# «Abstract From bidding data, we estimate the underlying value distribution for Forest Service timber. We nd that bidder values decrease $2=mbf ...»

There are 88 potential bidders for each of the 41 auctions open to all bidders, and 71 potential bidders for the ten SBA Set-Aside auctions. Two auctions had three losing bidders with unknown hauling distances. Those bidders were deleted from the analysis.

The observed bidder-speci c value components i are speci ed as i 1 HAULi + 2 SBAi 4.1 where HAUL is the distance from each rm's closest mill to the tract and SBA is a dummy indicating the SBA status of the rm. Timber is costly to haul and, ceteris paribus, the means of the value distributions for rms with mills closer to the tract are higher than the means for rms with mills farther from the tract. In addition, large rms may have economies-of-scale in production and, as Johnson 19, 20 notes, often possess a comparative advantage in building the permanent roads needed to remove the timber from its site. Smaller rm size and longer hauling distances lower a bidder's value for the tract.

Hauling-distance data are given in Brannman 6. The major weakness of these data is measurement error which derives from several sources. Many rms have more than one sawmill and the di erent mills are often specialized for processing particular grades of timber or producing particular products.

Part of the timber from a sale may be shipped to more than one mill. Firms may also sell their timber to other rms. This occurs when the winning rm is unable to process a particular part of the sale as e ciently as another rm with a mill better designed for the particular type of timber being sold. In addition, the method of constructing the hauling distance data is necessarily imprecise. Forest Service sale-location data at times have only a 1 4-mile error. Other times the data are less precise and may contain as much as an eight-mile error. The maps used to compute distance show all logging roads in the region but, since new ones are built daily, it is di cult 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. Finally, no allowance is made for topography. Hauling timber uphill is more costly than hauling timber downhill. This gives mills located downhill" from a particular tract an advantage over those that must haul logs up and over a crest."

Summary statistics for variables used in the analysis are presented in Table 1. Table 2 presents the FIML estimates of the value distribution.

Table 1: Summary Statistics for 51 Oral Timber Auctions

The results in Table 2 suggest that observed bidder heterogeneity has a signi cant impact on the probability of winning. Firms closer to the tract and larger rms win more frequently than smaller and more distant rms.

The large coe cient on the SBA dummy means that small rms win much less frequently than similarly-located large rms. In the data, SBA rms win only 13 of 41 open auctions 31:7 percent despite comprising 80:6 percent of the pool of potential bidders.

Note that the mean value of the common shock, EY in 2.6, is not identi ed because the spread parameter is estimated from di erences in losing bids. In the following simulations, we calibrate the estimated value distribution to the winning bid in each auction by adding the di erence between the winning bid and the expected winning bid to each bidder's value.

5 The E ects of Mergers or Bidding Cartels From 2.6, it follows that the expected pro t for bidder i surplus of value over winning bid weighted by the probability of winning is measured by EXmax, EBi pi =,1= log 1, pi : 5.1 Froeb, Tschantz, and Crooke 16 use this pro t function to develop a merger model. Suppose rms i and k merge or form a bidding coalition. Then the winning probability of the merged rm is pi + pk since the merged entity wins in every auction one or the other of its member rms would have won.

The winning probabilities of the other rms remain unchanged. Since the auction is e cient, the extra pro t to rms i and k is equal the reduction in seller's revenue at auction, and is given by H = hpi + pk , hpi, hpk =; hp , log1, p: 5.2 The loss of competition depends critically on the relative locations and sizes of the merging and non-merging mills, which determine the winning probabilities for each tract. The loss of competition from merger also depends on 1=, which underscores the importance of estimating the parameters of the value distribution as an element of merger policy.

Estimated merger price e ects follow from 5.2 and are shown in Figure 1 for the Maybee Slope auction. There were 88 potential bidders in this auction. Each bidder's expected price 2.6 and probability of winning 2.4 is denoted by a dot. The large dots represent the two bidders with the highest probability of winning. The price e ect of a merger between these two rms, the most anticompetitive merger at the auction, is computed as a movement along the price share relationship de ned by 2.6. The merged entity moves from its pre-merger shares of 15:2 percent and 28:5 percent to its post merger share of 43:8 percent. The average expected price paid by the two rms prior to the merger is $164=mbf, given by the top horizontal line in Figure 1. The computed post-merger average price for the merged rm is $157=mbf the bottom horizontal line, a change of 4:1 percent. Surplus to the merged rm, de ned in 5.1, increases by 6:9 percent. Average industry price, the change in the merged rms' average prices times their probabilities of winning, decreases by 1:77 percent.

Summary statistics for the expected merger e ects across all 51 oral auctions are given in Table 3. In each auction, the simulated merger is the PRICE 167.5

Figure 1: Simulated Merger Among Two Best Bidders most anticompetitive two- rm merger among the set of all potential two- rm mergers. We choose the most anticompetitive mergers to estimate an upper bound on merger price e ects. In Table 3, the rst row gives the expected market share" of the merged entity; i:e:, the sum of the estimated winning probabilities. The second row shows the change in the merged rm's winning bid. The third row shows the expected industry price e ects. This is the same as the expected revenue loss to the seller and equals the change in the merged rm's winning bid times the merged rm's probability of winning.

The fourth row gives the expected change in buyer surplus, the excess of value over winning bid. The last row, discussed below, is the reduction in marginal costs increase in value required o set the merger price e ects.

The computed merger e ects seem small when measured against the structural standards of the Horizontal Merger Guidelines 29. Even very large structural mergers have small price e ects. The worst merger in the data, with a combined share over 50 percent, raises industry price by less than three percent.

The trade-o between anticompetitive price e ects and merger e ciencies may be computed using the estimated value distribution. Because losing bidders set the price, merger synergies do not a ect the prices paid by the Table 3: Simulated Mergers Among Two Best Bidders Variable Min Max Median Mean

**Sum of Merging Shares 8:4 51:9 35:1 34:3**

Merged Firm's Winning Bid,0:4,5:4,2:7,2:6,0:03,2:6,0:9,1:0 Industry Price Merged Firms' Pro ts 0:19 12:05 4:2 4:8

**O setting MC 0:6 9:7 3:8 4:1**

merging rms. However, by making the merged rm a stronger losing bidder, merger e ciencies do raise prices paid by the non-merging rms. By providing additional competition for non-merging bidders, e ciencies can o set the anticompetitive price e ects of the merger. To benchmark the e ciency claims of merging parties, we propose computing the reductions in marginal costs increases in value necessary to o set the merger-induced price decreases. These compensating marginal-cost reductions are computed by equating the pre-merger expected industry price to the post-merger expected industry price, and solving for the location parameter of the merged rm.

If the merged entity is su ciently large then no amount of merger synergy can o set the anticompetitive price decline when the merging rms win.

This happens because the synergies increase price only in auctions that the merging rms do not win. If the merging rms are already winning most of the auctions, then making them stronger cannot o set the anticompetitive price decline. Note also that by keeping industry price constant, we implicitly evaluate the merger under a consumer-welfare standard, i:e: one that does not a ect price. This follows existing practice at the FTC, although the U.S. Department of Justice is more inclined to evaluate mergers under a total-welfare standard.

Figure 2 shows the marginal-cost reductions required to o set the merger price e ects. The line MC = 4Price is also plotted. This line seems to t the data fairly well. For every one-percent increase in industry price, computed using the merger model of 5.2, it takes at least a four-percent decrease in marginal costs to o set the merger-induced price e ect.

%∆MC

Figure 2: Compensating Marginal-Cost Reductions 6 The SBA Set-Aside Program and Bidder Preferences The estimated value distributions may be used to analyze the e ects of programs giving competitive advantages to some rms. Two examples, one real and the other proposed, are the SBA Set-Aside program and a system of granting preferences to smaller and more distant bidders.

6.1 The SBA Set-Aside Program The SBA Set-Aside program limits auction participation to small rms, dened by the SBA as those with less than 500 employees. Two identical mills can have di erent SBA classi cations depending on their parent rm's size.

The program is triggered if, in a given year, small rm purchases fall below their historical ve-year moving average. Small rms can still bid on open tracts after the program is triggered. These purchases add to the historical share of small businesses. The Set-Aside program has numerous analogies in other areas of government contracting where, for example, bidding is restricted to minority-owned rms Froeb and McAfee 14 .

The costs of the SBA program can be simulated by assuming that small high-cost rms evolve into large, more e cient rms. The expected price change under this hypothetical scenario is computed over all 51 auctions in Table 4. On average, price would increase by 14:8 percent. This $29:6=mbf simulated cost of the SBA Set-Aside program is much larger than Schneipp's 26 $13=mbf cost, estimated as the coe cient on an SBA dummy in a reduced-form price regression.

6.2 Bidder Preferences Froeb and McAfee 14 have suggested replacing the SBA Set-Aside program with a policy of bidding preferences which are phased out over time.

Bidding preferences granted to smaller and more-distant bidders make them stronger bidders. The winning price increases when they lose, but revenues are lost when they win because subsides must be paid. An optimal for the purpose of revenue-raising set of preferences equates the marginal gain in price against the marginal cost of the subsidies.

McAfee and McMillan 21 use simulation to compute optimal bidding preferences for high-cost domestic rms in government-procurement auctions. Using uniform value distributions, they nd that the optimal bidding preferences should be set at one-third of the cost di erence between the domestic and foreign bidders. Ayres and Cramton 1 nd that a 50 percent bidding preference to women and minority rms raised spectrum auction revenues by $45 million.

Bidder characteristics vary considerably across auctions, so we compute optimal bidding preferences on an auction-by-auction basis. Preferences would involve a subsidy to small rms and a per-mile subsidy to all rms.

Figure 3 shows the e ects of bidding preferences in the Maybee Slope auction. The subsidies shift the price share relationship up and reduce asymmetry in the winning probabilities. In Figure 3, preferences increase revenue by 3:8 percent but expected revenues increases by only 0:17 percent after the expected subsidies are paid.

Figure 3: Bidding Preferences

Hauling and rm-size subsidies for each of the 51 auctions are computed in Table 5. By using optimal bidding preferences, the Forest Service can increase its revenue by 0:07 percent. These estimates suggest that bidding preferences have little revenue-raising potential.

Of particular interest in Table 5 is the small size of the preferences, and their comparatively small e ects. These results di er signi cantly from those of Ayres and Cramton 1 who nd much larger e ects from much larger bidding preferences. One explanation is that bidders are more asymmetric in spectrum auctions due to capital constraints. However, it is di cult to compare the results directly because Ayres and Cramton do not explicitly estimate a value distribution for the spectrum licenses.

sis of mergers in di erentiated-products industries Willig 34 ; Werden and Froeb 32 . In this paper, we show that these same properties make the logit model an attractive tool for analyzing competition policy in auction markets.