Timber Sale, Value as a 

Forest Service Function of Sale Characteristics 

,rest and N u m be r of B i d d e r s Experiment Station 

Research Paper NE-657 

Paul E. Sendak 
Abstract 

Examines the effect of sale characteristics and number of bidders on sale value 

for timber sold by sealed-bid auction on the Green Mountain National Forest in 

Vermont. As anticipated from theory and previous empirical studies, increasing 

the number of bidders tended to increase the winning-bid value for the timber 

auctions studied. Tobit analysis was used because of the high number of timber 

sale offerings that received no bids. Efforts made to ensure that an offering 

received at least one qualified bid had a greater impact on sales revenue than 

efforts made to increase the high-bid value. In designing sales, managers should 

avoid setting appraisal value too high in relation to timber quality or should 

seek methods other than timber sales to regenerate poor quality stands. 

The Author 

PAUL E. SENDAK, forest economist, is Project Leader of the research unit on 

the economic potential of forest production in the North at the Northeastern 

Forest Experiment Station, Burlington, Vermont. He received a B.S. degree in 

forestry from Rutgers University, and an M.S. degree in forestry and Ph.D. 

degree in forest economics from the University of Massachusetts. He joined 

the U.S. Department of Agriculture, Forest Service in 1969. 

Acknowledgment 

This research resulted from a Cooperative Research Agreement between the 

US. Department of Agriculture, Forest Service, Northeastern Forest Experiment 

Station and the University of Montana, School of Forestry. I am indebted to 

Professor David H. Jackson's valuable contributions to the study design, data 

analysis, and final report. Any inaccuracies or errors that remain are the 

responsibility of the author. I am indebted also to the Green Mountain National 

Forest staff-in particular, Wayne Kingsley and Ginger Marx-for guidance 

through the timber sales record6 and sale procedures. 

Manuscript received for publication 11 July 1991 

Northeastern Forest Experiment Station 

5 Radnor Corporate Center 

100 Matsonford Road, Suite 200 

P.O. Box 6775 

Radnor, Pennsylvania 19087-4585 

December 1991 
Introduction 

Frederal timber auctions have been the subject of several 

empirical studies. This study focuses on timber auctions 

in the Green Mountain National Forest (NF) in Vermont 

and the influence that sale characteristics and number of 

bids submitted have on the winning-bid value. The study 

has implications for timber auction design in promoting 

competition and increasing revenues. The Green Mountain 

NF frequently has offered timber sales that received no 

bids. Thirty-two percent of the timber stands on the Green 

Mountain NF are of poor quality. These stands frequently 

are prescribed for regeneration cuts to convert them to 

higher quality. As a result, many of the timber sales in 

this study had a high percentage of poorer quality 

stands. 

According to Riley and Samuelson (1981), "the auction 

model is a useful description of 'thin markets' characterized 

by a fundamental asymmetry of market position." Typically, 

one seller faces a finite, and usually very small, number 

of potential bidders, whose valuation of the product is 

unknown to the seller. The auction follows an explicit set 

of rules, typically set by the seller, which includes how 

bids are to be submitted and how the winning bid is 

selected. 

The auctions for Green Mountain NF timber are first-price, 

sealed-bid auctions with a reservation price set by the 

seller. Sealed bids are submitted to the seller and the 

highest bid wins, with the winner paying the amount bid. 

The seller's reservation price sets a floor that all qualified 

bids must equal or exceed. 

It was hypothesized that a positive relationship exists 

between the number of bids -submitted on a timber sale 

and the winning bid. Tobit analysis was used to estimate 

two models that predict the winning-bid value because 

tlhe dependent variable was censored (Maddala 1983). 

The second of the two models included a transformation 

of the number of bids submitted as an ex~lanatory variable. 

The number-of-bids coefficient was statistically significant. 

Results are discussed in relation to the wood-using industry 

in Vermont and in reference to the objectives of timber 

sales on the Green Mountain NF. 

Timber Auction Studies 

A number of survey articles on auctions have been 

published and, rather than attempt an exhaustive review 

here, interested readers are referred to them. McAfee 

and McMillan (1987) survey the recent literature on auctions 

and bidding. Earlier literature is surveyed by EngelbrectWiggans (1980), and Stark and Rothkopf (1979) provide 

a comprehensive bibliography on competitive bidding. The 

literature on studies of federal timber auctions and the 

effect of number of bidders on winning-bid value is reviewed 

here in more detail. 

Auction theory predicts that winning-bid value tends to 

increase with increases in the number of bidders (McAffee 

and McMillan 1987, Engelbrect-Wiggans 1980). Several 

studies are concerned with examining the number of 

bidders participating in an auction. Mead (1 966) concluded 

that auctions with few bidders occurred because of the 

structure of the wood-using industries. There are few 

potential buyers because markets are constrained in area 

by the high.cost of hauling logs from woods to mill. This, 

coupled with an assumption that local timber supplies are 

relatively inelastic, led Mead to conclude that collusion 

among buyers of Douglas-fir timber is common. 

In a study of oral versus sealed bidding for Forest Service 

timber, Johnson (1979) found a positive relationship 

between the number of bidders and the winning-bid value. 

Number of bidders was one independent variable in a 

multiple regression model to predict winning-bid value, as 

estimated by ordinary least squares (OLS). 

Hansen (1986) also investigated oral versus sealed bidding 

for national forest timber. He estimated three high-bid 

models using least squares and maximum likelihood 

techniques in which the number of qualified bidders 

appeared in each model as a predictor variable. In all 

three cases, the number-of-bidders coefficient was 

statistically significant and positive. Brannman et al. (1987) 

tested theoretical predictions about the effects of number 

of bidders on winning-bid value in five auction settings, 

among them federal timber sales. They found that winning 

bid increases with the number of bidders. 

Buongiorno and Young (1984) modeled winning bid using 

OLS conditional on sales that received at least two bids. 

They recognized the potential for unsold offerings and 

that OLS regression would not be an adequate method 

when no bids were received. Huang and Buongiorno 

(1986), realizing the potential bias in ignoring unsold 

timber auctions, used Tobit regression. Number of bids is 

not a variable in their winning-bid model, although Tobit 

regression can be used to model the probability that an 

offering will sell (receive at least one bid) based on the 

other independent variables, will determine the appraisal 

value that will ensure a certain probability of sale, and 

will describe the demand schedule for timber on the forest 

of interest. 

Jackson and Gould (1 987)' and Niccolucci (1 989) modeled 

the number of bids using limited-dependent-variable 

techniques. Niccolucci used discriminant analysis and logit 

regression to discriminate between sold and unsold 

offerings. Jackson and Gould (1987) used logit regression 

to model the probability of single-bid auctions versus 

multiple-bid sales. They predicted winning-bid value using 

OLS. The market they investigated had no unsold offerings 

but many single sealed-bid sales. 

Setting a reserve price is a good strategy for the seller 

'~ackson, D.H.; Gould, E.M. 1987. Contractual arrangements, the level of competition, and value of national forest timber. 

Mimeo. 16 p. 
because theory shows that, on average, it will result in 

higher winning bids (McAfee and McMillan 1987). Riley 

and Samuelson (1981) show that for a broad family of 

auction rules, expected seller revenue is maximized if the 

seller announces an appropriately chosen reserve price. 

Methods 

Procedure for Green Mountain NF Timber Sales 

The Green Mountain NF advertises each sale in local 

newspapers and in a prospectus and solicits sealed bids 

from a list of approximately 80 potential bidders. A showing 

is scheduled for interested bidders to view the timber 

offered for sale. The winning bid must match or exceed 

the seller's appraisal value or reserve price. If no sealed 

bid is received, a purchaser can negotiate with the Forest 

Service, essentially match the appraisal value, and be 

awarded the sale. 

The sales in the sample population are lump-sum sales. 

The trees are marked for cutting before the sale and the 

timber volum.es'are estimated. Timber payments are not 

dependent upon the measurement of logs removed but, 

rather, on presale volume estimates. Lump-sum sales 

encourage the use of low-quality timber. 

Roads that are to become a part of the permanent road 

system, thus representing a capital investment in 

infrastructure, are often financed through purchaser credit 

in the National Forest System. Instead of paying the 

timber purchaser in cash for road construction, the Forest 

Service grants credit against the purchaser's timber payment 

account for building the roads. The credit is earned as 

the road is built. However, purchaser credits do not appear 

to be a significant factor on the Green Mountain NF. 

Few new roads are planned and since virtually all potential 

bidders are classified as "small business," bidders can 

have the Forest Service contract directly for permanent 

road construction. 

Transactions-evidence appraisal is used by the Green 

Mountain NF. Timber is advertised at the appraisal value, 

which is 85 percent of the average price of previous 

sales over the past 12 months. A sale may be appraised 

above or below the 85 percent standard if justified by 

sale attributes that deviate from the norm. But the advertised 

appraisal value cannot be lower than the base rate set 

by law. Three sale attributes used in adjusting the appraisal 

value are: percentage of pulpwood in the sale, slope, 

and yarding distance. Low quality timber is converted into 

wood pulp and high quality timber is converted into lumber, 

veneer, and specialty products. The Green Mountain Forest 

Plan recognizes the need to subsidize removal of poor 

quality timber with high quality timber in order to make 

sales more attractive to bidders (USDA For. Sew. 1985). 

Sample Data 

The sample population consisted of all sales on the 

Green Mountain NF with active harvesting operations 

during the first quarter of 1988. There were 45 sales with 

active harvesting operations sold at auction over the 

previous 10 years, but most of these sales (80 percent) 

had been awarded over the previous 4 years. In addition, 

data were gathered on 19 offerings advertised during the 

10-year period, but received no bids. Thus, the total sample 

of auctions was 64. 

The population of timber sale offerings may be divided 

into three groups: 1, offerings that received at least one 

qualified bid; 2, offerings that received no qualified bids 

but were later sold by negotiation; and 3, offerings that 

received no bids and were not sold by negotiation. For 

this study, the last two groups were combined into no-bid 

auctions because the focus is on auctions, and group 2 

was clearly not sold at auction. Simply put, offerings in 

group 1 were sold at auction; offerings in groups 2 and 

3 were not. Group 2 contained eight offerings. 

Five of the sixty-four sales sampled were advertised at 

the base rate. That is, the appraisal value for these sales 

was equal to, or less than, the legally mandated base 

rate. These five sales were relatively small in terms of 

timber volume and three received one bid while two 

received no bids. Two-thirds of the sales had at least 

one species of sawtimber or pulpwood advertised at the 

base rate. Most often, pulpwood was advertised at this 

rate, reflecting the poor market situation. But, most sales 

in the sample were advertised at an aggregate value 

significantly greater than would have resulted from applying 

the base rate. 

Information describing the characteristics of the sales was 

obtained from timber sale records maintained at the Forest 

Supervisor's office and, in some cases, Forest District 

offices. Data were gathered on the winning-bid value and 

21 potential explanatory variables. All dollar values were 

converted to constant 1982 value by the Gross National 

Product Implicit Price Deflator. All timber volumes were 

recorded in cubic feet to facilitate the comparison of sawlog 

and pulpwood volumes. 

Statistical Procedure 

lnitidl selection of explanatory variables for inclusion in a 

regression analysis was made using the pair-wise simple 

correlation coefficients among variables. Explanatory 

variables that had a statistically significant r value (~~0.05) 

when paired with the dependent variable were retained; 

others were eliminated from further analysis. Since many 

of the variables measured the same characteristics but in 

different units, such as total number of trees and total 

acres cut as measures of sale size, there was a problem 

of near collinearity between some explanatory variables. 

Backward deletion was used to eliminate redundant 

variables from the regression model based on a combination 

of their t values and the pair-wise correlations between 

explanatory variables. 

The Vermont timber market does not correlate well with 
national market indexes, such as lumber and pulp and 

paper production or lumber producer-price indexes. 

However, Vermont does publish a quarterly stumpage 

price report on regional prices, which gives a good measure 

of local timber market conditions. The value per cunit 

(VALUE) was calculated for each sale using the regional 

average stumpage prices for each species in the sale, 

weighted by the proportion of volume of that species 

relative to the total volume of the sale. For any species 

missing in the reports and for the few sales that occurred 

before the publication of Vermont stumpage prices, similar 

reports for northeastern New York counties were used. 

The winning-bid model was specified as a Tobit regression 

because the dependent variable, real-winning bid, is 

censored (Maddala 1983). That is, the winning bid (WIN) 

is observed for offerings that received bids equal to or 

greater than the advertised appraisal value (ADV). For 

offerings that received no bids, no winning bid is observed. 

The lower truncation point was the advertised appraisal 

value so it varied with sale. The model is defined in the 

following way: 

where WINi is the dependent variable, Xi is a vector of 

explanatory variables, p is a vector of unknown coefficients, 

and N is the number of observations. The error term, ui, 

is assumed to be independently normally distributed with 

zero mean and constant variance, u2. In equation (2), the 

winning bid is arbitrarily assigned a value of zero when 

the value of (Xip + ui) is less than the ADVi. 

Table 1 lists and defines the variables used in the study 

and gives their means and standard deviations by sales 

which received at least one-bid and no-bid offerings. The 

dependent variable, winning bid11 00 ft3 (cunit), is a volumeweighted average price and is the bid per unit volume on 

each timber species times the Forest Service estimate of 

the respective volume summed over all species and divided 

by the total volume in the sale. High-valued species tend 

to increase the bid per cunit, while low-valued species 

tend to reduce the bid. Independent variables used, in the 

analyses reflect timber quality, timber sale characteristics, 

and market conditions. Some of the variables are 

independent of managerial decisions, such as timing of 

timber sales to coincide with favorable markets. Other 

variables represent managerial choices in the design of 

timber sales, such as proportions of sawtimber and 

pulpwood, timber species, and trees chosen for harvest. 

Winning-Bid Value 

Two winning-bid models were estimated (Table 2). Model 

1 is similar to the Huang and Buongiorno (1986) approach 

to predicting the high bid. Sale characteristics and a 

market variable were specified in Model 1. Model 2 

differs from Model 1 in that the transformed number of 

bids [1/(1 +NOBID)] was added to the list of explanatory 

variables (Table 2). 

In Model 1, the likelihood ratio index (LRI), analogous to 

R2 in ordinary regression analysis, was 0.22 and 

statistically significant (p60.01). Three of the four 

explanatory variables were significant, but all coefficients 

had the expected sign. All significance tests for the 

estimated coefficients were based on a one-tailed test 

because of a priori expectations of signs. The three 

significant coefficients: HIVAL-percentage of total sawlog 

volume in high-valued species, HAUL-average timber 

hauling distance, and VALUE-sale value based on average 

regional prices, were positive for HlVAL and VALUE and 

negative for HAUL. The coefficient for DBH, average 

diameter of trees in the sale, was positive as expected, 

but not significant. 

HlVAL measured the relative quantity of high-valued 

species-the oaks, particularly northern red oak, white 

ash, and white pine-included in a sale. This variable 

Table 1.-Definition of variables, sample means, and standard deviations for timber sales with one or more 

bids (n =45) and no-bid offerings (n = 19) 

Sales with one 

or more bids No-bid offerings 

Variable Description Sample Standard Sample Standard 

mean deviation mean deviation 

ADV Advertised appraisal value per cunit (1 982 $) 11.16 8.31 8.27 8.23 

\NIN Winning bid per cunit (1982 $) 18.59 15.64 0 0 

IUOBlD Number of bids submitted 1.98 1.42 0 0 

INVBID Inverse of (1 + NOBID) 0.39 0.13 1 0 

IIBH Average diameter of trees in sale (inches) 11 .07 1.27 10.26 1 .15 

IiIVAL Percentage of sawlog volume in high valued species 

(red oak, white oak, white ash, white pine) 2.96 5.90 1.74 1.43 

HAUL Average timber hauling distance (miles) 42.65 13.78 49.47 14.82 

VALUE Sale value per cunit based on prevailing average 

stumpage prices (1 982 $) 20.42 7.26 16.59 6.66 
Table 2.-Estimated winning-bid models, without, and with, the number of bids as an explanatory variable 

Model 1 Model 2 

Estimated Standard Estimated Standard Variable coefficient error coefficient error t-statistic t-statistic 

INVBID - - - - 30.72 6.26 - 4.91 *** 

DBH 1.18 0.95 1.25 - 0.65 0.84 '- 0.77 

HlVAL 1 .16 0.19 6.1 9*** 1.06 0.1 5 7.1 3*** 

HAUL -0.18 0.08 - 2.30** -0.12 0.07 - 1.74* 

VALUE 1.22 0.1 8 6.94*** 1 .l 1 0.1 5 7.41 *** 

Constant - 17.80 10.84 - 1.64 16.83 11.03 1.53 

S 6.75 0.74 9.09*** 5.16 0.54 9.48*** 

Log-likelihood = - 1 60.1 6 Log-likelihood = - 135.93 

appeared especially critical because a typical sale included 

large volumes of sugar maple, yellow birch, and red spruce 

sawtimber. The estimated coefficient was highly 

significant. 

The estimated coefficient for VALUE was also highly 

significant. As expected, local timber-stumpage market 

conditions at the time of timber offering have a positive 

and measurable effect on the winning-bid value. The 

estimated coefficient for HAUL was negative because it 

represents a cost to the logger. The more distant the 

haul to market, the less valuable the timber, all else 

equal. 

In Model 2, INVBID, the transformed number of bids, 

was added as an explanatory variable to the four original 

variables. The addition of this variable to Model 1 had 

the potential to cause the problem of simultaneity bias. 

That is, the number of bidders may be thought of as 

having been influenced by some of the explanatory variables 

that determine winning-bid value. This confounds the 

interpretation of the beta coefficients. However, as the 

following analysis shows, the problem was not serious in 

this case. 

From Model 1 to Model 2 LRI increased from 0.22 to 

0.34 and the estimated coefficient for INVBID is significant 

(pa0.01). For the three significant variables in Model 1, 

the coefficients estimated in Model 2 were within two 

standard errors of the coefficients estimated in Model 1. 

The signs and significance of the coefficients were 

unchanged for HIVAL, VALUE, and HAUL. The coefficient 

for DBH was unexpectedly negative in sign, but still not 

significant. The addition of information about number of 

bids in Model 2 gives information not contained in the 

four variables in Model 1 and offers significant evidence 

of a positive relationship between number of bids and 

winning-bid value. 

Decomposition of Tobit Coefficients 

Tobit analysis can be used to determine both change in 

the probability that an offering will receive at least one 

bid (a bid that matches or exceeds the appraisal value), 

and the change in the winning-bid value if at least one 

bid is received. Thus, change in winning-bid value resulting 

from change in an explanatory variable may be decomposed 

into the marginal change in winning-bid value for offerings 

sold, and the change in probability that the offering will 

be sold (McDonald and Moffitt 1980). 

Decomposition of the Tobit coefficients, as presented by 

McDonald and Moffitt (1980) and applied to forestry 

examples by Huang and Buongiorno (1986) and Dennis 

(1989), provides additional information. Table 3 shows the 

results of the decomposition of Model 1, using the average 

values of the predictor variables: 

WIN= -17.80+1.18 DBH+1.16 HIVAL 

-0.18 HAUL+ 1.22 VALUE 

The coefficients of Model 2 were not decomposed because 

the number of bids was beyond direct control. 

In particular, section 1, Table 3, shows the estimate of 

expected high-bid value over all observations 

(unconditional), E(Y); section 2 the expected value 

conditional on being above the limit, E(Y*); and section 3 

the probability of being above the limit, F(Z), where F(.) 

is the cumulative normal distribution function and 

Z = ((- ADVi + XiB)/u). Section 4 shows adjustments to the 

Tobit beta coefficients needed to calculate the change in 

(a) E(Y), (b) F(Z), and (c) E(Y*) due to a change in the 

variable Xk. This obviously is conditional on the values of 

the X variables, so will change for any specific observation 

or combination of X values. The equations used to calculate 

the table entries are shown in the appendix. 

The change in sale revenue due to an increase in high-bid 

value is the product of the change in high-bid value of 

those auctions above the limit and the probability of being 

above the limit, section 5, Table 3. And, the change in 

sale revenue due to an increase in the probability of 

receiving at least one bid is the product of the change in 

probability of being above the limit and the expected 
Table 3.-Decomposition of Model 1 results using the 

total sample means 

Evaluated at 

Section Parameter estimated mean for sample 

z = 0.47 

1 Expected high-bid value (WIN) 

(1 982 $/cunit) E(Y) 11.60 

2 Expected high-bid value 

conditional on 2 ADV 

(1 982 $/cunit) E(Y') 17.05 

3 Probability of receiving at least 

one qualifying bid F(Z) 0.68 

4 Changes due to a change in 

variable X, 

(a) aE(Y)/aX, 1 .22Bk 

(b) aF(Z)/aX, 0.058, 

(4 aE(Y')/aX, 0.47~~ 

5 Change in the expected high bid 

due to increase in high-bid 

value (1982 $/cunit) 

F(Z)aE(Y')laX, 0.328, 

6 Change in the expected high bid 

due to increase in probability 

of receiving at least one bid 

(1 982 $/cunit) 

E(Y')aF(Z)/aX, 0.90Bk 

value of high bid if above the limit, section 6, Table 3. 

At the overall sample means, 26 percent [(0.32/1.22)X100] 

of the change in sale revenue is due to the increase in 

high-bid value and 74 percent [(0.90/1.22)XlOO] to the 

change in the number of auctions receiving at least one 

bidl. Thus, efforts resulting in fewer no-bid auctions potentially have a greater positive impact on sale revenue than 

eff~orts resulting in higher bid values for sales that received 

bidls: 

In summary, the relationship between number of bids and 

wirining-bid value is ignored in Model 1. Model 2 includes 

the transformed number of bids, 141 + NOBID). The number 

of bids significantly alters the model. The LRI increases 

from 0.22 to 0.34. The winning bid increases at a decreasing rate with the number of bids submitted. 

Discussion 

Auction theory predicts that seller revenue tends to increase 

with an increase in the number of bidders. Several empirical 

studies found evidence to support the prediction and this 

was found to be the case with federal timber sales on 

the Green Mountain NF in Vermont. 

The number-of-bidders variable is interesting because, like 

the winning-bid variable, it can be considered an indicator 

of the quality of the timber sale. Therefore, the number-ofbidders variable should be a function of some of the 

same timber sale characteristics as the winning-bid 

value. This interpretation is presented by Schuster and 

Niccolucci (1990). However, in this study, the number-ofbidders variable works as an explanatory variable. It may 

be an indicator of otherwise unmeasured market conditions 

at the time of sale or it may proxy for important sale 

characteristics missing from among the variables being 

used to describe the sales. 

The problem with Model 2, which includes the number-ofbidders variable, is that it cannot be used as a predictive 

model because number of bids is unknown until the timber 

auction. Schuster and Niccolucci (1990) avoided the 

problem by the use of instrumental variables and two-stage 

least squares. The procedure predicts the number of bids 

and this prediction can be used to estimate timber sale 

value and to avoid the potential simultaneity bias. 

A significant number of timber sale offerings on the Green 

Mountain NF received no bids. Also timber management 

policy on the NF has forced many recent sale offerings 

to include poorer quality stands. These two conditions 

imply that the seller's appraisal value is being set too 

high on some offerings. As Huang and Buongiorno (1986) 

noted, an increase in the reservation price acts in opposing 

directions-it increases the conditional high bid but 

decreases the probability of selling. 

To be sure, a small number of no-bid offerings can be 

an indication that appraisal value is not being set too 

low. Setting an appraisal value is a management decision 

that should consider the cost of reoffering the sale, including 

the postponement of revenue, as well as the cost of 

protecting the public's interest in the timber. 

Mead's (1966) observation-that collusion among buyers 

of Douglas-fir timber both avoids competition and results 

in few bids on sales-does not seem a likely explanation 

here. Quite simply, sales that are unattractive in terms of 

timber quality or value tend to attract few, and sometimes 

no, bids. This is weakly supported in Table 1 that compares 

the sale characteristic means of sales and no-bid offerings. 

All differences between the means of the five sale 

characteristics had the a priori expected sign, but only 

one of the five was statistically significant (~~0.05, onetailed test). A probability value of 0.05/5=0.01 was used 

to protect against the five sales-characteristics hypotheses 

and to ensure that the overall Type-l error rate was no 

larger than approximately 0.05. Only the difference between 

the means of average diameter of trees in sale (DBH) 

was statistically different from zero. 

There are major differences between western and eastern 

national forests. Among the most important are the smaller 

size, the lesser significance of timber production compared 

to other forest values, and the larger proportion of 

hardwoods in the East versus the West. The Green 

Mountain NF represents approximately 5 percent of the 

timber land area and 5 percent of the timber harvest in 

Vermont. With privately owned timber abundantly available 

in Vermont, the Green Mountain NF holds little monopoly 

power in selling timber. 
Vermont's saw and veneer mill industry consists of several 

hundred mills. In contrast to markets for sawlogs, pulpwood 

markets are characterized by a few distant purchasers. 

Depending on species, pulpwood cut on the Green Mountain 

NF is trucked to one of three mills in New York State, in 

some instances over 100 miles away. While there may 

be substantial returns to searching the market for the 

best sawlog prices, there are few options for marketing 

pulpwood. 

A large number of no-bid offerings is probably the result 

of an unacceptably high appraisal value relative to the 

quality of timber offered for sale. If the goals of management 

are being met by this process and tie added cost of 

sales administration is acceptable, .no change is 

recommended. However, poor quality stands could be 

cleared by low-bid contractors. Any merchantable timber 

could be sold at the landing to a high bidder, or included 

with an adjacent active sale. Other offerings might then 

be improved by the continued subsidizing of remaining 

lower quality timber by higher quality timber. By increasing 

the proportion of sawlogs, average diameter (DBH) and 

value (VALUE) will tend to increase and average haul 

distance (HAUL) will tend to decrease, because sawlog 

markets are much closer than pulpwood markets. Where 

possible, the species mix could also be improved, thus 

increasing the percentage of total sawlog volume in highvalued species (HIVAL) and also making the offering 

more attractive to potential bidders. 

Hansen, R. G. 1986. Sealed-bid versus open auctions: 

the evidence. Economic Inquiry. Vol. 24. 

Huang, Mey F.; Buongiorno, J. 1986. Market value of 

timber when some offerings are not sold: 

implications for appraisal and demand analysis. 

Forest Science. 32(4):845-854. 

Johnson, R. M. 1979. Oral auction versus sealed-bids: 

an empirical investigation. Natural Resources Journal. 

19(April):315-336. 

Maddala, G. S. 1983. Limited-dependent and qualitative 

variables in econometrics. Cambridge University Press. 

401 p. 

McAfee, R. P.; McMillan, J. 1987. Auctions and bidding. 

Journal of Economic Literature. 25:699-738. 

McDonald, J. F.; Moffitt, R. A. 1980. The uses of Tobit 

analysis. Review of Economic Statistics. 62(2):318- 

321. 

Mead, Walter J. 1966. Competition and oligopsony in 

the Douglas-fir industry. Berkeley, CA: University of 

California, 276 p. 

Niccolucci, M. J. 1989. A quantitative analysis of sold 

and unsold timber offerings in Region 1. Missoula, 

MT: University of Montana. 51 p. M.S. thesis. 

Literature Cited 

Brannman, L.; Klein, J. D.; L. W. Weiss. 1987. The price 

effects of increased competition in auction markets. 

Review of Economic Statistics. 69(1):24-32. 

Buongiorno, J.; Young, T. 1984. Statistical appraisal of 

timber with an application to the Chequamegon 

National Forest. Northern Journal of Applied Forestry. 

1 :72-76. 

Dennis, D. F. 1989. An economic analysis of harvest 

behavior: integrating forest and ownership 

characteristics. Forest Science. 35(4):1088-1104. 

Engelbrect-Wiggans, R. 1980. Auctions and bidding 

models: a survey. Management Science. 

26(2):119-142. 

Riley, J. G.; Samuelson, W. F. 1981. Optimal auctions. 

American Economic Review. (June):381-392. 

Schuster, E. G.; Niccolucci; M. J. 1990. Comparative 

accuracy of six timber appraisal methods. The 

Appraisal Journal. 58(1):96-108. 

Stark, R.; Rothkopf, M. H. 1979. Competitive bidding: a 

comprehensive bibliography. Operations Research. 

27(2) :364-391. 

U.S. Department of Agriculture, Forest Service. 1985. 

Draft environmental impact statement-land and 

resource management plan. Rutland, VT: U.S. 

Department of Agriculture, Forest Service, Eastern 

Region, Green Mountain National Forest. 532 p. 
Appendix 

Following are the equations for calculating the values in 

Table 3. Derivations can be found in McDonald and Moffitt 

(1 980). 

Sec. 1 E(Y)=XBF(Z)+uf(Z) 

Sec. 2 E(Y')=XB+uf(Z)/F(Z) 

Sec. 4(a) aE(Y)laX,=F(Z)aE(Y')IaX,+E(Y*)aF(Z)laX, 

Sec. 4(b) aF(Z)laXk=f(Z)Bkl~ 

Sec. 4(c) aE(Y')IaX,=B,[l -Z~(Z)IF(Z)-~(Z)~/F(Z)~] 

Where Z= (XB - L)/a, L is the lower truncation point in 

the Tobit analysis (ADV), f(.) is the unit normal density, 

and F(.) is the cumulative normal distribution function. 

Individual subscripts have been omitted to simplify the 

notation. 

For computational purposes, estimates of p and a were 

obtained using maximum likelihood techniques. Table 2 

reports estimates of the beta coefficients and of a, S. 

The values for f(Z) and F(Z) can be obtained directly 

from standard statistical tables. The values for sections 5 

an~d 6, Table 3, can be obtained from previously calculated 

values. 

As an example, the entries in Table 3 were calculated at 

the overall sample means using Model 1 coefficients: 

Variable 

DBH 

HlVAL 

HAUL 

VALUE 

Constant 

S 

ADV 

Mean Coefficient 

10.83 1.18 

2.60 1.16 

44.67 -0.18 

19.28 1.22 

1 .OO - 17.80 - 6.75 

10.30 - 

Ca.lculating XB = 13.48, XB - ADV = 3.1 8, and (XB - ADV)/ 

S =: 0.47. Statistical tables for the normal distribution give 

F(0.47) = 0.68 and f(0.47) = 0.36. Substituting these values 

in ,the equations listed above yields the values in Table 3. 
Sendak, Paul E. 1991. Timber sale value as a function of sale characteristics and number of bidders. Res. Pap. NE-657. Radnor, PA: 

U.S. Department of Agriculture, Forest Service, Northeastern Forest 

Experiment Station. 7 p. 

Examines the effect of sale characteristics and number of bidders on 

sale value for timber sold by sealed-bid auction on the Green Mountain 

National Forest in Vermont. As anticipated from theory and previous 

empirical studies, increasing the number of bidders tended to increase 

the winning-bid value for the timber auctions studied. Efforts made to 

ensure that a timber sale offering received at least one qualified bid had 

a greater impact on sales revenue than efforts made to increase high-bid 

value. In designing sales, managers should avoid setting appraisal value 

too high in relation to timber quality. 

Keywords: Appraisal, auctions, national forest, Tobit 

d. U.S. GOVERNMENT PRINTING OFFICE: 1991-548-088140,005 
Headquarters of the Northeastern Forest Experiment Station is in ~adnor,*~ennsyhrania. Field laboratories are maintained at: 

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Delaware, Ohio 

Durham, New Hampshire, in cooperation with the University of New Hampshire 

Hamden, Connecticut, in cooperation with Yale University 

Morgantown, West Virginia, in cooperation with West Virginia University 

Orono, Maine, in cooperation with the University of Maine 

Parsons, West Virginia 

Princeton, West Virginia 

Syracuse, New York, in cooperation with the State University of New York, 

College of Environmental Sciences and Forestry at Syracuse University 

University Park, Pennsylvania, in cooperation with The Pennsylvania State University 

Warren, Pennsylvania 

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the USDA. Discrimination in any form is strictly against agency policy, and should be 

reported to the Secretary of Agriculture, Washington, DC 20250. 

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