Potential competition and possible collusion in forest service timber auctions.

Brannman, Lance Eric

I. INTRODUCTION

Potential entrants to an imperfectly competitive market, in theory, limit the ability of existing firms to charge high prices. This claim has rarely been tested, due mainly to the problems of identifying potential entrants and determining whether established firms perceive them as future competition. In previous work, Neal [1987] finds option bid-ask spreads lower when they are eligible for multiple listing, Kuhlman and Johnson [1983] find winning highway construction bids insignificantly related to the number of firms buying plans for the particular project, and Hurdle et al. [1989] show that performance in the airline industry is affected by the number of potential entrants not deterred by economies of scale or scope.

This paper determines whether potential competition influenced winning bids in Forest Service oral and sealed-bid timber auctions held during 1977. Prior to 1977 oral bidding was the dominant method of selling timber in the Pacific Northwest. The National Forest Management Act of 1976 required that sealed bidding be used on all sales with exceptions made only by the Secretary of Agriculture. The sealed bidding requirement was overturned in 1978 after firms in communities dependent upon Forest Service timber complained that sealed bidding resulted in greater uncertainty in obtaining steady timber supplies.(1) Firms pay the government for the rights to harvest timber in Forest Service timber auctions and the highest bid wins. Bidding theory predicts that greater competition should result in higher winning bids.(2) The relevant measure of competition in an oral auction is the actual number of competitive bidders. Participants in a sealed-bid auction, however, should base their bids on the potential number of competitors.

Timber is costly to haul and timber transportation distances, from the sale site to the closest mill of potential competitors, are used to define two measures of potential competition. The first measure is a simple count of the number of firms whose closest mill lies within the geographical market for Forest Service timber auctions and is termed potential competition. The second results from a probit analysis relating auction participation to hauling distance and is called expected competition.

The results show that these measures are, as expected, considerably more important in explaining winning sealed bids. However, actual competition explains winning bids better than either potential or expected competition under both oral and sealed bidding. In addition, contrary to expectations, increases in hauling distances result in higher winning bids when sealed bidding is used.

Collusion in sealed-bid auctions and preclusive bidding (a type of collusion) in oral auctions are explanations for both of these results. The possibility of collusion in sealed-bid auctions is supported by an index, based on Stigler's [1964] theory of oligopoly and Feinstein, Block and Nold's [1985] research on bid-rigging in highway construction auctions, representing the likelihood that a given auction was rigged.

Mead [1966] was among the first to discuss the possibility of preclusive bidding in oral auctions. Preclusive bidding occurs when firms close to a sale site bid above levels which are profitable to firms farther from the site. Given that oral bidding entails greater participation costs (participants must be present), preclusive bidding or the threat of preclusive bidding deters outsider firms from bidding in future oral auctions. Firms close to the site benefit from the decreased competition and may win at a lower price. Oral and sealed-bid comparisons of winning bid variances, overbids, and numbers of bidders support the explanation of preclusive bidding in oral auctions.

Public policy should be concerned with obtaining the highest possible value for public timber and ensuring that it is awarded efficiently, to the firm having the highest timber value. The results indicate that sealed bidding best accomplishes these objectives, by widening the pool of potential bidders. Despite possible collusion in sealed-bid auctions, greater potential competition results in higher prices. In addition, timber seems to be awarded more efficiently in sealed bid auctions, i.e., to firms with higher timber values.

II. CURRENT BIDDING MODELS

Auctions vary considerably in form and environment, depending on their rules, the type of good being sold, and firm and industry characteristics.(3) In the independent private values model, bidders place different (independent) subjective values on an object offered for sale. All independent private valuations are treated as a random sample from some underlying value distribution which is known to all auction participants. Each bidder knows his own valuation, but not those of his competitors. The common value model assumes that the object offered for sale has a true but unknown value which is common to all bidders. Each bidder estimates the true value by independently drawing from a common distribution. Milgrom and Weber [1982] present a general bidding model which includes the independent private values and common value models as special cases.

Bidding strategies in both types of auction models depend on all available information, including the number of bidders, the value distribution of the object offered for sale, and the type of auction (e.g., Dutch, English, oral, sealed, etc.). In the independent private values model with risk neutral bidders, the expected winning bid equals the second-highest sampled value from the underlying value distribution in a wide variety of auction types, as explained by Myerson [1981] and Riley and Samuelson [1981]. More bidders (i.e., a larger number of samples from the value distribution) increase the expected value of the second-highest valuation at a decreasing rate. Using similar reasoning, expected winning bids also increase with the number of bidders when firms are risk averse in the private values model, but the actual movement depends on the degree of risk aversion among firms. Prior arguments about the relationship between expected winning bids and the number of bidders in the common value model are not as straightforward as in the private values model, being dependent on distributional assumptions and corrections for the winner's curse.

Timber auctions fit neither model. Initially the private values model seems appropriate since timber values differ across firms due to different hauling distances and product mixes. In addition, high setup costs limit the ability of firms to locate mills near each site. However, differences in location and product mix are probably known to all bidders prior to each auction. Furthermore, Johnson [1979] notes that large firms often have greater working capital and own specialized road building equipment, giving them a cost advantage over smaller firms in auctions requiring permanent road construction. These conditions violate the private values model's assumptions that values are randomly drawn from the same distribution and that a firm knows its own value but not those of other firms. Johnson analyzes this asymmetric bidding environment when there are two bidders and notes that the firm with the lowest costs maximizes expected profits by bidding higher than its expectations of the other firm's costs. Knowing this, the high-cost firm has an incentive to also bid higher. The result may be inefficient: a firm with higher costs may bid lower and win, relative to a firm with lower costs. However, this type of inefficiency decreases as the number of potential bidders increases.

Despite possible asymmetric information inefficiencies, available evidence indicates that increased competition leads to higher winning bids for Forest Service timber. Brannman, Klein, and Weiss [1987] find winning bids rising with the expected values of the highest and second-highest order statistics from a standard normal distribution. In Johnson [1977; 1979], winning bids are significantly affected by the logarithm of the number of bidders. Haynes [1980a] finds average overbids (winning bid minus the Forest Service appraisal price minus estimated permanent road construction costs, per thousand board feet (MBF) timber volume) highly correlated with the number of bidders across several regions of the country. Finally, Mead, Schniepp, and Watson [1981; 1983] find the logarithm of the number of qualified bidders significant in explaining average overbids when sealed bidding alone is used, and when oral and sealed bid auctions are pooled and the auction method is held constant.

III. THE MARKET FOR TIMBER

The market for a given timber auction depends on a number of influences, including whether firms are qualified to bid and how far they are from the sale site. One restriction on auction participation is institutional. Under the Small Business Administration (SBA) set-aside program, bidding for various sales is restricted to firms with less than 500 employees. The amount of actual, potential, and expected competition for SBA set-aside sales can therefore be no greater than the amount of competition for sales open to all firms.

The geographic market for timber is obtained using distances from various sale sites to the winning firm's closest mill. Brannman [1991] presents these data for a sample of 153 sales in Oregon's Lane and Douglas counties during 1977. These counties consistently have more sales than any other county in Oregon. The sample was reduced to 145 sales by requiring that all sales be on a "flat rate" pricing basis where the nominal winning bid remains constant and the winner makes payments to the government on an "as harvested" basis.(4) An additional oral auction was excluded because it was won by a firm that faced no competition and did not bid in any of the other auctions. This made it impossible to calculate an index for the likelihood that the firm colluded. Sealed-bid auctions accounted for 93 of the remaining 144 sales. Thirty-nine of these sales were SBA set-aside sales. In the 51 auctions held using oral bidding, 12 were SBA set-aside sales.

Timber has a low value per unit weight and the costs of transporting it help define the number of potential competitors for a given sale. An additional determinant is the distance the finished products must be shipped, from the winner's mill to its markets. This determinant is not as important since the value/weight ratio of finished products is considerably lower than that of timber. However, since sale sites are typically in remote areas, the distance from the site to the winner's closest mill and the distance from the winner's closest mill to metropolitan areas (representing product markets) should be inversely related.

Mead [1966, 94] concludes that high hauling costs limited the timber market in the Pacific Northwest in the early 1960s to buyers within a 75 mile radius of the timber stand. The highest hauling distance to a winner's mill in the present data set was 115 miles. Potential competition is defined as the number of firms with mills within this distance who had submitted a bid in any of the auctions. This criterion overcomes, at least roughly, the problems of identifying potential entrants and determining whether established firms perceive them as future competition.(5) Under this definition, the mean and dispersion of the distribution of distances to the closest mills of potential competitors should also be important in defining competition. An increase in the average distance from the sale site to rival mills lowers the competition that a given firm faces and, ceteris paribus, a firm is therefore able to bid lower than it would otherwise. Greater dispersion in the distribution of rival distances increase the chances that a rival mill is closer to the sale site and firms should adjust by bidding more than they would otherwise. A bidder, faced with an average distance to rival mills of forty miles and zero variation in rival distances is considerably less threatened and more able to submit a lower bid compared to a bidder whose rivals are the same average distance from the sale site but with considerable variation in their distances.

The expected competition measure results from a probit analysis of the relationship between distance to the sale site and auction participation. The expected number of bidders in this case is the sum of the estimated participation probabilities across firms. Beutel [1991], commenting on Meyer [1988], estimates competition in rice auctions using a probit model, arguing that an errors-in-variables problem occurs when the actual number of bidders is used as a proxy for expected competition, biasing its estimated coefficient towards zero. Johnston [1984] and Hausman [1978] show that the coefficient estimates are biased when the difference between the actual and expected number of bidders is correlated with the regression's disturbance term. The expected numbers of bidders resulting from a probit model is an instrument which solves this problem. The probit-derived expected number of bidders also implicitly contains information about the distribution of rival hauling distances. The mean and standard deviation of rival hauling distances are therefore excluded from the regression when the expected number of bidders appears in the equation.

The use of distances to the sale site to identify potential competitors may suffer from measurement error. Many firms have more than one sawmill and, in many cases, each mill is designed to process only a particular grade of timber. Part of the timber from a sale may be shipped to one mill, part to another, and the rest to still another. Firms may also sell their unused timber to other firms. This occurs when the winning firm is unable to process a particular part of the sale as efficiently as another firm with a mill better designed for the particular type of timber being sold. Finally, the method of constructing the hauling distance data is necessarily imprecise. Forest Service sale location data at times have only a one-quarter-mile error. Other times the data are less precise and may contain as much as an eight-mile error. The maps used show all logging roads in the region but, since new ones are built daily, it is difficult to know which were used to log a particular sale. In addition, there is no way to know when logging roads were used and when better quality roads or highways were used. Hauling costs are lower on high quality paved roads because truck speed is much greater.

IV. SPECIFICATION

The Forest Service is required by law to appraise the timber and sell it for an amount at least equal to this value. The appraisal process is based on the concept of derived demand. The Forest Service "cruises" the tract being sold and estimates a number of variables, including timber volume by species, the number of acres involved, road building requirements, different costs associated with harvesting and processing the timber, and the selling value of the products most likely to be produced. The appraised value is calculated by subtracting the estimated harvesting, manufacturing, and road building costs for a firm of "average efficiency" and a margin for "profit and risk" from the timber's estimated product selling value. This appraised amount, plus a credit given to the buyer for building any permanent roads, is the auction's reservation price and is known to all bidders prior to the auction. The appraised amount includes product and factor market conditions, but not the influence of potential or expected competition.

Regression analysis is used to estimate the effects of changes in actual, expected, and potential competition on winning bids. The dependent variable is the winning bid per thousand board feet estimated timber volume. Independent variables may be grouped into five categories: competition, the Forest Service appraisal and its elements, sale characteristics, bidder characteristics, and product market information. Auction theory predicts that increased competition raises winning bids at a decreasing rate. Competition is therefore measured by the natural logarithms of the actual, expected, and potential number of bidders.

An increase in the total appraised value (per thousand board feet) reflects a higher quality stand of timber and should raise winning bids. The appraisal components are included in the regression specification since the total appraised value does not accurately reflect true costs and revenues, as shown by Mead, Schniepp, and Watson [1985]. One reason is that the Forest Service bases its calculations on prior product market prices and the costs for a firm of "average efficiency" while the winner sells its products in the future and probably operates at above average efficiency. The appraisal element coefficients represent the degree to which the total appraised amount does not completely capture the market's evaluation of the sale.

Observed sale characteristics include the number of acres, percentage per-acre-material, whether or not the sale was a salvage sale, the amount of road construction required, the county in which the sale took place, and whether the sale was an SBA set-aside sale.(6) The number of acres, percentage per-acre-material, and whether the sale was a salvage sale are already included in the Forest Service appraisal components and should affect winning bids (in an a priori undetermined fashion) only when the appraisal components do not completely account for them. Similarly, since winners pay for the timber on an "as logged" basis after deducting credits allowed for the construction of permanent roads, estimated permanent road construction costs should affect winning bids when the credit given is greater or less than the true construction costs. The county dummy variable controls for possible differences between the two counties which might affect winning bids and which are not included in the appraised amount. Hansen [1986], for example, argues that buyer concentration is an important difference across geographic timber markets. Haynes [1980a, 25] suggests that there should be no difference in SBA set-aside versus open bid prices when the characteristics of the two types of sales (and the amount of competition) are held constant. However, as seen below, large firms appear to possess cost advantages in road construction.

Observed bidder characteristics are the hauling distance to the winner's closest mill and whether the firm is large or small. Higher hauling distances, ceteris paribus, make a firm less competitive and should result in lower winning bids. Large firms, due to their greater working capital and ownership of specialized road building equipment, are able to bid more when the auction involves constructing permanent roads. Public Law 94-588 gives small businesses the option of having the Forest Service construct permanent roads when the estimated cost exceeds $20,000. Despite this option, large firms appear to retain a cost advantage in road construction, winning 35/48 of the sample's open sales with estimated construction costs exceeding $20,000 but only 22/46 of the open sales with estimated costs less than $20,000. An interaction term, the product of a firm size dummy (= 1 if the firm is large) times estimated permanent road construction costs ($/MBF), is included to account for the advantage large firms have in constructing permanent roads. This variable should be positively related to winning bids.

Product market characteristics affect winning bids through lumber prices and contract duration. Since timber is harvested in the future, its estimated selling value should depend on expected future product prices.(7) Johnson [1977] provides evidence that Douglas-fir timber prices follow a random walk and predicts future lumber prices with the value of the wholesale lumber price index at the time of each auction. It might be argued that contract duration is a sale characteristic, rather than a product market characteristic. However, its influence on timber prices is through the product market, via the theory of financial options. Mead, Schniepp, and Watson [1985] note that longer contract durations (highly correlated with volume) increase the chance of observing higher product prices and thus increase winning bids. Firms essentially have an option at each point in time to either harvest the timber (exercise the option) or continue to let it grow, subject to the constraint that all harvesting must be completed during the duration of the contract. The Black and Scholes [1973] option pricing model formalizes the effect of time on option prices. The influences of expected future product prices and time on winning bids are captured by including average monthly lumber selling values for Pacific Northwest coastal mills for the month in which the sale took place and the duration of the contract in the regression equation.(8) An increase in the values of these variables should raise winning bids.

V. RESULTS

The data come from the Forest Service 2400-17 "Report of Timber Sale" forms and the Western Wood Products Association monthly price bulletins. A total of 104 different firms submitted bids in at least one of the sample's 144 auctions. Hauling distances to the closest mills of eighty-eight of these firms were calculated. Mill locations for the other seventeen firms, representing 5 percent of all bids and none of the winning bids, could not be identified and were excluded from the distribution of rival distances. Summary statistics on variables used in the regression analysis are given in Table I.

The probit-derived expected number of bidders in Table I is the sum of the estimated probabilities that each firm will participate, given its distance from the sale site. Each auction method/SBA set-aside sale combination was estimated separately because each implies different amounts of expected competition, affecting a firm's prior probability of winning and decision to participate.(9) The least amount of expected competition should occur when oral bidding is used and the auction is a set-aside sale. The greatest amount of expected competition should occur in sealed-bid sales open to all firms. The amount of expected competition in the other two categories, sealed-bid set-aside sales and oral auctions open to all firms, should be somewhere between these two levels.

Table II shows the estimated probit relationships for each combination. The number of bids submitted in each category is given in parentheses. Hauling distance, as expected, has a significantly negative effect on a firm's decision to bid in each case. Participation falls the most with greater hauling distances in sales open to all firms and the least in SBA set-aside sales. This is also as expected; in open sales an increase in a single bidder's hauling distance results in more competitors being closer to the sale site. The chance of winning therefore falls more, relative to SBA set-aside sales, and some firms compensate by not participating. The estimated relationships fit the data best in sealed-bid auctions, when participation costs are lower and there is less possibility of preclusive bidding.

The potential number of bidders using the geographic market definition (number of firms with mills less than 115 miles from the sale site) is significantly larger than the actual number of bidders or the expected number of bidders. This is because potential bidders were defined as all firms who had participated in at least one auction. No allowance was made for each firm's relative frequency of participation. However, as seen below, the natural logarithm of the significantly more numerous potential number of bidders, using the geographic [TABULAR DATA FOR TABLE I OMITTED] market definition, explains winning bids quite well.

Table III shows the winning bid regression results. Probability values, based on the expected coefficient signs, appear next to the coefficient estimates. For convenience, the alternative hypothesis for each variable is in parentheses next to the variable's name. The probability value for a one-tailed alternative hypothesis is less than 0.50 when the estimated coefficient has the expected sign and greater than 0.50 when the estimated coefficient has the wrong sign. A probability value close to one when the alternative hypothesis is one-sided indicates significant explanatory power, in the wrong direction. Due to rounding of the coefficient estimates, some of the displayed probability values are different from 0.5 or one when the corresponding coefficient estimates appear to equal zero.

Actual and potential or actual and expected competition measures are included in all equations in order to determine which provides the greatest explanatory power. The sample correlations between the number of actual and potential bidders were quite small, -0.11 (p-value = .28) in sealed-bid auctions and -.04 (p-value = .80) in oral auctions. The sample correlations between the number of actual and expected bidders were .05 (p-value = .52) in sealed-bid auctions and .09 (p-value = .55) in oral auctions.

[TABULAR DATA FOR TABLE II OMITTED]

The results generally confirm the predictions that actual competition matters in oral auctions and potential or expected competition matters in sealed-bid auctions. Both the potential and expected competition measures have the expected signs and considerably lower probability values in sealed-bid auctions. As expected, in oral auctions an increase in the actual number of bidders significantly increases winning bids while an increase in the potential or expected number of bidders has no significant effect on price. The greater significance of potential competition in sealed-bid auctions (p-value = 0.11) is noteworthy since the average number of potential competitors is substantially higher (sixty-eight in oral auctions and seventy in sealed-bid auctions) than average actual or expected competition.

The estimated mean and standard deviation of the distribution of rival hauling distances perform poorly. The average haul to rival mills has the expected sign and is mildly important (at the .13 level) only in oral auctions. The estimated standard deviation variable has considerable explanatory power in oral auctions, but its coefficient has the wrong sign. One explanation for these results is that timber hauling distances and lumber hauling distances (to the product market) should be inversely related. The rival hauling distance data therefore also include information about distance to product markets.

Differences in overall oral and sealed-bid behavior among bidders are mildly supported by the data. The test statistics for the equality of all the probit expected number of bidders and the geographical [TABULAR DATA FOR TABLE III OMITTED] potential number of bidders coefficients are 1.63 and 1.61. The F(17, 110) (expected competition) and F(19, 106) (potential competition) probability values associated with these statistics both equal .07.

The actual number of bidders fits better than the potential or expected number of bidders in sealed-bid auctions, contrary to expectations. Kuhlman and Johnson [1983] find the same perverse effect in their study of potential competition in highway construction auctions, attributing it to collusion among bidders. Collusion is a possible explanation in timber auctions as well, though previous work such as Mead [1966], Johnson [1977; 1979] and Brannman [1991] focuses on its potential for occurring in oral auctions. Hansen [1986], however, includes a variable capturing the ability of firms to collude (the concentration ratio for timber purchases across several counties) in his high-bid equation and rejects the notion that greater collusion occurs in oral auctions. Another explanation is measurement error in the calculation of the potential and expected number of bidders.

Hauling distance to the winner's closest mill has a positive effect on winning bids under both auction types and has considerable explanatory power in sealed-bid auctions. This result is unexpected but may be caused by differences in efficiency among bidders or the expected collinearity between timber hauling distances and distances to product markets. More efficient firms or those with a total hauling cost advantage (timber hauling plus product hauling) may be located farther from the sale site and are able to bid higher. The greater significance of hauling distance under sealed bidding supports this explanation since firms located farther from the sale site may be precluded more often under oral auctions, but not under sealed bidding. Systematic efficiency differences between large and small firms are indicated by the Large Firm x Permanent Road Costs interaction term. The estimated coefficient for this interaction variable has the expected sign and is significant across both auction types.

The effects of changes in the other variables generally conform to expectations but their explanatory power differs substantially between oral and sealed-bid auctions. With the possible exception of the salvage sale variable, the appraisal elements and sale characteristics contain significantly more information about oral winning bids. The SBA set-aside dummy variable is more important in oral auctions while the interaction term representing the cost advantage of large firms in permanent road construction is more important in sealed-bid auctions. The positive and, in the case of oral auctions, highly significant effect of contract duration on winning bids supports the idea that bidders view timber contracts as options to harvest within the specified time period. Contrary to expectations, increased lumber prices have negative effects on winning bids in both types of auctions. The effect is quite strong under sealed bidding. Lumber prices increased significantly during 1977 and bidders may have adopted mean-reversion expectations about future lumber prices, rather than the rational expectations found by Johnson [1977] in a different time period.

VI. POSSIBLE COLLUSION

Two results from Table III suggest possible collusion in oral and sealed-bid auctions. First, the actual number of bidders contains more explanatory power than either the expected or potential number of bidders in sealed-bid auctions. Second, increases in hauling distances raise winning bids in sealed-bid auctions, suggesting that more efficient firms may have been precluded from bidding in oral auctions.

Stigler [1964] notes that collusion is more likely to occur in oral auctions rather than sealed-bid auctions. Cartel detection and enforcement costs are lower under oral auctions and the incentive to cheat is less because the identities of all bidders and their bid amounts are immediately and costlessly known by all auction participants. The result is less cheating and greater cartel stability. Limited evidence appears to support Stigler's theory in the case of Forest Service timber sales. There were twenty-nine different winners among the ninety-three sealed-bid auctions and twenty different winners among the fifty-one oral auctions. However, the frequency distribution of wins by firm identity was highly skewed in the case of oral auctions, with the top two firms accounting for 36 percent of all wins and the top four firms accounting for 51 percent of all wins. The frequency distribution of wins was considerably more uniform under sealed bidding, with the top two firms accounting for 15 percent of all wins and the top four firms accounting for 28 percent of all wins.

Stigler's theory may be tested using indices developed by Feinstein, Block, and Nold [1985] and modified to suit the present sample. The sample was divided into four categories, according to the auction method used and the county in which the sale took place. Each category represents a market where the same firms are likely to repeatedly meet each other since high hauling costs limit the ability of firms to transport timber from one county to another. For each firm, an index H(i) is defined as the ratio of the number of different firms that firm i had bid with in the relevant sample to the total number of bids submitted in auctions that i had bid in, less the number submitted by i. Higher values of H(i) mean that i bid with many different firms. Since cartel detection and enforcement costs rise with the number of firms, a higher H(i) suggests a lower likelihood that firm i was part of a collusive agreement. Similarly, lower values of H(i) mean that i bid with fewer different firms and suggest a higher chance that firm i colluded.

A comparable index for each auction, Group, is the arithmetic average of the H(i) indices. Higher values of Group imply a lower chance that a given auction was rigged and therefore should be associated with higher winning bids. Lower values of Group imply a higher chance of collusion and should be associated with lower winning bids. According to Stigler's reasoning, the Group effect should be greatest in the environment most conducive to collusion, i.e., in oral auctions. However, when included in the Table III specification, its estimated coefficient in both types of auctions was significantly negative.(10) The most obvious reason for this anomaly is that an unweighted average of the H(i) indices in the present data set places too much emphasis on many firms that are not regarded as rivals by other firms since they rarely bid.

A modified Group variable, defined as a weighted average of H(i) indices, where the weights are the relative frequencies of participation by each firm across the relevant sample, controls for the situation of infrequent bidders receiving too much emphasis. Table IV shows the results of including this weighted Group variable in the regressions. As expected, higher-weighted Group values led to higher winning bids in both auction types. However, the effect was most important in sealed-bid auctions. This result indicates possible collusion in sealed-bid auctions and is consistent with the earlier finding that the actual number of bidders in sealed-bid auctions contains more explanatory power than either the expected or potential number of bidders.

Differences in overall oral and sealed-bid behavior among bidders when an allowance is made for possible collusion are supported by the data. The test statistics for the equality of all the probit-expected number of bidders and geographical potential number of bidders coefficients in Table IV are 1.75 and 1.78. The F(18, 108) (expected competition) and F(20, 104) (potential competition) probability values associated with these statistics equal -.04 and .03.

One explanation for the lack of weighted Group significance in oral auctions is that the greater chances for collusion in oral auctions (lower Group values) lead to decreases in average winning bids and, because of preclusive bidding (a type of collusion with its "win low-then preclude high-then win low" pattern of bidding), an increase in winning bid variances. This explanation is consistent with the data - the sample mean and standard deviation of winning oral bids were $187.72 and $46.24 per thousand board feet while the same figures for winning sealed bids were $205.83 and $42.74 respectively. Moreover, the unexpected positive effect of hauling distances is considerably stronger in Table IV, additional support for the idea that winning bidders farther from the site are more efficient than insider bidders.

Further evidence that oral auctions facilitate preclusive bidding is provided by Haynes [1980b]. Outsiders are defined by Haynes as bidders with their primary mill outside the "adjacent dependent community" or within the community but not having a record of previous timber purchases. Based on this definition he finds that sealed bidding did not result in greater outsider bidding. However, overbids on sales with outsiders were significantly higher than on sales without outsiders for both oral and sealed-bid auctions in Haynes's data set. The average overbid difference was $11.64 per thousand board feet in oral auctions and $5.50 for sealed-bid auctions. The higher difference at oral auctions is consistent with the idea that oral bidding is associated with preclusive bidding.

Similar tests may be conducted with the present data set using hauling distances to measure the likelihood of a firm being an insider. If preclusive bidding occurs, then the variation in winning bids for oral auctions won by firms close to the site should be greater than the variation in winning bids for oral auctions won by firms farther from the site. Insiders would win at a high price, then a lower price when the outsider does not participate, then a higher price, followed by a lower price, etc. In addition, since preclusive bidding is designed to deter future participation, the mean number of bidders at oral auctions won by firms close to the site should be more variable but less than the mean number of bidders at oral auctions won by firms farther from the site.

These hypotheses were tested by sorting the oral auction sample of fifty-one sales by the hauling distance to the winner's closest mill. The middle eleven auctions were eliminated, leaving two sets of twenty auctions, one corresponding to auctions won by firms close to the site and the other won by firms far from the site. The sample standard deviation of winning bids for the set close to the site was 35.05 and 46.52 for the set far from the site, contrary to expectations.(11) However, this difference was not significant since the null hypothesis that these variances are equal (versus the alternative that the oral winning bids have greater variance) could not be rejected at the .10 level. The computed F-statistic for testing equality of variances was 1.76, below the understated F(20,20) critical value of 1.79. In addition, the mean number of bidders for the set close to the site was 7.10 (s = 0.68) and 8.50 (s = 0.58) for the set far from the site, a significant difference and consistent with what is expected to occur under collusion. [TABULAR DATA FOR TABLE IV OMITTED] As expected, with less competition the average winning bid for the set won by firms close to the site ($197.56 per thousand board feet, s = $7.79) was less than the average winning bid for the set won by firms farther from the site ($218.38 per thousand board feet, s = $10.40).

VII. CONCLUSIONS

Theoretical auction models suggest that firms form their equilibrium bids based on the level of competition. In oral auctions the level of competition is the number of active bidders. In sealed-bid auctions firms should base their bids on the expected or potential number of bidders, not the unknown actual number of bidders. The effects of changes in expected and potential competition on winning bids in both types of auctions are as expected, significantly raising winning bids in sealed-bid auctions and having insignificant effects in oral auctions. Moreover, bidders appear to be more concerned with the number of potential competitors whose closest mill lies within a radius of 115 miles from the sale site, rather than the probit-derived expected number of bidders. Measurement error in the hauling distance data, upon which both the expected and potential competition measures are based, further strengthens these results.

Possible collusion in sealed-bid auctions and preclusive bidding in oral auctions (a type of collusion) explain the findings that actual competition matters more in sealed-bid auctions and that hauling distances have a strong and positive effect on winning sealed bids. Collusion in sealed-bid auctions, whether tacit or explicit, is further supported by the weighted average Group results in Table IV. The significant hauling coefficient under sealed bidding indicates that outsider firms that may have been more efficient in either their operations or total hauling costs were precluded from bidding in oral auctions. This explanation receives further support from comparisons of oral and sealed winning bid variances, winning overbids with and without outsider participation, and the mean number of bidders in oral auctions, ranked by the winner's distance to the sale site.

A finding that winning bids do not fluctuate with market pressures, in either type of auction, suggests that the government may need to become more involved in the design of timber auctions. Public policy should be concerned with obtaining the highest possible value for public timber and ensuring that it is awarded efficiently, to the firm having the highest timber value, whether or not that firm is part of the local timber-dependent community. Fehl and Guth [1987] outline non-incentive compatible pricing rules which address these objectives. The positive hauling distance coefficient and the effects of potential competition under sealed bidding suggest that efficiency and higher timber revenues seem to result more from sealed-bid auctions, despite possible collusion.

1. Hansen [1986] argues that auction method and winning bids, conditional on auction method, are simultaneously determined in the 1977 data set.

2. Porter and Zona [1993] argue that a well-designed phantom bidding scheme may also fit theory.

3. Milgrom [1985] and McAfee and McMillan [1987] provide bibliographies of the literature.

4. Some Forest Service price mechanisms share the risk of changes in product market prices with the buyer. Flat rate pricing does not allow adjustments in the amounts paid. Depending on expected future costs and revenues, the "flat rate" pricing basis may give winners an incentive to delay harvesting. Medema [1977] analyzes the effects of various price escalation mechanisms on timber prices.

5. Many firms have their own timber inventories or buy timber from other firms. They should not be regarded as competition. Identifying potential competitors by their participation during 1977 assumes that they had also participated prior to 1977, i.e., that the 1977 window adequately mirrors participation in other years.

6. Salvage sales involve picking up after the initial logging operation.

7. Nearly all contracts have a duration between one and five years. The Forest Service appraised selling value depends on prior product prices.

8. Average monthly lumber selling values for Pacific Northwest coastal mills on a FOB mill basis are calculated and published by the Western Wood Products Association.

9. The average numbers of bidders contain all firms and are greater than the corresponding probit estimates which include only firms with known mill locations.

10. The results are not reported to save space and are available from the author upon request.

11. The corresponding coefficients of variation were .50 and .44 respectively. Heteroskedasticity of winning bids was rejected, the sample variance of the lowest twenty winning bids ($/MBF - not sorted by hauling distance) was virtually identical to the sample variance of the highest twenty winning bids ($/MBF).

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