Economists need taught about physical constraints - but physicists need to learn about prices

Another excellent post from Tom Murphy entitled "Exponential Economist Meets Finite Physicist" is causing some interest. In the post the point is made that exponentially increasing use of energy is impossible, and that economic growth without energy use growth is difficult to imagine. These issues need to be more widely considered within economics, especially in these times of depressed output amid high energy prices. They are not simply for 400 years hence but are worth considering now - see relatively recent New Scientist article "How Clean is Green Energy?".

However certain points are made in the post that I don't think are justified and which are the sort of thing that is frequently stated without sufficient analysis at (informative and interesting) places like The Oil Drum and Our Finite World.

First of all, it is asserted that "If the flow of energy is fixed, but we posit continued economic growth, then GDP continues to grow while energy remains at a fixed scale. This means that energy—a physically-constrained resource, mind—must become arbitrarily cheap as GDP continues to grow and leave energy in the dust." This cannot be simply asserted - within most models it's simply not true, and the models in which it is true are the most unrealistic models (we would need elastic substitution of energy and other factor inputs but it appears that other factors can only substitute for energy on a very inelastic basis).

The baseline, first-order model of economic growth is the Ramsey model with Cobb-Douglas production and logarithmic utility (which the representative agent maximises in order to make consumption/investment decisions). If we suppose a constant returns to scale Cobb-Douglas production function with labour (fixed), energy (fixed) and capital (endogenous) subject to some exponentially growing productivity (*), then we derive a balanced growth path in which output, consumption and capital stock all grow at the rate of productivity growth (despite fixed labour and energy implying effective diminishing returns). The prices of the factors of production on the balanced growth path in this model are: constant for capital (i.e. interest rate is a positive constant); exponentially growing (at the rate of productivity growth) for energy and labour. This is because under Cobb-Douglas production, factors earn a constant share of output i.e. payments to energy are constant as a share of output, but the quantity of energy used is constant whilst output is exponentially growing: therefore energy's price must be exponentially growing.

So the first order model for describing economic growth predicts that if we had an economy with fixed energy inputs but positive economic growth, then energy prices would be growing, not falling. The post then relies on a floor for energy prices as it's mechanism in generating subsequent phenomena: but economic growth with constant energy input implies growing prices that do not run into this floor constraint, so the rest of the argument does not necessarily follow.

The post then also repeats various assertions that have been made for a steady state economy: "it’s not your father’s growth. It’s not ... , interest on bank accounts, loans, fractional reserve money, investment." I'm not sure where the idea comes from that a positive rate of interest on bank accounts relies on economic growth, but it's a meme that I've seen expressed before. It doesn't seem logical to me: a simple case is a model of generations in which the young work, consume and save (i.e. make loans) whilst the old consume out of their savings. These savings/loans are just pieces of paper so in reality the young work and their earnings provide the consumption goods for themselves and the older generation. The interest rate on the savings is just a price(**) that agents take when splitting their consumption from their own earnings into consumption whilst young and consumption whilst old - a high interest rate is perfectly compatible with a steady state economy if agents have a high rate of time preference. Fractional reserve banking likewise has nothing to do with economic growth. 

The post is fantastic at outlining an issue that economists have not grappled with, but in considering the economic impacts of the issue, the article makes clear a need for economists to provide some of the analysis!

(*) I'm not saying that this is a good model of long term growth, in particular I agree with this criticism of Noah Smith: "

Step 1: Take the parts of the economy you can't explain (i.e. the residuals) and label them either "culture" or "technology".
Step 2: Make ultra-confident pronouncements about the future behavior of culture and/or technology.
What I don't like, first of all, is that Step 2 just never makes any sense. The thing you are calling "culture" or "technology" is precisely the part that you couldn't explain with your models. Hence, it is the least likely thing for you to be able to predict going forward.
Admit it, economists: You don't know what is going to happen with technology. You don't know what is going to happen with culture. If you did, you would have included those things as endogenous variables in the model instead of simply labeling the residual."

(**) Though in steady state equilibrium it will be a positive function of both the growth rate and the rate of time preference.

The worst policy prescription

Former MPC member Andrew Sentance, has an article in the FT today in which he recommends a 'leaning against the wind' policy of raising interest rates to curb that inflation whose underlying cause is an excess of demand for energy over the available supply. This is the worst advice imaginable and seems to be driven by (a) considering this as purely a problem of excess demand; (b) the assumption that interest rate policy has no impact upon long run supply (so that central banks can concentrate solely upon managing inflation expectations).

However, the world's oil supply has stagnated with essentially zero growth in supply since 2005. Alternatives are difficult and so we can expect an extended period with little energy supply growth. It's facile to state, as Sentance does, that the inflation is "responsible for the slowdown in global growth". This gets causality backwards: to first order, growth in output is only possible with growth in energy inputs. With constant energy inputs, we cannot expect growth in output, so strengthening demand has to lead to higher prices rather than expanded output. The supply restrictions have caused the growth shortfall and the rise in prices, rather than the rise in prices causing the growth shortfall.

If energy supply stagnation leads to higher prices, how should we respond? I would recommend whatever policy response leads to fossil fuel substitutes being incentivised as quickly as possible. Sentance's prescription is higher rates - does this work? Higher rates depress demand, lowering energy prices and hence lowering incentives to invest in fossil fuel alternatives. Higher rates provide a higher yield on alternative investments to new energy infrastructure projects, raising the hurdle rate that these projects must achieve, lowering the incentive to invest in fossil fuel alternatives.

Sentance has it backwards: raising rates may well be the appropriate response to inflation caused by domestically generated wage-price spirals, but it is completely the opposite response to that required to the problem of global energy supply stagnation. The fact that we are running into supply constraints needs to be strongly signalled through the price mechanism so that there are incentives to invest in mitigating technologies. Interest rate rises are a demand depressing response to energy supply constraints. Since energy supply constraints will get worse over time if we do not develop alternatives, a policy which causes a contraction in demand rather than stimulating an alternative supply is a prescription for long term decline.

Phase Changes in the Oil Market

There was a recent flurry of interest (see e.g. Skeptical Science and Dosbat) in response to a Nature article "Climate policy: Oil's tipping point has passed" (behind a paywall), the gist of which is that the oil market has undergone a 'phase change' from a market in which supply grew in response to price increases, to a market in which supply is essentially constant but "prices swing wildly" in response to demand changes. See diagram below. 

The 'phase transition' terminology is by analogy with physics (in particular, but not limited to, the physics of solids, liquids and gases) and is a phenomenon that can be seen in other complex systems (e.g. the transistion from free flowing to congested traffic). As complex systems, clearly economic systems could be subject to the same phenomena. Multiple steady state models are perhaps the best examples of economic models that could fit this analogy, and I have done some work on such a multiple steady state model of the oil market exactly to explore this issue.

I initially came to the problem after reading Prophets of doom: the secrets of Soothsaying in the New Scientist in February 2011 which outlined the technique of detecting transitions between different steady states by observing 'Critical Slowing Down'. I then did some work in December 2011 on this (see paper (it's not reached the quality required be described as a working paper yet) and slides). I did not find any evidence of critical slowing down, or by implication, of a phase change as supplies plateaued. My explanation of this (negative) result is that a phase change would be due to some change in supplier behaviour, rather than being associated with a geological inability to increase supply. The shift in supplier behaviour in such a phase change would lead to a jump in the steady state e.g. from low price high quantity, A, to high price low quantity, B, in the diagram below:

We do not see this phase change, and so (potentially) only geological explanations remain. A geological explanation is consistent with a monotonic, but at some point very (infinitely) steep, supply curve, and no phase change.

I wanted to highlight the work I had done on this for two reasons: (a) there was the flurry of interest created by the Nature article that came after I had done my work; (b) I then read Noahpinion's Sketch of a model of higher education where he says "Anyone can, of course, feel free to take this model and run with it if you like it (and if you do, feel free to include me as a co-author, or not, as you like)."

This is kind of where I am with this project: I found no evidence to support any suggestion of a 'phase change' - which I thought was an outlandish idea that might just be true. A negative result though was, I thought, equivalent to stating "No evidence found for phenomenon that no-one thought would be there anyway", which I surmised would not be a very interesting paper. However, given the Nature paper, clearly this is an idea that people are proposing and so perhaps my rejection of it is of interest? And in case I don't get round to working on this before somebody else does, this blog post is, to some extent, stating my claim to the idea. I would modify Noah Smith's quotation to read "Anyone can, of course, feel free to take this model and run with it if you like it - and if you do, please consider including me as a co-author!"