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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