"Cake without Flour" -- Duncan Foley on the Dilemmas of Economic Growth

The following excerpt is from Duncan Foley's outgoing Presidential Address to the Eastern Economics Association, "Dilemmas of Economic Growth," presented March 9, 2012 (Reprinted by permission from Macmillan Publishers Ltd: Eastern Economic Journal (2012) 38, 283–295 published by Palgrave Macmillan). The title is an allusion to Herman Daly's parody of Cobb-Douglas production function hyperbole "as implying that it is possible to bake a cake without eggs or flour as long as the cook whisks the empty bowl faster and faster."

CAKE WITHOUT FLOUR

Some growth economists might regard the considerations we have just reviewed as rather quaintly anachronistic in putting so much emphasis on the material nature of economic production. Well-established patterns of economic growth show that as incomes rise, the proportion of output as measured by such indexes as real GDP consisting of material goods steadily declines. The major sources of growth in incomes (and, given the way we measure GDP, in indexes of output) shift to the tertiary sector, particularly services. The chief input to services is human intelligence, and at least in some accounts, intelligence is an unlimited resource. So why couldn't real GDP, measured to include the use-value of services, continue to grow without limit?

There are some immediate problems with this conception. Strictly speaking the production of almost all services does require material and energy inputs, as the gigantic server farms required for information technology are a concrete reminder. Maintaining the human capital to provide a glittering array of intellectual services requires material and energy inputs, and these very likely increase as the quality of intellectual output rises.

But this vision of endless growth without material or energy inputs requires some re-examination of just what it is that we regard as output and try to measure in indexes like real GDP. Some rapidly growing service industries, such as finance, seem to be able to produce increasing measured output without much input increase, even of human employment, at all [Basu and Foley 2011; Foley 2011]. An examination of the issues raised by the growing significance of service industries, which have no measurable output, raises some deep questions about the conception of economics.

The paradigmatic economic interaction for economic theories rooted in the marginalist revolution, such as neoclassical economics and its various descendants, is a transaction in which one good moves from the possession of an agent who subjectively values it less to the possession of another agent who values it more, in exchange for another good (in many transactions money). As the familiar Edgeworth-Bowley box construction illustrates, this type of transaction puts both agents on a higher (or at least no lower) indifference curve, and thus achieves a Pareto-improvement in the allocation of existing resources. Many financial transactions are of this type, for example, initial public offerings to take companies public, real estate brokerage, insurance contracts, and other more exotic forms of financial arbitrage. It is important to remember, however, that the transfer of existing goods or assets in these transactions is not production. When financial intermediaries appropriate some part of the economic surpluses generated in these transactions as revenue, however, economic statisticians have felt compelled to regard the resulting incomes as part of national income, and to invent an imaginary product, financial services, to put on the product side of the accounts as a counterpart.

It is hard to imagine limits to the magnitude of subjective economic surpluses that could be realized through transactions of this type. If, for example, policies or the historical evolution of the division of labor increase economic insecurity by eroding the institutions of traditional societies, one can easily imagine an unlimited expansion of insurance transactions as a result. But from the point of view of classical political economy, it is the increase in material productivity of labor, not the increase in economic insecurity associated with the expansion of the division of labor, which is the source of improvements in economic welfare. This point of view is deeply embedded in the methods of national income accounting, for example, in the fundamental rule that transactions involving the transfer of existing assets do not constitute production of goods and services, no matter how much economic surplus they may represent.

The classical political economists and Marx addressed these issues through the concepts of "productive" and "unproductive" labor. In the version of this distinction, Marx distilled from his critical review of Adam Smith, productive labor (whether it produces material goods or services, since providing haircuts is hard to distinguish from making hats) returns the costs of production with a profit, while the cost of unproductive labor is paid out of revenues without any recovery or return. This classical-Marxian line of thinking puts the origin of the incomes from the production of "services," such as finance, in a different perspective.

This perspective is perhaps most clearly articulated in Marx's analysis of wage labor and the origins of surplus value. Productive labor is responsible for the whole value added in production, but receives only a fraction of the value added in the form of the wage. The resulting surplus value constitutes a pool of potential revenue for which capitalist producers, landowners, intellectual property owners, financial firms controlling money capital, and the state compete. The implications of this analysis, which, unfortunately, is for the most part systematically excluded from the modern economics curriculum, are far-reaching. No particular capitalist firm, no matter how large in revenue and employment, can have much direct effect in increasing the pool of surplus value. Thus "money-making" in capitalist society is proximately based on taking surplus value away from others. In an economy where resources and intellectual property command enormous rents, there may be a vanishingly small connection between the revenue of any entity and its actual contribution to production of useful output.

Many people today are dazzled by the apparently magical ability of innovators to appropriate enormous revenues on the basis of ideas and their manipulation alone. This phenomenon has understandably spawned theories of a "new" economy, supposedly based on new principles of the creation of value. Classical-Marxist political economy, in contrast, locates incomes to innovation not in new principles of the creation of value, but in new (or newly important, since most of these "business models" have actually been around for a long time) modes of appropriation of surplus value. As Slavoj Žižek vividly points out, increasing returns in the appropriation of rents for intellectual property simultaneously obscure the origin of the resulting enormous incomes in the pool of surplus value appropriated from productive labor and mystify the factors behind the increasing inequality in the distribution of these revenues [Žižek 2012]. The origin of the rent of a particularly exploitable resource like a waterfall or a petroleum deposit is hard enough to understand, but at least the owner of a waterfall cannot allow an unlimited number of cotton mills to exploit the resulting usable energy. By contrast, the owner of the rights to distribute a piece of software that, due to network externalities, becomes a technical standard, can allow an effectively unlimited number of users to install the software and charge each of them a fee.

It would be, however, a peculiar political economy that convinced itself that the increasing returns in the rents to artificially created assets, such as systems software, were a remedy for thermodynamically imposed decreasing returns to resource use in material production.

Optimization and Its Discounts

Trying to reconcile cost shifting with the discounting of future climate change costs and benefits has taken me on some unexpected detours. I was initially thinking about bills of exchange and their role in the early modern era of concealing church-outlawed "usury" in the guise of a more palatable commercial transaction. Discounting was an arithmetical accounting exercise that arose out of the discounting of bills of exchange.

Both compound interest and discounting partake of the same exponential function -- from different ends of the calculation -- so it is easy (and misleading) to think of the discounting of a bill of exchange as a kind of loan. Discounting a bill of exchange is a sales transaction. The credit involved is commercial credit extended from a supplier to a purchaser. The bank then buys the bill of exchange from the supplier at a discount from its face value.

If one insists on seeing a loan from the banker in the transaction, it would only be an indirect loan to the purchaser of the goods, not to the supplier who sold the bill of exchange to the bank. But that loan would be secured by the goods that were the original object of the transaction that originated the bill of exchange... (Unless, that is, the bill of exchange was only speculative, a circumstance that Marx labeled a swindle.)

The important point is that bills of exchange originated in real transactions of goods, not in purely financial transactions. This has serious implications for the use of "discounting" in cost benefit analysis of public investments.

If the discount rate is meant as a metaphor it is a peculiarly bad one. The goods in question -- costs and benefits of climate change mitigation, for example -- have both negative and positive values but more importantly they have not been contracted for by the interested parties -- there is no "bill of exchange" to be discounted. Furthermore, the beneficiary of the discounted price is not society but the polluting firm who has shifted part of its costs to society and the environment. This perverse distribution of costs and benefits (and incentives) is concealed by the aggregate generality of the climate economy models that construe everything as one big happy economy.

Put it this way: discounting the future costs and benefits of greenhouse gas emissions provides a subsidy to the most prolific emitters of greenhouse gases that they can then reinvest at compound interest. This is hardly a matter of being "neutral" on questions of distribution. Nor is it a question of generational equity. This is simply taking the bankers' perspective on financial accumulation and proclaiming it "socially optimal."

Been Discounted So Long It Looks Like Up To Me

The monks ascending the steps on the outside of the wall are growing the GDP, while the monks descending the steps on the inside are abating carbon dioxide emissions. Climate change mitigated -- emissions decoupling accomplished!

"Business profit," Schumpeter tells us, "is a prerequisite to the payment of interest on productive loans... The entrepreneur is the typical interest payer." There are three cost-reduction strategies that firms may pursue to maximize profits. The most opportunistic is cost-shifting, in which some third party, society or the environment gets stuck with the cost rather than the firm. The cost doesn't go away, it just becomes external to the accounting entity's balance sheet and thus is an "externality." Greenhouse gas emissions are such an externality. They are a cost-shifting success for the profit maximizing firm.

Carbon trading schemes and Pigouvian taxes are supposed to "internalize" those externalities so that the users of fossil fuels, for example, are made to pay the full cost -- or at least a larger proportion of the cost -- of their production processes or consumption preferences. Assessments of the costs and benefits of such policies typically discount the present value of future costs and benefits. The appropriate discount rate, it is often argued, should reflect market interest rates or else it may result in spending that is less efficient than would occur through the market. William Nordhaus in A Question of Balance:

The choice of an appropriate discount rate is particularly important for climate-change policies because most of the impacts are far in the future. The approach in the DICE model is to use the estimated market return on capital as the discount rate. The estimated discount rate in the model averages 4 percent per year over the next century. This means that $1,000 worth of climate damages in a century is valued at $20 today. Although $20 may seem like a very small amount, it reflects the observation that capital is productive [S'man: no, it reflects the assumption that capital is "productive"]. Put differently, the discount rate is high to reflect the fact that investments in reducing future climate damages to corn and trees should compete with investments in better seeds, improved equipment, and other high-yield investments. With a higher discount rate, future damages look smaller, and we do less emissions reduction today; with a lower discount rate, future damages look larger, and we do more emissions reduction today.  

Update:  But... if profitability is a function of cost shifting, the market interest rate a function of profit, the discount rate a function of the market interest rate and cost/benefit optimization of GHG abatement a function of the discount rate, doesn't said optimization embed a circular reference? No, this is both too simple and too forgiving an interpretation of the relationship between discounting and cost shifting. More on this soon...

Nordhaus, again:

In thinking of long-run discounting, it is always useful to remember that the funds used to purchase Manhattan Island for $24 in 1626, when invested at a 4 percent real interest rate, would bring you the entire immense value of land in Manhattan today. 

Professor Nordhaus here simply updates and tones down the hallucinations of Dr. Richard Price, who exclaimed in 1774:

One penny, put out at our Saviour's birth to 5 per cent compound interest, would, before this time, have increased to a greater sum, than would be contained in a hundred and fifty millions of earths, all solid gold. 

As Marx began the chapter in Capital in which he cited Price's dazzled fancy:

The relations of capital assume their most externalised and most fetish-like form in interest-bearing capital. We have here M — M', money creating more money, self-expanding value, without the process that effectuates these two extremes. 

In his discussion of discounting, Nordhaus doesn't distinguish between compound interest and the process that brings about the apparent productivity of capital that he extols. What makes this lack of distinction particularly telling is that he is supposedly discussing solutions to a problem that results from the very process that makes capital productive of profits sufficient to sustain interest payments on money capital. It is as if the greenhouse gases are unrelated to the industrial processes that emit them.

Compound interest does not emit greenhouse gases. What people do to make the profits to pay the compound interest does. Money capital does not compound itself. The discount rate is no more independent of the cost-shifting that engenders it than it is of the greenhouse gas emissions whose costs are being shifted. D.I.C.E. thrown will never annul chance.

"From him exact usury whom it would not be a crime to kill."

The truth about usury lies somewhere beyond St. Ambrose's condemnation and Jeremy Bentham's cavalier apologetics. In a very brief but valuable essay, Francis Bacon counselled,

It is good to set before us the incommodities and commodities of usury, that the good may be either weighed out or culled out; and warily to provide, that while we make forth to that which is better, we meet not with that which is worse. 

Strictly speaking, compound interest is usury. Discounting is compound interest, ergo discounting is usury.  Bentham, who upheld usury in a series of letters addressed to Adam Smith, also was a pioneering proponent of cost-benefit analysis for public investments. Considering that usury has both incommodities and commodities, a proper cost-benefit analysis would need to evaluate the costs as well as the benefits that arise from the discounting of future value.

The typical way of handling traditional objections to usury is to cite scripture and the interpretations of it offered by religious authorities. This was the method followed by Benjamin Nelson in The Idea of Usury, whose analysis was taken up by Lewis Hyde in The Gift and by David Graeber in Debt: the first 5000 years. But the biblical injunctions are laconic and subsequent interpretations may partake more of rationalization than impetus. Bentham was right when he observed,

It is one thing, to find reasons why it is fit a law should have been made: it is another to find the reasons why it was made: in other words, it is one thing to justify a law: it is another thing to account for its existence. 

Bentham's defence of usury, though, was as verbose and meandering as the infamous passage from Deuteronomy about brethren and strangers was terse. His account of the grounds for the prejudice against usury was frivolous and dismissive. "To trace an error to its fountain head," Bentham cited Lord Coke, "is to refute it." What Bentham meant by "trace" was "assert." According to him, the prohibition of usury was motivated by the perverse asceticism of early Christians, foolish abstractions of Aristotle and ill-tempered envy toward the wealthy by the profligate debtors.

More concisely and substantively, Francis Bacon presented, in one paragraph, a catalogue of seven disadvantages arising from usury. A second paragraph elaborated on three advantages. Bacon's fourth criticism of usury is of particular interest:

…it bringeth the treasure of a realm or state into a few hands; for the usurer being at certainties, and others at uncertainties, at the end of the game most of the money will be in the box; and ever a state flourisheth when wealth is more equally spread…

In favour of usury, Bacon's second point is his most compelling:

…were it not for this easy borrowing upon interest, men's necessities would draw upon them a most sudden undoing, in that they would be forced to sell their means (be it lands or goods), far under foot; and so, whereas usury doth but gnaw upon them, bad markets would swallow them quite up.

In modern parlance, Bacon's most compelling arguments, both for and against usury, refer to what Marshall called the "external economies" -- or positive and negative externalities -- of the loan transactions. For better or worse then, compound interest is a vehicle for the shifting of costs and benefits. It is well to remember, in this connection, Joan Martinez-Alier's observation that "one can see externalities not as market failures but as cost-shifting successes."

One doesn't need to assume that cost shifting is necessarily a bad thing. Insurance, including social insurance, is a form of cost shifting. But when the project being evaluated in a cost-benefit analysis has the overt purpose of internalizing the cost of externalities -- such as in the analysis of abatement of greenhouse gas -- it is disingenuous to overlook the role of compound interest in enabling the social cost shifting in the first place and of perpetuating it over the period being analyzed. In other words, part of the value allegedly being "added" by capital in the analysis is not in fact being produced but is merely being appropriated by capital through social cost shifting.

(See also "Why Is the Discount Rate So Important?" page 9 in "More than Meets the Eye: The Social Cost of Carbon in U.S. Climate Policy, in Plain English.")

Weitzman's Burden: do we dare to question economic growth?

Do we dare to question economic growth? asks Warwick Smith in a Comment is Free op-ed at the Guardian:

We live on a finite planet. 

That’s it. How, you might wonder, can such a simple statement of obvious fact undermine the tenets of modern society?

According to Paul Krugman, though, "there’s a lot of room to reduce emissions without killing economic growth. If you think you've found a deep argument showing that this isn't possible, all you've done is get confused by your own word games."

O.K., let's play some serious "word games," then, and try not to get confused.

Actually, these are word games about pictures. One of them is Wittgenstein's discussion of the duck-rabbit picture. The other is Keynes's discussion of the newspaper beauty contest in which contestants are asked to guess which pictures the most contestants think are prettiest.

But let's start with another quote from Paul Krugman, "So what I end up with is basically Martin Weitzman’s argument: it’s the nonnegligible probability of utter disaster..." What the probability of utter disaster does in Weitzman's argument is render the standard cost-benefit analysis, based on a market-based discount rate, inoperative. What's a discount rate? It's an interest rate, or more specifically, according to Investopedia,

The discount rate also refers to the interest rate used in discounted cash flow analysis to determine the present value of future cash flows. The discount rate in discounted cash flow analysis takes into account not just the time value of money, but also the risk or uncertainty of future cash flows; the greater the uncertainty of future cash flows, the higher the discount rate.

So a discount rate is an interest rate. What is an interest rate? In the retrospective, "From Usury to Interest," Joseph Persky explained,

Our modern word 'interest' derives from the Medieval Latin interesse. The Oxford English Dictionary explains that interesse originally meant a penalty for the default on or late payment of an otherwise legitimate, nonusurious loan. As more sophisticated commercial and financial practices spread through Europe, fictitious late payments became an accepted if disingenuous way of circumventing usury laws. Over time, 'interest' became the generic term for all legitimate and accepted payments on loans.

A discount rate is an interest rate is a (formerly) usurious charge on a loan. Now, if I were to say next that "economic growth is another aspect of compound interest" or that "usury is what propels growth and what makes it imperative" an economist would insist that I am some kind of a crank. I won't say that.

I won't say it because what we're dealing with here are not economic growth and interest rates but accounts of economic growth and interest. These accounts are like pictures and here is where Wittgenstein can be of help. Paul Krugman, and EconoSpeak's own Peter Dorman, are fond of reminding us that critics of growth "mistakenly" identify GDP with "stuff." They point out that it is value, not stuff, that gets added up in the national income accounts. This is a bit like saying the duck-rabbit picture is a picture of a rabbit, not of a duck.


GDP certainly is not stuff. It is an account of something. And it is most definitely an account of something that many -- possibly most -- people perceive of as stuff. The question then arises whether the "value" that economists attribute to GDP would continue to carry the same weight if the people who formerly perceived of GDP as accounting for stuff stopped having that perception. This is another way to pose the question, "what is liquidity?"

What is liquidity? Clearly Keynes thought that liquidity-preference resulted from uncertainty and that changes in liquidity-preference are implicated in slumps to the extent that the rate of interest required to induce people to not hoard liquid assets exceeds the expected rate of return on productive investments. In other words, while GDP is indeed not stuff, whether it is perceived to be an account of stuff may well have a bearing on private investment decisions.

Furthermore, whether an individual investor does or does not believe that GDP is an account of stuff doesn't matter as much as what that investor believes is the average perception of investors. Keynes illustrated this condition with his beauty contest story.

In conclusion, Weitzman presented a compelling case for the inappropriateness of using market interest rates as a discount rate for cost-benefit analysis of policies for abatement of GHG emissions. There are no grounds for assuming that capital markets would react benignly to such policies, however prudent and appropriate they may be.

Is there "a lot of room to reduce emissions without killing economic growth?" as Paul Krugman asserts or "do we dare to question economic growth?" as Warwick Smith wants to know.

A throw of the D.I.C.E. will never abolish chance

In Building a Green Economy, NYT Magazine, April 7, 2010, Paul Krugman wrote,

As Harvard’s Martin Weitzman has argued in several influential papers, if there is a significant chance of utter catastrophe, that chance — rather than what is most likely to happen — should dominate cost-benefit calculations. And utter catastrophe does look like a realistic possibility, even if it is not the most likely outcome. 

Weitzman argues — and I agree — that this risk of catastrophe, rather than the details of cost-benefit calculations, makes the most powerful case for strong climate policy. Current projections of global warming in the absence of action are just too close to the kinds of numbers associated with doomsday scenarios. It would be irresponsible — it’s tempting to say criminally irresponsible — not to step back from what could all too easily turn out to be the edge of a cliff.

... 

So what I end up with is basically Martin Weitzman’s argument: it’s the nonnegligible probability of utter disaster that should dominate our policy analysis. And that argues for aggressive moves to curb emissions, soon.

So far, so good. But Krugman's conclusion produced this pretzel of cognitive dissonance:

...there has to be a real chance that political support for action on climate change will revive. 

If it does, the economic analysis will be ready [no, it isn't]. We know how to limit greenhouse-gas emissions [no, we don't]. We have a good sense of the costs [nope] — and they’re manageable [how could we know?]. All we need now is the political will.

Krugman apparently assumed that the cost estimates developed, for example, in Nordhaus's "dynamic integrated climate-economy" (DICE) analyses are independent of when the greenhouse gas abatement actions are taken. But the rationale for delaying abatement is that the discount rate assumed in the model makes it cheaper to wait to do the abatement. Weitzman's critique doesn't present cost estimates. Contra Krugman, there is not even a consensus about what needs to be done or how to do it, let alone "a good sense of the costs" of doing... it? Whatever "it" is.

The bottom line (literally) is that a key consideration of the structure and assumptions of the conventional models was facilitating economic growth and relying on that economic growth to finance the costs of abatement. The DICE were loaded for growth! To put it somewhat crudely, delaying abatement was supposed to make a large part of the cost "pay for itself" through the dividends earned on the money saved by not doing it now. You cannot have your cake and eat it too. Nor can you finance a current expenditure from revenues you would have earned if you hadn't made the expenditure.

The excerpts and abstracts below are not from people Krugman would ridicule as "degrowthers." There seems to be a dawning awareness that the assumptions of the conventional integrated assessment models need to be, at the very least, radically revised, which is essentially the point those silly anti-capitalist degrowthers on the left (going back to that silly anti-capitalist leftist Nicolaus Georgescu-Roegen)  have been making all along.

"Climate Change Policy: What Do the Models Tell Us?" Robert S. Pindyck

Very little. A plethora of integrated assessment models (IAMs) have been constructed and used to estimate the social cost of carbon (SCC) and evaluate alternative abatement policies. These models have crucial flaws that make them close to useless as tools for policy analysis: certain inputs (e.g., the discount rate) are arbitrary, but have huge effects on the SCC estimates the models produce; the models’ descriptions of the impact of climate change are completely ad hoc, with no theoretical or empirical foundation; and the models can tell us nothing about the most important driver of the SCC, the possibility of a catastrophic climate outcome. IAM-based analyses of climate policy create a perception of knowledge and precision, but that perception is illusory and misleading.

"Climate Policy: Science, Economics, and Extremes," Anthony C. Fisher and Phu V. Le

Economic models help illustrate the links between the climate and the economy, and they are an important component of the multidisciplinary analysis that is needed to address climate change. However, there are major problems with the estimates of potential damages in the IAMs... First, damage functions and estimates appear to have little connection to the empirical findings from econometric studies of sectoral impacts, particularly on agriculture, as we discuss later. More generally, economy-wide damage functions are simply not known, especially at the global level. Thus, as Pindyck (2013b) argues, there is little empirical, or for that matter theoretical, foundation for the specification of functional forms and parameters in the models. This suggests that their quantitative results and policy prescriptions are somewhat arbitrary. 

We agree with Stern (2013) that there are gross underestimations of damages in economic impact models and IAMs, and we discuss some additional issues that are not adequately addressed in the models including the importance of nonlinearities, environmental impacts, extreme events, and capital losses.

"Endogenous growth, convexity of damages and climate risk: how Nordhaus' framework supports deep cuts in carbon emissions." Simon Dietz and Nicholas Stern

'To slow or not to slow' (Nordhaus, 1991) was the first economic appraisal of greenhouse gas emissions abatement and founded a large literature on a topic of great, worldwide importance. In this paper we offer our assessment of the original article and trace its legacy, in particular Nordhaus' later series of 'DICE' models. From this work many have drawn the conclusion that an efficient global emissions abatement policy comprises modest and modestly increasing controls. On the contrary, we use DICE itself to provide an initial illustration that, if the analysis is extended to take more strongly into account three essential elements of the climate problem -- the endogeneity of growth, the convexity of damages, and climate risk -- optimal policy comprises strong controls. To focus on these features and facilitate comparison with Nordhaus' work, all of the analysis is conducted with a high pure-time discount rate, notwithstanding its problematic ethical foundations. [We have argued elsewhere that careful scrutiny of the ethical issues around pure-time discounting points to lower values than are commonly assumed (usually with little serious discussion).]

"Climate Risks and Carbon Prices: Revising the Social Cost of Carbon," Frank Ackerman and Elizabeth A. Stanton

Once the social cost of carbon is high enough to justify maximum feasible abatement in cost-benefit terms, then cost-benefit analysis becomes functionally equivalent to a precautionary approach to carbon emissions. All that remains for economic analysis of climate policy is to determine the cost-minimizing strategy for eliminating emissions as quickly as possible. This occurs because the marginal damages from emissions have become so large; the uncertainties explored in our analysis, regarding damages and climate sensitivity, imply that the marginal damage curve could turn nearly vertical at some point, representing a catastrophic or discontinuous change.  

The factors driving this result are uncertainties, not known facts. We cannot know in advance how large climate damages, or climate sensitivity, will turn out to be. The argument is analogous to the case for buying insurance: it is the prudent choice, not because we are sure that catastrophe will occur, but because we cannot be sufficiently sure that it will not occur. By the time we know what climate sensitivity and high-temperature damages turn out to be, it will be much too late to do anything about it. The analysis here demonstrates that plausible values for key uncertainties imply catastrophically large values of the social cost of carbon.
…
Our results offer a new way to make sense of the puzzling finding by Martin Weitzman: his “dismal theorem” establishes that under certain assumptions, the marginal benefit of emission reduction could literally be infinite (Weitzman 2009). The social cost of carbon, which measures the marginal benefit of emission reduction, is not an observable price in any actual market. Rather, it is a shadow price, deduced from an analysis of climate dynamics and economic impacts. Its only meaning is as a guide to welfare calculations; we can obtain a more accurate understanding of the welfare consequences of policy choices by incorporating that shadow price for emissions.

Slow steam, fat tails and a dismal theorem

Paul Krugman's column the other day, invoking William Nordhaus's "demolition" of the forecasting model in The Limits to Growth, got me wondering about how well Nordhaus's indictment has stood up over the years. So I started poking around in the archives.

Twenty years after publication of Limits to Growth, the research team reconvened in 1992 for Beyond the Limits, an  update of the earlier analysis. Nordhaus, too, followed up his earlier "blistering" review with a critique of the second version. This second review was more conciliatory, albeit still critical of the Limits to Growth and Beyond the Limits assumptions and conclusions:

While the LTG school argued that economic decline was inevitable and economists argued that the LTG argument was fallacious, the argument is ultimately an empirical matter. Put differently, critics would have gone too far had they claimed that the postulated pessimistic scenario could not hold.

Instead of simply "demolishing" the LTG model, in his second review, Nordhaus responded with his own simple model, using more a conventional generalized Cobb-Douglas production function.

Like LTG models, the general model given in the last section shows the tendency toward economic decline. In addition, there are no less than four conditions, each of which is satisfied in the LTG model, that will lead to ultimate economic stagnation, decline, or collapse...  

[However]...the entire argument can be reversed with a simple change in the specification of the model; more precisely, I will introduce technological change into the production structure and assume that the Cobb-Douglas production function accurately represents the technological possibilities for substitution.

"Ultimately, then," Nordhaus concluded his discussion of simple growth models,

...the debate about future of economic growth is an empirical one, and resolving the debate will require analysts to examine fundamental structural parameters of the economy... How large are the drags from natural resources and land? What is the quantitative relationship between technological change and the resource-land drag? How does human population growth behave as incomes rise? How much substitution is possible between labor and capital on the one hand, and scarce natural resources, land, and pollution abatement on the other? These are empirical questions that cannot be settled solely by theorizing.

One of the discussants for Nordhaus's 1992 Brookings paper was Martin Weitzman, who described it as "an outstanding paper." that "represents the economic state of the art, circa 1992, in dealing seriously and honestly with the major limits-to-growth arguments." One could almost imagine hearing the scalpel being quietly honed as Weitzman administered that subtle anesthesia.

Fast forward another two decades and it is Nordhaus's turn to comment on a paper by Weitzman, "On modeling and interpreting the economics of catastrophic climate change."

In an important paper, Weitzman (2009) has proposed what he calls a dismal theorem. He summarizes the theorem as follows: "[T]he catastrophe-insurance aspect of such a fat-tailed unlimited-exposure situation, which can never be fully learned away, can dominate the social-discounting aspect, the pure-risk aspect, and the consumption-smoothing aspect." The general idea is that under limited conditions concerning the structure of uncertainty and societal preferences, the expected loss from certain risks such as climate change is infinite and that standard economic analysis cannot be applied.

Nordhaus concluded his discussion of Weitzman's theorem on a somber and humble note:

In many cases, the data speak softly or not at all about the likelihood of extreme events. This means that reasonable people may have quite different views about the likelihood of extreme events, such as the catastrophic outcomes of climate change, and that there are no data to adjudicate such disputes. This humbling thought applies more broadly, however, as there are indeed deep uncertainties about virtually every issue that humanity faces, and the only way these uncertainties can be resolved is through continued careful consideration and analysis of all data and theories.

The word "growth" doesn't appear in Nordhaus's 16-page commentary. Pascal's wager, anyone?

Krugman, straw man, beggar, thief

In his "Slow Steaming..." column today, Paul Krugman blatantly misrepresented and trivialized Mark Buchanan's argument:

Buchanan says that it’s not possible to have something bigger — which is apparently what he thinks economic growth has to mean — without using more energy.

Wrong. Buchanan said bigger things, as a rule, use more energy. He also said that efficiencies of scale don't overturn that rule. He referred to data about economic growth and energy use, not "what he thinks economic growth has to mean":

Data from more than 200 nations from 1980 to 2003 fit a consistent pattern: On average, energy use increases about 70 percent every time economic output doubles. This is consistent with other things we know from biology. Bigger organisms as a rule use energy more efficiently than small ones do, yet they use more energy overall. The same goes for cities. Efficiencies of scale are never powerful enough to make bigger things use less energy.

Krugman disparaged Buchanan for reprising the claims and title of the book that William Nordhaus "demolished so effectively forty years ago":

...not only does he make the usual blithe claims about what economists never think about; even his title is almost exactly the same as the classic (in the sense of classically foolish) Jay Forrester book that my old mentor, Bill Nordhaus, demolished so effectively forty years ago.

I'll leave it to posterity whether or not Nordhaus "demolished" Limits to Growth. Forty years on, Brian Hayes wrote a less "blistering" critique, published in American Scientist, judging Forrester's mathematical model to be "more of a polemical tool than a scientific instrument" but concluding the book's message of limits is worth listening to. Defenders of the book have argued that Nordhaus misunderstood or misrepresented the structure of the model and whether or not the model used historical data (it did) -- the title of Nordhaus's review was "World dynamics: measurement without data."

But, following the Krugman's link to his earlier article reveals that the "foolishness" or otherwise of the book Nordhaus supposedly demolished is really beside the point. Krugman's conclusion in that earlier article directly contradicts the Pollyanna claims he is now making:

You might say that this is my answer to those who cheerfully assert that human ingenuity and technological progress will solve all our problems. For the last 35 years, progress on energy technologies has consistently fallen below expectations. 

...

But anyway, while the Limits to Growth stuff of the 1970s was a mess, the history of energy technology doesn’t support extreme optimism, either.

You've really got to follow the links.

Keep asking the wrong question, Paul Krugman, and you won't have to think about the answer.

Krugman: "But it is, I think, a useful corrective to the rigorous-sounding but actually silly notion that you can’t produce more without using more energy."

Of course you can produce more while using less energy. That is what has been happening throughout history. That is the wrong question, though. The problem has to do with maintaining employment while reducing the absolute amount of energy used. Producing more with less energy doesn't solve that problem.

UPDATE: Krugman proved Mark Buchanan right: economists ARE blind to the limits of growth!