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
Descriptive statistics are given for the simula- tion parameters in Table 1. The simulation 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 S
t d
= S
t − 1 d
+ G
t − 1 d
− C
t − 1 d
− H
t − 1 d
S
t − 1 d
− B
t − 1 d
3 Similarly, changes in the coniferous stock are
represented by S
t c
= S
t c
+ G
t − 1 c
− C
t − 1 c
− H
t − 1 cA
S
t − 1 c
− H
t − 1 cQ
S
t − 1 c
− B
t − 1 d
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 coniferous 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
172 198 468 88 660 532
127 394 932 −
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
Upper 95 confidence interval 180 393 047
188 574 794
Fig. 1. Mean and confidence interval for 20-year time path of net income.
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 B 90 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
