when can improvements in agricultural productivity help industrialization? An old literature assumed that any such improvement would help: the newly rich agricultural workers would demand more manufactured goods, and since manufactured and agricultural products are complements, rising agricultural productivity would shift workers into the factories. Kiminori Matsuyama wrote a model (JET 1992) showing the problem here: roughly, if in a small open economy productivity goes up in a good you have a Ricardian comparative advantage in, then you want to produce even more of that good. A green revolution which doubles agricultural productivity in, say, Mali, while keeping manufacturing productivity the same, will allow Mali to earn twice as much selling the agriculture overseas. Workers will then pour into the agricultural sector until the marginal product of labor is re-equated in both sectors.

Now, if you think that industrialization has a bunch of positive macrodevelopment spillovers (via endogenous growth, population control or whatever), then this is worrying. Indeed, it vaguely suggests that making villages more productive, an outright goal of a lot of RCT-style microdevelopment studies, may actually be counterproductive for the country as a whole! That said, there seems to be something strange going on empirically, because we do appear to see industrialization in countries after a Green Revolution. What could be going on? Let’s look back at the theory.

Implicitly, the increase in agricultural productivity in Matsuyama was “Hicks-neutral” – it increased the total productivity of the sector without affecting the relative marginal factor productivities. A lot of technological change, however, is factor-biased; to take two examples from Brazil, modern techniques that allow for double harvesting of corn each year increase the marginal productivity of land, whereas “Roundup Ready” GE soy that requires less tilling and weeding increases the marginal productivity of farmers. We saw above that Hicks-neutral technological change in agriculture increases labor in the farm sector: workers choosing where to work means that the world price of agriculture times the marginal product of labor in that sector must be equal to world price of manufacturing times the marginal product of labor in manufacturing. A Hicks-neutral improvement in agricultural productivity raises MPL in that sector no matter how much land or labor is currently being used, hence wage equality across sectors requires workers to leave the factor for the farm.

What of biased technological change? As before, the only thing we need to know is whether the technological change increases the marginal product of labor. Land-augmenting technical change, like double harvesting of corn, means a country can produce the same amount of output with the old amount of farm labor and less land. If one more worker shifts from the factory to the farm, she will be farming less marginal land than before the technological change, hence her marginal productivity of labor is higher than before the change, hence she will leave the factory. Land-augmenting technological change always increases the amount of agricultural labor. What about farm-labor-augmenting technological change like GM soy? If land and labor are not very complementary (imagine, in the limit, that they are perfect substitutes in production), then trivially the marginal product of labor increases following the technological change, and hence the number of farm workers goes up. The situation is quite different if land and farm labor are strong complements. Where previously we had 1 effective worker per unit of land, following the labor-augmenting technology change it is as if we have, say, 2 effective workers per unit of land. Strong complementarity implies that, at that point, adding even more labor to the farms is pointless: the marginal productivity of labor is decreasing in the technological level of farm labor. Therefore, labor-augmenting technology with a strongly complementary agriculture production function shifts labor off the farm and into manufacturing.

That’s just a small bit of theory, but it really clears things up. And even better, the authors find empirical support for this idea: following the introduction to Brazil of labor-augmenting GM soy and land-augmenting double harvesting of maize, agricultural productivity rose everywhere, the agricultural employment share rose in areas that were particularly suitable for modern maize production, and the manufacturing employment share rose in areas that were particularly suitable for modern soy production.

August 2013 working paper. I think of this paper as a nice complement to the theory and empirics in Acemoglu’s Directed Technical Change and Walker Hanlon’s Civil War cotton paper. Those papers ask how changes in factor prices endogenously affect the development of different types of technology, whereas Bustos and coauthors ask how the exogenous development of different types of technology affect the use of various factors. I read the former as most applicable to structural change questions in countries at the technological frontier, and the latter as appropriate for similar questions in developing countries.

Debraj Ray on Piketty’s Capital

As mentioned by Sandeep Baliga over at Cheap Talk, Debraj Ray has a particularly interesting new essay on Piketty’s Capital in the 21st Century. If you are theoretically inclined, you will find Ray’s comments to be one of the few reviews of Piketty that proves insightful.

I have little to add to Ray, but here are four comments about Piketty’s book:

1) The data collection effort on inequality by Piketty and coauthors is incredible and supremely interesting; not for nothing does Saez-Piketty 2003 have almost 2000 citations. Much of this data can be found in previous articles, of course, but it is useful to have it all in one place. Why it took so long for this data to become public, compared to things like GDP measures, is an interesting one which sociology Dan Hirschman is currently working on. Incidentally, the data quality complaints by the Financial Times seem to me of rather limited importance to the overall story.

2) The idea that Piketty is some sort of outsider, as many in the media want to make him out to be, is very strange. His first job was at literally the best mainstream economics department in the entire world, he won the prize given to the best young economist in Europe, he has published a paper in a Top 5 economics journal every other year since 1995, his most frequent coauthor is at another top mainstream department, and that coauthor himself won the prize for the best young economist in the US. It is also simply not true that economists only started caring about inequality after the 2008 financial crisis; rather, Autor and others were writing on inequality well before date in response to clearer evidence that the “Great Compression” of the income distribution in the developed world during the middle of the 20th century had begun to reverse itself sometime in the 1970s. Even I coauthored a review of income inequality data in late 2006/early 2007!

3) As Ray points out quite clearly, the famous “r>g” of Piketty’s book is not an explanation for rising inequality. There are lots of standard growth models – indeed, all standard growth models that satisfy dynamic efficiency – where r>g holds with no impact on the income distribution. Ray gives the Harrod model: let output be produced solely by capital, and let the capital-output ratio be constant. Then Y=r*K, where r is the return to capital net of depreciation, or the capital-output ratio K/Y=1/r. Now savings in excess of that necessary to replace depreciated assets is K(t+1)-K(t), or

Y(t+1)[K(t+1)/Y(t+1)] – Y(t)[K(t)/Y(t)]

Holding the capital-output ratio constant, we have that savings s=[Y(t+1)-Y(t)]K/Y=g[K/Y], where g is the growth rate of the economy. Finally, since K/Y=1/r in the Harrod model, we have that s=g/r, and hence r>g will hold in a Harrod model whenever the savings rate is less than 100% of current income. This model, however, has nothing to do with the distribution of income. Ray notes that the Phelps-Koopmans theorem implies that a similar r>g result will hold along any dynamically efficient growth path in much more general models.

You may wonder, then, how we can have r>g and yet not have exploding income held by the capital-owning class. Two reasons: first, as Piketty has pointed out, r in these economic models (the return to capital, full stop) and r in the sense important to growing inequality, are not the same concept, since wars and taxes lower the r received by savers. Second, individuals presumably also dissave according to some maximization concept. Imagine an individual has $1 billion, the risk-free market return after taxes is 4%, and the economy-wide growth rate is 2%, with both numbers exogenously holding forever. It is of course true true that this individual could increase their share of the economy’s wealth without bound. Even with the caveat that as the capital-owning class owns more and more, surely the portion of r due to time preference, and hence r itself, will decline, we still oughtn’t conclude that income inequality will become worse or that capital income will increase. If this representative rich individual simply consumes 1.92% of their income each year – a savings rate of over 98 percent! – the ratio of income among the idle rich to national income will remain constant. What’s worse, if some of the savings is directed to human capital rather than physical capital, as is clearly true for the children of the rich in the US, the ratio of capital income to overall income will be even less likely to grow.

These last couple paragraphs are simply an extended argument that r>g is not a “Law” that says something about inequality, but rather a starting point for theoretical investigation. I am not sure why Piketty does not want to do this type of investigation himself, but the book would have been better had he done so.

4) What, then, does all this mean about the nature of inequality in the future? Ray suggests an additional law: that there is a long-run tendency for capital to replace labor. This is certainly true, particularly if human capital is counted as a form of “capital”. I disagree with Ray about the implication of this fact, however. He suggests that “to avoid the ever widening capital-labor inequality as we lurch towards an automated world, all its inhabitants must ultimately own shares of physical capital.” Consider the 19th century as a counterexample. There was enormous technical progress in agriculture. If you wanted a dynasty that would be rich in 2014, ought you have invested in agricultural land? Surely not. There has been enormous technical progress in RAM chips and hard drives in the last couple decades. Is the capital related to those industries where you ought to have invested? No. With rapid technical progress in a given sector, the share of total income generated by that sector tends to fall (see Baumol). Even when the share of total income is high, the social surplus of technical progress is shared among various groups according to the old Ricardian rule: rents accrue to the (relatively) fixed factor! Human capital which is complementary to automation, or goods which can maintain a partial monopoly in an industry complementary to those affected by automation, are much likelier sources of riches than owning a bunch of robots, since robots and the like are replicable and hence the rents accrued to their owners, regardless of the social import, will be small.

There is still a lot of work to be done concerning the drivers of long-run inequality, by economists and by those more concerned with political economy and sociology. Piketty’s data, no question, is wonderful. Ray is correct that the so-called Laws in Piketty’s book, and the predictions about the next few decades that they generate, are of less interest.

A Comment on Thomas Piketty, inclusive of appendix, is in pdf form, or a modified version in html can be read here.

“On the Origin of States: Stationary Bandits and Taxation in Eastern Congo,” R. S. de la Sierra (2013)

The job market is yet again in full swing. I won’t be able to catch as many talks this year as I would like to, but I still want to point out a handful of papers that I consider particularly elucidating. This article, by Columbia’s de la Sierra, absolutely fits that category.

The essential question is, why do states form? Would that all young economists interested in development put their effort toward such grand questions! The old Rousseauian idea you learned your first year of college, where individuals come together voluntarily for mutual benefit, seems contrary to lots of historical evidence. Instead, war appears to be a prime mover for state formation; armed groups establish a so-called “monopoly on violence” in an area for a variety of reasons, and proto-state institutions evolve. This basic idea is widespread in the literature, but it is still not clear which conditions within an area lead armed groups to settle rather than to pillage. Further, examining these ideas empirically seems quite problematic for two reasons, first because states themselves are the ones who collect data hence we rarely observe anything before states have formed, and second, because most of the planet has long since been under the rule of a state (with apologies to James Scott!)

De la Sierra brings some economics to this problem. What is the difference between pillaging and sustained state-like forms? The pillager can only extract assets on its way through, while the proto-state can establish “taxes”. What taxes will it establish? If the goal is long-run revenue maximization, Ramsey long ago told us that it is optimal to tax elements that are inelastic. If labor can flee, but the output of the mine can not, then you ought tax the output of the mine highly and set a low poll tax. If labor supply is inelastic but output can be hidden from the taxman, then use a high poll tax. Thus, when will bandits form a state instead of just pillaging? When there is a factor which can be dynamically taxed at such a rate that the discounted tax revenue exceeds what can be pillaged today. Note that the ability to, say, restrict movement along roads, or to expand output through state-owned capital, changes relevant tax elasticities, so at a more fundamental level, capacity by rebels along these margins are also important (and I imagine that extending de la Sierra’s paper will involve the evolutionary development of these types of capacities).

This is really an important idea. It is not that there is a tradeoff between producing and pillaging. Instead, there is a three way tradeoff between producing in your home village, joining an armed group to pillage, and joining an armed group that taxes like a state! The armed group that taxes will, as a result of its desire to increase tax revenue, perhaps introduce institutions that increase production in the area under its control. And to the extent that institutions persist, short-run changes that cause potential bandits to form taxing relationships may actually lead to long-run increases in productivity in a region.

De la Sierra goes a step beyond theory, investigating these ideas empirically in the Congo. Eastern Congo during and after the Second Congo War was characterized by a number of rebel groups that occasionally just pillaged, but occasionally formed stable tax relationships with villages that could last for years. That is, the rebels occasionally implemented something looking like states. The theory above suggests that exogenous changes in the ability to extract tax revenue (over a discounted horizon) will shift the rebels from pillagers to proto-states. And, incredibly, there were a number of interesting exogenous changes that had exactly that effect.

The prices of coltan and gold both suffered price shocks during the war. Coltan is heavy, hard to hide, and must be shipped by plane in the absence of roads. Gold is light, easy to hide, and can simply be carried from the mine on jungle footpaths. When the price of coltan rises, the maximal tax revenue of a state increases since taxable coltan production is relatively inelastic. This is particularly true near airstrips, where the coltan can actually be sold. When the price of gold increases, the maximal tax revenue does not change much, since gold is easy to hide, and hence the optimal tax is on labor rather than on output. An exogenous rise in coltan prices should encourage proto-state formation in areas with coltan, then, while an exogenous rise is gold prices should have little impact on the pillage vs. state tradeoff. Likewise, a government initiative to root out rebels (be they stationary or pillaging) decreases the expected number of years a proto-state can extract rents, hence makes pillaging relatively more lucrative.

How to confirm these ideas, though, when there was no data collected on income, taxes, labor supply, or proto-state existence? Here is the crazy bit – 11 locals were hired in Eastern Congo to travel to a large number of villages, spend a week there querying families and village elders about their experiences during the war, the existence of mines, etc. The “state formation” in these parts of Congo is only a few years in the past, so it is at least conceivable that memories, suitably combined, might actually be reliable. And indeed, the data do seem to match aggregate trends known to monitors of the war. What of the model predictions? They all seem to hold, and quite strongly: the ability to extract more tax revenue is important for proto-state formation, and areas where proto-states existed do appear to have retained higher productive capacity years later perhaps as a result of the proto-institutions those states developed. Fascinating. Even better, because there is a proposed mechanism rather than an identified treatment effect, we can have some confidence that this course is, to some extent, externally valid!

December 2013 working paper (No IDEAS page). You may wonder what a study like this costs (particularly if you are, like me, a theorist using little more than chalk and a chalkboard); I have no idea, but de la Sierra’s CV lists something like a half million dollars of grants, an incredible total for a graduate student. On a personal level, I spent a bit of time in Burundi a number of years ago, including visiting a jungle camp where rebels from the Second Congo War were still hiding. It was pretty amazing how organized even these small groups were in the areas they controlled; there was nothing anarchic about it.