Table 8 Price and fire risk simulation summary statistics: net income, years 1–20
Annual net income statistic Lowest of annual
Average of annual Highest of annual
Depreciation approach 60 405 755
Mean 241 060 264
137 330 540 −
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.
Unlike the depreciation approach, the wealth approach uses information related to future rev-
enue flows to value current stock changes. There- fore, to determine the value of stock changes,
future revenue flows must be projected. As Brekke 1997 suggests, these revenue projections can be
based on an optimal extraction path or any other production scenario. As we show in this paper, if
risks make the production regime andor revenue flows uncertain, we can determine the expected
net preset value of revenue flows by accounting for the probability of these risks. The wealth
approach allows the change in future resource flows that results from cutting or fires in the
current period to be captured in the net income estimate for the current period. Therefore, if the
timber stock volume decreases to near zero, net income does not decline as drastically as when the
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
6
It is assumed that the salvage value is minimal. Burnt wood fibre would contaminate pulp production; however, in
some cases, timber from burned areas can be recovered for other uses.
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
− 1 677 701
− 314 708
Lower Upper
5 302 874 269 821
5 254 349
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 distribution
a¯ = exp m + s
2
2 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.
The simulations also show the importance of giving industry the means by which to hedge
against financial risks. Currently, forestry compa- nies engage in a number of risk hedging activities.
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
