apply the approach consistently with the value- added method of summing the contributions of
individual economic units to obtain traditional net national product NNP.
Appropriate economic and accounting method- ology raises a further issue, however, of whether it
is worthwhile to implement green accounting: the practices of the traditional national accounts and
green accounting are, in a sense to be elaborated, equivalent.
For the
commercial aspects
of forestry, traditional NNP is arguably superior to
green NNP. For non-priced amenities, on the other hand,
green accounting would be a giant step forward. Because market prices do not exist, we revert to
an aggregate model to obtain expressions for the shadow prices of the amenities. We argue that the
interpretation by Weitzman 1976 of NNP as an index of welfare requires that valuation be done
at the margin, excluding consumers’ surpluses. If there are international environmental externali-
ties, green NNP may not capture all flows in the balance of trade unless adjustments are made in
the external accounts.
2. The forest as a purely commercial resource
2
.
1
. A re6iew of Faustmann
’
s analysis Suppose that the best use of a parcel of land for
the foreseeable future is as forest land, the opti- mal choice of species being replanted after each
harvest. Also suppose that the prices in all mar- kets are shadow values for the economy, so that
maximizing the value of the forest using these prices leads to socially optimal decisions. Let the
quantity of useful wood in a forest of age t \ 0 be qt, and have price pt and harvest cost Ht.
Let the cost of planting a new rotation be P, the appropriate interest rate be r, and variable profit
be pt = ptqt − Ht. A commercial forester’s problem is to choose the optimal rotation period
time between planting and felling, T, so as to
max
T
− P +
n = 1
[pT − P]e
− rnT
n
= L.
In the solution, the value of the land in sup- porting forestry is L, and
p ; T=rpT+rL.
1 At the temporal margin, the rate of increase in
profit from holding the trees an instant longer, p
; T, is equal to the interest on the capital tied up in the forest in the form of trees rpT and
forest land rL. At time t = 0, just after a harvest, a forestry
firm is holding only bare land, and the value of the forest, Vt, is given by V0 = L. Moreover,
if capital markets are in equilibrium so that there is no further opportunity for arbitrage, then an
instant after planting the value of the forest land with seedlings is given by V0
+
= L + P. This is the net present value, on the assumptions 1 that
the trees are left to grow until exactly time T and 2 that the rotation is repeated forever thereafter.
At time T, the value has grown to VT = V0
+
e
rT
= L + Pe
rT
. We can also express the value at time T as the
net contribution of the forest products plus the value of bare land:
L + Pe
rT
= VT = pT + L.
2 It is worth observing that, while the forest can
be imagined to be an even-aged stand on a given area, it could as easily be a stand with multiple
ages, with selective cutting of trees of age T, possibly on a sustained basis. In this case, the
same type of analysis would be used to derive the optimal value of T. Presumably there would be
higher costs of planting P and cutting HT; for example, economies of scale might not be fully
exploited. Ceteris paribus, this would imply a smaller value of L. The use of selective harvesting
would presumably be chosen in order to reap other amenities from the forest. Such practice
would increase the social value of bare land, as compared with considering only its commercial
values see Section 3 below.
2
.
2
. Green accounting By Eq. 2, the revenue, pTqT, realized
from the sale of the forest products is equal to [HT + L + Pe
rT
− L]. At time T, there is an
increase in social consumption opportunities of pTqT. A part of this value, HT, is a pay-
ment to factors, and is treated in well-understood ways. The remainder, [L + Pe
rT
− L], is the de-
cline in value of the forest, or depreciation, at time T.
The variable profit of the firm, pTqT − HT, is called the rent of the forest. Therefore,
depreciation at T exactly offsets the rent obtained at T. It would appear that, properly measured,
the net income should be exactly offset in the national accounts by an entry for depletion of the
forest. An implication is that the net contribution of the forest to national income is nil, for the
resources making up the harvest cost HT could have been used elsewhere in a fully employed
economy, producing a value of HT at the mar- gin. This is the widely held perception mentioned
above, and would imply that NNP is not so large as measured by the national accounts.
But this is not a complete view of the contribu- tion of the forest. At time T
+
, there is an invest- ment
of P
in planting
the next
rotation. Depreciation net of this investment is L +
Pe
rT
− 1. The portion Pe
rT
− 1 is the depreci-
ation of the accumulated value of the investment made at time 0 in the producing stand.
1
This component of the rent, then, is a quasi rent to the
investment to the human contribution. The re- maining portion, Le
rT
− 1, is the depletion of
natural capital
:
Le
rT
− 1 = pTqT − HT − Pe
rT
. 3
Some have argued that depletion is less than the total rent; our analysis indicates that the
reason is the appropriate accounting for invest- ments made in planting. Depletion is also less
than the net cash flow, [pTqT − HT − P].
Some have viewed the problem of forestry ac- counting as being analogous to accounting for a
nonrenewable resource, except that the forest can grow as well as be extracted. Analysis based on
this view yields a relationship for rent at the margin which is analogous to Hotelling’s rule. The
distinction between marginal and average rent becomes an issue. This formulation is inconsistent
with the point-output nature of the problem. Eq. 3 indicates that the relevant magnitudes are
incremental, not marginal.
2
An intuitive way to perceive the distinction being made here is to note that, at the chosen
harvest time, all trees of the relevant cohort are harvested. The forester adjusts the timing of the
harvest at the margin, not production one tree more or less to be harvested now or left for the
future. There is no analogy to Hotelling’s rule for a nonrenewable resource, and it is not germane to
distinguish between marginal and average magni- tudes. Eq. 1 resembles Hotelling’s rule. But it
holds only at T, not through time.
At any time t 0, T], the value is what the land with trees of age t would fetch in a perfect capital
market, or Vt = L + Pe
rt
. In Fig. 1, the value Vt rises from L
+
P at time t = 0 to L + Pe
rT
at T. The rate of growth of the instantaneous profit from harvesting the
trees at time t B T is faster than the rate of growth
Fig. 1. The solution to Faustman’s Problem.
1
At time T, there is a reinvestment of P, and hence there is an explicit expectation that an investment of P for T periods in
this forest will have a return of r. A similar point holds for the reinvestment of L.
2
Indeed, Hotelling’s rule is not useful for green accounting for even a mine Cairns, 2000a see below.
of capital value until T, when the two are equal. As there is no thought of harvesting before or
after time T, either of which would result in a loss of value, the rate of growth of the trees for t B T
is not pertinent to the valuation of the resource. Rather, at time t, there is an appreciation of the
6alue of the forest,
V : t=rL+Pe
rt
= rVt.
4 In the green accounts, this appreciation would
be accounted as an investment.
3
Also, at times t = nT, n = 0, 1, 2, 3, …, planting costs P would
be accounted as an investment. As is necessary for correct accounting, the undiscounted sum of the
investments in the forest is equal to the net value at any time, in particular, at time T:
L + P +
T
rL + Pe
rT
dt = L + Pe
rT
.
2
.
3
. Comparison of traditional and green accounting
The differences of traditional national account- ing from the green method above are that
there is no attribution of an increase in social welfare resulting from growth in value for
t 0, T, as V : t is not recognized as an invest-
ment; and
there is no accounting for depletion of the forest at the time of harvest, T.
At time T, the addition to traditional NNP is 1. an addition to consumption of pTqT on
the income side, income to harvesters, HT, and variable profit pT, plus
2. an addition to investment of P with corre- sponding entries on the income side, minus
3. depreciation of the original investment at t = 0 of P,
a net total at time T of pTqT. Green net national expenditure recognizes an
investment at t = 0 of P. At times t 0, T, it recognizes further investments of V
: t=rL+ Pe
rt
, having undiscounted sum L + Pe
rT
− 1.
At time T, there are investment P, depreciation [Le
rT
− 1 + Pe
rT
], and consumption pTqT. The undiscounted net total over the interval 0, T]
is pTqT. In both methods, the contribution of a national
forest is the sum over its component stands, as reported by economic units such as firms. In both
methods, at time t = 0 the contribution to NNP, P, is the same. For t \ 0 there is the same undis-
counted total, pTqT.
4
Therefore, for the com- mercial aspects of forestry, green and traditional
NNP are equi6alent, in the sense that they give the same total NNP over the harvest cycle. The equiv-
alence arises because in this model it is assumed that there is no feature of the forest which is not
captured in market prices.
Green NNP explicitly recognizes the growth of a forest’s value through time, and hence contribu-
tions in the form of ‘investments’ through forgo- ing the harvest until time T to intertemporal
social well-being. Manipulation of Eqs. 2 – 4 shows that the growth of value can be expressed
as V
: =r[pT−P]e
rt
e
rT
− 1. In terms of dis-
crete, annual measurements, with 1 + i = e
r
, the change in value in year t is
V
t + 1
− V
t
= i[pT − P]1 + i
t
[1 + i
T
− 1]
. Since value is increasing at rate 1
+
i , most of the attributed investment occurs toward time T,
the point at which traditional NNP attributes the full rent as net income. Suppose that T = 50. For
typical interest rates, the investment even in year 40 represents less that 4 of the net cash flow,
4
It could also be that the firm leases the land from a landowner. In this case, the amount rL would be accounted as
rental income to the landowner at each instant t. If the firm had other sources of profit, this amount would reduce the
firm’s profit at that instant. In that case, the net effect on traditional net national income would be nil. If the firm had
no other source of income, rental payments would be deducted at time T from pTqT − HT. Green accounting would
have no effect on total undiscounted NNP over the cycle.
3
This is consistent with the formula of Weitzman 1976, which is a special case of the asset – market equilibrium equa-
tion, C = rV − V : : the instantaneous payment is equal to the
sum of interest on the capital value and depreciation. Con- sumption of the forest at time t 0, T is nil. Any allocation at
time t 0, T between land and planting between nature and forester is arbitrary because the investment of L + P is sunk
on 0, T.
p 50 − P. The proportion of investment at-
tributed to the last 10 years is
t = 41 50
1 + i
t t =
1
50
1 + i
t
; for an interest rate of 5 this works out to over 40; for 10 to about 60. If
the national forest includes other ages, the total effect of a change to green accounting will be
attenuated, even if the ages are not evenly dis- tributed.
In sum, green accounting has a purely short- run effect on the national accounts, and does not
capture the long-run concerns which motivate the perceived need to do green accounting. In prac-
tice, the changes may not be significant.
Moreover, the changes in value, V
t + 1
− V
t
, in the green method are not observed in a market,
but are imputed.
5
An advantage of traditional NNP is that the accountant does not have to
impute values, but uses only observed transac- tions in markets. In effect, in traditional NNP, the
appreciation of the forest is realized at the same time as its depreciation, with a net effect of zero.
Also, timber and pulp prices fluctuate in practice, and the rate of growth of trees is not deterministic
but dependent on climatic factors. These stochas- tic features could affect the path of ptqt
through time, and hence the realized value of T through the stochastic analog of Eq. 1. By deal-
ing with realized values of variables, traditional practice obviates the need to make complicated
imputations of option value. Furthermore, the traditional accounts measure directly the level of
human economic activity in an industry, which is what they were devised to measure, and the mon-
itoring of which remains central to macroeco- nomic policy.
In this point-input, point-output problem with prices equal to social shadow values, there would
seem to be information lost in using green NNP rather than traditional NNP, despite the addi-
tional effort required for making imputations.
2
.
4
. Non-optimality, old growth and deforestation While we have made reference to Faustmann’s
analysis as a motivator of the present one, there is no need to assume that the chosen rotation period
is the optimal one, for the current or any future rotation. If the chosen harvest time is not optimal,
then the main other change is that the value of the land is lower than the optimal value, L. Under the
assumption that market prices are equal to social shadow values, traditional NNP correctly values
the lower contribution of the forest to social well-being. For example, if the rotation period is
longer than optimal, green NNP attributes spuri- ous capital gains for times t 0, T if Faust-
mann’s formula is used, and must impute capital losses for t \ T, up to the chosen harvest time.
Therefore, traditional NNP is more practical than green NNP if the actual rotation period is not the
optimal one.
Consider the harvest of a forest primeval. It is easiest first to assume that the forest is cut all at
once. Below we allow harvesting to occur through time. If L is the market value of bare
land, and other variables are as above, then the value of the forest at the time of harvest, T
, is VT
= pT qT
− HT + L.
After harvest but before planting, the value of the land is L. This would be the value determined
as above for the forest assuming new rotations, or else in some other use. Whatever that value may
be, the depletion at time T is equal to the full
rent, pT qT
− HT , and depreciation is this
magnitude less the planting cost P or other ready- ing of the land. We are attributing the original
‘investment in planting’ the forest to nature. The option to leave the trees growing past age
T would give rise to changes in the value because
of changes in price and possibly harvest cost. In keeping with our discussion, it would seem futile
to estimate these changes in the national accounts. Rather, economists would point to the losses in
national income and welfare resulting from sub- optimal policy.
If, on the other hand, the forester’s plan is to harvest the forest at rate qt from time t = T
to t = T
+ S, then the present value at T
is
5
In practice, both T and [pT − P] would have to be projected. In some countries there are markets for forests. But
there are not transactions for each piece of land at each date, as would be required actually to observe each value V
t
and hence each change in value V
t + 1
− V
t
.
VT =
T +
S t = T
ptqt − Hqt 1 + i
t − T
. Some have observed that this forest has analo-
gies to a mine, especially if it is not to be re- planted. Even so, we do not have recourse to
Hotelling’s rule, nor find any use for what some have called ‘Hotelling rent’ for details see Cairns,
2000a. Consider the part of the stand to be cut at time t \ T
. It has present value 6
t
T =
ptqt − Hqt 1 + i
t − T
. During time s B t, there is an appreciation of
the value of this part of the stand, equal to 6
t
s + 1 − 6
t
s = i ptqt − Hqt
1 + i
t − s
. This could be imputed as an appreciation. The
total undiscounted appreciation of the value of this part of the stand to time t is then
A =
T +
t − 1 s = T
[6
t
s + 1 − 6
t
s] = 6
t
T +
t − 6
t
T .
In this case, the depreciation of this part of the stand is
D = ptqt − Hqt = 6
t
T +
t. Therefore, the total net depreciation of the
stand is D − A = 6
t
T ,
and the total over all stands is VT , the value at
the time it is decided to cut the forest. Alterna- tively, the value VT
could be recorded at time T
, and be depreciated over time. Ideally, the depreciation
would be
6
t
T = [ptqt −
Hqt]1 + i
t
, so that the net contribution to NNP from the harvest at time T
+ t would be
N
t
= ptqt − Hqt − 6
t
T =
[ptqt − Hqt] 1 −
1 1 + i
t − T
n
. The net gain, N
t
, is the total of the appreciation above; it arises because interest increases the value
of this part of the stand from 6
t
T at time T
to 6
t
T +
t at time T +
t. In practice, an account- ing formula could be used for the depletion of the
full value VT .
An environmentalist might react to this analysis by remarking that the preference for traditional
over green NNP arises because Faustmann’s forest is a sustained forest, and that a major
environmental concern is deforestation. Suppose that a forest is taken into another use, and in this
use has a different value from that in forestry. Some have argued that a special treatment of this
change in value should be made in the accounts. But, so long as the 6alues in question are all
commercial, the appropriate treatment of the change in value is conceptually not different from
that applied to other assets which change their uses, such as buildings or rezoned urban land.
Indeed, the source of environmentalists’ concern about deforestation is loss of non-commercial
value.
Therefore, as far as the purely commercial as- pects of forestry are concerned, there is no com-
pelling reason to change the current practice of accounting for forests. Even if the forest is ex-
ploited suboptimally, the economic and account- ing implications are comparable with those in
non-resource industries. The equivalency we have noted arises because accounting methods have
been designed over the centuries to provide the maximal obtainable information about the effi-
ciency of commercial activities.
The only exception is the harvesting of a forest directly from its pristine state. In this case, as we
have observed above, depletion should be at- tributed. The reason is that the original planting,
by nature, is not ‘priced’. Non-priced features constitute a systematic problem.
3. Non-priced amenities