3. dynamic value tva

3.1 Differential rates of change

The TVA undertaken in the first part of this report assumes that the demands for both the extractive and protective uses of the forest areas are constant through time. This is clearly not the case in reality. A more appropriate analysis involves these values changing through time to reflect changes in economic and social circumstances. Importantly, recognition should be given to the ways in which the rates of change applying to extractive and protection values differ. In this part, such a “dynamic value” TVA is undertaken. A consideration of the factors that may underpin differential rates of change is outlined first².

3.2 Extractive values

The extractive uses of the forest involve the conversion of natural resources into intermediate products that in turn satisfy demands for the production of final products. For instance, hardwood timbers are cut and converted into structural timbers in order to satisfy the demand for products such as house frames. Wood chips are harvested to produce pulp and thence paper and card. In all cases, the outcomes are “producible” goods. This implies that the supply of these goods (both at the intermediate and final stages) can be enhanced over time. Furthermore, substitutes for both the final and the intermediate products exist. This improves the potential for supply enhancement over time. Hence, any increase in the demand for house frames may be met by enhanced production from existing hardwood forests, especially with the introduction of more advanced growing, harvesting and milling methods resulting from technological improvements. In addition, supplies of laminated softwoods or even alternative non-timber products such as steel may meet those increases in demand.

These characteristics imply that the value of the benefits derived from extractive uses of the forest may fall through time. The nature of the fall is dependent on the rate of technological advancement. When this falling value is discounted, it is clear that the present value of extractive benefits under the dynamic value model will be less than that calculated under the constant value model. The static model therefore overestimates the extent of the opportunity costs associated with protecting the forest. The threshold value that the protective values must exceed for forest protection to be a superior resource allocation to forest extraction is lowered under the dynamic value model.

3.3 Protective values

The situation where protective uses of the forest resource are involved is in marked contrast to the case described above for extractive values. For protective uses, the services provided by the forest enter directly into the utility function of the individual. That is, the benefits of forest protection are enjoyed directly by people. Furthermore, the services supplied by protected areas are not producible. Hence, their supply cannot be increased in response to increasing demands. It is also the case that once the supply has been reduced (say due to extractive use) it may be the case that the reduction is irreversible. That is, the regrowth of the forest after harvesting may not be able to supply the same services as the original, old growth forest.

The implication of these characteristics is that substitutes for the protective use of the forest are not as readily forthcoming as they are for the extractive use products. Hence, as demand for the protective use increases through time, the benefits so derived will increase.

A feature of this relationship is that the growth rate acts to counteract the effect of the discounting process. If the rate of growth of the protective values is greater than the discount rate, then the present value of the stream of protective values through time is infinite. Under the more reasonable scenario of the growth rate being positive but less than the discount rate, the effect is one of moderating the rate at which future values are discounted.

A number of factors influence the rate of growth of protective benefits. These are, in essence, the factors that drive and constrain increases in the demand for protective values. It is likely that, because of these factors, the growth rate will be non-uniform. In other words, because the factors driving and constraining demand increases will change through time, the rate of growth of protective benefits will vary through time.

To understand the way in which the growth rate varies through time, it is important to understand the factors that affect and define the demand for forest protection. First, demand is affected by the rate of growth in peoples’ willingness to pay for any given level of forest protection. This, in essence, is a reflection of changing tastes in the community and can be effectively proxied by the rate at which per capita income is growing (w). A factor that can be used to define demand growth is the rate at which forest protection services have been growing given a zero price (c).

The growth in demand that these two factors indicate is likely to slow through time. As far as direct use of the protected areas is concerned, the primary reason for this slowing is the carrying capacity of the areas. The value of c must therefore be carefully defined through time to account for the impact of the capacity constraint. Four different phases through time can be expected for the value of c:

1. From the outset to the time at which the carrying capacity constraint is reached (in year k), c could be expected to be maintained at current levels;
   
2. After the capacity constraint is reached, c could be expected to decline over time (as c*) until it falls to equal the rate of growth of the population (in year m);
   
3. For a further period of time (until year z), c remains equal to the rate of growth of the population (c_m); and,
   
4. The final phase involves no growth at all.

The effect of this process is, overall, to decrease the impact of the discounting process on the extent of the present value of protective benefits. The exact magnitude of this impact is determined by the values of all the parameters that define the model.

3.4 Re-estimating foregone extractive values

To re-estimate the foregone extractive values detailed for the constant value analysis in a dynamic value context, an additional piece of information is required: the rate at which substitution is possible between the existing output of the South Coast sub-region forests and alternatives. This rate, to a large extent, is driven by the rate of technological advance. Estimates of this rate are very difficult to derive. In the past, substitution for hardwood products has been made possible by numerous technological advances, primarily relating to the use of plantation softwoods in the construction industry and in the production of papers and packaging. As a conservative estimate, it is assumed that the rate of technological change affecting the timber products industry will be in the order of one per cent per annum.

In Table 4, the foregone extractive values relating to the scenario for the South Coast sub-region is displayed given a one per cent change in technology every year, at two discount rates.

3.5 Forest protection values over time

The calculation of the present value of a stream of forest protection benefits in the dynamic value context depends on:

• the magnitude of the initial year’s protection benefit
  
• the discount rate; and,
  
• the factors that influence the extent to which the benefit grows through time: w, c, k, z, c_m, and c*.

The values of these parameters are now discussed.

w

The rate at which willingness to pay for protected forests increases is defined in w. It is an estimate of the rate at which the demand curve shifts up the vertical axis through time. Krutilla and Cichetti (1972) argue that this rate should be a reflection of the rate at which per capita real income is growing. In Australia, this rate has in recent times averaged between 3 and 5% per annum. The model estimated below uses the 3%, 4% and 5% rates to test for sensitivity of the results to this parameter specification.

c

The rate of growth of consumption of protected forest benefits at a zero price, up to the carrying capacity, is defined as c. There are few studies that have investigated this rate. Krutilla and Fisher (1975) report US data indicating a range from 10 to 45%. Saddler et al (1980) use a more conservative range of estimates between 7.5 and 12.5%. This is in line with the more recent findings of Worboys (1997).

k

The carrying capacity of the protected forests is defined as k. There are little data regarding current use levels and even less regarding what can be regarded as a carrying capacity. Necessarily, the latter is a subjectively defined parameter because of differing perceptions of what is the carrying capacity. The approach used by Saddler et al (1980) is advocated here. The carrying capacity is assumed to be at 20 times the current use level. Combining this judgement with the assumed values for c and it can be calculated that k is 40 years when c is 7.5%, 30 years when c is 10% and 25 years when c is 12.5%.

m

The time at which the rate of growth of consumption falls to the population growth rate is defined as m. There is little on which to base this estimate. 50 years is used by Saddler et al (1980) for Australia over 10 years ago. Hence 40 years is used here.

z

The time at which no further growth is experienced. Again, an assumption is made that this occurs at 50 years.

c_m

Population growth rates in Australia are assumed to be stable at around 0.6% in 30 years time

c*

The rate of growth in consumption is assumed to decline between time period k and time period m. This rate c* is therefore determined by the parameters k, m and cm. The decrease in c*, using a straight line decay function is:

when c = 7.5%    c* decreases at 0.0 % per annum (note: k=m)
            =10.0%                  “ 0.94 %               “
            = 12.5%                 “ 0. 79 %              “

The model is implemented by calculating the present value of $1 initial year’s benefit from the protected forest areas under the range of parameter values specified above. Through this process, the sensitivity of the results to changes in the values of the parameters can be tested. The results of the model calculations are presented in Tables 5 and 6.

Hence:

• at a discount rate of 8% (i);
  
• with incomes rising at 4% (w);
  
• consumption of protected forest areas rising initially at 10% (c); and,
  
• consumption falling to equal the growth in population in 40 years time (m);

the present value of $1 worth of current year forest protection benefits is approximately $98.

3.5.1 The initial year’s threshold

To estimate the threshold value for protection benefits in the initial year, the present values of the extractive values foregone, are divided by the present values of protective benefits growing from an initial value of $1 as calculated in the previous section. These dynamic value thresholds are displayed in Tables 7 and 8.

Again using the scenario of:

• a discount rate of 5% (i);
  
• with incomes rising at 4% pa (w);
  
• consumption of protected forest areas rising initially at 10% pa (c); and,
  
• consumption falling to equal the growth in population in 40 years time (m);

then the current year threshold value for the protective benefits provided by the Current Commitments scenario is $2125.

In other words, the protective benefits of the forests reserved under the Current Commitments scenario in the current year, given the situation outlined by the assumed parameter values, would need to be greater than $2125 for the reservation decision to be desirable from a community wide perspective.

The data in Table 7 demonstrates the sensitivity of the threshold values to the range of parameter assumptions that have been made. Of particular note are the impacts made on the threshold values by the choice of:

• discount rate (the increase in discount rate from 5% to 8% causes the threshold value to increase by about 30%)
  
• income (cutting the rate of income growth from 5% to 3% causes the threshold value to rise by approximately 50%)
  
• consumption trends (reducing the rate of growth of protected forest use from 12.5% per annum to 7.5% per annum results in an increase in the threshold value by approximately 40%)

The selection of these parameter values is of great importance to the decision making process. However, once they have been chosen, the critical decision for policy makers is whether the protective benefits of the alternative scenarios that will be enjoyed in the space of the current year are worth their threshold values. This determination would be benefited by some quantification of those protective benefits, however, such an exercise is not undertaken here. Rather, an analysis of benefit estimates generated by other studies is used to provide some perspective for the threshold value estimates.

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