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Sunday, August 24, 2014

Sustained Growth On A Finite Planet

In recent years, it has been increasingly popular to make statements along the line that exponential* economic growth cannot forever in a finite planet. (One of the more popular examples of this argument was the essay Exponential Economist Meets Finite Physicist, by Tom Murphy, an Associate Professor of Physics at the University of California, San Diego.) I follow what I would describe as a minimal Peak Oil viewpoint, but I believe that this framing of the issue in terms of a finite planet is largely incorrect in terms of analysing the economy. My reading of the situation is that under a non-catastrophic Peak Oil scenario, economic growth in the developed world will continue much as it has been doing for a fairly long horizon (30 to 50 years?). Much longer horizons (100 years, for example) is when very serious problems would show up in the economic data.

Tim Harford discussed this in his book, The Undercover Economist Strikes Back, which I previously reviewed. My analysis is similar to his, although I appear to be more pessimistic in the long term. One could summarise the argument in a way that would be very non-controversial amongst economists: GDP growth - which is what most economists are referring to when they refer to "growth" - is not the same thing as "resource usage growth". (The chart below shows how real GDP growth in the United States has decoupled from the number of miles driven as one example of this.) Physicists and petroleum engineers are free to define "growth" however they want, but it is strange that they are lecturing economists on how to use economic technical jargon. Most economists would not make arguments that physicists are using technical terms (such as "energy") incorrectly.
Chart: U.S. Miles Driven, Real GDP

A Minimal Peak Oil Scenario

There is a great deal of controversy around the notion of "Peak Oil", partly because too much attention is paid to the concept of the point of maximum production (the peak). I have never attempted to make energy production forecasts, but I followed the literature because energy prices are an important component of inflation breakeven forecasting. Unfortunately, the controversy and hyperbole makes it harder to discuss the subject in technocratic circles. I will instead focus on a reasonable baseline scenario for the developed countries, although I am not concerned about exact details. I am more interested in covering the theoretical question whether "sustained" growth is possible under a peak oil scenario.

I want to emphasise that my scenario here is for a horizon of 30-50 years, which is a far longer horizon than markets can deal with. I discuss a more pessimistic long run scenario (100 years?) below.
  • The date of peak production does not really matter. I have glanced at some recent mainstream energy production forecasts, and the production of "liquid petroleum" (which includes conventional and unconventional oil) is expected to continue to slowly rise for at least a decade. (Since the unconventional oil production requires energy inputs, some of this represents a conversion of one type of an energy to convenient liquid form. The Albertan Tar Sands is an example of unconventional oil.) After the peak, production will slowly decline (as oil fields travel down the back side of a roughly bell-shaped production curve). But from the point of view of developed countries, any continued growth in production only matters from the point of view of carbon dioxide emissions - the amount of oil that will be available to the developed world will slowly decline. Emerging markets, in particular oil producers, will bid away oil supply.
  • I assume that there are no major oil discoveries or technological "silver bullets" (for example, thorium reactors) which can ramp up the supply of energy. I have limited justification for this assumption, but I need it in order for the rest of the article to make sense.
  • Conversely, there are no catastrophes that hit society, from any number of possible directions (for example, global warming). Modern societies are remarkably resilient, so this is not totally unreasonable.
  • Absolutely disastrous policy, such as we see in the euro area at present, are not sustained over the scenario period. This is perhaps only a hope, but there is a certain amount of Darwinian selection in the long term for failed policies.
  • Energy price spikes will only cause temporary disruptions that are eventually absorbed by automatic stabilisers.
  • Price signals within an economy will eventually  lead to something resembling "optimising" behaviour (that is, movement away from energy-intensive products).
  • These price signals will eventually lead to adaptive policy changes as well. My summary of the situation is that nothing will be done until it needs to be done.
    (For what it is worth, my recommended policy would be to enact an "Energy Added Tax" which punishes energy consumption, which also catches imported goods. It should start small, and ramp up along a pre-determined schedule, to give people time to adapt.)
  • "Peak Food" matters, and is fundamentally more important than Peak Energy (for reasons I discuss below). Peak energy poses problems to the industrial farming model, and so the issues are related. But the constraints on fresh water, fertiliser and other inputs could bite even before energy limits hits agricultural production. I assume that hard limits will not be reached within the forecast horizon, but food production will act as a drag on growth.
  • There is a lot of activity in modern economies that is not of fundamental importance. Many energy-intensive activities can be dropped without the underlying character of society changing. (As a small example, consumption of fruit transported by air could be replaced with more traditional sources, such as eating canned fruit.)
  • Demographic data indicates that populations in the developed world are either slowly declining or have a small positive growth rate due to immigration. This reduces the pressure on resource constraints.
The situation in the developing economies is somewhat different. I do not follow those economies enough to be confident in discussing them, but my bias is not to be too optimistic about countries that need to import food and energy. The developed countries, by contrast, have considerable food security.

How Nominal GDP Grows

It is easy to demonstrate that nominal GDP can continuously grow, regardless of the energy scenario. Nominal wages grow steadily due to custom, and that nominal growth rate is generally faster than any decline in the working population (although this has not been true for Japan). 

Although the number of workers can fall due to rising unemployment, unemployment rates cannot rise forever as a result of the automatic stabilisers. Therefore, total nominal wages will rise on a sustained fashion over time. Within national income, there is also the profit share of the total. The profit share moves around (it is relatively high now), but its movement will not be enough to derail the trend in rising nominal income. And since Gross Domestic Income is equal to Gross Domestic Product (measurement issues aside), nominal GDP will rise.

One could argue that this misses the point - real GDP matter, not nominal. (Nominal GDP growth could just represent inflation.) But it does matter for things like debt service burdens. If you are modelling fiscal dynamics, nominal GDP growth is far more important than real GDP growth.

How Real GDP Grows

(Note: in this section, I am going to talk about a "closed economy", which is really only true for the Earth as a whole. I note the international complications below.)

Real GDP growth can be thought of as multiplying the number of workers employed by the average volume of output per worker. And the output is not measured in terms of energy or some other construct, it is (generally) based on market transactions. 

In order for real GDP to grow on a trend basis, the trend output per worker needs to grow more than the trend decline of the working population. Since population decline rates are generally not very large, the hurdle rate for productivity growth in order for there to be aggregate growth is not that high (1% should do it).

Peak oil impacts the productivity of the workers in the energy industry - more people need to work in order to get the same output. However, the productivity of energy-using sectors is not impacted. If I am using a chainsaw to chop down trees, raising the cost of my fuel raises my cost of doing business, but I can still cut down trees at the same pace. 
Chart: Canadian Employment In the Extraction Industries

And the reality is that oil extraction is not labour-intensive. We do not have hundreds of millions of workers toiling with picks, shovels and buckets to extract petroleum; the work is done by a handful of workers. As an example, the chart above shows that the employment in the entire resource extraction sector in Canada - a major commodity producer - is a small percentage of the population. Even if their measured productivity is dropping, it is not large enough to drop the measured productivity of the labour force in aggregate.

I emphasised measured productivity for a reason - it has a bias towards higher productivity, as long as the mix of goods and services produced changes. Higher energy prices may induce tumult in production patterns, which will accentuate this bias. As production of new goods and services ramps up, economies of scale kick in, and so measured productivity will rise. On top of that, added experience and technology should create efficiencies (which is what people normally associate with productivity). It is entirely possible that the new goods and services are less satisfying on some absolute scale relative to previous energy-intensive goods, but that is a value judgement that government statisticians do not attempt to make. All they can do is measure the value of goods in market prices, and infer productivity based on the volumes of production.

Open Economy Considerations

A country that is reliant upon energy imports will suffer a terms-of-trade shock: the volume of the goods it exports need to cover the same volume of energy imports will rise. This will result in a loss of purchasing power, which will depress real GDP. This will happen even if there is no drop in domestic productivity.

For the world as a whole, imports and exports net out (or at least they are supposed to, published statistics do not do so). But most developed countries have access to a lot of fresh water, and so the gains on food trade may cancel out the losses on energy imports. And obviously, the situation varies from country-to-country.

The Long-Term Threat To Growth

I discuss in the Appendix below how it appears possible for a hypothetical sustainable economy to have real GDP growth "forever". But the real world growth scenario I discuss above runs into problems on a longer time horizon (for sake of argument, say 100 years from now).

Remember my example of how the increasing price of oil does not drop the productivity of the user of a chain saw? Well, as many of my readers will have observed, my productivity in tree chopping will collapse if am forced to use a human-powered buck saw due to a lack of fuel for my chainsaw.

My reading of the energy scenarios is that there will be enough supply so that the "high productivity" activities will be able to bid away energy from the "low productivity" frivolous energy uses. But on a long enough horizon, energy production limits would start to force people to replace external energy sources with human or animal power for critical tasks. 

To my mind, the key is agriculture. We cannot substitute other goods and services for food. A reversion to non-intensive non-industrial farming would force a secular rise in agricultural employment, reversing the urbanisation of previous centuries. Improved knowledge should mean that crop yields are higher than they were historically (assuming soils are not too degraded), but productivity gains from year-to-year would be low. Depending on the amount of energy available, life would become very similar to centuries ago, where there was limited economic dynamism. The end result would be collapse of productivity to a low level, and progress from that low level will be limited.

I would note that this scenario is a re-wording of the thesis of John Michael Greer (such as in the book The Long Descent) in technocratic economic jargon. He argues that industrial civilization is following earlier civilizations towards collapse, but at a sedate pace (that is, not in the form of a sudden apocalypse that is now popular in fiction). He also highlights how our society has an ingrained belief in progress, which makes such a scenario almost unthinkable. Given the extremely long time frame, all I can say is that the scenario is plausible, but far from certain. 

Appendix - How Real GDP Can Grow "Forever"

In "Exponential Economist Meets Finite Physicist", Professor Murphy argues in "Act Three" that it is impossible to have steady energy usage and growing real GDP. I believe that this is possible in a (hypothetical) sustainable society. I will note that I have not worked through the entire real GDP growth rate calculation, but the mechanism I outline below should work.

Imagine that we have an economy that runs on renewable resources and has a relatively fixed population. Nominal GDP is $100/year, energy costs are $10/year, and the physical amount of energy used is fixed (which implies that the unit price of energy is fixed). 

However, there is a continual rotation of new goods and services that are produced within the economy. The $90 in non-energy spending therefore buys a different mix of goods and services over time.

Now, imagine that spending is reallocated from a less popular existing product A to a new product B in year t+1 (relative to year t). The price for 1 unit at time t is $1 for both products A and B. The logic is slightly different for a physical good than for a service.

  • If the product is an insubstantial service, it is entirely possible that the producer of B could produce 1.1 units for a selling price of $0.91 (=$1/1.1). The total dollar revenue is unchanged per unit, but a greater number of units of B are sold. Take for example the possibility of selling more concert tickets in a hall that is below seating capacity. This can be done without hitting physical constraints, at least for the calculation year.
  • If both products are goods that require physical inputs, we have to be more careful. Assume that the production of 1 unit of A or B in year t requires 1 unit of some physical input. However, we assume that product B was new, and there is less physical wastage in its production in year t+1. It will be possible to increase the number of units of B produced by more than the drop in the production of the number of units of A. Since we assume that dollar revenue paid for the two products is unchanged, it implies a drop in the price of B in year t+1.
Nominal GDP is unchanged, but the price level dropped. By implication, real GDP rose. By continuously creating new goods and services which enter the economy at a relatively high price level and then drop, the price level can be in a continuous state of deflation. (Note that the logic would break down if there was only a small fixed set of products that are produced each year with similar weightings; there are limits to engineering efficiency gains.) This allows real GDP to grow "forever", even with a fixed energy share of (nominal) GDP.

(I have not worked out the economy-wide calculations, and so I am unsure what happens to the ratio of the real energy component of GDP versus aggregate real GDP. I believe that it would collapse, as the rest of the economy is growing in real terms. But because of effects such as this, real GDP price levels are rebased every so often.  This rebasing shows up in things like referring to "GDP in chained 2009 dollars"; 2009 is the base year used for prices, and for that year, the weightings in real GDP of components of GDP will match that for nominal GDP. This means that in this example, the published data would revert to a 10% energy weighting in real GDP periodically.  Since the components of real GDP are not additive, there can be considerable drift in components that follow a price trajectory that diverges from the aggregate, such as computers.)

In the epilogue of his article, Professor Murphy noted that he was aware of possibilities like this:
So I can twist my head into thinking of quality of life development in an otherwise steady-state as being a form of indefinite growth. But it’s not your father’s growth. [emphasis mine - BR] It’s not growing GDP, growing energy use, interest on bank accounts, loans, fractional reserve money, investment. It’s a whole different ballgame, folks. 
Economies have switched over to a heavy weighting in services decades ago, and therefore most of the economy is insubstantial stuff like software. But the money earned by software companies matters. This creates some strange effects in real GDP calculations. But we cannot drop services out of GDP just to meet the biases of physicists who just want to focus on physical quantities.


* From the point of view of economics, adding "exponential" as a qualifier to "growth" is redundant, since economic growth rates are invariably presented as percentage growth rates. An economy growing in a linear fashion (for example) would have a "growth rate" that converges to zero.

See Also:

(c) Brian Romanchuk 2014


  1. Just discussing this with an engineer yesterday. His view is that real resources aren't so much the issue owing to technological innovation that can increase efficiency and produce substitutes. So we could still hit a more or less steady state in which a prosperous living standard is distributed globally and also enjoy a possibly rsing stand through innovation that increases efficiency.

    His concern is chiefly physical constraints like the Second Law and increasing heat. Using energy to do work results in entropy in the form of ambient heat in the environment. The planetary heat sinks are the large bodies of water, principally the oceans, and the atmosphere.

    At present, the oceans are bearing the brunt but as their waters warm up, increasingly that job will also fall on the atmosphere. Ambient heat cannot be packaged and shipped off into space. While there may be reason to believe it can be harnessed, so far there is no scalable method for doing so.

    So with the level of population and technology involving energy use, there's a real problem building with heat accumulation that is affecting climate and weather, as well as vital sources like water. This is already an issue.

    Secondly, electricity is a huge energy source and the fact that electricity is grounded results in Earth potential rise. The "danger zone" is generally limited and can be handled safely with care. However, no one really knows what the long term effects of small changes are.

    Same with all the wave emission now, which is greatly increasing with technology and no end it sight. It's true that the flux diminishes quickly from the source, with the square of the distance iaw the inverse square law. But there's still a lot of low level emission that no one really knows the effect of on biological systems that may be sensitive to small changes.

    Something similar is happening with GMO's. Some scientists I talk to are concerned that we are rushing into scaling up a technology that is not sufficiently tested which could have deleterious unintended consequences. One even turned back a sizable grant when he became concerned that potential risk was being intentionally ignored.

    Issues like these may be where we are like children playing with matches.

    1. In terms of children playing with matches, the worst examples appear to be in various types of pollution and even things like food additives. Things are better in the developed countries, but that is partially because the most toxic processing was outsourced to developing countries.

    2. "... Ambient heat cannot be packaged and shipped off into space ..."

      It can, ask Boltzmann.

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