The forest as a purely commercial resource

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