A Valuation Case Study: the Great Barrier Reef

Posted on July 15, 2017 by Adam Bailey

A valuation of the Great Barrier Reef illustrates many common issues in the economics of environmental valuation.

A recent report by Deloitte Access Economics (1) estimates the asset value of the Great Barrier Reef at A$56 billion (2).  This is the sum of:

  • Value to local recreational users and tourists from elsewhere in Australia: A$32 billion, estimated by the travel cost method (pp 39 & 40).
  • Value to Australians of the Reef’s existence, regardless of having visited it or intending to do so; A$24 billion, estimated by contingent valuation (p 34).

The main data source was a representative survey of over 1,000 Australians (p 30). The survey also included 500 residents of 10 other countries world-wide.

The report also identifies the following components of value for which it does not offer numerical estimates:

  • Value to tourists from outside Australia: not estimated due to data limitations (p 85).
  • Existence value to non-Australians: not estimated as difficult to allow for contextual cultural factors, language barriers and purchasing power differences in using survey responses from some countries (p 35).
  • The value of certain ecosystem services provided by the Reef such as maintenance of water quality and storm protection for the adjacent coast (pp 40 & 42): not estimated as difficult to separate from ecosystem services provided by neighbouring terrestrial and river ecosystems (p 84).
  • “Traditional owner value” to peoples who have lived in the vicinity of the Reef since before Australia was settled by Europeans, relating to cultural heritage, sacred sites and archaeological sites: not estimated because such unique sites lack the substitutability on which non-market valuation relies (pp 45-7).
  • Brand value, that is, the contribution of the Reef to “Brand Australia”. This is given a whole chapter of the report (pp 50-7) which is not easy to summarise.  One key point is how far the contribution is from the existence of the Reef and how far from perceptions of Australia’s performance as guardian of the Reef (p 56).

Taking the above together the report suggests, reasonably, that the full value of the Reef is much more than A$56 billion.  Some, though not all, of the points below tend to reinforce that conclusion.

There are other components of value which the report does not mention.  One is the possible medicinal use of plants and animals found in the Reef (3).  A negative component – illustrating the general point that natural capital is often associated with natural hazards  –  is its role as a shipping obstacle and hazard (4).

As is common with environmental valuation studies, therefore, the components of total economic value fall into three categories: those that can be measured with the available data; those that are in principle measurable but for which the necessary data is difficult to obtain; and those that are intrinsically unmeasurable (but still perhaps important).

As a contingent valuation sceptic (see this post), I would have been inclined to put the existence value of the Reef in the unmeasurable category.  A specific difficulty with the approach adopted is that respondents were asked how much they would be willing to pay weekly to “guarantee” that the Reef is “protected”, having been told that such a payment would be in the context that all Australians would have to pay (p 80). This is a strange question given that global climate change is a major threat to the Reef.  It seems quite possible that some respondents viewed the payments as to guarantee that the Australian government would do what it could to protect the Reef (eg from risks originating within Australia such as mining activity), while others viewed them as guaranteeing the preservation of the Reef, implying protection against all risks including climate change.

The remainder of this post considers the method used to estimate the value of the Reef to tourists from within Australia. The individual version of the travel cost method was used, given that individual data was available and showed good variation between individuals in visit numbers (p 78), so that it could be expected to give more precise results than the alternative zonal method (5).  The variation between individuals was not just due to luck: it was facilitated by the decision to ask respondents how many times they had visited the Reef in the last five years (not merely the last year).

With the individual method, the first step is to regress individual visit numbers against individual travel costs to the Reef and other variables that may influence visit numbers.  The report does not state the full regression model, but from the survey questions (pp 76-82) it appears that the other variables included age, gender and education.  Variables that seem not to have been included are income and travel costs to one or more substitute sites.  Although income is mentioned in discussion of the method (p 85), there is no indication that income data was collected.  This may have been because it was anticipated that such data would be difficult to obtain (US studies often collect income data but it may be that willingness to disclose one’s income varies between cultures).  The issue of substitute sites may have been ignored because of the complexity of allowing for many possible substitutes, and lack of consensus in the literature as to how this should be handled.  Whatever the reasons, omission of these variables can result in omitted variable bias leading to a biased estimate of the travel cost coefficient and hence of the site value, although the magnitude and direction of bias will depend on the circumstances (6).

Mention of substitute sites may seem surprising given the unique nature of the Great Barrier Reef.  But a substitute, in economics, does not have to be a perfect substitute.  One definition is that two goods are substitutes if their cross-elasticities of demand are positive.  Applied to two tourist sites, that would be the case if a higher travel cost to either were associated with a higher demand for visits to the other – a plausible scenario.

The decision effectively to ignore travel time (p 85) is surprising. Common practice is to include the value of time as well as expenditure on transport and accommodation within travel cost to the study site.  The report cites three Australian studies which applied a zero value to travel time, but this is rather selective even among Australian studies (7), and certainly not representative of the global literature including US and UK studies.  Admittedly there is no consensus on how the value of time should be determined.  But to assume a nil value is likely to result (other things being equal) in under-estimation of the value of the Reef.  A fairly simple and still conservative alternative would have been to value time at a suitably small fraction (say a quarter) of the average hourly wage, and to include the effects of different fractions in the sensitivity analysis.

The statistical methods used to estimate the trip-generating function and then derive the value (consumer surplus) per visit (A$662) are not described in full, but appear from the outline provided (pp 85-6) to have been appropriate.  As is common in individual travel cost studies, negative binomial regression was used because of overdispersion (p 86), which is a slightly misleading term for a feature (not a defect) often found in the distribution of individual visit numbers, namely that the variance is greater than the mean.

I would have liked to see some consideration of what potential visitors might have done instead if the Reef had not existed.  Many would probably have visited other tourist sites, increasing the value of those sites and offsetting to some degree the lost value associated with the Reef.  A case can be made that the most useful concept of value for a recreational site is not the gross site value but the contribution which the site makes to the total value of all such sites (8).

To obtain the total annual value to tourists, value per visit was multiplied by the annual number of visits to the Reef, which was estimated as 2.3 million (p 86).  This number was inferred from Tourism Research Australia (TRA) data on numbers of visits within Australia to regions adjacent to the Reef.  However, these numbers include visits to the regions but not to the Reef itself, and some crude round-number assumptions, claimed to be conservative, were made to eliminate such visits (p 86).  An alternative approach would have been to include in the survey a question designed to distinguish visits to the Reef itself from visits to the adjacent regions, and to use that data to estimate, for all visitors to those regions, the proportion who visit the Reef itself.

The final step was to capitalise the stream of annual values so as to obtain the asset value.  The result is heavily influenced by the choice of time horizon and discount rate, as is illustrated by the sensitivity analysis (p 88).  A time horizon of 33 years was adopted, one stated reason being the severe threats to the future health of the Reef (pp 87-8).  Within that time frame, annual consumer surpluses as calculated from the survey data were discounted at a rate of 3.7%, determined using the Ramsey formula (p 87):

Social discount rate  =  Rate of time preference + [Annual growth rate of consumption

                        x Minus the elasticity of marginal utility with respect to consumption]

Given assumptions of a very low rate of time preference (0.05%) and an elasticity of 1, the discount rate largely reflects the growth rate of consumption, which was assumed to equal the average GDP growth rate over the previous 30 years (which can be inferred to have been 3.65%).

While the particular figures used in the capitalisation could be challenged, there are some more fundamental issues here.  One could value the Reef on the assumption that it will degrade along a defined path, or on the basis of its remaining in its current condition.  The key question here is not which of these scenarios is more likely, but which basis of valuation will yield more useful information.  If what we are interested in is the value which is potentially at risk from degradation of the Reef, then it is valuation on  the ‘current condition’ basis which is more useful, and the ‘degradation’ argument for the 33-year time horizon does not apply.

Whether future economic growth is likely to be at a similar rate to that of the previous 30 years can be debated.  My instinct would be to calculate the central estimate of value on a zero-growth basis, and to consider the effect of positive rates within the sensitivity analysis.  If, however, a positive growth rate is assumed, then for consistency it needs to be considered that, since expenditure on tourism is discretionary, demand for tourism is likely to be highly income-elastic.  Subject to the condition of the Reef,  and to the adequacy of infrastructure to accommodate visitors, demand for visits might be expected to grow even faster than GDP.  The report, however, does not consider whether the number of visits to the Reef may change in future.  The implicit assumption is that annual visits and annual consumer surpluses will remain as estimated (9).

Notice that the combination of a very low rate of time preference and a zero rate of economic growth will yield, via the Ramsey formula, a very low discount rate.  In conjunction with a long time horizon this could imply an asset value many times higher than the report’s A$56 billion.

Notes and References

  1. Deloitte Access Economics (2017) At what price? The economic, social and icon value of the Great Barrier Reef  https://www2.deloitte.com/content/dam/Deloitte/au/Documents/Economics/deloitte-au-economics-great-barrier-reef-230617.pdf   All page references are to this report.
  2. A$ = Australian dollars. A$56 billion is equivalent to GB£33 billion or US$43 billion.
  3. Bruckner A (2002) Life-Saving Products from Coral Reefs Issues in Science and Technology XVIII(3) http://issues.org/18-3/p_bruckner/
  4. See for example The Guardian (6/4/2010) The Great Barrier Reef scandal https://www.theguardian.com/world/2010/apr/06/great-barrier-reef-ship-aground
  5. King D M. & Mazzotta M Ecosystem Valuation – Options for Applying the Travel Cost Method  http://www.ecosystemvaluation.org/travel_costs.htm#OPTIONS
  6. Re omission of substitute site variables see Caulkins P, Bishop R & Bouwes N (1985) Omitted Cross-Price Variable Biases in the Linear Travel Cost Model: Correcting Common Misperceptions Land Economics 61(2) pp 182-7
  7. Two Australian studies which applied positive values to travel time are: a) Lansdell N & Gangadharan (2003) Comparing Travel Cost Models and the Precision of their Consumer Surplus Estimates: Albert Park and Maroondah Reservoir Australian Economic Papers 42(4) p 403  b) Whitten S & Bennett J (2001) A travel cost study of duck shooting in the Upper South East of South Australia  Private and Social Values of Wetlands Research Reports No. 7  https://crawford.anu.edu.au/pdf/staff/jeff_bennett/wtlndrr07.pdf
  8. This point is briefly noted in Bateman I (1993) Valuation of the environment, methods and techniques: revealed preference methods, in Turner R (ed) Sustainable Environmental Economics and Management: Principles and Practice Belhaven Press, London  pp 218-9
  9. This is shown by the fact that a stream of consumer surpluses of A$662 x 2.3 million = A$1.523 billion annually for 33 years, discounted at 3.7% per annum, approximates to the A$29 billion stated on p 39.
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Energy and Environment in China

Posted on May 27, 2017 by Adam Bailey

Arthur Kroeber’s book on China’s economy includes an excellent section on energy but a rather selective account of its environmental issues.

Arthur Kroeber’s book China’s Economy in Oxford University Press’s What Everyone Needs to Know series (1) deserves a wide readership.  Admittedly it’s rather dry: those who like their reading on serious and important topics to be spiced with anecdotes or cultural references had better look elsewhere.  But for the general reader (in English) who wants to understand China’s development and possible future – to go beyond journalistic impressionism and simplistic or politically-motivated judgment – I doubt whether there is anything better.  This is a properly researched book at a well-chosen level, a serious piece of description and analysis which avoids over-technicality.  The chapter on ‘Changing the Growth Model’, for example, makes extensive use of key ratios such as the capital-output ratio while avoiding the complexities of, say, total factor productivity.  The tables and charts are helpful and not overdone. Also helpful is the division of each chapter into sections headed by questions.  Sensitive issues such as corruption and possible exchange rate manipulation are treated in a fair-minded and temperate manner.

A full review would be beyond the scope of this blog, but I offer here some comments on Chapter 8 entitled Energy and the Environment.

Starting with energy, I commend the book for using consistent, well-defined and sensible units (p 150).  Writings on energy often confuse matters by switching between different units, using vague units (“enough to power a million homes”) or, worst of all, failing to distinguish between units of energy and units of power (2).  By contrast, Kroeber sets out very clearly the main facts of China’s energy use. The total in 2014 was 22 billion barrels of oil equivalent, as compared with 17 for the US, 12 for the European Union and 95 for the whole world. Of China’s 22, 14 are from coal (which is about half of world coal consumption) and another 5 from other fossil fuels, underlining the importance of China in worldwide efforts to address climate change by limiting greenhouse gas emissions.

Kroeber also presents two important per unit measures of energy use.  As might be expected given China’s huge population, its per capita energy use is not especially high: much less than the US, less than the EU, and only slightly above the world average. More surprisingly, perhaps, China’s energy use per unit of output (GDP), also termed energy intensity, is more than twice that of the US and the EU, and almost twice the world average.  This is despite considerable improvements in energy intensity already achieved, eg a 19% improvement during 2005-2010 after the government had set energy efficiency targets for large firms in heavy industry (p 160).

China’s high energy intensity calls for explanation, and Kroeber identifies three causes (pp 150-2 & 161).  One is the structure of its economy, with industry accounting for a high proportion of output, agriculture smaller proportionally than in many poorer countries, and services as yet smaller proportionally than in most developed countries.  Because industry is more energy-intensive than agriculture or services, and because a high proportion of China’s industry consists of especially energy-intensive heavy industry such as steel and cement manufacturing supporting its housing and infrastructure boom, its overall energy-intensity is high.  A second cause is China’s unusually high reliance on coal, which is a less efficient energy source than natural gas for generating electricity.  This is a consequence of the geographical accident that it has large reserves of coal but much less oil and gas.  The third cause relates to the efficiency with which China uses its energy sources. Here the picture is mixed.  Many of China’s coal-fired power stations have been built relatively recently to modern standards, and are somewhat more efficient than older power stations in the US.  Its fuel efficiency standards for vehicles compare reasonably well with those in developed countries. However, the energy efficiency of homes and offices is often poor, and many old, unprofitable and energy-intensive industrial plants have been kept open by local governments seeking to maintain employment and tax revenues.  Energy prices, though not especially low by international standards, are subject to controls which can reduce incentives to make energy-saving investments.

Kroeber does not attempt to quantify the overall effect of these causes, but it does seem plausible that together they go a long way towards explaining China’s high energy intensity.  A point he might have added is that the annual temperature range in much of China is such that homes need both heating in winter and air-conditioning in summer.

Like many countries, China has sought to diversify its energy sources in order to reduce its reliance on coal which is both a major source of local air pollution and a major contributor to global greenhouse gas emissions (pp 152-4).  It has become a major oil importer (although the IEA’s statistics do not seem to support Kroeber’s claim that in 2013 it became the world’s largest (3)).  It also imports natural gas.  Over the last decade, China has more than doubled its output of nuclear power and hydropower, and increased its output of electricity from renewables almost twentyfold.  However, the effect of all this in reducing coal’s share of China’s energy mix has been relatively small. In absolute terms coal consumption has continued to grow (from which it may be inferred that China’s overall energy use has also been growing).  Its coal consumption may now be close to peaking, although Kroeber advises caution on this point, both because of the short-term effect of macroeconomic fluctuations on energy demand, and because of possible under-reporting of output by smaller coal mines.

Kroeber states, correctly, that China produces over 90% of the coal it uses, and that its coal imports are only a modest proportion of its total use.  It might be added that in the context of world trade in coal, China is nevertheless a major player, and was the largest importer in 2014 (4).  Because its imports are the difference between two huge numbers (its demand and its domestic production), there is considerable potential for fluctuations in its imports to have a major impact on the pattern of trade in coal.

Because of its huge energy consumption and reliance on fossil fuels, China is the world’s largest emitter of greenhouse gases, accounting in 2012 for 24% of the global total.  Kroeber considers, but seems to me to do less than justice to, the fact that some of China’s emissions relate to the production of goods for export, and arguably should be attributed to the importing countries in any international apportionment of responsibility for climate change (pp 154-5).  I cannot see why he links the issue to that of multinational companies moving their production to China, as if exports produced by Chinese companies are irrelevant in this context.  He also states that most of China’s emissions relate to heavy industries supporting domestic construction and not to export industries.  It would have been useful to have quantified or given a source for this claim, and to have noted that domestic construction includes construction of factories producing goods for export and transport links to carry such goods.

Turning to other environmental issues, the book focuses mainly on the much-publicised issue of air pollution, treating other issues only indirectly via an environmental performance index.  Understandably perhaps given the broad scope of the book, it says little about soil and water other than noting their “extreme degradation” due to industrialisation (p 155).  A fuller treatment would have considered each of the following, and efforts to address them: soil erosion (5), soil pollution (6), reduced river flows (7), depletion of groundwater (8), and water pollution (9).  These are not minor or merely local issues.  Unless effectively addressed, they have the potential to constrain China’s food production and so increase its demand for food imports with impacts on world food prices (10); and the costs of addressing them are likely to divert significant resources from elsewhere in the economy.

As in other countries, air pollution in China includes both gases – notably sulphur dioxide – and particulates of various sizes.  Over 50% is attributable to burning of coal, 15-20% to vehicle emissions, and the remainder to other sources (pp 159 & 161).  Although Kroeber seems to suggest that the problem is most serious in Beijing and other northern cities (pp 155 & 161), he does not offer a systematic description of the geographical pattern of air pollution.  If, as seems likely, the air is cleaner in much of the countryside, then that surely needs to be taken into account in any assessment of rural-urban inequality (a topic discussed by Kroeber elsewhere in the book (pp 30-5))?

China has made some progress in addressing air pollution in that emissions of sulphur dioxide have been reduced, although concentrations of small particulates have continued to rise (p 161).  What progress there has been seems to have been achieved largely via improvements in energy efficiency and some diversification away from coal as described above.

Kroeber rightly rejects the idea that China’s environmental problems are “uniquely attributable” to its growth model or political system, pointing out that Japan, the UK and the US all experienced severe air pollution in the mid-twentieth century (p 156).  He argues however that its problems are particularly severe for a country at its stage of development.  As evidence for this he presents a version of the Environmental Kuznets Curve (a formulation of the tendency for countries to give a higher priority to environmental issues as they become richer), plotting scores on Yale University’s Environmental Performance Index (EPI) (11) against gross national income for 30 of the world’s most important countries (p 157).  This shows a fairly clear relation between EPI and income, albeit with, as is to be expected, some spread of points about the line of best fit.  China’s EPI  score is some 14% less than might be predicted from its income level.

Kroeber suggests that this can be explained in terms of China’s political system, its ‘East Asian’ approach to development, with an unusually high premium on maximising economic growth, and its aspiration to be a superpower (pp 157-8).  This seems questionable.  A possible alternative explanation starts from the fact that environmental improvement is usually a gradual process. This is for various reasons: some pollutants have a finite life over which they gradually degrade; fish stocks take time to recover from a pollution incident; newly planted trees take many years to mature; and so on.  When a country initiates the sort of environmental improvements typical of its income level, therefore, it is likely to take some years for the full benefit to be realised.  If the country’s economy has grown rapidly, as China’s has, then this time lag may result in a lower EPI score than that of another country which has a similar income level but has reached that level more gradually.  If for example countries A and B have similar income levels but A’s economy has grown annually at 8%  and B’s at 1%, then an average time lag of about 2 years would be sufficient to give A a score 14% below B.

Looking to the future, addressing air pollution is now a stated priority of the Chinese government (p 159).  The main policy instruments likely to be used are stricter environment laws and stricter enforcement.  Other approaches used in western countries, such as emissions trading schemes and class-action lawsuits against polluting companies, Kroeber suggests, are unlikely to be successful in the Chinese context (p 158).  On the other hand, the fact that a high proportion of emissions are from a small number of heavy industries may make the problem easier to address, especially, it might be added, as some of the companies in those industries are state-owned (p 100).  At any rate, Kroeber is optimistic that the next few years will see accelerated progress against air pollution.

Notes and References

  1. Kroeber, A R (2016) China’s Economy: What Everyone Needs to Know Oxford University Press.  Page references in the text are to this book.
  2. Difference Between Energy and Power http://www.differencebetween.net/science/difference-between-energy-and-power/
  3. International Energy Agency Key World Energy Statistics 2015  p 11 ftp://ftp.energia.bme.hu/pub/energetikai_alapismeretek/KeyWorld_Statistics_2015.pdf
  4. International Energy Agency, as 3 above, p 15
  5. Xinhuanet (15/3/2017) Central China Province to Spend 2 Billion Yuan on Erosion Control http://news.xinhuanet.com/english/2017-03/15/c_136131474.htm
  6. Xinhuanet (18/1/2017) China Sets Up Lifelong Accountability System to Control Soil Pollution http://news.xinhuanet.com/english/2017-01/18/c_135994290.htm
  7. Earth Observatory Yellow River Delta https://earthobservatory.nasa.gov/Features/WorldOfChange/yellow_river.php
  8. Qiu J (13/7/2010) China Faces Up to Groundwater Crisis Nature News  http://www.nature.com/news/2010/100713/full/466308a.html
  9. Xinhuanet (22/4/2014) China’s Underground Water Quality Worsens: Report http://news.xinhuanet.com/english/china/2014-04/22/c_126421022.htm
  10. OECD-FAO (2013) Agricultural Outlook 2013-2022 Chapter 2 Feeding China: Prospects and Challenges in the Next Decade  See especially Risks and Uncertainties pp 83-7  http://www.oecd.org/berlin/OECD-FAO%20Highlights_FINAL_with_Covers%20(3).pdf
  11. Yale University Environmental Performance Index  http://epi.yale.edu/
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Net National Product and Sustainability

Posted on May 17, 2017 by Adam Bailey

National product, calculated net of a deduction for depletion of natural resources, could in theory provide some indication of whether current consumption is permanently sustainable.  But the conditions that would be needed to make net national product into a practical sustainability indicator cannot be met.

When gross national product (GNP) and related economic aggregates were first developed by Kuznets and others in the 1930’s and 1940’s, there was debate as to whether the aim should be to measure activity and output, or welfare and well-being.  Against a background of mass unemployment and then World War II, the debate was won by those who wanted the former (1).  To this day, GNP as calculated in most countries remains a measure of activity and output, and (as many critics have pointed out) it is easy to find examples of activities which raise GNP but do not enhance and may even lower welfare.

It has always been recognised that net national product (NNP), which equals GNP less an allowance for depreciation of capital assets is in some ways a more meaningful measure. Most countries publish estimates of NNP as well as GNP.  Nevertheless, most economic discussion focuses on gross aggregates, including GDP (gross domestic product, which is similar to GNP but excludes certain international income flows).  This seems to be partly because of the short-term link between activity and employment, and partly because of difficulties – both conceptual and practical – in measuring depreciation (2).

In the 1970’s, growing interest in environmentalism and concerns regarding resource depletion (3) led some economists to explore long-term macroeconomic models in which the essential inputs to production include non-renewable natural resources.  This led to the idea that NNP might be adapted – by including a suitable deduction for resource depletion –  to provide an indicator of sustainability.  Much of the academic literature on this topic stems from Weitzman’s 1976 paper On the Welfare Significance of National Product in a Dynamic Economy (4). 

Weitzman explored the properties of NNP within a long-term model whose assumptions included the following (5):

  • A single consumption good (or a single number representing consumption).
  • Many capital goods, taken to include not only equipment and infrastructure but also human capital and non-renewable natural resources.
  • A production possibility set determined as a function of the available capital goods.
  • A fixed own rate of interest r on the consumption good.

NNP was taken to be measured as consumption plus the value of net investment in capital goods.  For a non-renewable resource, it would include a deduction for any depletion. 

Given initial quantities of the capital goods, there can be determined within the model an optimal consumption stream, that is, one which maximises the discounted present value of future consumption, taking the fixed own rate of interest as the discount rate.  To achieve that path requires an optimal balance at all times between consumption and net investment and, within net investment, between investment in and depletion of the various capital goods.

Whatever the present value of the optimal consumption stream may be, there must exist a rate of consumption which, if maintained constant forever, has the same present value.  Weitzman calls this the stationary equivalent of future consumption: others have called it, more conveniently, constant-equivalent consumption, and I shall use the latter term here. 

We can now state Weitzman’s main conclusion as follows: NNP equals constant-equivalent consumption (6). I shall refer to this as Weitzman’s equality.  His formulation of the equality (7) shows that NNP depends on the discount rate, so it is appropriate to write NNP(r); constant-equivalent consumption, being calculated from the optimal consumption stream for a particular discount rate, also depends on the discount rate.

The impact of Weitzman’s paper went beyond the academic literature.  It was an important influence on Nature’s Numbers (1999), a report commissioned by the US government on expanding the US national accounts to “include the environment” (8).  According to this report:

“One of the most surprising results of modern economic theory is the output-sustainability correspondence principle …. This … holds that under idealized conditions, net national product and sustainable income are identical.” (9)

Now there are two problems with this statement. One is that, even if it were technically correct, making it in a report to government carries a strong implication that it is practically important.  That requires that the necessary “idealized conditions” are a reasonable approximation to reality or, more precisely, any differences between those idealized conditions and reality are such that net national product is a reasonable approximation to sustainable income.  I shall show below that this is not the case.  The second problem is that the statement is not even technically correct. As I shall explain shortly, it is a basic misunderstanding to interpret Weitzman’s constant-equivalent consumption as sustainable income.

It is worth noting that the term “output-sustainability correspondence principle” has not found favour with economists (or anyone else).  On googling it, I obtained few hits, most of them linking to Nature’s Numbers itself.  As a name for Weitzman’s equality, the term is doubly misleading: sustainability is not constant-equivalent consumption, and “output” does not convey the subtleties of Weitzman’s concept of net national product.  

If we are concerned to use economic analysis to assess the sustainability or otherwise of an economy that uses non-renewable resources, then we will want to develop long-term models similar in some respects to that of Weitzman.  But there is one fundamental difference.  The natural way to define sustainability within such a model is in terms of the feasibility of a constant rate of consumption continuing forever.  We might ask whether a particular rate of consumption, for example the current rate, can continue indefinitely, or we might ask what is the maximum rate of consumption that can be so sustained.  In either case, we are concerned with a putative actual rate of consumption, a rate that (subject to its distribution) would determine the living standard of the people living at any time.  Weitzman’s constant-equivalent consumption, however, is merely a theoretical construct.  We cannot assume that constant consumption at that rate is feasible within the parameters of his model (indeed, Weitzman shows that it is not feasible (10)).  Even if the optimal consumption stream were achieved, actual consumption would be more than constant-equivalent consumption at some times, and less at others, and for those unfortunate enough to live at times when it was less, it would be no consolation (even if it were so) that constant-equivalent consumption would have been sufficient for their needs or aspirations.

So does Weitzman’s equality have any bearing on the question of sustainability?  In fact, a  link can be made as follows. For a given model, given initial values, and discount rate r, we make the following definitions:

  • PVOC(r) is the present value of the optimal feasible consumption stream OC(r) at discount rate r.
  • PVCE(r) is the present value of constant-equivalent consumption CE(r) at discount rate r.
  • PVCC*(r) is the present value at discount rate r of the maximum feasible rate of constant consumption CC*. Note that we do not write CC*(r): the maximum feasible rate depends only on the initial quantities of capital goods, including natural resources, and the production technology.

From the definition of constant-equivalent consumption, PVOC(r) = PVCE(r).  Since OC(r) is optimal given r, we must have PVCC*(r) ≤ PVOC(r) and therefore PVCC*(r) ≤ PVCE(r). Because CC* and CE(r) are both constant rates, we can infer that CC* ≤ CE(r). Given Weitzman’s equality NNP(r) = CE(r), this implies CC* ≤ NNP(r).   Importantly, this argument does not depend on the value of r.

So from Weitzman’s equality we can infer what might be termed a partial sustainability indicator: if a putative rate of constant consumption CC* exceeds NNP(r), then it is not sustainable forever.  But if CC* is less than NNP(r), then it may be sustainable. 

Before proceeding, it will be useful to show that this indicator can be expressed in another way.  Writing C for consumption, I for the vector of net investments in each of the capital goods, and q for the vector of prices of those goods, we have NNP(r) = C + qI.  The above indicator implies that for sustainability we must have C ≤ CC* ≤ NNP(r), from which we can infer C ≤ C + qI and therefore qI ≥ 0, a condition sometimes termed the genuine savings indicator.  This can also be put the other way round: if qI < 0, then current consumption is definitely unsustainable.

The fact that the above indicator is only partial is no reason to belittle it.  On the contrary, assessing long-term sustainability is both an important and a complex matter, so any contribution should be welcome.

The real problem with this indicator is that it relies on the assumptions underlying Weitzman’s equality – or as Nature’s Numbers put it, the idealized conditions.  Weitzman’s paper is quite concise and, as with much of the literature on this topic, it is not entirely straightforward to discern the precise assumptions on which its results depend.  That’s not just my opinion; Asheim’s 2003 paper Green National Accounting for Welfare and Sustainability: A Taxonomy of Assumptions and Results (11) begins with a similar sentiment.

Asheim proceeds to consider five possible assumptions that long-term models might or might not make, and to identify conclusions which can be drawn from particular combinations of those assumptions. In relation to sustainability as defined above, the two most relevant assumptions are:

  • Optimality: the economy is on a path which maximises the present value of the consumption stream, and prices of capital goods are such as to support that path. I take the latter to mean that the time paths of prices are such that, if producers act at all times so as to maximise their profits given those prices, then the choices of goods produced and inputs used at any time will be such that the present value of the consumption stream will be maximised.
  • Stationary technology: there is no technical progress and therefore the amount and composition of output at any time depends solely on the quantities of inputs and the allocation of inputs to the production of different goods.

Asheim’s conclusions regarding sustainability are summarised in a table (12), the blanks indicating combinations of assumptions from which no conclusions can be drawn.  What is striking is that without the optimality assumption, no conclusions can be drawn, regardless of whether other assumptions hold or not.  Our indicator above, in the form that current consumption may be sustainable if qI ≥ 0 and is unsustainable if qI < 0 (I cannot see why Asheim switches between these equivalent formulations) is shown as requiring both optimality and stationary technology.

These two assumptions are in fact both implicit in Weitzman’s paper, though perhaps not stated as clearly as they might have been.  His initial definition of NNP includes C for consumption and K for capital (13), but the fact that these letters soon acquire asterisks serves as a warning sign that something is going on.  The something is that C* and K*, together with the prices of each capital good, are on paths determined within, or just as if they were within, a competitive economy with perfect foresight.  The paths are such as both to maximise income at any time and to meet the condition for intertemporal efficiency (14).  These conditions ensure that the paths optimise the present value of the consumption stream, subject to the constraints of the initial quantities of capital goods and the production possibility set.

What this means, in simple terms, is that the optimality assumption is built into Weitzman’s concept of NNP.  That has two implications.  Firstly, it means that his NNP is very different from any NNP calculated using actual prices determined in real markets that are often imperfectly competitive and lack perfect foresight.  I say “any” NNP because that includes NNP as conventionally estimated by national income statisticians, but also estimates of “Green NNP” which make allowance for natural resource depletions but value those depletions on the basis of actual prices.  Consequently, Weitzman’s equality, and the sustainability indicator derived from it, is not valid for NNP based on actual prices; only for his concept of NNP.

The second implication is that to estimate Weitzman’s NNP so as to use it in applying the above sustainability indicator would raise enormous practical difficulties.  Instead of valuing net investment in a capital good using its actual price, it would be necessary to use a price that made full allowance for the future, a price that reflects the direct and indirect contributions to output the good can make into a far distant future in which natural resources may be much scarcer and man-made capital more plentiful than at present.  More precisely, the price would need to be the shadow price as it would be calculated from a giant dynamic optimisation problem with no time horizon seeking to maximise a constant level of consumption subject to the constraints of a production function and initial quantities of each capital good and natural resource.  Without knowing what prices such a model would yield, it is fairly obvious that they would not always correspond very closely to actual prices.  Consider for example the sharp fall in the price of oil in 2008, which surely had much to do with the effect of problems originating in financial markets on short-term demand for oil, and little to do with long-term considerations? 

Solving such a dynamic optimisation problem may be possible (with suitable computing power), notwithstanding the very large number of goods that would need to be considered.  But the nature of such problems is that small changes to the terms of the problem sometimes result in large changes to the solution.  As explained in this post, we cannot estimate a production function with sufficient accuracy for future circumstances in which the ratio of man-made capital to non-renewable natural resources may be many times higher than at present.  Nor in many cases can we measure current reserves of natural resources with the necessary accuracy; moreover the issue for many resources is not so much their finite quantity as the increasing cost of extraction from progressively less accessible sources, which would further complicate the problem.  The practical conclusion is that we do not have the necessary knowledge to calculate Weitzman’s NNP.

If, however, we did have that knowledge, we could simply infer the maximum constant level of consumption from the solution to the problem.  There would be no need to follow the roundabout approach of using the prices determined by the problem to calculate Weitzman’s NNP as a basis for applying the sustainability indicator.

Turning to the assumption of stationary technology, Weitzman adopted a neat device to broaden the scope of circumstances that can be considered to satisfy that assumption.  His broad definition of capital goods enabled him to treat technical progress of a gradual, step-by-step kind as capital accumulation in the forms of increasing stocks of knowledge and enhancements to the human skills used in applying knowledge.  In so far as technical progress can be handled in this way, it implies no change to the functional relation between the the inputs to production and the production possibility set, just more inputs resulting in more production.  It does however add an extra complication to the measurement of NNP by adding to the complexity of the production relation, and to the number and type of capital goods for which net investment must be measured and valued.  Thus it renders even more impracticable what we have already identified as impracticable because of the optimality assumption.

Weitzman also recognised, however, that this device would not do for sudden and unanticipated inventions.  In such a case, he asserted, the discounted present value of the increase in the future consumption stream made possible by the invention should immediately be capitalised by increasing NNP (15).  Whatever the merits of that approach, it means that NNP will suddenly peak and then (barring another such invention) revert to something like its previous level.  Such fluctuations in NNP imply that in those circumstances it will no longer equal constant-equivalent consumption, which should increase to reflect the invention but not subsequently fall.

A further very important issue in assessing sustainability is how to bring population growth within the scope of the analysis.  Weitzman suggests, without developing the point, that one could simply calculate everything on a per capita basis (16).  Certainly, the natural interpretation of sustainability in circumstances of growing population is constant consumption per capita.  But that leads to the problem that the appropriate prices for valuing net investment will depend on the future consumption levels needed to ensure constant per capita consumption, which will depend on future population growth, the extent of which in the long term is unpredictable. 

A final feature of Weitzman’s NNP is that it is to be calculated not as a total for a period but as a rate at a point in time within a continuous time framework.  In this respect also it differs from NNP as measured by national income statisticians, who start (for flow variables such as consumption and investment) from data for a period.  In principle, this could make a significant difference where net investment in a capital good within the period is large, so that if its shadow price could be measured it would be found to have changed during the period.  It is hard to say how much difference this might make in practice, but it is one more difficulty in making the leap from practical measurement of NNP to a reliable sustainbility indicator.

The conclusion I draw from all this is that NNP does not provide a practical sustainability indicator. That also applies to the genuine savings reformulation.  I should perhaps add that this is not to say I believe any other sustainability indicator to be better.  The problem of assessing long-term sustainability just is extremely challenging.

This post was substantially amended on 15 January 2019 to focus more clearly on the key points and eliminate some errors.

Notes and References

  1. Coyle, D (revised and expanded edition 2014) GDP: A Brief but Affectionate History Princeton University Press  pp 12-16
  2. OECD (second edition 2009) Measuring Capital: OECD Manual Ch 5 pp 43-51  https://www.oecd.org/std/productivity-stats/43734711.pdf
  3. See for example Meadows D H et al (1972) The Limits to Growth Universe Books  https://www.clubofrome.org/report/the-limits-to-growth/
  4. Weitzman M L (1976) On the Welfare Significance of National Product in a Dynamic Economy  The Quarterly Journal of Economics  90(1) pp 156-162
  5. Weitzman, as above, pp 156-8
  6. Weitzman, as above, p 160
  7. Weitzman, as above, equation (10) p 161
  8. Nordhaus W D & Kokkelenberg E C (eds) (1999) Nature’s Numbers: Expanding the National Economic Accounts to Include the Environment https://www.nap.edu/catalog/6374/natures-numbers-expanding-the-national-economic-accounts-to-include-the
  9. Nordhaus & Kokkelenberg, as above, p 36
  10. Weitzman, as above, pp 159-160.
  11. Asheim G B (2003) Green National Accounting for Welfare and Sustainability: A Taxonomy of Assumptions and Results  Scottish Journal of Political Economy  Vol 50(2) pp 113-130
  12. Asheim, as above, Table 2 p 128
  13. Weitzman, as above, Identity (2) p 157
  14. Weitzman, as above, p 158
  15. Weitzman, as above, p 162
  16. Weitzman, as above, p 157

 

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Managing Natural Capital

Posted on January 19, 2017 by Adam Bailey

A critical analysis of Dieter Helm’s ‘Natural Capital: Valuing the Planet’.

Contents

Introduction

The Asset-Based Approach

The Importance of Natural Capital

Valuing Natural Capital

Natural Goods – and Bads

Sustainability and Renewable Natural Capital

Sustainability and Non-Renewable Natural Capital

National Accounting and the Capital Maintenance Charge

Conclusion

Introduction

This book (1) addresses big and important issues about the relation between the economy, the environment and the well-being of future generations.  Its starting point is the scale of the challenge we face from environmental degradation associated with past and likely future economic growth.   To address this, it advocates an approach to economic policy-making designed to produce sustainable growth.  Central to this approach is what Helm terms the aggregate natural capital rule.

The book was presumably intended for a variety of readerships: environmentalists; economists; policy-makers; and ‘the educated layperson’.  What readers make of it may well depend on where they are coming from.  Although the book is very readable, with many examples to illustrate its general arguments, and no formulae or diagrams, I did not find it straightforward to understand how the elements of Helm’s approach fit together. The nearest he comes to attempting an overall summary of his position is in his description of three steps, according to which the aggregate rule is to be applied only after applying cost-benefit analysis to evaluate potential projects and correcting prices to reflect environmental costs (pp 132-3). Whether this is consistent with his emphasis elsewhere (pp 8, 241) on the central role of the aggregate rule is not entirely clear.

Readers with little economic background may wonder about the origins of the aggregate natural capital rule – especially if they google that precise phrase and find that the relatively few hits all lead back to Helm (2).  In fact (as the notes to Chapter 3 indicate), the rule has been developed within a considerable body of literature on the economics of sustainability, notable contributors being Robert Solow, who proposed that capital, including resources, should be “maintained intact” (3, 4), and David Pearce, who advocated “constant capital”, defined as including natural and man-made capital (5).  Solow, in turn, made his proposal in the context of earlier literature on the properties of long-term economic models in which it can be shown that consumption can be maintained indefinitely if investment follows what is known as the Hartwick Rule (6). Specifically, he showed that to maintain intact an “appropriately defined stock of capital” was equivalent to following the Hartwick Rule.

Economists will not be surprised to find that Helm sees a large role – much larger than at present – for prices in providing incentives to encourage conservation and discourage environmental degradation (pp 117-130 & 139-168). These might take the form of compensation payments, taxes or prices of tradeable permits: what is important is that they should reflect the environmental costs (externalities) of the activities of developers, producers and consumers.  Given sufficient information in a case of, say, pollution, the price can be set to induce an optimal balance between the damage done by the pollution and the costs of reducing that damage (p 164).  At the level of individual markets and particular environmental problems, then, Helm advocates policies designed so far as possible to optimise, to maximise economic efficiency with environmental costs included in the assessment of efficiency.  Since I broadly agree with this approach, which is a mainstream view among economists who study environmental policy, I shall say little more about it, focusing instead on other parts of the book.  Whether the public can be persuaded to accept environmental pricing on the scale proposed by Helm is open to question, but he certainly does a service in presenting the case for pricing to a wide audience.

When he considers the economy and the environment in aggregate and addresses the issue of sustainable growth, Helm’s approach is much more pragmatic.  Although informed both by economic analysis and ethical values, it is also influenced by considerations of political and practical feasibility.  He is not concerned, except in some brief critical comments (p 56), with the sort of economic models that consider levels of capital stock, resources and consumption for many years ahead and seek to identify sustainable or optimal paths.  The aggregate natural capital rule is presented not as an ideal policy that would lead to some sort of optimum in balancing the interests of the current and future generations, but as “a line in the sand” (pp 8 & 241) – a challenging yet achievable target which would be a big improvement on the status quo, and one which we should be able to go beyond (p 73).  The rule is an example of what Solow calls a “rule of thumb” intended to ensure that long-term interests are not neglected (7).

Despite its sub-title and many references to the importance of valuation, the book does not discuss in any detail the methods commonly used by economists to value non-market environmental goods, such as the travel cost, hedonic and contingent valuation methods.  These are mentioned only briefly (pp 124-6) and not by name.  Given my interest in the travel cost method, I found this slightly disappointing, but most readers will probably be content to be spared such technicalities.

Those familiar with company accounting may be intrigued by Helm’s frequent references to the need for balance sheets within national accounts (pp 86ff).  It is clear that these would include a nation’s assets, including natural assets.  But I could find no answer in the book to the question of what would be the balancing items on the other side of such a balance sheet.  What Helm means, it seems, is a single-sided account showing the values of assets and changes thereto, perhaps better described as an asset account.

One final introductory point.  Helm rejects, for good reasons, the idea that we should aim for zero economic growth in order to ease pressures on resources (pp 37-8).  But once he has made that point, economic growth features in the book as a background assumption, something that technological progress will more or less inevitably make possible.  Although there is a chapter entitled “Sustaining Economic Growth”, there is little discussion of policies to achieve growth.  It is no criticism – given that one book cannot cover everything – to point out that technological progress is taken for granted, and that the focus is on sustainability, in the sense of ensuring that growth is not undermined by depletion of natural capital.

The Asset-Based Approach

The aggregate natural capital rule is an example of a sustainability rule.  Helm presents it as a sensible intermediate position between two other rules that have been widely discussed (p 63).  Advocates of strong sustainability hold that we should maintain all natural assets, and that man-made assets can never adequately substitute for natural assets (consequently they are opposed to economic growth and favour what they might term ‘living in harmony with nature’).  Weak sustainability, on the other hand, permits depletion or degradation of natural assets, provided that this is compensated for by appropriate investment in other assets.

Before considering the merits of different sustainability rules, it is worth noting something they have in common, namely, a focus on assets.  Helm regards this as a matter of considerable importance, describing his approach as “asset-based”. This has two aspects.  One is the extension of national accounting to include the asset account.  Whether that is worthwhile depends partly on the feasibility of valuing assets, which is considered below.

The second aspect concerns planning for future generations. In this context, Helm is at pains to explain why an asset-based approach is better than an alternative which he calls an “income or consumption-based approach” (pp 55-8). His target here appears to be a type of long-term economic modelling which makes detailed assumptions about the preferences of  people in the future and tries to plan for their happiness.  Such assumptions, he suggests are both impracticable (“extremely informationally demanding”) and inappropriate (interfering in “the personal domain”).  Noting the Brundtland definition of sustainable development which refers to “the ability of future generations to meet their own needs”, Helm suggests that what the next generation needs is not a detailed plan, but a set of assets that will enable them to achieve their own conception of a good life (p 57).

At one level this argument is correct.  It can be read simply as an application to the long term of well-known criticisms of detailed central planning.  As an argument against any form of planning for future consumption, however, it is unconvincing.  Admittedly we cannot know what preferences people in 30 or 50 years’ time will have in respect of, for example, lifestyles, fashion, entertainment and holidays, nor what new sorts of devices and technologies consumers will have available.  We can however make reasonable assumptions about their basic needs.  Indeed, on the very next page (p 58) Helm refers to the needs of future generations for what he terms “social primary goods” – including health, housing, education and electricity – together with infrastructure and systems to deliver those goods.  If we reject, as we should, the idea of comprehensive planning for the needs and preferences of future people, the obvious alternative is a much more modest form of planning focusing on such primary goods and leaving plenty of flexibility in other respects.

The real reason why we should focus on assets, which Helm never states, is simply this.  The main way in which one generation can affect the circumstances of the next is through the assets it passes on.  Can income be passed on?  Yes, but before it can be passed on it must be saved, and the very act of saving converts income, a flow, into a stock of value, or asset.  Can current research on solar power help the next generation to avoid an energy shortage?  Yes, but only in so far as that research leads to the passing-on of suitable infrastructure, installations, skills or knowledge, all of which are assets of sorts.  Indeed, if assets are broadly understood to include all forms of capital – physical, financial, natural, human, social, institutional – then it becomes a tautology that anything of value that can pass to the next generation is by that very fact an asset.

While Helm’s focus on assets, or capital, is entirely appropriate, therefore, it is not quite as substantive a point as he suggests; nor does it have much to do with respecting future generations’ right to their own conception of a good life.  The crucial issues are which kinds of assets are most important or most at risk, to what extent different kinds of assets can substitute for each other, and what guidelines and policies should be adopted to maintain and manage assets.

A balanced approach to planning for future generations should also have regard to population growth. We might consider population an asset in its role as the source of labour and a repository of knowledge and skills.  But when we think of people as ends rather than means, as consumers, and as putting pressure on nature by virtue of their numbers and needs, we adopt a different perspective.  Another way in which one generation can affect the circumstances of the next, therefore, is through the extent to which it allows its population to grow, increasing future needs for goods of all kinds.  Helm does discuss the impact of population trends (pp 23-4), but is I suggest too dismissive of policies to moderate population growth as a way to improve the lives of future generations (p 246).  Such policies need not imply coercion: for poor countries with rapidly growing populations, as in sub-Saharan Africa, a case can be made for aid to support education in birth control.  A limitation of any approach to sustainability which focuses exclusively on assets, therefore, is that it ignores the potential trade-off, in terms of marginal benefits, between money spent on conservation projects and on family planning programmes.

The Importance of Natural Capital

Having made a case for focusing on assets, Helm proceeds to argue for the special importance of natural capital, defined (p 3) as “elements of nature [that] directly or indirectly produce value to people”.  I find his distinction between ethical and instrumental arguments (pp 58, 60) puzzling: ethical and instrumental considerations surely need to work together, the former to justify objectives, and the latter to show the importance of natural capital to their achievement?  His best argument, and it is a powerful one, is that elements of natural capital are essential factors of production that future generations will need to provide themselves with social primary goods (pp 58-61).  He refers in particular to the brick and tarmac of cities as derived from nature, and the dependence of agriculture on soil ecosystems.  He might equally have referred to water and energy sources as vital factors of production.

A slightly separate argument relates to the physical, mental and spiritual benefits of access to nature (pp 59-60).  This relates only to some aspects of nature: not for example to coal or oil reserves. Moreover the benefits are to some extent a matter of individual preference, culture or circumstance (if we live in a city with polluted air we may value more the cleaner air of the surrounding countryside).  Whether access to nature should be considered a social primary good is debatable.  Although this argument is valid, it is much less important than the factors of production argument: even for those like me who love to walk in the countryside, in our hierarchy of needs it is well below food and a home.

Valuing Natural Capital

The aggregate natural capital rule requires that elements of natural capital be valued: economic value is the only possible basis for aggregating, say, hectares of forest and cubic metres of fresh water.  There is, admittedly, one circumstance in which the rule can be applied without values, namely, when any loss or depletion is compensated for on a like-for-like basis.  But as Helm recognizes (p 155) like-for-like replacement is rarely possible.  Although he suggests that valuation is unnecessary if we aim simply at  “holding … the aggregate line” (p 90), and only needed if we aim to improve or expand the asset base, I cannot see any basis for that.  If we attempt to hold the line by substituting B for A, we need to know whether B has the same value as A.  A comprehensive asset account would also require valuation of elements of natural capital.

Some would argue that to value nature in economic terms is wrong in principle.  Helm quite properly counters this by pointing out that, since we do not have the resources to conserve all natural capital, values can help select priorities for conservation (pp 4, 116).  But that only shows that it would be useful to be able to value natural capital: whether and to what extent it is possible are further questions.

The practicality is that, depending on the type of asset, or service provided by an asset, our ability to estimate economic values using techniques from a large economic literature on the valuation of environmental assets ranges from fairly good to very poor. Consider a forest, sustainably managed with growth of new trees offsetting logging of mature ones.  In the fairly good category we can place the value of the timber, which has a market price, although even in that case there is scope for argument about how that price may change in future, and about discounting of future revenues.  At the other extreme, suppose the plants in the forest include an endangered species, present only in a few sites around the world, of no known practical value, but which might one day be found to have some use for medicinal or other purposes. Any attempt to value the presence of the plant would be highly speculative.  Somewhere between these extremes is the value of the forest in sequestering carbon: the mass of carbon sequestered can be estimated fairly accurately, but there is plenty of scope for argument about the appropriate carbon price per unit mass, reflecting the benefit of carbon sequestration in moderating climate change.  Also between the extremes is the recreational value of the forest, which in principle can be estimated from the costs incurred by visitors in travelling to the forest, but which in practice raises many questions including the value to be placed on visitors’ travelling time and the most appropriate statistical methods for estimating a value from survey data (8).

There is a further problem.  To a large extent, what valuation techniques do is value specific environmental assets in their actual current circumstances.  Suppose for example that a country has many similar forests.  Recreationists who decide to visit a forest will mostly choose the one that is nearest to them and least costly to visit.  If the forests were fewer and further apart, then some of those visitors would choose to make longer, more costly trips (just as some Europeans and Americans make expensive trips to Africa to see animals that they cannot see in the wild in their own countries).  A valuation of a forest derived from actual visit costs will not capture that willingness to incur higher costs. That may be fine if the valuation is to be used in appraising a proposal to convert that one forest site for alternative use, while retaining all the other forests.  But it will not do if the aim is to find the aggregate value of all the forests.  For that purpose, we need to include the full willingness of potential visitors to incur costs of travelling to a forest, and that cannot be inferred from their current behaviour if their nearest forest is relatively close.  Visitors could instead be asked how much they would pay to visit a forest if there were far fewer forests (as in contingent valuation (9)), but how reliable their responses might be given the extremely hypothetical nature of that scenario is open to question.

Helm recognizes that estimating values for natural assets is often difficult (pp 125-6, 136), but  offers several arguments in defence of valuation.  Approximate values, he suggests, are often good enough (p 127).  If the cost of preserving an ecological site is known, then a decision to preserve the site can be based on knowledge that the value of the site is more than that cost, and it does not matter whether it is twice the cost or ten times the cost.  But that is in the context of evaluating a possible project.  For the aggregate rule to be workable, a degree of approximation would be acceptable, but if many of the larger items added together are subject to a wide range of uncertainty, the overall figure will not be very meaningful.  Another argument is that valuations, even if imperfect, are to be preferred to judgments by experts or regulators subject to lobbying by interest groups (p 136).  That seems dubious, since application of valuation techniques itself often requires judgments (eg in choosing between alternative statistical techniques).

An argument more relevant to the aggregation rule is that it does not require valuation of every element of natural capital, because to monitor any change in the aggregate value it would suffice to consider just the value of changes of those elements that have changed.  This is not explicitly stated by Helm, but is a possible interpretation of several passages (pp 10, 90, 104).  The example of a sustainably managed forest illustrates both the strength and the limitations of the argument.  In the absence of a relevant change, nothing about the forest will have contributed to any change in the aggregate value of natural capital, and there is therefore no need for any valuation in respect of the forest.  If, in a period, most assets satisfy the ‘no relevant change’ condition, then the scale of the valuation problem will be greatly reduced.  The difficulty here is what sort of changes should be considered relevant.  Even if the forest itself does not physically or biologically change, any of the following might be considered grounds for treating its value as having changed: a change in the market value of timber; a change in the worldwide population of the endangered plant species, increasing or reducing its risk of extinction; a change in the appropriate carbon price following new scientific evidence on climate change; or a change in the number of recreational visitors due to a change in population in the surrounding area.  In any year, the proportion of natural assets subject to some such change might be high.  There are complex issues here which, so far as I can see, Helm does not address.

Whatever the merits in principle of the aggregate natural capital rule and of a comprehensive asset account, I conclude, obtaining the valuations that their application would require would be extremely difficult, rather more so than Helm seems to suggest.  This is not to deny the importance of environmental valuation: its main roles, however, are in the appraisal of potential projects, enabling the monetary value of changes to environmental assets to be included in cost-benefit analyses, and in the assessment of environmental externalities as a basis for determining the appropriate level of policy instruments such as taxes, subsidies and compensation payments.

Natural Goods – and Bads

Among Helm’s examples of natural capital are some that can cause harm: species, which include pests and pathogens; land, which can be earthquake-prone; air, which can bring hurricanes; and oceans, which can bring surge tides.  It would be unfair to suggest that Helm ignores the downside of nature, which is clearly recognised in his discussion of flood defence (pp 186-8).  Nevertheless, the book conveys, to me at least, an impression of nature as largely benign to the human race.  For those of us who live in southern England, with its relatively mild climate, moderate year-round rainfall and rarity of serious natural disasters, that may seem a plausible view.  Inhabitants of many other regions of the world may incline more to a view of nature as indifferent to humans, to be coped with and managed.  China’s environmental statistics, for example, record (in each case figures are for the latest available year): 623 deaths from 20 earthquakes; 482 deaths from other geological disasters (eg landslides); 19,000 hectares of forest destroyed by fire, with 112 casualties; 3,000,000 hectares of total crop failure due to extreme weather conditions, flood and drought; and 52,000,000 hectares of grassland harmed by rodent and insect pests (10).

Given that there exist, from a human perspective, ‘natural bads’ as well as ‘natural goods’, it needs to be considered how they will be handled within any sustainability rule and any scheme for valuing nature. One approach, to bring natural bads within an asset account as a basis for applying a sustainability rule, would be to treat every bad as merely the absence of the corresponding good.  Thus an asset described as ‘absence of serious earthquakes’ would appear in England’s asset account, but not in Japan’s.  That might seem a neat way to justify an exclusive focus on goods, but it does not really work.  England then has in its account an ‘asset’ which, so far as is known, is a permanent feature of its geology, not at risk and not requiring any maintenance – a rather pointless piece of record-keeping.  Japan, on the other hand, has a serious natural risk which it mitigates by measures such as appropriate construction of buildings, but there is no entry in its account to indicate a need for such mitigation.  Unless we recognise both the goods and the bads in our assessment of nature, and the dual role of investment in man-made capital in mitigating the bads as well as complementing and substituting for the goods, we will have only a partial view of the relation between the economy and the environment.

Even in England, much investment in man-made capital is wholly or partly to mitigate natural bads.  Coastal and flood defences are examples, but so is any investment in the production of goods intended (perhaps as one of various functions) to provide comfortable temperatures and protection from the elements.  That includes housing, heating and air-conditioning (both appliances and the energy they use), and clothing.  Also of this nature is investment in health services, in so far as it is to address diseases of natural origin.

In considering possible sustainability rules, therefore, we should ask how, if at all, they will apply to natural bads.  Most fundamentally, should we regard the mitigation of natural bads as broadly desirable, or should we reject all such mitigation on the grounds that it is a form of interference with nature?  I take it that most people would accept the former, and that, for example, very few would argue that the appropriate response to flood risk is always either to live with the risk or if possible to move home, and never to build defences.  There are then questions about substitution.  Can the mitigation of a natural bad be an acceptable substitute for depletion or degradation of a natural asset?  Suppose for example it were possible to eliminate malaria from a region, but at the price of damage to other elements of the region’s ecosystems.  Would that be an acceptable project, subject only to the benefit being shown to exceed the cost?  Or should it be subject to the further requirement that the damage be compensated for by equivalent enhancement of other natural assets?  If moreover we formulate a sustainability rule in terms of maintaining an aggregate, can we simply net the natural bads against the natural assets?  These sorts of questions are not considered by Helm, but are I suggest quite fundamental ones for his approach.

Sustainability and Renewable Natural Capital

So far as renewable natural assets are concerned, Helm’s sustainability rule has only one version: the aggregate level should be kept at least constant (p 64).  But what exactly is renewable natural capital?  Helm refers to its “potentially infinite yield at zero cost” and its ability to renew itself or reproduce (pp 3, 50).  His examples – pansies, peat bogs, fish and trees – perhaps suggest that renewable natural capital must be biological.  And when he argues that depletion of renewables is “the real concern” (more serious than depletion of non-renewables) because they are subject to thresholds below which they cannot renew and regenerate themselves (p 35), it is clearly biological assets – species and ecosystems – that he means.  But sunlight, rainfall and wind are surely also renewable natural capital – both as essential support for the biosphere and as renewable energy sources?  They are certainly not non-renewable: the only alternative would be to have a third category, perhaps described as permanent natural capital.

Renewable natural capital is thus a very diverse category, and that presents a difficulty for Helm’s sustainability rule.  Why should we focus on the aggregate level of renewable natural capital, unless we consider that one element or type of such capital can substitute for another?  Helm gives the example of substitution at the margin of habitats for newts by habitats for nightingales (p 155).  However, there is nothing in the rule that limits substitution to marginal changes, to species of little practical value or concern to most people, or even to the biosphere as a whole. Prima facie, it suggests that it would be acceptable to substitute, for example: squid for cod; oak trees for skylarks; micro-organisms for elephants; or forests for lakes.

Within Helm’s overall approach, there are several considerations which to some extent limit the permitted substitutions.  Firstly, the sustainability rule is not supposed to be considered on its own: rather, it is preceded by cost-benefit analysis of potential conservation projects (pp 132-3).  In any particular set of circumstances, therefore, many possible substitutions via projects would be rejected because, in cost-benefit terms, they were less advantageous than others.  Secondly, Helm notes the importance of keeping the level of a species above the critical threshold below which it would no longer be able to reproduce itself (p 10), an example of a sustainability constraint.  Thirdly, the practical unit for such thresholds is often a habitat or ecosystem rather than a single species (pp 51, 104-6).  Hence many one-species-for-one-species substitutions are simply impracticable, because changes in levels of those species would also affect other species within their respective ecosystems.

While the effect of these considerations is significant, they do not go far enough in limiting the sort of substitutions that should be considered acceptable.  Explicit regard should be had to the functions or services provided by the respective assets.  If for example ashwoods (woods in which ash trees are the predominant species) are dying from ash dieback, oakwoods are in several respects a good functional substitute.  Both ash and oak (like all trees) sequester carbon; being deciduous and forming airy canopies, both allow light for plants on the woodland floor, especially in spring; and both yield hardwood timber.  Woods of spruce, a species which is evergreen, forms a dense canopy and yields softwood, would be functionally a less good substitute; while many other types of renewable natural capital, especially animals and non-biological assets, would be even less good.  Our focus, I suggest, should be less on very broad aggregates such as renewable natural capital, and more on multiple smaller aggregates of assets with similar functions.  This would counteract the tendency which broad aggregates have to encourage unacceptable substitutions.  An important additional advantage would be that, within any one functional group, aggregation could be to a much larger extent on the basis of physical measures, reducing reliance on questionable monetary valuations.

Sustainability and Non-Renewable Natural Capital

For non-renewable natural assets, Helm states two versions of the aggregate rule.  The weak version requires that depletion of non-renewables be compensated by investment in general capital, that is, in some combination of man-made and renewable natural capital (p 64).  That is quite close to the rules of Solow and Pearce, and requires valuation both of the depletion and of the compensating additional capital.

The main objections to the weak rule are the same as those identified above for the aggregate rule as it applies to renewable natural capital. It places too much reliance on valuations, and not enough on functions, in determining acceptable substitutions of one asset for another.  Indeed, these objections apply with even greater force, simply because of the huge variety of assets embraced by ‘general capital’.  Consider for example investments in entertainments, tourism and works of art, assets which (though they contribute to a broad view of a good life) have little or no impact on the provision of social primary goods.  Investing in these sorts of assets is fine, but it would be fallacious to regard it as compensating for the depletion of non-renewable natural capital.  Such investments do have monetary value, and that value may help to ensure that the aggregate value of natural and man-made capital is maintained. But they cannot substitute, functionally, for the depletion of non-renewable factors of production such as fossil fuels and other minerals.

The strong version of the aggregate rule differs from the weak rule in two respects.  Firstly, it does not permit depletion of non-renewables to be compensated for by investment in man-made capital: the compensation has to be in renewable natural capital.  Secondly, the terms of compensation are not to be based on asset valuations: instead, the amount of the compensating investment is to equal the economic rents from depletion of non-renewables (p 64).  Economic rent in this context, in simple terms, is the return to the owner of a resource arising from the difference between the market value of the resource and its extraction cost.  A possible advantage of this rule is that it could be applied without having to consider the sort of valuation issues identified above for the case of forests: for example, should the valuation of fossil fuel reserves be adjusted in response to new research findings on greenhouse gases and climate change?  Economic rents, based on current market prices and current costs, can be more straightforward to identify.

I shall argue however that the strong rule – and specifically, it’s requirement for compensating investment to be in renewable natural capital – is too restrictive.  Consider how it would apply to the depletion of fossil fuels.  Given such depletion (and to limit greenhouse gas emissions), we need to invest in developing alternative energy sources.  What is less clear is which alternative sources should be chosen, and the best mix will vary between countries and regions, with solar, wind and various biofuels among the options.  Solar and wind energy are often described as renewable, but that does not mean that to invest in them is to invest in renewable natural capital.  The  investment is in equipment such as solar panels and wind turbines – forms of man-made capital – to capture energy from those renewable (or permanent) sources.  On any normal approach to valuation, the investment adds to the value of man-made capital, but there is no addition to the value of renewable natural capital, which is what the strong rule requires.  A possible rejoinder is that the aggregate value of renewable natural capital should include a value for sunlight and wind, and furthermore that this value should be adjusted to reflect increases in our ability, via more and better solar panels and wind turbines, to capture their energy.  Barring that very problematic approach, the strong rule would discourage investment in solar and wind energy, and encourage investment in those renewable sources where the investment really would increase renewable natural capital – biofuels, perhaps.  And this would be regardless of the relative efficiency of these different energy sources, or of their respective implications for land use, air pollution and greenhouse gas emissions.

Let’s pursue the argument a little further, on the supposition that we have been thus encouraged to opt for biofuels as an alternative energy source.  There is then a question of what type of biofuel should be chosen, and some biofuel crops will be more efficient sources of energy than others, having regard to the climate and soil in particular locations.  The strong rule, however, would tend to encourage the selection of perennial crops (eg sugar cane and oil palms), which have a capital value based on their expected stream of future harvests, rather than annuals (eg wheat and corn), again regardless of their relative efficiency.

The upshot is that the strong rule tends to discourage a sensible energy policy, unless we either adopt the radical course of putting a monetary value on sunlight and wind, or else let the rule be over-ridden by other considerations.  There isn’t a strict incompatibility here, since we could always ensure compliance with the rule by some other investment in renewable natural capital, unrelated to energy – but that would involve costs.  The crucial point is that the discouragement of a sensible energy policy would be for no good purpose: if a part of non-renewable natural capital has no significant function other than as an energy source, and if the best alternative source of an equivalent amount of energy happens not to require investment in renewable natural capital, then there can be no harm in allowing the depletion of that particular part without any compensating investment in renewables.

The scope of this argument is not limited to fossil fuels.  Take copper, a mineral used in plumbing and wiring (and for various other purposes), present in abundance in the Earth’s crust, but with only limited reserves economically viable given current prices and technologies (11).  It would be sensible to invest in technologies for extracting copper at lower cost from less accessible or lower concentration reserves, and in alternatives to copper for use in plumbing and wiring.  It is quite difficult to see how investment in renewable natural capital might make an effective contribution here: investment in suitable man-made equipment or in extraction of alternative minerals appears much more promising.  Whatever the merits of different investments to address a potential copper shortage, the choice should not be influenced by a requirement to compensate for depletion of copper reserves by investment in renewable natural capital.  Similar considerations apply to other metallic minerals.  As in the case of energy, adherence to the strong rule tends to distort the allocation of resources, including capital investment, for no good purpose.

Can we perhaps argue that the strong rule is nevertheless a useful “line in the sand”: a rule which will usually point us in the right direction, even if cases can be identified in which it would lead to sub-optimal decisions?  No, because fossil fuels and metallic minerals are not minor exceptions, they are among the most important examples of non-renewable natural capital.

The other side of this is that the strong rule would tend to lead to over-investment in renewable natural capital. How can that be?  Surely there is no shortage of potentially beneficial projects to restore and enhance the natural environment?  Indeed there are, and that could be an attraction of such a rule for some.  For environmental groups campaigning to clean up polluted sites, protect habitats, and save endangered species, the idea that the depletion of fossil fuels and other minerals should have to be compensated for by correspondingly large investments in renewable natural capital must be very exciting.  But as Helm points out (pp 4, 119), we do have to make choices.  We cannot afford to do everything, and most people, conscious of the importance of primary goods, would regard investments to maintain energy supplies and electrical and water infrastructure as an essential part of our response to depletion of non-renewables.  This is not to deny the importance of renewables, or even to reject Helm’s assertion (p 35) that depletion of biological renewables is potentially the more serious threat to growth and sustainability. The point is simply that our response to depletion and degradation of ecosystems should be decided on its own merits, and not artificially linked to depletion of minerals.

National Accounting and the Capital Maintenance Charge

The key features of Helm’s proposed approach to national accounting  are an asset account (‘balance sheet’) and a capital maintenance charge.  The asset account would be a list of assets (natural and man-made) and their values, though for reasons of practicality it might initially be limited to the most important and most at-risk assets (p 89).  Presumably it would also record changes in those assets including depletion, degradation, natural growth, maintenance and enhancement.  A number of countries including the US (12) have explored the preparation of such accounts, but few if any have adopted them as a routine part of their national accounting (13).  Given the difficulty, described above, of valuing natural capital, this is perhaps not surprising.

The capital maintenance charge has two aspects.  It is an adjustment to GDP, to ensure that it reflects damage to the environment and depletion of natural resources.  In this aspect it is one of various adjustments to GDP that have been proposed by environmental economists. The second aspect is that it would mean raising a huge sum to pay for capital maintenance via some combination of pollution taxes, higher utility bills, ending of perverse subsidies, rents from depletion of non-renewables, and reductions in other public expenditure (pp 92 & 223-8).

Whatever their merits, these two aspects do not have to go together: one could adjust GDP, as a measure of economic performance and to inform policy-making, without any cashflow or tax implications.  For Helm, it seems, national accounting is not just data-gathering and publication of aggregate information, important though that is, but also accounting in the sense of national revenue collection, perhaps more properly termed public finance.  I shall say no more about this, since such large-scale fund-raising and investment raises broader questions about the role of the state and the balance between the public and private sectors that are not specific to environmental and natural resource issues.

Let’s return now to the capital maintenance charge as an accounting adjustment.  Environmental adjustments to GDP may have either of two motivations.  One is to provide a more comprehensive measure of current welfare.  Conventional GDP does not reflect the harm done by pollution, except to the extent that it affects the sorts of output that GDP measures.  So the current welfare perspective suggests a deduction for the estimated value of the current harm due to pollution.  From this perspective, however, there is no reason for a deduction for depletion of non-renewable resources, because such depletion does not reduce current welfare.

The second motivation is quite different, in that it is concerned with the future as well as the present.  It aims to measure, not actual current welfare, but the level of current welfare that could be sustained in the future, sometimes termed Net National Product or Green GDP.   This implies a deduction for depletion of non-renewable resources, because such depletion potentially impacts on future welfare.  So far as pollution is concerned, it implies a deduction for emissions of cumulative pollutants which will eventually cause harm, even if their current levels in the environment are low enough to be harmless.  This has been the motivation of most economists who have explored environmental adjustments to GDP, including for example Solow (14), and it also seems to be Helm’s motivation in proposing that GDP be reduced by the capital maintenance charge, which he links to depletion of non-renewable assets (p 92).

Whether this sort of adjustment to GDP is feasible and useful is a matter of controversy among economists.  This partly concerns valuation: theory suggests that depletion of mineral reserves should be valued at prices that, putting it simply, make full allowance for future needs (15).  Current market prices are unlikely to meet that requirement. So one focus of dispute is whether the ‘right’ prices can be identified with sufficient accuracy, either by showing that market prices, perhaps with adjustments for gross distortions such as the effect of OPEC, provide a reasonably good approximation to the ‘right’ prices, or by showing that appropriate adjustments to market prices can be calculated from other data such as estimates of future needs for factors of production.

A second difficulty concerns the fact that man-made capital tends to wear out, or need repair, a phenomenon generally described as depreciation.  If we consider that income and welfare can be sustained, even without technical progress, because depletion of non-renewable resources can be offset by sufficiently large investment in other capital including man-made capital, then it is incumbent upon us to consider the depreciation of the ever-increasing stock of man-made capital.  Given the standard assumption that annual depreciation is a constant proportion of capital, it must eventually exceed income, leaving no part of income for consumption to support welfare, or for investment in additional capital (16).  Without technical progress, therefore, there would be no level of welfare that could be sustained indefinitely.

That leads to the third and in my view most fundamental difficulty with adjusting GDP to try to achieve a measure of sustainable welfare. To avoid the above conclusion, which would result in adjusting GDP to zero, we have to make one or more arbitrary assumptions.  One possibility is to set a time horizon of X years, and find the level of welfare that could be sustained for that period.  Another would be to make an assumption about future technical progress – for example that the output achievable from given inputs will increase annually by n% – and find the welfare level that could be sustained indefinitely on that assumption.  Population growth is another consideration where a more or less arbitrary assumption is likely to be needed: even if world population eventually stabilizes, it makes a significant difference to the feasibility of a given average welfare level whether it settles at, say, 9 billion or 10 billion. It is fine for economists to make assumptions on these matters and see what they imply.  But they are not the sort of matters on which there is any prospect of reaching a consensus.  It is not going to be possible, with such assumptions, to arrive at a single adjusted GDP figure which can be considered a correct measure of sustainable welfare and which will command, or merit, credibility with policy-makers and the general public.

Conclusion

There is much in this book with which I can agree.  I agree that much greater use should be made of taxes and other price-based policy instruments to address environmental externalities. I agree that valuation of specific natural assets has an important role to play in setting such policies, and in estimating the costs and benefits of proposed projects that impact on the environment.

Most fundamentally, I agree that depletion and degradation of natural capital is a serious and growing problem, and that the economy should be managed in a way which gives a much more central place to environmental and resource issues, and has much more regard to the interests of future generations.  However, I am not persuaded that adherence to the aggregate natural capital rule would point the economy in a more sustainable direction.  The strong version of the rule would encourage a misallocation of investment resulting in  sub-optimal adaptation of the economy to depletion of fossil fuels and other minerals.  The weak version would place too much reliance on questionable valuations and, because it would permit bizarre substitutions of one natural asset for another, would have to be supplemented by other rules to produce sensible results.  Moreover, neither version embraces investment to mitigate natural bads.

My proposed alternative would include the following elements:

  1. A greater focus on targets relating to functional groups of assets, with less focus on aggregation over the very diverse category of natural capital as a whole. Some possible examples of functional groups are: sources of fresh water; sources of energy; waste sinks; and food crop pollinators (there would need to be many more than that).  Functional groups would not be limited to those relating directly to human needs, but would also include, for example, supporting ecosystems.
  2. More reliance on appropriate physical and biological measures, and less on valuations, in defining targets for particular functional groups of assets, and in determining the terms of acceptable substitutions of one asset for another within groups. The starting point in setting targets would be an assumption that for each functional group we should at least maintain a suitably defined aggregate, although in some cases more or less demanding targets might be justified by particular circumstances.  Targets should have regard to the likely needs for social primary goods of future generations.
  3. A greater focus on natural bads and investment to mitigate them, with clear recognition that investment in long-term mitigation of natural bads is an important part of what we leave for future generations. Examples include: long-lasting flood and tidal defences together with building of new homes in areas not at risk of flooding;  development of more drought-resistant food crops; and permanent medical advances (such as the eradication of smallpox).
  4. Extension of national accounting to include an asset register recording natural assets (and bads) in physical and biological terms (but in most cases without valuations), changes thereto, risk assessments, and classification by functional group (with many assets contributing to more than one group). The register would provide the detailed data needed to monitor performance against the targets for functional groups.

I readily accept that the above is far from fully worked out, but suggest that a framework along these lines would be less likely than the valuation-based aggregate natural capital rule to lead to mis-allocation of investment, and more likely to carry credibility with decision-makers.

Notes and References

  1. Helm D (2015) Natural Capital: Valuing the Planet  Yale University   All page references above are to this book.  Dieter Helm is Professor of Energy Policy at Oxford University and Chairman of England’s Natural Capital Committee.
  2. Based on my search on 4 January 2017.
  3. Solow R M (1986) On the Intergenerational Allocation of Natural Resources Scandinavian Journal of Economics  88(1) pp 141-9.  See Abstract p 141.
  4. Solow R M (1992) An Almost Practical Step Toward Sustainability https://haskayne.ucalgary.ca/files/haskayne/RobertSolow_AnAlmostPracticalStepTowardSustainability_Sep93.pdf p 169  (This paper is recommended as a non-mathematical way in to the literature on the economics of sustainability.)
  5. Pearce D (1992) Green Economics  Environmental Values 1(1)  pp 3-13  http://www.environmentandsociety.org/sites/default/files/key_docs/pearce_1_1.pdf   See Fig 1 p 6.
  6. Hartwick J (1977) Intergenerational Equity and the Investing of Rents from Exhaustible Resources American Economic Review 66 pp 972-4.
  7. Solow, as 3 above, p 148.
  8. See for example the Ecosystem Valuation website’s account of the Travel Cost Method: http://www.ecosystemvaluation.org/travel_costs.htm
  9. http://www.ecosystemvaluation.org/contingent_valuation.htm
  10. National Bureau of Statistics of China China Statistical Yearbook 2015  http://www.stats.gov.cn/tjsj/ndsj/2015/indexeh.htm   The figures quoted are derived from tables 8-27, 8-30, 8-31, 8-32 & 8-35.
  11. Wikipedia Copper  https://en.wikipedia.org/wiki/Copper
  12. US Bureau of Economic Analysis (1994) Integrated Economic and Environmental Satellite Accounts. See Table 1: https://www.bea.gov/scb/account_articles/national/0494od/table1.htm
  13. Some countries, eg Canada, Germany and the Netherlands, publish “environmental accounts” which are essentially compilations of environmental statistics with few if any monetary valuations of non-market assets.
  14. Solow, as 4 above, pp 162-3.
  15. Solow, as 4 above, p 169. Solow’s argument is also described in Perman R, Ma Y, McGilvray J & Common M (3rd edn 2003) Natural Resource and Environmental Economics  Pearson Addison Wesley p 632.
  16. Buchholz W, Dasgupta S & Mitra T (2005) Intertemporal Equity and Hartwick’s Rule in an Exhaustible Resource Model Scandinavian Journal of Economics 107(3) pp 547-61.  Modelling of depreciation is introduced on p 551 and the relevant result is on p 553 (case θ = 1 and δ > 0).  See also my post Constant Consumption with Resource Depletion.
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