GDP or NDP on the depletion of national resources

Salah el Serafy (1927-2016) stated the following about GDP and NDP (Gross and Net Domestic Product):

  • “Selling natural assets and including the proceeds in the gross domestic product, GDP, is wrong on both economic and accounting grounds.”
  • Even though NDP is rarely estimated, depreciation of produced assets is fairly small and predictable. Declines in natural assets, on the other hand, may be large and volatile, and are not reflected at all in the estimates of GDP commonly used for macroeconomic analysis.”
  • “For economic purposes, a better approach would be to calculate the user cost component of resource declines, and either subtract this from GDP as capital consumption or (much better) exclude it from the gross product altogether.”

The term “user cost” merely indicates the investments that are required to maintain the resource level and quality.

Two flows

In the RES Newsletter El Serafy (2014) recalled:

“Exploiting finite natural resources without replenishment is akin to mining and Marshall had taken pains to explain that the surplus realized in mining, often miscalled rent, should be split into proper ‘rent’ which is income and ‘royalty’ which is capital.”

George Santopietro (1998) summarized El Serafy’s position as:

“El-Serafy (1989) argued that the surplus for a depletable resource represents two values: (1) a true income component which can be consumed; and (2) a separate depletion cost. The depletion cost is the amount that needs to be reinvested in order to sustain the economy’s ability to provide future generations with the ability to enjoy a non-declining level of consumption. In this line of thinking, the net price method overstates the true depletion cost. Von Amsberg took El-Serafy’s method and applied the strong sustainability criterion to it by calling for a depletion cost sufficiently large that when invested in the production of a substitute, future generations will be able to enjoy a non-declining flow of similar services.”

It was actually John Hicks who distinguished fundist and materialist capital in accounting. In both cases there is Hicks’s accounting principle of keeping capital intact for income estimation purposes. El Serafy puts emphasis on fundist capital, thus with monetary value. A depletion of a natural asset can be compensated by a gain in other capital. The alternative is to look at the physical stock of goods. El Serafy: “damaged or depleted natural capital cannot easily be replaced with manufactured capital.”

A small model

Wondering what to make of this, I came upon the following small model. When you sell your house then the proceeds are not your income, so much is obvious. You might rent out a room to pay for the maintenance costs. Farmers sell the proceeds from their crop but keep some seeds for next year.

Since Keynes, macro-economics has tended to link consumption to income but let us now relate it to the capital stock that might be depleted.

Assume that the price of a depletable resource is p = 1, and that the resource stock K is capital too: K ~ p K. The first is in physical units and the second would be in money, but let us take the resource as the numeraire, so that K = p K.

  • For investment: Let physical investment J = b K. Let g be the physical return factor on physical investment. Then economic (gross) investment I = r K = (dK with d depreciation and i a rate of interest. We also have I = g J = g b K so that r = g b.
  • For consumption: Let w L be services without use of capital. For consumption of the depletable resource we distinguish a fraction s that is sustainable and a fraction u that is unsustainable. Total consumption is C = (s + u) K + w L, and we have sustainability when u = 0. Below relations allow us to deduce that s = (g – 1) b, so that sustainable consumption is determined by the physical return factor of physical investments.
  • From these two: u K are the user costs or investment that are required to keep the resource intact. When consumption is sustainable = 0 then such costs are not incurred.

In accounting of expenditure flows, it may happen that u currently is not even included in D, so that also NDP is off-track.

If u is in D then we find: NDP gives substainable consumption s K + w L, while the figure of GDP will be polluted by unsustainable depletion u.

Physical, sustainable if u = 0 Nominal, with p = 1
C = (s + u) K + w L C = (s + u) K + w L
J = b K I = r K = (i + d) K       (gross investment)
K[t+1] = (1 – sub) K + g J K[t+1] = (1 + r) KD
K[t+1] = (1 – u) K D = d K = (s + u + b) K = (r + u) K
s = (g – 1) b r = s + b = g b,     1 – u = 1 + i
d = s + u + b GDP = Y = C + S = C + I = (s + u + r) K + w L
0 ≤ s + u + b ≤ 1 NDP = YD = s K + w L = (g – 1) b K + w L

El Serafy rather wants to see that also GDP is income, which can be achieved by a separate deduction from the stock:

Physical, sustainable if u = 0 Nominal, with p = 1
C = (s + u) K + w L C = (s + u) K + w L
J = b K I = r K                                  (gross investment)
K[t+1] = (1 – sub) K + g J K[t+1] = (1 + r) KD* – Δ   with Δ = u K  as user cost
K[t+1] = (1 – u) K D* = d* K = (sb) K = r K     (without user cost)
s = (g – 1) b r = s + b = g b,   and r = i* + d* means i* = 0
d = s + u + b GDP* = Y* = C + S = C + I – Δ = (s + r) K + w L
0 ≤ s + u + b ≤ 1 NDP = Y*D* = s K + w L = (g – 1) b K + w L

An example is selling the natural resource, putting the proceeds into a bank, and live from the perpetuity. With i the money rate of interest, then sustainable income is s K = i K, so that s = i. Then b = 1 because all money is in the bank, and g = 1 + i = r. It follows that GDP = (1 + 2 iK + w L and NDP = i K + w L. Normally we do not regard the whole capital as the investment but for money it makes sense. In practice money in the bank is only a financial arrangement and the true return must still come from productive investments.

Environmental sustainability

Above model can be extended with environmental sustainability by replacing s + u with es + eu, with es ≤ s and eu ≥ u. For example, the home owner must put aside additional investments for an extension to the house to make room for solar panels or heat pumps, or to relocate it because of flooding. Sustainability and environmental sustainability have the same model here, and only different data. However, practical modeling can be different. Mere sustainability might rely on actually observed values of the going rate of depleting, while environmental sustainability with es and eu would require more involved modeling to come to grips with the current (conservative) expectations on future development.

Intermediate conclusion based upon this small model

I tended to favour GDP as based upon expenditure flows, since depreciation of produced capital tends to use accounting schemes that seem rather arbitrary. Now, however, it is clearer to me that depletion of natural resources may pollute these GDP data. Now I am starting to think that NDP would tend to be a better yardstick, provided that statisticians find adequate estimates of depletion of course. If those estimates are deficient then the use of NDP provides only the illusion of improvement though.

PM. This simple model seems quite tricky. A one time deviation from sustainability causes a one time GDP growth, but also forces to continue to deviate from sustainability for ever more, with K[t] = (1 – u)^t K[0] merely to maintain the income level without any growth. It is only a simple model to clarify a basic idea. Salah el Serafy has more sophistication with the user cost.

Salah el Serafy again

El Serafy (2014) however advises that resource depletion is removed from income altogether (with my comments):

“Any presumption that removing ‘royalty’ (the capital element) from GDP entries relating to natural resources might be taken care of at the level of estimating NDP cannot be accepted for more than one reason.
First, NDP is not often reckoned at all, and if reckoned there is no unanimity over the amount to be used for the capital consumption involved. (TC: But would there be unanimity for correction at the level of GDP ?)
Second, natural resource deterioration due to commercial exploitation is not ‘depreciation’ in the accepted sense; it does not conform to standard wear-and-tear allowances applied at year-end to asset categories, and may in fact amount to as much as 100 per cent of the asset. In the latter case proceeds of the asset sale will all be a User Cost and must be exiled altogether from GDP. (TC: This is a matter of definitions. If Gross is taken as expenditure flows, then Net can be taken as depletion and standard depreciation. However, expenditure flows are not income indeed.)
Third, if stock erosion is viewed correctly as Marshall advised as emanating from ‘Nature’s store’, accounting conventions dictate that using-up stocks must be dealt with at the gross income estimation stage. Clearly natural resources are not ‘fixed capital’ but inventories, and the User Cost implicit in using them up should be recognized for correct accounting. (TC: But the situation becomes blurred, when the stocks can be used for investments to maintain the stocks, see above small model. In that case it makes some sense to define Gross as the expenditure flows, and deduct depletion with depreciation. However, expenditure flows are not income indeed.)
Such economic reasoning appears to escape the concerns of the estimators who have taken charge of the accounts resisting the economic logic behind the ‘greening’ quest.”


El Serafy did his doctorate in economics at Oxford in 1957, supervised by John Hicks, one of the giants in economics, and also famous for his insistence on proper accounting. El Serafy laments that this heritage has gotten lost:

“However, as the economists’ interest in studying social accounting faded the accountants and statisticians have taken over, often disregarding the concerns of economics, and disclaiming any hint that the national accounts should be estimating income.”

“Their message in brief is that no adjustment for environmental losses can be expected within the mainframe of the national accounts. This in effect is a death sentence on ‘green accounting’.”

Salah el Serafy has a point. The point has also been made by Tinbergen & Hueting.


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