Abstract
The adoption of the System of Environmental-Economic Accounting 2012: Central Framework as a UN statistical standard is a landmark in environmental accounting. The SEEA has the same authority and weight as the System of National Accounts in the pantheon of official statistics. The SEEA defines the unit value of depletion of an exhaustible resource to equal the average unit value of the asset (the total asset value divided by the physical stock of resource). By applying this definition to a non-optimal Dasgupta–Heal–Solow model of an extractive economy, we show that ‘depletion-adjusted net saving’ as defined in the SEEA supports a generalized version of the Hartwick Rule. This measure of saving can guide policies for sustainable development in extractive economies, in particular fiscal policies concerning consumption and investment expenditures funded by resource rents. The conditions required to support this finding are (i) that extraction declines over time at a constant rate, and (ii) that the marginal cost of resource extraction is constant. A less general result holds in the case of increasing marginal extraction costs.
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Notes
Note that Solow (1974), Hartwick (1977) and Dasgupta and Heal (1979) all assume that produced capital does not depreciate at a fixed rate. The reason is that, with a wasting asset, produced capital must grow without bound in order to offset declining resource inputs to production. With a neoclassical production function this implies that the marginal product of capital must also approach 0. The result is that the effective interest rate (the marginal product of capital minus the fixed depreciation rate) will turn negative in finite time as the resource is depleted. The ‘solution’ to this problem is endogenous technical change; exogenous technical change effectively makes the sustainability problem disappear. The comments of two anonymous reviewers are acknowledged with thanks. The usual caveats apply.
The intuition behind this finding is discussed in Sect. 3.
Consider an economy that is recovering from a major disaster—in the short run consumption will decline in order to finance investment in reconstruction. By the Pezzey (1989) definition this economy is unsustainable owing to declining consumption. If the initial period of declining consumption is finite, then social welfare will increase at each point in time if the rate of time preference is sufficiently low—the economy will be sustainable by the Dasgupta and Mäler (2000) definition.
Dasgupta and Heal (1979) famously show that the optimal policy for this economy—the policy that maximizes social welfare—leads to a path for consumption that falls asymptotically to zero. Optimality requires two dynamic conditions to hold: the Ramsey Rule, which equates the cost of deferring a unit of consumption to the interest rate defined by the marginal product of capital; and the Hotelling Rule, which assures that marginal resource rents rise at the rate of interest. The sustainability results of Solow (1974) and Hartwick (1977) require the Hotelling Rule to apply, but not the Ramsey Rule.
Wei (2015) shows that a slightly different parameterization of the model of Hamilton and Ruta (2009) leads to an accounting price for natural resources that is equal to the change in total wealth per unit of resource extracted. But he does not show whether this measure of depletion can lead to constant consumption under the Hartwick Rule. Section 2 turns to this question.
In Dasgupta and Mäler (2000) the concept of an allocation mechanism is very general. It is essentially a program or set of rules that defines a unique future path for the economy, taking initial stocks as given. While conceived as a way to parameterize a non-optimal economy (one which does not maximize social welfare), optimal development paths can be considered to be underpinned by specific allocation mechanisms which ensure that the Ramsey Rule, for example, holds at each point in time.
El Serafy (1989) made an important contribution by showing that the total rent on resource extraction can be partitioned into an income component and a capital consumption component. This builds on notions of Hicksian income and the Permanent Income Hypothesis. However, his formula for valuing resource depletion is equivalent to measuring the change in the total value of the resource stock which, as established in expression (11), leads to unsustainability.
Morovati Sharifabadi (2013) estimates the elasticity of the (conventional) oil extraction cost function in Texas to be \(\epsilon = 4.08\) in 2006.
These assumptions parallel those in Arrow et al. (2003) for a resource discovery function.
Note, however, that by construction \(N\) will approach \(\left( {F_{R} - \gamma }\right) S\) as the mine nears depletion, so the growth rate of \(p\) will approach the discount rate. The Hotelling Rule is approached asymptotically, but it is important not to over-emphasize this point: Livernois (2009) finds virtually no evidence for the Hotelling rule actually being observed in resource markets.
For brevity, in this paragraph we suppress the proviso that depletion-adjusted net saving should also be growing at a rate less than the interest rate.
In practice, a variety of royalty and corporate taxes are typically used to capture rents, complicated by the information asymmetry between producers and governments.
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Hamilton, K. Measuring Sustainability in the UN System of Environmental-Economic Accounting. Environ Resource Econ 64, 25–36 (2016). https://doi.org/10.1007/s10640-015-9924-y
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DOI: https://doi.org/10.1007/s10640-015-9924-y