Every theory or, to use the term famously coined by Thomas Kuhn, paradigm is based on a set of assumptions. Some assumptions are more, others less important for the overall theoretical system that is built upon them. This has to do with the ease with which they can (or cannot) be relaxed if shown not valid. It is, however, a truism that every model, theory or paradigm must be based on simplifying assumptions and that “closeness to reality” is seldom a relevant criterion for their evaluation (this latter statement must be, of course, qualified, which I will do below). Resource economics, i.e., the branch of economic theory that deals with the exploration, extraction and markets for (non-renewable) resources is no exception from this rule. One of my professors at the university used to present empirical findings regarding important assumptions of economic theory (such as the interest rate parity) by stating: “This is one of the few economic assumptions that stand up to reality.” The so-called Hotelling’s rule, one of the crucial models and assumptions of resource economics, is not one of those few.

What is the Hotelling’s rule (not to be confused with Hotelling’s law–it’s the same Harold Hotelling, but a wholly different issue)? It is the result of a formal model presented by Harold Hotelling, one of the luminaries of 20th century economics, in his 1931 publication *The Economics of Exhaustible Resources*. It might be considered the birth event of modern resource economics. Hotelling was interested in the way exhaustible resources are extracted by rational agents, and the effects of their respective calculus on social welfare. He built a model based on the following assumptions, most of which are typical for mainstream economic theory: the owner maximizes the net present value of the income he acquires by selling the resource; the discounting rate used to calculate the net present value is the market rate of interest; the resource’s owner and the resource itself have the same lifetime; the amount of the resource is known; demand is time-independent (i.e., demand today is not influenced by demand yesterday). The results of Hotelling’s model are incorporated in many resource economic models (including integrated assessment models of climate change) until today. Its central result is that the extraction rate of an exhaustible resource is monotonously sinking, while its price is increasing. The process’s pace is determined by the market rate of interest (the actual Hotelling’s rule). So, everything is nice and clean–but for the fact that empirical observations do not confirm the rule. As can be seen in the figure below, world market prices of the most important non-renewable resources have been floating up and down, with no significant long-term trend identifiable.

How is it then with the assumptions made by Hotelling? Why doesn’t his formally oh-so-nice model work as expected? Well, to answer this it might be a good idea to first consider what epistemology, i.e., the branch of philosophy that deals with how knowledge is created, tells us about assumptions. Basically, three broad classes of assumptions can be distinguished: negligibility assumptions, domain assumptions and heuristic assumptions. Negligibility assumptions are the classic case when the researcher thinks or knows that a certain variable has no significant effect on the process of interest (say, the influence of the number of sunspots on the choice of travel mode by commuters). In the language of econometrics, we might also speak of a zero restriction. Such assumptions may be arbitrarily “unrealistic” since they do not influence the model. Domain assumptions are epistemologically more problematic, they are close to “immunization strategies” in the sense of Karl Raimund Popper: the researcher may restrict the validity of his model to a certain “domain” if he recognizes that it has no universal validity. Heuristic assumptions are known to be wrong in the sense of negatively influencing the explanatory power of a model–but they are used in order to extend the model: first, the model is built with the heuristic assumption which then is relaxed to show what difference this relaxation makes. And then, of course, there are assumptions which simply are not valid: they negatively influence the explanatory power of the model but are not relaxed for whatever reason. Hotelling’s rule, when used as assumption in modern models, is an invalid assumption:

The assumptions [of the authors’ model] are obviously debatable a priori and they also have some implications that are difficult to reconcile with historical data. In particular, they imply that aggregate fossil fuel use should follow the famous Hotelling rule, which implies falling quantities and increasing prices, a pattern notoriously at odds with reality. [Source]

The reason why this is so lies in Hotelling’s own assumptions, which he built his model upon. Two of them are crucial and have been criticised by other scholars. First, Hotelling assumed that the owner of the resource in question has the same lifetime as the resource and that he will retain the ownership over that time span. Second, he assumed that the amount of the resource is perfectly known.

Hans-Werner Sinn, an acknowledged German economist, once has shaken up the climate change debate when he criticised standard economic models of climate change for ignoring the supply side in energy markets. According to him, most climate policy measures are directed towards demand/consumption of energy–be it taxes, cap-and-trade systems etc. However, if supply is not elastic, i.e., if e.g. the OPEC countries do not adjust their supply to changes in demand (and thus prices), demand-based policies will be ineffective, as they will only lead to demand shifts (e.g., from European towards East-Asian consumers)–unless, of course, the policies have global reach, as then there is no place demand could shift to. Sinn based his argumentation on the observation that property rights over crucial fossil fuels–particularly petroleum–are anything but stable. A large part of the world’s fossil fuel reserves are located in politically unstable regions (particularly the Middle East, the Niger delta and the Maghreb). The stability of ownership cannot thus be assumed, and so we cannot take for granted–as Hotelling did–that resource owners will response to changes in market prices/reserves as rational choice theory predicts. But if they don’t, the Hotelling’s rule is likely invalid.

Another weakness of the Hotelling model was pointed out, among others, by the Swiss economist Hans Christoph Binswanger in his book *The Growth Spiral* (*Die Wachstumsspirale*). When we talk about non-renewable resources, two processes are important: exploration and extraction. Hotelling ignored the former, focussing entirely on the latter. The extraction of resources changes the amount of reserves in that it reduces them–the more is extracted, *ceteris paribus,* the less is left in the ground. But no resource extracting company will limit its activities to extraction–they undertake exploration as well, i.e., they search for new reserves. Thus, exploration has an effect on reserves that counteracts that of extraction–it increases their amount. There are many different mechanisms that can lead to an increase in reserves: new ones may just be found where no-one had expected them; but technological progress and price increases, too, may make formerly marginal resources profitable. The assumption that we know in advance how much resource we are going to extract over the years is extremely problematic. And this leads to a difference, pointed out by Binswanger, between the expected and the realized extraction/price path. At every single point in time, a rational resource owner will, based on his knowledge about the amount of the resource, expect this amount to decrease continually and the price to rise accordingly. This is what Hotelling assumed. However, as in every period the known reserves change due to exploration, the realized path will not follow the expected path. And therefore the whole Hotelling’s rule will not work in reality.

As suggested by the quotation above, resource economists are aware of the problem. Nevertheless, so far no satisfactory alternative to Hotelling’s rule has been found–and thus, this highly problematic assumption continues to be included in models which influence some of the most important environmental debates of our time.

**Literature**:

- Alan Musgrave (1981): ‘”Unreal Assumptions” in Economic Theory: The F-Twist Untwisted’.
*Kyklos*34(3). pp. 377-387. - Hans Christoph Binswanger (2012): ‘The Growth Spiral: Money, Energy, and Imagination in the Dynamics of the Market Process’. Berlin/Heidelberg: Springer.
- Hans-Werner Sinn (2008): ‘Public policies against global warming: a supply side approach’.
*International Tax and Public Finance*15(4). pp. 360-394. [open access]