Valuing a log : alternative approaches

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eat x fey es :

A

United Stat
USDA Destine riot
Ca) Agriculture

Forest Service

Pacific Northwest
Research Station

Research Note
PNW-RN-541
February 2003

Abstract

Introduction

Valuing aLog:,_
Alternative Approaches
Rao V. Nagubadi, Roger D. Fight, and R. James Barbour’

The gross value of products that can be manufactured from a tree is the starting
point for a residual-value appraisal of a forest operation involving the harvest of trees
suitable for making forest products. The amount of detail in a model of gross product
value will affect the statistical properties of the estimate and the amount of ancillary
information that is provided. Seven data sets from forest product recovery studies

of western conifers were used in the evaluation of three models of gross product
value. The evaluation of these models was based on the need for information and the
statistical properties of the estimators. The most detailed method provided additional
information, but at some loss in the precision and accuracy of the prediction of gross
value of products from a log.

Keywords: Residual-value appraisal, log value, alternative approaches.

Residual value is a common approach used to estimate the value of forest operations
involving the removal of trees suitable for making wood products (Duerr 1993). The
residual-value approach begins with an estimate of the gross value of products that
can be produced from the logs of a tree. This approach was once used by the USDA
Forest Service for appraising timber sales but was abandoned in favor of a transac-
tions-evidence appraisal system. Residual-value methods are especially helpful for
understanding the components of costs and revenues associated with a timber ap-
praisal and are therefore useful in research applications.

The purpose of this study was to evaluate three models for estimating the gross prod-
uct value that is required for using the residual-value approach. All three models were
based on data from empirical lumber recovery studies but use different amounts of
detail in deriving the estimates. The evaluation of the models was based on the need
for information and the statistical properties of the estimators.

The seven empirical lumber recovery data sets used in this evaluation come from
lumber recovery studies (Stevens and Barbour 2000). Each data set provides (1) an
estimate of gross product value per cubic foot of log for a species (or species group)
for a particular type of lumber product and set of product prices; (2) the proportion of
the volume of the log ending up in three products: lumber, chips, and residues; (3) the
proportion of lumber that falls in each lumber grade; and (4) diameters and lengths of
the logs. These data are available for each of the logs in the data set. These values
and transformations of them are used in regression equations to estimate gross prod-
uct value.

7 Rao V. Nagubadi was a forester, Roger D. Fight is a principal
economist, and R. James Barbour is a research forest products
technologist, Forestry Sciences Laboratory, P.O. Box 3890, Port-
land, OR 97208-3890. Rao V. Nagubadi is currently a post-doctor-
al fellow with the School of Forestry and Wildlife Sciences, Auburn
University, 108 M. White Smith Hall, Auburn, AL 36849-5418.

Data and Methods

Calculated Gross
Product Value of Logs

A description of the database used in this study is available in Stevens and Barbour
(2000). Logs for this study include ponderosa pine (Pinus ponderosa Doug]. ex Laws)
from the intermountain West and Douglas-fir (Pseudotsoga menziesii (Mirb.) Franco),
western hemlock (Tsuga heterophylla (Raf.) Sarg.), and true fir species (Abies) from
western Oregon and Washington. Table 1 provides a description of the data used in
the study. The logs studied in this analysis are from small-diameter trees with an aver-
age small-end diameter ranging from 8.8 to 10.5 inches, average taper ranging from
0.12 to 0.17 inch per foot of log, and average log length ranging from 14.7 to 23.7 feet.
We believe that these three variables are the most important in determining the value
of a log. Although log grade and knots are key variables in determining the value of
logs, we could not include these variables in our models because relevant data are
not available in the data sets nor would it be available in potential applications of the
models.

In pricing lumber to determine the gross product values for logs in the database, vol-
umes in each of the lumber grades were multiplied by the 1999 prices. For the detailed
method, lumber grades were combined into a workable number of grade groups as
shown in table 1 and weighted average prices were applied for these grade groups
(Chmelik et al. 1999). For ponderosa pine, 1999 average prices were for dry surfaced
lumber from the inland region (WWPA 2000b). For Douglas-fir, 1999 average prices
were for green-surfaced lumber from the coast region (WWPA 2000a). For western
hemlock and true firs (hem-fir), prices were for dry hem-fir lumber from the coast
region (WWPA 2000a).

Lumber volumes were measured in board feet, and the corresponding prices in dol-
lars per board foot were applied. The chips and residues (Sawdust and planer shav-
ings) portions produced from these logs were measured in cubic feet of solid wood
equivalent (SWE), and the corresponding prices in dollars per cubic foot were used in
all three methods. Details of the calculation of the gross product value of logs in the
database are shown below.

The gross product value of logs in dollars per cubic foot of log volume was calculated
by summing values of detailed lumber grades, chips, and residues portions as follows:

n
L,x P.|+CxP.+RxP
Gross value = be | ; he (1)

CFLog

DuixF

where 7 ' is the sum of value of lumber in various grades; i = 1 to 48 for
ponderosa pine, and 1 to 16 for Douglas-fir, western hemlock, and true firs; C x P_ is
the value of chip portion; R x P_ is the value of residues portion in a log; L; is the quan-
tity of lumber in board feet in the i-th grade of lumber; C and R are quantities of chips
and residues in cubic feet SWE; P. is price of lumber in dollars per board foot for the
i-th grade of lumber; P, and P_ are prices of chips and residues in dollars per cubic foot
SWE; and CF, ,, is the total volume of the log in cubic feet. These values were calcu-
lated for each log in the seven data sets and were the basis of comparison between
the alternative methods of estimation of gross product value of logs.

Table 1—Details species, products, logs, lumber grades, and average values of variables used
in the study

No. of Average value of variables
lumber ——
Tree species and lumber type No. of logs grades? SED°(D) Taper(T) Length (H)

---- Inches - - -- Feet

Ponderosa pine:
Old growth, Dimension 66 48 10.44 0.14 15.56
Old growth, Appearance 266 48 10.48 AS 14.49
Young growth, Dimension 178 48 8.79 AS) 1511
Young growth, Appearance 418 48 8.93 17 14.68
Douglas-fir: Dimension SITS 16 9.65 8} 18.89
Western hemlock: Dimension 321 16 8.96 WZ 23.64
True firs: Dimension 1,663 16 10.00 ITS 15.49

2 There was a small amount of volume in some of these studies that was originally graded into grades that are no longer
commonly used, and that volume was reassigned to the current most nearly equivalent grade.
© SED = small-end diameter.

The three alternative methods are (1) direct method: value was estimated directly

by regressing the actual value of log per cubic foot on small-end diameter in inches,
taper in inches per foot of log length, and log length; (2) intermediate method: value
per cubic foot was estimated by using regressions for lumber recovery factor (board
feet per cubic foot of log) for lumber (LRF), average price per board foot, and recovery
proportions for chips and residues (in cubic feet of SWE per cubic foot of log); and (3)
detailed method: value per cubic foot was estimated by using regressions for detailed
grade recovery equations, LRF, and recovery proportions of chips and residues. In all
three methods, a value of the log in dollars per cubic foot was estimated for compari-
son. These three methods are described below.

Direct Method The simplest model of gross product value for logs was based on a regression of the
value per cubic foot of log as a function of log small-end diameter, taper (computed
from log diameters and length), and length of log. This provided a single regression
equation for a log manufactured into the specified lumber product; for example, visu-
ally graded Douglas-fir Dimension lumber. This will be referred to as the direct method.
In this method, the value of a log was estimated by using an equation of the following
form:

Value (direct) = f(D, T, H), (2)

where D is small-end diameter in inches, 7 is taper in inches per foot of log, and H is
length of log in feet.

The dependent variable used in the equation came from the gross product value of
logs calculated in equation (1). Various forms of small-end diameter (D, D?, 1/D, and
1/D?), taper (T and 7), and length of log (H, H?, 1/H, and 1/H?) were tried in a step-
wise regression equation, and the equation with the highest R? was selected, (the
p-values selected for entry and retention of independent variables are 0.15 and 0.10,
respectively). If more than one form of a variable were retained in the final selection
of the step-wise regression, two forms for the small-end diameter, and one form each

Intermediate Method

for taper and length of log were selected based on highest partial R2. In this method,
there is only one prediction equation. By definition, the mean value of log estimated
from this direct method is always equal to the mean of the gross product value of log
calculated in the previous section. In this method, the only information predicted is the
value of log in dollars per cubic foot based on the predictive regression equation. No
other information is derived from this method.

An approach intermediate in complexity was based on regressions of the average
value per board foot of lumber from the log and the proportion of log volume going into
lumber, chips, and residues (as in the previous method). These regressions also were
based on log small-end diameter, taper, and length. These estimates were combined
with prices for lumber, chips, and residues to get gross product value per cubic foot of
log. This method does not involve equations for the proportion of lumber in each grade
or grade group and is therefore unable to provide any information about the quality

of lumber other than its average value per board foot. This will be referred to as the
intermediate method.

This method uses predictive equations for LRF, recovery proportion for residues (R,,):
price in dollars per board foot of lumber (P,,), and recovery proportion of lumber (L

),
rp
which were estimated as follows:

ERE = f(D) 7, Hy): (3a)
ey = (DY 16 Ind) (3b)
P,, = f(D, T, H), and (3c)
ee =" 1(D ame): (3d)

where LFF is the lumber recovery factor (board feet of lumber per cubic foot of log
volume), D is small-end diameter in inches, T is taper in inches per foot of log, H is the
length of log in feet, R,, is proportion of the log that ends up as residues, P,,is price of
lumber in dollars per board foot, and Le is the proportion of log that ends up as lumber
(CF/CF of log volume). As in the direct method, various forms of D, T, and H were tried
in a step-wise regression, and the equation with the highest R? value was selected.
The recovery proportion of chips (C,,) in the log was estimated by subtracting recov-
ery proportions of lumber (L_,) and residues (R,,) from 1 (C,, = 7 - Eee R.,)- Here, the
distinction between LRF and L should be noted. The unit of LRF is the number of
board feet per cubic foot of the part of log volume that is made into lumber, whereas

L_, is the proportion of log volume in cubic feet that is converted into lumber from the
total volume of log in cubic feet. The total volume of log is composed of Ly Cy and

R

ee
fa method, the value of a log in dollars per cubic foot was estimated as:
Value (intermediate) = LRF x P,, (Lumber portion)
+ Re x P_ (Residues portion)
+ (ee P. (Chips portion) , (4)
where LRF is lumber recovery factor in board feet per cubic foot of log volume, P,,
is price of lumber in dollars per board foot, R_, and C,, are recovery proportions of

residues and chips in the total volume of log, and P_ and P. are prices for residues
and chips in dollars per cubic foot SWE.

Detailed Method

In this method, there are four predictive equations; i.e., for LRF, recovery proportion
of residues (R,,.), price of lumber per board foot (P,,), and recovery proportion of lum-
ber (L,)- Thus, in addition to the estimated value of a log, information can be gener-
ated on LRF; recovery proportions of lumber, residues, and chips; and price of lumber
in dollars per board foot based on the predictive equations.

The most complex model of gross product value was based on regressions of the
proportion of lumber in each of several grade groups and the proportion of log volume
going into lumber, chips, and residues. These regressions were based on log small-
end diameter, taper, and length. These estimates were combined with prices for chips,
residues, and each grade group of lumber to get gross product value per cubic foot

of log. This method provided information not available from the other methods but
required many more equations. This will be referred to as the detailed method.

In this method, the volume of lumber in board feet for each of the grade groups for
each log is estimated as:

G = f(D, T,H) for all i (/= 1, 2, ..., L) (5a)
LRF = f(D, T, H) (5b)
L, “= SLAP l CF. ‘ralli=1, 2b). (5c)

where G, are the proportions of lumber in lumber grade groups, LRF is the lumber re-
covery factor (board feet per cubic foot of log) for each log, L, is the volume of lumber
in board feet in the log in the /-th grade, CF, ,, is the total volume of a log in cubic feet,
and L is the total number of lumber grades produced from the logs.

The value of the log in the detailed method in dollars per cubic foot was estimated as:

DLixP, +CxP,+RxP.
Value (detailed) = | — (6)

CF, 06
n
DbixP
where 4-7 is the lumber portion, C x P_ is the chips portion, R x P. is the resi-
dues portion, and CF, ,, is the log volume, P; are the weighted average prices of /-th
lumber grade group in the detailed method, and P, and P_ are prices for chips and
residues in dollars per cubic foot SWE.

The detailed method provides extensive information on the volumes, lumber grades,
and values of all the products derived from the logs manufactured from each tree
based on the predictive equations and the prices provided. This detailed information
can often be useful for various purposes. This method was adopted in the financial
evaluation of ecosystem management activities (FEEMA) and FEEMA WS (west-
side) software developed by the USDA Forest Service, Pacific Northwest Research
Station (Fight and Chmelik 1998). This software and documentation is available at
http://www. fs.fed.us/pnw/data/soft.htm.

Evaluation Criteria

The value of a log in dollars per cubic foot was estimated for each log in all of these
methods for ponderosa pine, Douglas-fir, western hemlock, and true firs. The esti-
mated values obtained in the three models were compared with the actual gross value
of the log with a specified set of market prices. For this purpose, statistical measures
such as average deviation and average absolute deviation of the predicted values in
the direct, intermediate, and detailed methods from the actual gross value of logs were
derived. Average deviation indicated the estimated bias, and average absolute devia-
tion measured the estimated accuracy (Max et al. 1985) and were derived as:

n
Average deviation = Ly Uy) (7a)
n
n
Average absolute deviation = pa ly -¥i | , and (7b)
n
n
Average deviation squares = 2 (i - vi)" (7c)
n

where y, is the actual value of a log; y, is the estimated value of a log in the direct,
intermediate, or detailed methods; and n is the number of observations.

These three models also were compared by model selection criteria, Akaike Informa-

tion Criterion (AIC), and Bayesian Information Criterion (BIC). These criteria are simi-

lar to R? in that these reward good fit but also penalize the loss of degrees of freedom
(Greene 1993). The difference between these two criteria is that BIC imposes a larger
penalty for the extra coefficients. The information criteria are estimated as:

AIC
BIC

In (62) + (2k/n) (8a)
In (62) + (k In (n) /n) , (8b)

where G6? is RSS/n, RSS is the estimated residual sum of squares obtained by sum-
ming the squared residuals between actual value that was estimated under calculated
gross product value and the predicted values obtained in the different methods (i.e.,
direct, intermediate, and detailed methods), n is the number of observations, and k is
the number of estimated parameters in the entire model. Because there were differ-
ing numbers of equations in each method, the number of parameters (k) including the
intercept was counted for each method. From a statistical standpoint, the model with
the lowest value of AIC or BIC is preferred as these criteria select a model with lowest
RSS consistent with keeping the risk of including spurious correlations in the model at
an acceptable level.

Results and
Discussion

The purpose of this research was to evaluate alternative models of valuing a log so
that its value would be as close as possible to the calculated gross value in dollars
per cubic foot considering the amount of information provided by each model. As
mentioned before, the gross value was estimated by using the quantities of lumber
manufactured from a log and prices of all available lumber grades. The gross value
estimated in equation (1) was the base with which the estimated values obtained in
different methods were compared.

Tables 2 through 4 show the predictive equations for estimating the value of a log in
the direct, intermediate, and detailed methods. The signs of the coefficients are along
expected lines in most cases. The number of equations was reduced from a total of 61
in the detailed method to 28 in the intermediate method, and to 7 in the direct method.
Note, however, that these equations were used to predict different things in each of
these three models as explained in the “Data and Methods’ section.

Table 5 provides a comparative summary of R2 values from the three methods. Note
that the R? values in the direct method are higher than the lowest R? values in the
other two methods. The R? values were higher in the direct and intermediate methods
than the highest R? values in the detailed method for all ponderosa pine data sets. The
highest R? values in the detailed method were higher than the highest R? values in the
direct and intermediate methods for the equations for other species.

The coefficient of variation (standard deviation as a percentage of the mean) pro-
vides a measure of variation in the estimated values in each particular method. The
coefficient of variation in the estimated values of logs was highest in the intermedi-
ate method and lowest in the detailed method for all data sets except the Douglas-fir
and western hemlock data sets (table 6). The coefficient of variation for actual gross
values of log, however, was higher than those in all three methods.

The values of logs in direct, intermediate, and detailed methods were estimated by
using equations (2), (4), and (6), respectively. Mean values and other statistics for the
three different models for ponderosa pine, Douglas-fir, western hemlock, and true firs,
for comparison, are shown in table 7. The estimated mean values of logs in the direct
and intermediate methods were close, and the difference in value of logs between
these two methods did not exceed $0.02 per cubic foot. The difference between the
direct and detailed methods ranged from $0.12 to $0.63 indicating a deviation of 4.56
to 21.95 percent from the actual value of logs. The detailed method underestimated
the value of logs for three data sets (old- and young-growth Dimension ponderosa
pine and Douglas-fir) and overestimated for the remaining four data sets.

As already mentioned, the gross calculated value and the value estimated by the
direct method are equal by definition, and consequently the average deviation, which
measures the average bias, from the calculated (observed) gross value was zero for
the direct method. Between the two remaining methods, average deviation from the
gross calculated value was less for the intermediate than for the detailed method for
all the data sets.

Average absolute deviations, which measure the estimated accuracy, were about the
same in the direct and intermediate methods for all data sets. Average absolute devia-
tion was higher for the detailed method for all cases. Mean deviation squares were
also higher for the detailed method than for the direct and intermediate methods for all
data sets without exception.

Table 2—Estimated equations for the direct method

Small-end diameter (D)

Tree species and Number of
lumber type Intercept (1) (2) Taper (T) Length (H) R? observations
Ponderosa pine:

Old growth, Dimension 2HGs 0.01(D?)? — — -88.20*(1/H*)° 0.57 66

Old growth, Appearance -3.15? .91(D)? 13.93(1/D)? -7.56(T)? — .63 266

Young growth, Dimension 1.972 .008(D7)? — 1.06(T)° -57.96(1/H)? 46 278

Young growth, Appearance -.45. 32(D)? i SAAVIDAE = aAAn)= .0017(H?)? 52 418
Douglas-fir, Dimension 2.249 .11(D)? -.70(1/D) -2.68(T)? — .23 1 4117/
Western hemlock, Dimension 2.602 .04(D)? — -2.14(T)? -33.65(1/H7)? 2 321
True firs, Dimension 4.76? -21.11(1/D)? 50.95(1/D*)?_— -2.46(T) -59.48(1/H?)? .29 1,663

— = variable not entered or retained in the step-wise regression; variables were selected by step-wise regression with significance level to
enter = 0.15 and significance level to retain = 0.10; when more than one form of the same variable was selected in the step-wise regression,
two forms of D, and one form for each of T and H with the highest partial R? were retained in the final estimated equations.

? Significance at 1-percent level.
2 Significance at 5-percent level.
© Significance at 10-percent level.

The results indicate that the mean values of logs in the direct and intermediate meth-
ods are closer to the actual value. In the detailed method, the number of equations
involved in the prediction was higher than in the intermediate method. The reason for
the higher deviations in the detailed method is that it involved more equations with low
R? values. Although the detailed method used fewer lumber grade groups, the inter-
mediate method used more lumber grades with the corresponding prices.

The AIC and BIC values were highest for the detailed method in all cases and lowest
for the direct method. Because of the higher number of equations and more estimated
parameters involved in the estimation, the detailed method resulted in higher AIC and
BIC values. This also resulted in higher average deviation and average absolute devia-
tion from the actual gross values in the detailed method. Hence the detailed method.
does not give any better estimates than those given by the direct and intermediate
methods. However, the value of the detailed method lies in the information about the
quantity and quality of lumber grade groups it generated.

Given the above tests and comparisons, valuing a log can be simplified by the direct
and intermediate methods by using fewer equations and incorporating more detailed
lumber grade prices into the process of prediction than in the detailed method. The
value of logs predicted by the direct and intermediate methods was closer to the calcu-
lated gross value than that predicted by the detailed method.

The direct method is the simplest method and is therefore desirable when estimates
of the value of the log are all that are desired. When some information on the relative
proportions of log value that are derived from lumber, chips, and residues is of interest,
then the intermediate method offers a good alternative that is still computationally easy
to derive. When specifics about the change in the proportions of grade groups with
increasing log diameter are of interest, the detailed method is needed. The detailed
method allows users to infer information about which grade groups increase and which
decrease when the average lumber value changes. This is not always obvious from

Table 3—Estimated equations for the intermediate method

Tree species
and lumber type

Small-end diameter (D)

recovery variables? Intercept (1) (2) Taper (T)
Ponderosa pine:
Old growth, Dimension:
LRF 10.85? -28.31(1/D7)° — -5.77(T)?
Rie 10 -.006(D)° 0.0004(D?)? -.17(T?)
ae A482 -.05(D)? .004(D?)? _—
s 834 -.88(1/D)? — -.34(T)?
Old growth, Appearance:
LRF 12.56? -74.79(1/D)* 177.00(1/D2)? -2.34(T)?
Ro 092 .0006(D) - .18(1/D)° -.03(T)?
Per 322 .002(D7)? 2.46(1/D2)? -.23(T)?
b
i. 242 .04(D)? -.74(1/D?) -.22(T)
Young growth, Dimension:
LRF 7.48? a2) 2 — —
Ro 05? 00015(D*)? .15(1/D2)° —
Pe 392 -.03(D)? .002(D?)? —
a 47? .01(D)? —
Young growth, Appearance:
LRF 3.342 29(D) -3.46(1/D?) -4.09(T)?
Re 092 0004(D) -.15(1/D) -.07(T7)?
eee 322 001(D?)? -.16(T)? —
= -.45 32(D)2 7-57 @/D2)¢ -2.76(T)?
Douglas-fir, Dimension:
LRF By OF .29(D)? — -4.29(T)?
Rp 06? .002(D)? — -.04(T)?
Pe 402 00001(D?) -.13(1/D)? -.45(T)?
Lp 362 .02(D)? — -.32(T)?
Western hemlock, Dimension:
LRF 9.572 —--10.80(1/D)? ws ‘a
RS 08? -.05(1/D)° — -.07(T)?#
Pe 382 -.23(T)# — 23(T)?
ee 692 -.82(1/D)? —
True firs, Dimension:
LRF 12.19? -43.28(1/D)* 100.41(1/D2)# -6.36(T)?
Re 07? .001(D)? = -.06(T)?
Pie 432 -1.06(1/D)? 2.70(1/D2)? -.07(T)?
ee 612 007(1/D)® ~—- -.69(1/D2)? -.42(T)?

Length (H)

-261.66(1/H2)?
-1.80(1/H2)°
-6.78(1/H2)
-18.98(1/H2)°

.00007(H2)?

-151.59(1/H2)?
-3.49(1/H2)?
-9.42(1/H2)?

-16.72(1/H)?
16(1/H2)
-.00001(H2)?
-1.14(4/H)?

-167.27(1/H2)?
-.19(1/H)?
-2.06(1/H2)?
-13.23(1/H2)?

R2

Number of
observations

— = variable not entered or retained in the step-wise regression; variables were selected by step-wise regression with significance level to
enter = 0.15 and significance level to retain = 0.10; when more than one form of the same variable was selected in the step-wise regression,
two forms of D, and one form for each of T and H with the highest partial R? were retained in the final estimated equations.

? Significance at 1-percent level.

e Significance at 5-percent level.

© Significance at 10-percent level
lumber recovery factor, Ree

ILRF=
lumber.

= recovery portion of residues, P,,, = price of lumber in dollars per board foot, L

(p = recovery portion of

Table 4—Estimated equations for the detailed method

Small-end diameter (D)

Tree species
and lumber grade

Ponderosa pine:

Old growth, Dimension—
No. 2 and better
Utility
Economy
2 Commons and better
3 Commons
4 Commons
Chips
Residues
Lumber recovery factor

Old growth, Appearance—
Moulding and better
No. 1 Shop
No. 2 Shop
No. 3 Shop
2 Commons and better
3 Commons
4 Commons
5 Commons
Chips
Residues
Lumber recovery factor

Young growth, Dimension—
No. 2 and better
Utility
Economy
2 Commons and better
3 Commons
4 Commons
Chips
Residues
Lumber recovery factor

Young growth, Appearance:
Moulding and better
No. 1 Shop
No. 2 Shop
No. 3 Shop
2 Commons and better
3 Commons
4 Commons
5 Commons
Chips
Residues
Lumber recovery factor

10

Intercept

(1)

29.30(D)°
-1.55(D)?
-7.58(D)?
-6.39(D)°
81.01(1/D)?
-.65(D)°
-28.31(1/D2)°

.06(D2)?
.02(D2)?
-3.12(D)?
3.02(D)?
-.13(D2)?
-.14(D2)?
04(D)
-3.81(D)
.06(D)
-74.79(1/D)?

16.46(D)?
-.05(D2)°

54.99(1/D)?
-4.85(D)?
-3.83(D)?

'9.64(D

(2)

-1.58(D2)?
49(02
43(D2)?
04(02

a

—

293.24(1/D2)2
21(D2)
278.25(1/D)°
-142.32(1/D)°
-.02(D2)?

-17.98(1/D)°
177.00(1/D2)2

-.99(D2)?

-1066.2(1/D2)°
14.55(1/D2)°

0.12(D2)2
131.17(1/D)?
-0.56(D2)?

-15.1(1/D)
-3.46(1/D2)

Taper (T)

97.84(T)?
-16.56(T2)?
-5.77(T)?

-85.00(T)?
62.57(T)?
72.37(T2)?
46.17(T)?
-3.33(T)?
-2.34(T)?

55.64(T2)°
14.73(T)°
218.71(T2)2

63.47(T)?
-7.01(T2)?
-4.09(T)?

Length (H)

-3387.0(1/H2)°

4108.1(1/H2)?

-.95(H)?
2286.3(1/H2)?
-180.41(1/H2)°
-261.66(1/H2)°

.007(H?)?

-2714.9(1/H?)?

214.67(1/H)?
1294.6(1/H2)?

-151.59(1/H2)?

.007(H2)°

425.81(1/H)
-1658.1(1/H2)?
1053.9(1/H2)?

.005(H2)?
003(H2)2

R2

Number of
observations

Table 4—Estimated equations for the detailed method (continued)

Small-end diameter (D)

Tree species ——— Number of
and lumber grade Intercept (1) (2) Taper (T) Length (H) R? observations
Douglas-fir: Dimension—
Select structural 31.04? -6.24(D)? .50(D?)? —_ -69.44 (T)? — 25 1,517
No. 2 and better -44.20? .62(D?)? -69.69(1/D) 3.33(H)? .63 1,517
No. 3 and Utility -14.03? .12(D?)? — 274.15(T)? .02(H)? .28 1,517
Economy 6.12° -3.14(D)? .22(D*)? 127.94(T?)? .01(H?)? .20 1,517
Chips 58.55? -2.31(D)? — 35.70(T)? — .23 1,517
Residues 5.78? .19(D)? — -3.81(T)? — IS 1,517
Lumber recovery factor 5.10? .29(D)? — -4.29(T)? — .23 1, 17/
Western hemlock: Dimension—
Select structural -3.76 0.18(D?)? — -50.74(T)? .01(H)? 31 321
No. 2 and better -43.942 (AF — 93.28(T)? .07(H*)? .68 321
No. 3 and Utility -55.102 .33(D?)? — 200.1(T)? .05(H)? .66 321
Economy -19.972 .12(D)? — 72.27(T)? .014 (H?)? 43 321
Chips 26.307 90.42(1/D)? — — 901.41(1/H?)? 09 321
Residues 9.172 -5.68(1/D)° — -6.08(T)? -.03(H)? 10 321
Lumber recovery factor 9.57? -10.80(1/D)? — — -16.72(1/H)? 10 321
True firs: Dimension—
Select structural 6.442 0. ee -130.16(1/H)? 18 1,663
No. 2 and better -66.37? 56(D?)? 216. 34( 110? -76.20(T)? 3.82(H)? .67 1,663
No. 3 and Utility -17.13? 12(D?)? 8.69(T)? 1.18(H)? 24 1,663
Economy -2.34° 04(D)? — 6.71(T)? .02(H?)? .08 1,663
Chips 40.50? 4 voy 2 +185.69(1/D2)2 48.05(T)? 1448.71(1/H?)? 22 1,663
Residues 6.612 11(D)? — -5.59(T)? -18.74(1/H)? 18 1,663
Lumber recovery factor 12.197 -43. 28(1/D)? 100.41(1/D2)? -6.36(T)? -167.27(1/H?)? .26 1,663

— = variable not entered/retained in the step-wise regression; variables were selected by step-wise regression with significance level to enter
= 0.15 and significance level to retain = 0.10; when more than one form of the same variable were selected in the step-wise regression, two
forms of D, and one form for each of T and H with the highest partial R? were retained in the final estimated equations.

2 Significance at 1-percent level.

2 Significance at 5-percent level.

© Significance at 10-percent level

Table 5—Summary of R? values for estimated equations in the different methods

Intermediate method R2 Detailed method R2

Tree species and Direct method
lumber type R?2 Lowest Highest Lowest Highest
Ponderosa pine:
Old growth, Dimension O57, 0.28 0.65 0.12 0.53
Old growth, Appearance .63 24 oi .00 49
Young growth, Dimension 46 18} 02 02 43
Young growth, Appearance Bz 5) 02 .0O 49
Douglas-fir: Dimension 8) .09 24 tke) .63
Western hemlock: Dimension 12 .08 24 .09 .68

True firs: Dimension .29 11 .26 .08 .67

11

12

Table 6—Coefficient of variation of values of logs in the different methods?

Tree species and lumber type

Ponderosa pine:
Old growth, Dimension
Old growth, Appearance
Young growth, Dimension
Young growth, Appearance
Douglas-fir: Dimension
Western hemlock: Dimension
True firs: Dimension

? Coefficient of variation = (standard deviation/mean) =x 100.

Item

Ponderosa pine:
Old growth, Dimension—
Mean
Average deviation
Average absolute deviation
Average deviation squares
Number of lumber grades

Number of regression equations

Number of parameters
AIC?
BIC?

Ponderosa pine:
Old growth, Appearance—
Mean
Average deviation
Average absolute deviation
Average deviation squares
Number of lumber grades

Number of regression equations

Number of parameters
AIC?
BIC?

Ponderosa pine:
Young growth, Dimension—
Mean
Average deviation
Average absolute deviation
Average deviation squares
Number of lumber grades

Number of regression equations

Number of parameters
AIC?

Detailed
method

19.13
29197
20.14
21.87
17.70

8.57
13.06

Gross Direct Intermediate
value method method
33.97 25.63 29.34
47.63 SV fella) 38.67
33.49 22.67 23.90
41.80 30.19 30.44
28.43 14.48 14.23
25.04 8.56 8.11
33:50 17.99 18.39
Table 7—Comparison of mean values of log under different methods
Direct Intermediate Detailed
method method method
33 3)1|22 2.90
.00 01 23
54 53 56
48 46 61
48 48 6
1 4 9
3 177 29
-.23 18 .66
-.24 ike} 58
3.44 3.44 3.63
.00 -.01 -.19
iz WL .80
99 1.00 1.16
48 48 8
1 4 11
4 Ir 35
.03 se wo
.03 as) 38
2.56 2.55 2.29
.00 .00 Pf
50 50 1S
40 .40 48
48 48 6
1 4 9
4 13 30
-.36 -.26 02
-.35 -.24 .06

Bicz

Table 7—Comparison of mean values of log under different methods

(continued)

Item

Ponderosa pine:

Young growth, Appearance—
Mean
Average deviation
Average absolute deviation
Average deviation squares
Number of lumber grades
Number of regression equations
Number of parameters
AIC?
BIC?

Douglas-fir, Dimension—
Mean
Average deviation
Average absolute deviation
Average deviation squares
Number of lumber grades
Number of regression equations
Number of parameters
AIC?
BIC?

Western hemlock, Dimension—
Mean
Average deviation
Average absolute deviation
Number of lumber grades
Average deviation squares
Number of regression equations
Number of parameters
AIC?
BIC?

True firs, Dimension—
Mean
Average deviation
Average absolute deviation
Average deviation squares
Number of lumber grades
Number of regression equations
Number of parameters
AIC?
Bic?

4 AIC = Akaike Information Criterion.
BIC = Bayesian Information Criterion.

Direct
method

Intermediate Detailed
method method
2.62 2.85
.02 -.21
.58 64
.593 .66
48 8

4 10
19 39
-.14 01
-.11 07
2.85 D3
.02 .63
5i/ .80
Sif .98
16 4
4 7
13 27
-.23 .03
-.22 105
2.62 D'S
01 -.12
46 49
16 4
39 44
4 i
14 26
-.32 -.19
-.30 -.15
2.40 2.57
02 -.16
54 56
48 52,
16 4
4 6
19 27
-.30 -.25
-.28 -.23

118)

Conclusions

Acknowledgments

Metric Equivalents

14

the average, and understanding how the proportion of lumber grade groups change
in relation to each other is sometimes important in understanding the effects of forest
management on resource value.

Our results show that the mean values per cubic foot of log were close in the direct
and intermediate methods but diverged in the detailed method from the actual value
by either overestimating or underestimating the value of logs. This suggests that users
can select the least complex computational method that gives them the desired infor-
mation and feel confident that the value of log estimated by using either of the other
methods would be relatively close.

These methods reflect the tradeoff between simplicity and the amount of informa-

tion developed. The detailed method provides extensive information on the volumes
of different lumber grades as well as a means to do a complete analysis of forest
management activities; the other two methods do not. If users wish to make a simple
calculation of value of a forest stand based on the small-end diameter and taper of
logs, the direct method would suffice. If more detailed information is needed, such as
an estimate of the value of a forest stand based on the LRF, recovery proportions of
chips and residues, and price in dollars per board foot, the intermediate method would
give the most accurate estimate. Although the detailed method enables us to get more
information pertaining to recovery of lumber in different grade groups, it does not en-
able us to get a better estimate of log value than the direct and intermediate methods
as it tends to overestimate or underestimate the values.

In this study, three alternative approaches for predicting the value of a log were
examined. Taking the calculated gross value of logs obtained by applying all detailed
grades and available prices as the base method, the estimated value of logs in three
models—direct, intermediate, and detailed—were compared with the calculated gross
value of logs. The average deviations, average absolute deviations, average devia-
tion squares, and model selection criteria showed that the direct and intermediate
models produced predictive values of logs closer to the calculated gross value for
most samples. Direct and intermediate models also have the advantage of relying on
fewer predictive equations and more detailed grades and prices than does the detailed
method. Although the detailed model uses fewer lumber grade groups and respective
prices, it enables us to derive extensive information on the values and volumes of lum-
ber products from a forest. The detailed model, however, produced values that devi-
ated more from the calculated gross value than did the other two models. Depending
on the need for detailed information, any of these models can be used in valuing logs
in a forest stand. The simplest one is the direct model in that it gives only the value of
the forest stand quickly and the detailed model is more sophisticated because it gives
an array of detailed information. Although the estimated value in the intermediate
model is closer to the calculated gross value, it enables us to get limited information
on proportions of lumber, chips, and residues.

The authors gratefully acknowledge the critical comments received from Timothy Max,
Xiaoping Zhou, and David Nicholls on an earlier draft.
When you know Multiply by To get:

Inches 2.540 Centimeters
Feet 0.305 Meters

Literature Cited

Chmelik, J.T.; Fight, R.D.; Barbour, R.J. 1999. Softwood lumber prices for
evaluation of small-diameter timber stands in the intermountain West. Res.
Note. FPL-RN-0270. Madison, WI: U.S. Department of Agriculture, Forest
Service, Forest Products Laboratory. 4 p.

Duerr, W.A. 1993. Introduction to forest resource economics. New York: McGraw-
Hill. 485 p.

Fight, R.D.; Chmelik, J.T. 1998. Analysts guide to FEEMA for financial analysis of
ecosystem management activities. Gen. Tech. Rep. FPL-GTR-111. Madison, WI:
U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 5 p.

Greene, W.H. 1993. Econometric analysis. Englewood Cliffs, NJ: Prentice Hall. 791 p.

Max, T.A.; Cahill, J.M.; Snellgrove, T.A. 1985. Validation of a butt log volume
estimator for Douglas-fir. Forest Science. 31(3): 643-646.

Stevens, J.A.; Barbour, R.J. 2000. Managing the stands of the future based on the
lessons of the past: estimating western timber species product recovery by using
historical data. Res. Note. PNW-RN-528. Portland, OR: U.S. Department
of Agriculture, Forest Service, Pacific Northwest Research Station. 8 p.

Western Wood Products Association. 2000a. Coast F.O.B. price summary.
December, 1999. Portland, OR. 8 p.

Western Wood Products Association. 2000b. Inland F.0.B. price summary.
December, 1999. Portland, OR. 13 p.

15

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