On Limits to Growth

It’s a good idea to read things you criticize; checking your sources doesn’t hurt either. One of the most frequent targets of uninformed criticism, passed down from teacher to student with nary a reference to the actual text, must be The Limits to Growth. In writing my recent review of Green & Armstrong (2007), I ran across this tidbit:

Complex models (those involving nonlinearities and interactions) harm accuracy because their errors multiply. Ascher (1978), refers to the Club of Rome’s 1972 forecasts where, unaware of the research on forecasting, the developers proudly proclaimed, “in our model about 100,000 relationships are stored in the computer.” (page 999)

Setting aside the erroneous attributions about complexity, I found the statement that the MIT world models contained 100,000 relationships surprising, as both can be diagrammed on a single large page. I looked up electronic copies of World Dynamics and World3, which have 123 and 373 equations respectively. A third or more of those are inconsequential coefficients or switches for policy experiments. So how did Ascher, or Ascher’s source, get to 100,000? Perhaps by multiplying by the number of time steps over the 200 year simulation period – hardly a relevant measure of complexity.

Meadows et al. tried to steer the reader away from focusing on point forecasts. The introduction to the simulation results reads,

Each of these variables is plotted on a different vertical scale. We have deliberately omitted the vertical scales and we have made the horizontal time scale somewhat vague because we want to emphasize the general behavior modes of these computer outputs, not the numerical values, which are only approximately known. (page 123)

Many critics have blithely ignored such admonitions, and other comments to the effect of, “this is a choice, not a forecast” or “more study is needed.” Often, critics don’t even refer to the World3 runs, which are inconvenient in that none reaches overshoot in the 20th century, making it hard to establish that “LTG predicted the end of the world in year XXXX, and it didn’t happen.” Instead, critics choose the year XXXX from a table of resource lifetime indices in the chapter on nonrenewable resources (page 56), which were not forecasts at all.

As an example, Bjorn Lomborg writes in The Skeptical Environmentalist (pg. 121), “Along with numerous other resources, Limits to Growth showed us that we would have run out of oil before 1992.” What he refers to is the table entry on pg. 58 of Limits showing static reserve life indices (SRLI) and dynamic equivalents for petroleum If you read the accompanying text, it’s clear that the table has little to do with forecasting exhaustion. Instead it simply makes the point that the SRLI (=reserves/current use) is a poor measure of the true lifetime of a resource with exponentially growing use. Limits also recognizes the distinction between reserves and resources, and includes a second column of dynamic indices at arbitrary 5x reserves (to make the point that even large discoveries can be overwhelmed by growth). For oil, this yields a dynamic reserve lifetime of 50 years (again, not a forecast and not model-based, but implying exhaustion in 2022, not 1992). Lomborg happily ignores these subtleties and publishes a table of updated SRLIs a few pages later.

Such misattributions become more and more remote from reality as they are handed down from author to author without verification:

Another example is the celebrated ‘World Model’ of the Club of Rome, published in the 1970s best-seller, The Limits to Growth (Meadows et al. 1972). This model predicted major shortages of natural resources by the end of the twentieth century that would cause commodity prices to skyrocket. In fact, not only did prices fail to increase at the predicted rate, they did not increase at all. At the end of the twentieth century, the prices for nearly all natural resources were lower than at the time the model was built (Moore 1995). – Naomi Oreskes, The Role of Quantitative Models in Science

The problem is, those allegedly wrong forecasts simply aren’t there. Limits didn’t predict much of anything for the end of the twentieth century – its time horizon was far longer. Prices couldn’t “fail to increase at the predicted rate” because there was no predicted rate. In fact, the whole section on nonrenewable resources in Chapter 2 hardly mentions price. The closest it comes to a general forecast is, “Given present resource consumption rates and the projected increase in these rates, the great majority of the currently important nonrenewable resources will be extremely costly 100 years from now.” Last time I checked, it wasn’t 2072 yet. The only commodity for which actual numerical results are shown is a hypothetical analog of Chromium. Simulations are shown for 1x and 2x reserves, with costs remaining relatively constant until about 2030 and 2050, respectively. Again, not yet a forecast failure. (Chromium turns out to be an interesting special case, because its resource base is quite vast, but also exceptionally concentrated in a single location).

Limits goes on to say,

Added to the difficult economic question of the fate of various industries as resource after resource becomes prohibitively expensive is the imponderable political question of the relationships between producer and consumer nations as the remaining resources become concentrated in more limited geographical areas. Recent nationalization of South American mines and successful Middle Eastern pressures to raise oil prices suggest that the political question may arise long before the economic one. (page 67)

That doesn’t sound so bad now, with increasing concentration of remaining conventional oil resources in politically unstable regions and commodities revisiting their historic highs. But it’s also not a proof of limits any more than cheap oil in the 90s was a refutation. It’s important to remember that prices are not a complete basis for judging long term scarcity. Prices are good reflections of short term market clearing conditions, but long term prices also reflect expectations and allocations of property rights. Over the long haul, expectations can be quite wrong, and allocations can be incomplete or perverse. Reasoning based on prices can easily be circular, for example when governments freely allocate mineral rights with the expectation that low prices indicate abundance.

The problem with focusing on the forecast performance of the model is that it diverts attention from what the model was really about. The fundamental message of the model is that a system with rapid exponential growth and long delays in propagation and perception of problems is prone to overshoot. A lot of critics evidently just don’t want to consider that proposition, and prefer to dismiss the idea on the basis of short term evidence that has no actual bearing on its correctness. To really learn and communicate, one must get beyond data bites, and consider not only whether the past 30 years of history is consistent with the model, but also whether the model properly articulated the arguments of limits and technological optimism and whether improved models would yield different answers.

Certainly data is relevant, but the real focus of thinking about Limits should be model structure. There have been several intelligent attempts to critique Limits and formulate alternative models, which I’ll detail in a future post.

As a counterpoint to the polemics, there’s an unusually good article and accompanying Econ one on one revisiting Limits in yesterday’s Wall Street Journal. Both the article and the discussion are quite thoughtful and thought-provoking. A few excerpts:


A similar pattern could unfold again. But economic forces alone may not be able to fix the problems this time around. Societies as different as the U.S. and China face stiff political resistance to boosting water prices to encourage efficient use, particularly from farmers. …

This troubles some economists who used to be skeptical of the premise of “The Limits to Growth.” As a young economist 30 years ago, Joseph Stiglitz said flatly: “There is not a persuasive case to be made that we face a problem from the exhaustion of our resources in the short or medium run.”

Today, the Nobel laureate is concerned that oil is underpriced relative to the cost of carbon emissions, and that key resources such as water are often provided free. “In the absence of market signals, there’s no way the market will solve these problems,” he says. “How do we make people who have gotten something for free start paying for it? That’s really hard. If our patterns of living, our patterns of consumption are imitated, as others are striving to do, the world probably is not viable.”

The dynamic today appears different. So far, the oil industry has failed to find major new sources of crude. Absent major finds, prices are likely to keep rising, unless consumers cut back. …

New technology could help ease the resource crunch. Advances in agriculture, desalination and the clean production of electricity, among other things, would help.

But Mr. Stiglitz, the economist, contends that consumers eventually will have to change their behavior even more than then did after the 1970s oil shock. He says the world’s traditional definitions and measures of economic progress — based on producing and consuming ever more — may have to be rethought.

In years past, the U.S., Europe and Japan have proven adept at adjusting to resource constraints. But history is littered with examples of societies believed to have suffered Malthusian crises: the Mayans of Central America, the Anasazi of the U.S. Southwest, and the people of Easter Island.

Those societies, of course, lacked modern science and technology. Still, their inability to overcome resource challenges demonstrates the perils of blithely believing things will work out, says economist James Brander at the University of British Columbia, who has studied Easter Island.

“We need to look seriously at the numbers and say: Look, given what we’re consuming now, given what we know about economic incentives, given what we know about price signals, what is actually plausible?” says Mr. Brander.

Indeed, the true lesson of Thomas Malthus, an English economist who died in 1834, isn’t that the world is doomed, but that preservation of human life requires analysis and then tough action. Given the history of England, with its plagues and famines, Malthus had good cause to wonder if society was “condemned to a perpetual oscillation between happiness and misery.” That he was able to analyze that “perpetual oscillation” set him and his time apart from England’s past. And that capacity to understand and respond meant that the world was less Malthusian thereafter.

The “Limits to Growth” debate raises a key issue: how much consumption do we need to live a “good life?” Why is the “American Dream” our dream? As China and India grow richer, will their new middle class seek to live a more restrained lifestyle or will they embrace our conception of the “good life?” By making people think through the social consequences of their own consumption goals, the “Limits to Growth” advocates may actually help to mitigate the “crisis.”

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