The Carbon Cycle and the Value of Canadian Forests

Mohammed Dore, Mark Johnston, and Harvey Stevens
Department of Economics, Brock University, St Catharines, Canada
Dore@adam.econ.brockU.ca

Abstract

In the theory of renewable and non-renewable natural resources, what is the appropriate concept of scarcity rent remains controversial. A review of literature on this subject shows that a number of economists have divergent views. Brown and Field (1978) and Fisher (1979) argue that measures of scarcity suffer from serious conceptual shortcomings. If attention is confined to exhaustible resources, even here, what constitutes scarcity rent (or `user cost' or `royalty rate') and how it changes over time remains controversial. In the standard Hotelling model, it is argued that the scarcity rent rises monotonically over time at the social rate of discount. In contrast, both Heal (1976) and Hanson (1980), using very different cost functions, show that the scarcity rent must decline monotonically to zero, as the resource approaches exhaustion.

The divergence of views is replicated in the empirical studies too. For instance, Barnett and Morse (1963), Barnett (1979) and Johnson et al. (1980) all find that unit extraction costs in real terms have declined, so that these resources are in some sense becoming less scarce. Nordhaus (1974) also found that real prices of 11 major minerals fell over the period 1900 to 1970. In contrast, Smith (1979), Slade (1982), and Hall and Hall (1984) all find that real prices of natural resources are rising.

If we turn to renewable resources such as fish and forestry, it is not at all clear whether scarcity rent is deemed appropriate at all. The forestry literature is mainly concerned with optimal harvesting, although a number of forest ecologists have argued that forests are fast `disappearing', so that the remaining forests are becoming scarce. But as far as we are aware no attempt has been made to compute a shadow price or scarcity rent of forests in mitigating global warming; it is this which is a central objective of this paper.

In an attempt to reconcile the divergent and conflicting approaches to scarcity rent of natural resources, Farzin (1992) presents a generalized model which shows that in general the scarcity rent is non-monotonic. He shows that rising scarcity rent of exhaustible resources is a special case. He also presents an important corollary, that when the discount rate is zero (due say to intergenerational equity considerations) then contrary to the Hotelling rule, scarcity rent of an exhaustible resource always decline monotonically over time to zero, irrespective of the form of the extraction cost function.

Our paper is concerned with valuing forests for an important ecological function, namely the ability of forests (at least those in Canada) to sequester carbon and so mitigate global warming. It turns out that Canadian forest are a net `sink' of carbon - they capture more carbon than the release to the atmosphere.

An optimal control model (that maximizes value added) is used to derive a shadow price of forests. From the optimal solution, the value of forest is computed via econometric techniques, with value-added as numeraire. From this the marginal social opportunity cost of forests per hectare is computed. It is argued that it is this opportunity cost that must enter any harvesting decision model, or any other social cost-benefit calculation.

Our model is consistent with the results of Farzin (1992), mention above. The computed shadow price of forests obtained by normalizing the shadow price which is consistent with an ecological constraint, is shown to be non-monotonic in general, and a monotonic shadow price can be obtained as a special case. We use trend analysis and ARIMA models to determine the marginal social opportunity cost of a hectare of forest.

The econometric estimates of the shadow price of the forests and the resulting MSOC value of forests per hectare are obtained by a time trend model (Model 2) and an ARIMA model (Model 3). We regard the ARIMA model estimates to more representative of current conditions, and the estimated shadow price of the forests (in 1990) is a premium of the order of 25 to 32 percent. The corresponding MSOC value of a hectare of forest is between $ 350 to $ 412 in 1986 constant dollars. Naturally the estimates are subject to the limitations of the data.