Information about each sale was found in official sale 

 records, such as the timber sale report and appraisal 

 summary. 



Cost allowances and bid premiums were used as de- 

 pendent variables, both expressed in dollars per thousand 

 board feet (M bd ft) of timber harvest. Detailed cost infor- 

 mation, such as allowances for felling and bucking costs, 

 slash disposal costs, and so on, was obtained directly from 

 the timber sale appraisal summary (Forest Service Form 

 2400-17). Similarly, information from sale summary was 

 used to calculate bid premium as the difference between 

 advertised rate and high bid. All dollar information was 

 expressed in 1985 dollars, using the GNP Implicit Price 

 Deflator (BOC 1987). 



Sale characteristics were used as the independent vari- 

 ables. Various timber sale records provided information 

 on 40 sale characteristics, including sale features such as 

 volume harvested and miles of road construction and sale 

 requirements such as dust control and haul restrictions. 

 Sale features were measured as continuous variables. 

 Sale requirements were binary, measured as or 1, pres- 

 ent or absent. 



Cost allowance equations were estimated in four steps. 

 First, linear correlation analysis eliminated all but the 26 

 most promising or useful sale characteristics. Subsets 

 from these 26 characteristics were used as potential inde- 

 pendent variables to estimate each cost equation. Second, 

 traditional multiple linear regression analysis was next 

 used to identify the best subset of the 26 potential vari- 

 ables for each cost allowance model (see Draper and 

 Smith 1981 on adjusted R 2 and Mallow's Cp). Third, 

 using those variables, cost equations were reestimated 

 with the Seemingly Unrelated Regression routine of 

 SORITEC software (Sneed and others 1986). Finally, 

 equations were tested for compliance with underlying 

 statistical assumptions (see Weisberg 1980 on Box- 

 Ti dwell analysis) and two transformations adjusted for 



Figure 1 — The Northern Region and Intermountain 

 Region of the Forest Service. 



nonlinear relationships: the reciprocal transformation 

 (Y = 1/X) and the square root transformation (Y = X 112 ). 

 If any of the previously identified variables became non- 

 significant in the reestimated equations, they were dis- 

 carded and the equation again reestimated. Ultimately, 

 19 sale characteristics were used as independent vari- 

 ables; the rest were dropped from further consideration. 



Although bid premium depends on both market circum- 

 stances and errors in cost allowances, we were interested 

 only in the cost allowance portion. It is quite difficult, 

 however, to ascertain how much of the bid premium is due 

 to cost allowance errors and how much to the effect of 

 market circumstances. Our approach was therefore re- 

 strained, purposefully limiting the portion of bid premium 

 ascribed to errors in cost allowance. The bid premium 

 equation was estimated with traditional multiple linear 

 regression through a three-step process. In the first step, 

 bid premium was modeled as a function of market-related 

 variables only — number of bidders and the selling price of 

 lumber. This effectively ascribed the maximum amount of 

 bid premium to market circumstances. In the second 

 step, the five cost categories were added as independent 

 variables to that model, and the model reestimated. 

 Statistically nonsignificant cost categories were discarded, 

 and the model was again reestimated in the third step. 

 Coefficients on cost category variables depict the influence 

 of cost allowance errors on bid premium. 



RESULTS 



In total, 12 equations were estimated — six (the five cost 

 categories plus the bid premium equation) for the North- 

 ern Region and six for the Intermountain Region. The 

 listing below shows that allowances for stump-to- truck 

 costs were most important, accounting for more than half 

 of the $153/M bd ft overall averages in allowances: 



Northern and 

 Intermountain Regions 

 average allowance 



1985$IMbdft 



Stump to truck 



$82.15 



Transportation 



38.54 



Slash 



13.59 



Specified roads 



18.13 



Temporary roads 



.97 





$153.38 



Bid premium 



-26.39 





$126.99 



These cost allowances combine with overbids to account 

 for total adjustments. The variation in the cost allow- 

 ances explained by the equations ranged from 35 percent 

 to 91 percent, averaging 58 percent. Equations for the 

 Intermountain Region were above the average, the North- 

 ern Region below. 



The 19 variables used in final models are defined in 

 table 1. All but one described sale characteristics; the sole 

 sale requirement variable concerned dust control. As 



2 



