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 andor
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,
H
t d
= 0.007439S
t d
1 H
t c
= 0.002358 + 0.006618S
t c
2 where H
t c
= H
t cA
+ H
t cQ
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 deciduous 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.
Since it is assumed that harvest levels are pro- portional to stock levels, changes in stock levels
over time must be characterized. It is assumed that the deciduous stock changes over time ac-
cording to the following equation:
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
− 19.82560
Minimum 1.0000
2.16502 Maximum
Range 21.99062
1.0000 −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
