ANALYSIS
Incorporation of risk in regional forest resource accounts
Michel K. Haener *, Victor L. Adamowicz
Department of Rural Economy,Uni6ersity of Alta,Edmonton,AB,T6G2H1Canada
Received 13 May 1999; received in revised form 8 November 1999; accepted 13 December 1999
Abstract
To be an appropriate indicator of sustainability, a net income measure projected into the future should consider risk. Several authors have demonstrated how risk can be formally incorporated into welfare measures like Green Net National Product (NNP), however, the resulting measure can be considerably more complex than its deterministic counterpart. A practical alternative to formally incorporating risk is to use simulations of the type outlined in this paper to provide information about the expected impact of risk. This information can be used to apply a stochastic version of a sustainability rule that requires that the expected value of net income be non declining. This paper discusses the importance of risk and uncertainty to welfare measurement and more specifically the measurement of net income from forest services in a region of northern Alberta. Two different approaches to valuing resource extraction are compared. The depreciation approach and the wealth-based approach provide very different projec-tions of net income. We demonstrate that when a renewable resource is subject to risk, the wealth-based approach provides a more appropriate measure of the influence of resource use on future consumption possibilities and the sustainability of net income. © 2000 Elsevier Science B.V. All rights reserved.
Keywords:Resource accounting; Risk; Forest resources; Income measurement
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1. Introduction
Theoretical literature related to resource ac-counting suggests that net national product (NNP) is the most defendable accounting aggre-gate and that extensions of income measurement to include the environmental sector should use
NNP as a starting point (Weitzman, 1976; Aronsson et al., 1997). Numerous economists have derived measures of ‘Green NNP’ from gen-eralized and simplified models of economies with environmental and resource sectors, including Hartwick (1990), Dasgupta and Ma¨ler (1991), Ma¨ler (1991), Dasgupta et al. (1994). Their work suggests that Green NNP should be adjusted to include the value of flows (goods and services consumed in the current period) and account for how current changes in capital stocks will affect * Corresponding author. Tel.: +1-780-4921518; fax: +
1-780-4920268.
E-mail address:[email protected] (M.K. Haener)
future wellbeing. Accounting for changes in capi-tal stocks, requires that the value of the stock change be included in the measure. Essentially, the depreciation or appreciation of capital stocks must be included in the income measure.1
Other more recent work related to national product related welfare measures considers how relaxing certain assumptions in the underlying model of the economy, influences the Green NNP expression and its appropriate measurement. The influences of technological change, population growth, variable interest rates and future resource discoveries, have all been considered in the litera-ture; however, in this paper we consider the influ-ence of uncertainty on the net income generated by a small open economy.
This paper will discuss how fire and price risk can be incorporated into the resource accounting framework and the implications for the measure-ment of regional net income. The analysis builds on the resource accounting framework developed for a region of public forestland in northern Al-berta in Haener and Adamowicz (1999).
The paper is organized as follows. Firstly, re-cent literature related to the incorporation of uncertainty in national product related welfare measures, will be discussed. Secondly, the meth-ods used to simulate the effects of fire and price risks on the future values of the case study re-gion’s net income are outlined and the empirical results are presented. Next, the implications of these simulations are discussed. The paper con-cludes with a brief summary, discussion of recom-mendations and suggestions for future research.
2. Incorporating uncertainty in NR accounting2
Most literature which examines the measure-ment of Green NNP assumes a closed economy. Under this assumption Dasgupta and Ma¨ler (1991), Aronsson and Lo¨fgren (1993, 1995), Aronsson et al. (1997), Hung (1993), Dasgupta (1995) have mathematically illustrated how differ-ent types of uncertainty can be incorporated into national product related welfare measures. The resulting welfare measures are often much more complicated than their deterministic counterparts. The measurement of income in a small open economy, where interest rates, terms of trade and prices are not likely to be constant over time, has been given less attention in the literature. There are however, notable exceptions, including Asheim (1986) and Brekke (1997). Brekke (1997) suggests that ‘for a small open economy, income could be estimated through estimation of the na-tional wealth’ (p. 517). Using this approach, wealth can be computed for any production plan and set of future prices if we assume the economy has access to perfect credit markets. Furthermore, ‘no assumption about preferences are needed to compute Hicksian income’ (p. 518).3 From the wealth estimate, maximum sustainable consump-tion can be computed.
Of most interest here is Brekke (1997)’s consid-eration of income measurement under uncer-tainty. Firstly, Brekke suggests that in the case of uncertainty resource wealth should be defined as ‘the expected present value of future net revenues’ (p. 521). The concept of sustainable consumption must also be extended. According to Brekke (1997, p. 521),’since future rents are uncertain, we cannot determine a consumption level that can be sustained under all sets of circumstances’. Brekke (1997) suggests that a more reasonable sustain-ability rule in these circumstances is one that 1An implicit assumption underlying the Green NNP
mea-sure is that of weak sustainability. Weak sustainability as-sumes that natural and human-made capital are substitutes; therefore, depletion of natural capital can be counter-balanced by investment in human-made capital. Strong sustainability, on the other hand, does not assume substitutability between natural and human made capital; therefore, to remain on a sustainable path natural capital stocks must be non decreasing (Hanley et al., 1997). We focus solely on weak sustainability in this paper.
2In this paper, we use the terms risk and uncertainty interchangeably. However, some people define risk as random-ness with a known probability distribution and uncertainty as randomness with an unknown distribution (Lutz and Munas-ingnhe, 1994).
requires that the expected value of income flows be non declining over time or in other words that ‘ expected future consumption should be at least as large as current consumption’ (p. 521). If we ignore uncertainty and use a deterministic income measure, we may make inaccurate conclusions regarding sustainability. The reason being that there will be an inherent amount of variability in income that results from risk.
Brekke (1997) compares the wealth-based in-come calculations described in his paper to other approaches to measuring resource stock changes. The depreciation approach put forth by Repetto et al. (1989) values the total change in stock in the current year at current prices. Brekke describes why this approach is not consistent with the wealth approach. Another approach is El Serafy’s user cost approach, which was derived to calcu-late the appropriate measure of income from non renewable resource extraction. Brekke successfully argues that this approach is ‘a special case of the wealth approach’ which assumes constant prices and production over time (p. 523). In this paper, we further illustrate the usefulness of the wealth approach when future risks to resource revenues are significant. We also show how the deprecia-tion approach inadequately accounts for these risks.
3. Importance of risk and uncertainty to forest income flows
Uncertainty and risk are associated with future income flows from forest resources. The uncer-tainties associated with income generated from timber harvesting stem from uncertainty regard-ing both future environmental and market condi-tions. Changes in environmental conditions can alter the growth and characteristics of the timber stock and thereby influence commercial forestry, recreational activity, biodiversity and other forest services. For example, the weather can influence harvest costs and the amount harvested in a given year. Market conditions can also influence future income flows from the forest. Timber flow and stock values can change in response to output price fluctuations stimulated by factors such as
consumer preferences, development of substitutes and technological advancements.
Many aspects of future conditions cannot be anticipated, however, there are some parameters for which an equation or probability distribution could be used to characterize movements over time. Fire risk, an environmental risk, and price risk, a market-related risk, are examples. A num-ber of different fire risk models can be used to attach a probability to the likelihood of a fire occurring in an area. It is expected that incorpo-rating the distribution of fires over time in forest resource accounts will influence the volume of timber harvested and the size of the timber stock in future periods, thereby affecting the value of net income in future periods. The historical vari-ability in market prices, pulp and lumber prices in this case, can also be used to obtain a reasonable estimate of the distribution that future prices are likely to follow.
4. Case study
1996. Commercial forestry comprises :62% of the total. Refer to Haener and Adamowicz (1999) for a brief description of the region and discussion of the methods used to estimate net income.
Haener and Adamowicz (1999) apply the ‘Green NNP’ approach but they do not consider the influence of uncertainty on the measurement of regional net income. Fire and price risks were identified as potentially important forms of risk in the case study region. If these forms of risk are significant, the literature discussed in the pre-vious section suggests that the net income mea-sure for the region should account for the influence of these forms of risk on future rev-enue flows. Without these adjustments, the in-come measure will be inaccurate and use of the index to assess sustainability may be inappropri-ate.
Formally adjusting the net income measure for the region requires re-formulating the model of the economy to account for stochasticity. A stochastic differential equation, which character-izes the influence of risk on future revenue flows, would have to be added to the problem. How-ever, a number of other complicating factors would also have to be considered. Hartwick (1990) and Ma¨ler (1995) explain that only unan-ticipated (or partially anunan-ticipated) shocks to the economy are relevant to current measures of wellbeing. Correctly anticipated changes have ‘al-ready been capitalized in other prices and there-fore, already been included in the net national income concept’ (Ma¨ler, 1991, p. 13). Estimating contingent shadow prices could be complicated, since it may be difficult to determine the degree to which current prices already reflect risk.
The practical question that must be addressed is whether it is enough to simply qualify our interpretations of net income or whether the net income measure for the region should be for-mally adjusted to account for risk. Simulation exercises such as the one carried out in this pa-per, provide a practical alternative to re-formula-tion of deterministic welfare indices. The simulation allows the significance of risk and its expected influence on sustainable income to be assessed.
5. Simulations
A series of simulations were conducted to demonstrate how fire and price risks influence regional resource revenue flows and timber stocks. The simulations use value estimates from the 1996 resource account developed for the region in Haener and Adamowicz (1999).
The simulations illustrate the effect of fire and price risks on the realization of the study region’s net income over a 20-year period. Only the effect of these risks on commercial forestry (pulp and lumber production, changes in the stock of timber capital) is considered. All simulations assume that fire and price risk do not influence other components of net income. Therefore, the sum of the other component values (i.e. produced capital depreciation in the forest industry, commercial fishing and trapping recreational activity, traditional aboriginal land use, biodiversity maintenance and carbon sequestration) stay constant at $10.56 million. In reality, the other components of the net income measure would also be influenced, especially in the case of fire risk.
As noted, the simulations predict revenue flows and stock changes for the next 20 years. This simulation period is used since this corresponds to the duration of the FMA and to the planning horizon used in a typical general development plan (Land and Forest Service (LFS), 1998). For each of the 20 years, 500 draws are made from the probability distribution characterizing fire and/or price risk. A large number of draws is required, because, as will be seen, the distributions are highly stochastic. It was anticipated that 500 draws would be sufficient to characterize the shape of the distribution of the annual net income values. A greater number of draws would give a more precise picture, but would also be more computationally demanding.
In all cases, income measures are reported in 1996 $Cdn. Annual values are not discounted and therefore, represent the net income predicted to occur in that year. Firstly, fire risk is simulated, then price risk and finally both types of risk are simulated together.
6. Fire risk simulations
Armstrong (1999) analyzes the distribution of fire risk over time for a region in northeastern Alberta that closely corresponds to the case study region. In his analysis, Armstrong (1999) com-pares several spatially explicit models that incor-porate variables such as vegetation type and topography. He finds that his relatively simple non spatial stochastic characterization of fire risk predicts as well as these other models. Armstrong finds that the distribution of fire risk, when ac-counting for suppression efforts, can be character-ized as a lognormal with a mean annual burn rate of 0.006296% of forest area and S.D. 2.853. Five hundred 20-year random draws from this distribu-tion were simulated.
The simulations require a number of assump-tions. It is assumed that deciduous and coniferous harvest levels (H) depend solely on the level of the respective timber stock (S). Harvest levels are assumed to be a constant percentage of the timber stock based on the amount of stock harvested in 1996, but limited to a maximum of 5% above the
harvest level in 1996. The reason for using con-stant harvest rates is that forest management reg-ulations in Alberta dictate that harvest levels be based on sustained yield (i.e. even flow) con-straints. Companies are required to remain within 5% (above or below) the annual allowable cut calculated, based on sustained yield, unless cir-cumstances are beyond their control (i.e. fire). Therefore, the regulatory structure results in fairly constant harvest rates. Another option would be to use the historical pattern of harvest rates; however, there is little historical data related to harvest rates in the region because Alberta-Pacific has only been cutting since about 1993 and opera-tions have stabilized only recently. Finally, we opted not to try to determine a harvest plan based on an optimal rotation model, since it would not be relevant to reality. As Brekke (1997) points out ‘we can compute wealth for any given production plan, optimal or not’. We follow the suggestions of Brekke and try to make our production plan mimic expectations.
In 1996, Alberta-Pacific harvested about 0.7439% of the deciduous stock and 0.2358% of the coniferous stock in the region. Quota holders harvested about 0.6618% of the coniferous stock. Therefore,
The superscripts d and c are used to differenti-ate between deciduous and coniferous timber and the superscripts A and Q are used to differentiate between Alberta-Pacific and quota holder conifer-ous harvest. It is assumed that all deciduconifer-ous harvest over the 20-year period can be attributed to Alberta-Pacific. The relative proportion of coniferous stock harvested by Alberta-Pacific and quota holders is assumed to remain constant at the 1996 level.
Table 1
Summary statistics for fire risk simulation parameters
Ln rate Rate
−9.02915 0.0051457 Mean
Standard deviation 2.84245 0.041551 2.4539E-09
(−9.0848, (4.5701E-7, 95% confidence
−8.9734)
interval 0.034018)
Using the above equations and the random draw of burn rates, volumes of timber harvested and annual stock changes are predicted for the next 20 years. The averages of the high and low rent estimates from Haener (1998) are used to determine the revenue associated with the annual harvests. It is assumed that other components of net income remain constant at 1996 levels.
7. Results
Descriptive statistics are given for the simula-tion parameters in Table 1. The simulasimula-tion pro-cess results in a sample of 500 20-year paths of timber revenues and stock changes. Therefore, for each of the 20 years, there are 500 predictions of the path of net income using the depreciation approach and 500 predictions of the path of net income using the wealth approach. Descriptive statistics for the predicted net income values for the 20 years are provided in Table 2. Some of the highlights of the results are briefly reviewed in this section. The significance of the results of all three sets of simulations is discussed in Section 5.
The information generated by the simulations was used to calculate annual net income estimates using the depreciation approach and the wealth approach to calculate the adjustment associated with stock changes. Fig. 1 shows the mean of yearly net income values and the 95% CI around the values for the two approaches. The CI shows
St
Similarly, changes in the coniferous stock are represented by
Stc=Stc+Gtc−1−Cct−1−HtcA−1(Stc−1)
−HtcQ−1(Sct−1)−Btd−1 (4)
where G is growth, C is volume lost to land use conversion and B is volume burned. Annual growth and land use conversions are also assumed to remain constant proportions of the stock based on 1996 levels. Annual growth of the deciduous stock is set at 1.0784% and annual growth of the coniferous stock is set at 1.2299%. Annual land use conversion is set at 0.006680% of the decidu-ous stock and 0.006604% of the coniferdecidu-ous stock; these represent the 1996 levels.
Table 2
Fire risk simulation summary statistics: net income, years 1–20
Average of annual Highest of annual
Annual net income statistic Lowest of annual
Depreciation approach
Mean 127 394 932 88 660 532 172 198 468
−1 066 302 314 −65 430 098
−511 764 178 Lower 95% confidence interval
245 000 957 240 487 312 235 161 260
Upper 95% confidence interval Wealth-approach
176 412 759 180 273 909
Mean 172 578 664
79 403 011 177 168 282 123 853 227
Lower 95% confidence interval
184 689 639
the area on the graph, which, if all 500 simulated time paths were drawn, would encompass 476 paths.4
When the depreciation approach is used, the path of net income displayed is highly uncertain. Fig. 1 reveals that the confidence interval for the 500 draw values for a given year is extremely large (over $1 billion in some years). This variability occurs because large fires periodically cause the timber stock to decline to near zero. Since the depreciation approach adjusts current income flows by the value of the change in stock for that year, the variability in stock levels is reflected directly in the net income measure.
The path of mean or expected net income that results when the wealth-approach is used is much smoother. The confidence intervals increase over time but they do not fluctuate greatly. In addi-tion, the path of net income is higher than the one that results from the depreciation approach.
Visual representations of the simulated net in-come values are also provided for selected years. Year 10 was selected to illustrate the distribution of the 500 draws for a given year. The distribu-tions for other years are very similar. Fig. 2 shows a histogram and cumulative frequency curve for the net income values for year 10, for both the depreciation and the wealth approach. For the depreciation approach, the first interval in the chart (B90 million $) includes some very small values, since the net income predictions for a given year include values as low as about $1 billion. However, most values are grouped tightly around the upper end of the distribution in the $220 – $230 million interval. The corresponding chart for the wealth approach shows a distribu-tion with a very similar shape but much smaller range. Most values lie between $180 and $190 million. There are fewer values at the extreme left of the distribution and the absolute minimum is about $10 million.
8. Price risk simulations
As with the fire risk simulations, the simulation of price risk requires the distribution of future prices to be explicitly defined. In this case, the distributions of pulp and lumber prices were esti-mated using historical time series data. Lumber prices for western spruce – pine – fir (f.o.b. mill net or factory gate) were obtained from Natural Re-sources Canada (1996) and Warren (1997) which report annual average prices. Northern bleached hardwood and softwood pulp prices were ob-tained from the Pulp and Paper North American Fact Book (1996).5
Price movements over time can be modeled in many different ways. Here the characterization of future price movements is relatively simple. The following regression equations were estimated for each price series:
Autoregressive 1 (AR1):
Pt=a1Pt−1+g+et (5)
Autoregressive 2 (AR2):
Pt=a1Pt−1+a2Pt−2+g+et (6)
Logged Autoregressive 1 (lnAR1):
lnPt=a1lnPt−1+g+et (7)
Logged Autoregressive 2 (lnAR2):
lnPt=a1lnPt−1+a2lnPt−2+g+et (8)
The above equations were estimated using his-torical annual average prices that were converted to 1996 Canadian dollars. A combination of fac-tors including overall model significance (P -value), coefficient significance, examination of residuals was used to select the equations that would be used in the simulations. For hardwood and softwood pulp the AR2 relationship appeared to explain price movements best, whereas for lum-ber, lnAR1 was found to provide the best fit. A time variable was added to these specifications but was not found to be significant.
5Since, f.o.b. mill net pulp prices were not available, prices for pulp delivered to the US are used. This is accounted for in the estimate of average variable cost (AVC).
Table 3
Equations for future price movementa
Equation type Coefficient
Number of years Intercept
Price series Standard error
(g)
(n) (a1) (a2) (se)
AR2 0.75598
HBKP 20 −0.54057 652.56185 151.87626
SBKP 20 AR2 0.86759 −0.62316 699.86508 141.20234
lnAR1 NA 0.70015 1.75496
Lumber 22 0.201
aHBKP, hardwood bleached kraft pulp; SBKP, softwood bleached kraft pulp.
The parameters of the regressions used to pre-dict future prices are listed in Table 3.
Note the relatively high standard error values for all three regressions. Even the selected models leave much of the variation in prices unexplained. As noted above, the method for predicting future prices is kept relatively simple in this analysis, however, a variety of more elaborate methods might be applied. For example, the pulp and lumber market are sensitive to a number of fac-tors including the interest rate, exchange rates and trade policy (i.e. softwood lumber tax). Predic-tions of the future path of these variables might also be used to forecast future pulp and lumber prices. Similarly, the futures markets for pulp and lumber could be used to assist in predicting future prices.
In order to isolate the influence of future price, the annual deciduous and coniferous harvests are kept at a constant percentage of the stock equal to that which applied in 1996. This means that opening and closing stocks and the equations that determine stock volumes over time in the fire simulations are not required. The annual harvest level and change in the stock remain at the same volumes as in 1996. The average variable cost estimates in Haener and Adamowicz (1999) is used with the projected prices to calculate pulp and lumber rent. As with the fire simulations, 500 draws of 20 years each are made from the error term distributions.
9. Results
Tables 4 – 6 provide descriptive statistics for the parameters of the HBKP, SBKP and lumber price
simulations. As in the fire risk section, Table 7 illustrates the resulting net income values for the 20 years of the simulation. Figures corresponding to those in the fire section are also provided (see Figs. 1 and 2).
For the 10 000 draws, Tables 4 – 6 report the mean rent values to be $71.32 for HBKP, $75.68 for SBKP and $36.90 for lumber. The pulp rent values are significantly higher than the average rent values estimated for 1996 ($46.56 for HBKP and $50.57 for SBKP), whereas the lumber rent is much lower ($60.89 in 1996).
Table 4
Summary statistics for hardwood bleached kraft pulp (HBKP) price simulation
Summary statistics for softwood bleached kraft pulp (SBKP) price simulation
Minimum 76.96 −66.60
473.75 1696.65 209.79 Maximum
1002.07
Table 6
Summary statistics for lumber price simulation
LnP Price ($) Rent ($/m3)
Error term
5.8875
Mean −0.00116 375.39 36.90
0.2856 108.23
0.2031 25.22
Standard deviation
4.7525 115.88
Minimum −0.8364 −23.56
7.0043 1101.32
0.7346 206.05
Maximum
2.2517 985.44 229.61
Range 1.5710
Under the depreciation approach, Fig. 1 shows that the time path of net income has fairly stable confidence intervals over time compared to those generated when fire risk is simulated. The upper and lower CIs are far apart (about $500 million) but appear to be equidistant from the mean. Table 7 reports that for the 20 years mean net income ranges from about 133 million to $374 million. The difference in the time paths generated using the depreciation and the wealth approach is less marked in this case. The shapes of the curves are similar; however, the wealth approach generates a time path, which is less variable. Under the depre-ciation approach, mean net income ranges from 116 to $270 million and the 95% CI around the annual mean ranges from 6.9 to $381 million.
Fig. 2 shows that for a given year the distribution of net income values for the depreciation and the wealth approach is very similar. Again, the depre-ciation approach results in a distribution with a slightly larger range and the middle of the distribu-tion is higher.
10. Fire and price risk simulations
In reality, timber capital is subject to both fire and price risk. Therefore, simulating both types of risk together may provide more realistic and appli-cable results. The final set of simulations uses the fire risk and price risk parameters from the previous simulations to illustrate the combined effect of these two types of risk on the value of net income.
11. Results
As with the previous simulations, the results of this combined simulation are summarized in a table of descriptive statistics (Table 8) and a series of figures (Figs. 1 and 2). (As with the price risk simulation, a cumulative frequency diagram and histogram are only shown for year 10.)
Fig. 1 shows that when the depreciation ap-proach is used the mean yearly net income values produce a somewhat unstable path. The upper CI
Table 7
Price risk simulation summary statistics: net income, years 1–20
Lowest of annual
Average of annual Highest of annual
Annual net income statistic Depreciation approach
288 936 520 132 652 963
Mean 374 045 681
130 393 535 Lower 95% confidence interval 64 341 341 −34 121 181
509 822 227
Upper 95% confidence interval 297 607 298 614 569 846
Wealth approach
269 709 346 116 018 452
212 688 904 Mean
47 157 086
Lower 95% confidence interval −9 061 119 179 095 907
372 642 633
Table 8
Price and fire risk simulation summary statistics: net income, years 1–20
Annual net income statistic Average of annual Lowest of annual Highest of annual Depreciation approach
60 405 755
Mean 137 330 540 241 060 264
−1 357 505 422
−642 290 552 −82 846 996
Lower 95% confidence interval
497 696 587
Upper 95% confidence interval 315 087 376 591 251 783
Wealth approach
Mean 208 402 188 115 950 744 268 417 402
−23 932 034 177 537 244 Lower 95% confidence interval 30 473 649
185 849 964 448 431 123 376 991 472
Upper 95% confidence interval
of this path is relatively stable in comparison to the lower confidence interval, which is highly spo-radic across years. Table 8 confirms the variability in the yearly means, which range from about $60 million to $241 million. The influence of fire risk appears to dominate since the resulting figure closely resembles the corresponding chart for fire risk.
Again, the time path of net income that results when the wealth approach is used is less stochastic than the path generated when the depreciation approach is used. Yearly means are still somewhat variable, ranging from 116 to $268 million; how-ever, the CIs around the means are much tighter than the confidence intervals in the depreciation approach. In addition, the chart resembles the price risk chart suggesting that price risk is the dominant influence on net income.
From Fig. 2, we can see, that again the depreci-ation approach generates a distribution of annual values for year 10 with a greater spread. The tails of the distribution extend further and contain more values than the corresponding chart for the values generated by the wealth approach. The middle of the distribution also occurs at different points; the median of distribution generated by the depreciation is between $50 and $100 million larger.
12. Discussion
As Brekke (1997) notes ‘the income measures that Repetto et al. (1989) obtain, fluctuate sharply over time’ (p. 523). Our results also show, that
income calculations based on the depreciation approach fluctuate sharply over time compared to the measure of income using the wealth-based approach. When the depreciation approach is ap-plied, the entire appreciation (depreciation) in re-source stock for the current year is valued and added (subtracted) from income flows or the year. Therefore, if the volume or the price of the re-source stock fluctuates over time then net income will as well. However, in the case of renewable resources like timber, this type of adjustment overestimates changes in the productive capacity of the resource. For example, the approach does not account for the fact that if the stock of timber decreases due to cutting or to fire, the land can regenerate to productive forest and provide in-come flows in the future periods.
depreciation approach is used. There is still a degree of fluctuation in net income since fires and prices are stochastic, but the path of net income is much smoother. Therefore, we find that, particu-larly where a renewable resource is subject to risk, the wealth approach is a more appropriate method for valuing stock changes.
The simulations suggest that fires and price changes play an important role in determining the annual net income of the region. Due to the influence of these risks on commercial forestry, the net income of the region can be expected to fluctuate from year to year. The simulations using the depreciation approach give the impression that fire risk is the dominant influence. However, as we have discussed, the depreciation approach does not account for the ability of the resource to regenerate in future periods, therefore, it over-weights current declines in stocks, essentially treating them as permanent deletions. We argue that the wealth approach provides a more appro-priate estimate of net income. Using this ap-proach, it appears that price risk plays a larger role in determining expected annual net income in future periods.
The simulations provide some valuable insights regarding the expected path of net income in the case study region. Based on the arguments above, we rely on the results of the wealth approach. The first set of simulations isolates the influence of fire risk. The distribution of the net income predicted for a given year is highly skewed with most values predicted to be relatively close to the mean, but several values far below the mean. The reason for this result is related to the lognormal distribution of forest fires. Although the mean burn rate is very small, the lognormal form combined with the high variance of the burn rate distribution means that some draws select a burn rate that is 1 or very near to 1 (i.e. the entire forest or almost the entire forest burns). For these draws, the flow of income falls to near zero since there is no stock to harvest.6 Fig. 1 shows that net income declines
into the future. This is partly due to the way in which the adjustment for the change in stock is calculated. Since we limit our time horizon to 20 years, we consider revenue flows for this time only. Therefore, as we approach the end of the time horizon (i.e. year 17), we have few years of future revenue flows remaining (i.e. 3). As there are fewer years of future revenues, the annuity equivalent of the expected net present value of these revenues is smaller and more variable since there are fewer years for the forest to regenerate after large fires. This result illustrates the impor-tance of providing companies with stable and long-term tenure. If a company believes that its rights will be terminated in the near future, it will prefer to harvest more in the current period since the resource could burn in the next period and there would not be sufficient time for the trees to regenerate.
In the price risk simulations, the amount of harvest is assumed to remain constant at the 1996 level. Therefore, any changes in annual net in-come are directly attributable to pulp and lumber price fluctuations. The price risk simulation pre-dicts much more variability in yearly net income values and the mean values are higher than when only fire risk is considered. In 1996, pulp prices were relatively low; therefore, it is not surprising that net income is expected to increase in future periods. The distribution of net income for year 10 closely resembles the normal. This is expected to an extent since the simulated error terms for SBKP and HBKP were normally distributed. However, the influence of the error term for lum-ber prices, which was drawn from a lognormal distribution, is less apparent. If we compare this graph with the corresponding graph of year 10 values for the fire risk simulation, it is apparent that the spread of the values when price risk is considered is much larger. This explains why the CIs in for price risk are much larger than for fire risk in Fig. 1. The influence of the two types of risk is much different. Fire risk causes infrequent but large declines in net income. Future price changes, on the other hand, are generally positive with a fairly large but normally distributed error. The results of the combined simulation show that when fire and price risk considered together 6It is assumed that the salvage value is minimal. Burnt
the variability of expected net income for a given year increases. In addition, the possible 20-year path of net income is more difficult to determine as illustrated in Fig. 1. In comparison to the corresponding figure for the price risk simulation, the 95% CI is slightly wider. The distribution of draws for a given year shows that price risk plays the main role in determining the value of net income. Fig. 2 shows that the distribution of year 10 values, takes on a relatively normal shape similar to that depicted for the price risk simula-tion. The influence of the distributions simulated for the fire risk error terms is masked by the price risk distribution. The overall effect is that the two forms of stochasticity compound each other slightly, however, the effect of price risk dominates.
From the simulations it can be concluded that risk plays an important role in determining net income in the case study region. This suggests that using changes in net income to assess the sustain-ability of income flows from the region must consider the role of risk in causing net income to fluctuate over time. According to Ma¨ler (1991), Dasgupta (1995), Aronsson et al. (1997) and oth-ers, sustainable development requires that NNP (or net income in this case), be non decreasing over time. However, such an interpretation relies on the assumption that the welfare measure is the stationary equivalent of current and future wellbeing.
As discussed in Haener (1998), for this to be the case the model used to derive the welfare must accurately depict the evolution of the economy over time and include all factors that influence welfare. The net income measure in developed in
Haener and Adamowicz (1999) fails to incorpo-rate all components of welfare, however, even so, there is still the potential to use the measure to assess whether the income flows from the compo-nents included in the measure are sustainable. The simulations suggest that using the net income measure to assess sustainability must be further qualified. The stochasticity of risk means that fluctuations in net income are to be expected and, for the most part, these fluctuations cannot be avoided. Thus, the reason for including a risk adjustment factor in the net income measure in stochastic setting is apparent.
The results of the simulations can be used to provide an estimate of the magnitude of the risk adjustment factor to be applied to the estimate of regional net income from Haener and Adamowicz (1999). The value of the change in the timber stock used to estimate regional net income in Haener and Adamowicz (1999) was about $52 million using the depreciation approach. Using the wealth approach we can account for changes in future revenue flows including the influences of fire risk and expected price changes. Table 9 reports the expected value of the change in timber stock for 1996 that results from the three sets of simulations.
As Table 9 reports, the expected value of the change in stock is estimated to be about $2.1 million, when both fire and price risk are consid-ered. The expected value of fire risk is negative; however, price risk has a larger positive expected value. In 1996, pulp prices were quite low com-pared to the prices predicted to occur in subse-quent years. Therefore, there is value in leaving
Fig. 3. Comparison of net income measures for the study region.
Table 9
Wealth approach: expected value of income from change in timber stock in 1996
Simulation scenario Adjustment
($)
Fire and Fire risk Price risk
price risk
−219 809 2 360 320 2 091 862 Mean
−1 996 225 −314 708 −1 677 701 Lower
part of the stock so that it can be harvested in the future when prices are higher.
The other components of net income in 1996 summed to about $180.1 million; therefore, using this approach, 1996 net income is estimated to be about $182.2 million. These estimates can also be compared to the estimate of net income that would be obtained from conventional income ac-counting methods. Fig. 3 compares the net in-come measures.
As noted earlier, the simulations do not ac-count for all factors necessary to provide an exact estimate of the adjustment required; however, the magnitude of the suggested adjustment appears to be reasonable. Formal incorporations of fire and price risk into the net income measure would provide a more accurate estimate of the adjust-ment required. Besides the incorporation of the probability distributions, which characterize these risks, other adjustments to the deterministic model may be needed. The extent to which fire and price risks are already reflected in current prices must be considered when estimating shadow prices. For example, using price forecasts, Alberta-Pacific can attain a reasonable idea of future prices, at least in the near term. Alberta-Pacific may be able to hedge against fire and price risk to a limited extent by keeping an inventory of wood fibre which can be drawn down when re-quired or built up if prices are low.
The influence of fire risk and price risk on other components of forest income would also have to be considered. The simulations only consider the influence of risk on the income generated by commercial forestry. In reality, these risks may alter the value of other forest services. Fire influ-ences plant and wildlife populations, which in turn affects trapping, subsistence resource use and passive use values associated with biodiversity. However, the impact of fire is not easy to predict since although a fire may destroy certain plants and wildlife habitat in an area, other species thrive in the early successional stages that domi-nate in recently burned areas. Fire will also influ-ence recreational values if the aesthetic quality of recreation sites declines and big game are more difficult to hunt. Fires play a role in the carbon cycle by releasing carbon dioxide into the
atmo-sphere. Therefore, the carbon sequestration ser-vices provided by the forest will be tied to the frequency and size of fires. If the influence of fire on these and other components of net income were considered the predicted regional net income would probably be even more sporadic and the adjustment to current net income needed to ac-count for this risk would be larger.
There are also other forms of price risk that could have been considered in the simulations. Price variability also occurs in the commercial trapping and fishing sectors. If the stock of furbearers and fish had been incorporated in the model of the regional economy then this risk would have to be considered when estimating the shadow price associated with changes in these stocks.
The simulations provide some insights related to forest policy. It appears that some benefits could be realized by decreasing the risk of fire and in particular the occurrence of very large fires. In statistical terms, decreasing the S.D. of the burn rate would decrease the expected income losses. This is also apparent when examining the equa-tion for the mean of a lognormal distribuequa-tion
a¯=exp
m+s 22
(9)where a refers to annual burn rate and m is the
median of the population (Armstrong, 1999). The Alberta Land and Forest Service (1998) and the forest industry in the region already partake in fire suppression activities; however, it appears that additional measures may be beneficial. However, it should be kept in mind that fire plays an important ecological role in the Boreal Forest and is part of the forest’s natural disturbance regime (Hunter, 1992; Armstrong, 1999). The long run ecological implications of disrupting this regime by increasing fire suppression efforts beyond cur-rent levels and limiting large fires are not certain. The trade-off between the benefits of additional fire suppression to commercial forestry may be outweighed by the ecological consequences.
Companies can hedge against the risk of fires to an extent by maintaining an inventory of wood fibre. Inventories can also be used to hedge against price risks since the company can choose to accumulate its inventory of logs instead of processing the logs and selling pulp or lumber when prices are low. The company can also purchase fibre from private woodlots and sawmills or sell salvaged timber to mills that are able to use it. It would be interesting to investigate whether or not current levels of risk hedging are optimal or whether there would be net benefits associated with additional measures. To the extent that net benefits could be realized, perhaps government regulation and policy would have a role.
In our simulations, we implicitly assume weak sustainability in our calculation of net income. We incorporate existing regulatory constraints that are intended to promote sustainability (even flow con-straints on harvest). Strong sustainability could be imposed by constraining future harvests so that the timber stock is never depleted (i.e. only net growth is harvested). However, in the case where fires are expected to occur, it would be impossible to keep the timber stock intact unless fire suppression efforts were 100% effective. This would be pro-hibitively expensive and have negative ecological consequences since natural disturbance is an im-portant part of the forest ecosystem. The fact that the frequency of fires is uncertain precludes the possibility of keeping the timber stock at a constant volume. The existence of fire and other natural disturbances means that some fluctuation in stock levels is to be expected and is not reasonably avoidable. Another possibility would be to impose constraints on the amount of particular habitat types that are maintained, or constrain the timber stock to a lower limit.
In this paper, we have focussed on fire and price risks since they are likely to be important in the case study region. However, there are many other types of risk that could be simulated in the same type of framework that we have used. Brekke (1997) gives examples of other risks and uncertainties that influence the value of wealth and sustainable con-sumption. Interest rates could be modeled as changing over time or population growth rates could also be simulated. Other types of ecological
risks such as the implications of climate change on timber volumes or the frequency and stochasticity of fires could be incorporated. The productivity or growth rate of timber could be simulated as de-creasing due to declining soil or air quality.
13. Summary and conclusions
The derivation and measurement of a welfare index that incorporates the implications of current activities on future utility, requires making assump-tions regarding the future state of economy. In most cases, these assumptions include the absence of risk and uncertainty. Therefore, most resource accounting systems paint a deterministic picture of the world implying that the future is known with certainty, or at least that, future uncertainties cannot be meaningfully characterized. However, recent literature has shown that in a stochastic setting, a wealth-based approach can be used to determine the income associated with changes in resource stocks, by calculating the expected maxi-mum sustainable consumption associated with the expected value of changes in resource stocks.
The practical question that must be addressed in resource accounting applications is whether it is enough to simply qualify our interpretations of net income or whether the net income measure should be formally adjusted to account for risk. The answer to this question is likely to depend on the particular situation. As has been discussed, adjust-ing the net income measure would require re-for-mulating the model to account for stochasticity. The nature of risk may not lend itself to quantifi-cation. The probability distribution associated with the stochastic variable may be complex and it may be difficult to determine the degree to which current prices already reflect risk. In other cases, incorpo-ration of risk may be rather straightforward.
reality perfectly, but they can provide useful infor-mation related to the role of risk and the relative magnitude of the risk adjustment factor that the-ory prescribes should be incorporated into the welfare index in a stochastic setting.
Acknowledgements
The authors wish to thank the Sustainable Forest Management Network Centres of Excel-lence for Financial Support.
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