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Comparative antitrust damages in bid-rigging cases: some findings from a used vehicle auction.

I. Introduction

In order to recover antitrust damages, the plaintiff in a bid-rigging case must be able mi prove the amount of the price change suffered as a result of a conspiracy. However, despite a large theoretical literature on auctions and competitive bidding, there are only a few published studies of the possible effects of bid-rigging on auction prices.(1) One result of this lack of empirical evidence is that the determination of damages in civil Antitrust litigation is much less certain.(2) and as Froeb points out, bidding rings are often so stable that absent the risk of Antitrust sanctions, a bidder always has reason to join and remain a member of a ring.(3)

In a recent study of a sealed-bid procurement auction, Howard and Kaserman examined alternative approaches to damage estimation for a construction industry bid-rigging case.(4) Their general purpose was to analyze the legal, practical, and economic aspects of proving damages in bid-rigging cases. More specifically, they estimated comparative damages using five different empirical methods and a small sample of seven rigged construction contracts and 39 competitively-bid contracts. Howard and Kaserman concluded that the results obtained for three alternative statistical approaches were broadly robust with regard to average damages.(5) Thus, while there are always practical problems associated with any damage estimation method, their study provides a tentative basis for arguing that a statistical approach to damage estimation is reliable and accurate for determining average (and therefore total) damages.

The objective of this study is to provide a comparative analysis of damages resulting from alleged bid rigging at an English auction of used state police cars. The damage estimates are hypothetical because the antitrust suit was settled out of court and there was no finding of guilt or admission of wrongdoing. Consequently, for purposes of this article, certain facts and all names in the case have been suppressed.(6)

Following the procedures outlined by Howard and Kaserman, three different statistical estimation methods are examined: the ratio approach, the dummy variable approach, and the forecasting approach. However, the present study differs in several ways from Howard and Kaserman's work. First, the auction in question is a repeated oral auction of multiple units of like-model vehicles. With multiple units, it is important to control for the number of units auctioned as well as the number of bidders. Only the latter control was important in Howard and Kaserman's study; they examined a sealed-bid auction of relatively unique construction job& Second, a larger sample is available in the present study which makes it possible to consider some of the shortcomings of the dummy variable approach that were discussed by Howard and Kaserman. The sample consists of 340 vehicles sold at 13 auctions, including 81 vehicles that possibly were affected by bid rigging. Third, the study attempts to show how a government regulation can divide a market so as to limit the number of effective competitors and thereby encourage collusion. I show below that an important aspect of the market for used police cars is a New York City regulation on conversion of used vehicles to taxicabs. This regulation has the effect of sharply dividing bidders' valuations into "high" and "low" valuation groups. The present study is therefore an example of how a government regulation can inadvertently restrict competition and facilitate collusion.

The remainder of the article is organized as follows: Section II provides background on the auction. Section III describes the data and presents some descriptive statistics. Section IV contains the comparative estimates of damages for the three alternative statistical approaches. Section V contains the conclusions.

II. Background on the auction

A. The auction

A state government's used vehicles are sold at a public auction held in the northeastern U.S. The auction is conducted monthly or whenever enough used vehicles have been obtained to make up a sale lot of about 200 vehicles. Approximately 150 of these vehicles will be passenger cars in serviceable condition, with the remainder made up of trucks, utility vehicles, and wrecks. The vehicles are available for public inspection for 2 weeks prior to and on the day of the sale.(7) Each vehicle is identified by an item number on the windshield, and each vehicle has a window sticker containing information on the make and model of the car, mileage, and the state agency that used the vehicle. The window sticker also contains the agency's rating of the mechanical condition of the car on a scale of "poor," "fair," or "good," a similar rating of the exterior/interior condition, and a similar rating of the vehicle's tires. Specific mechanical defects that could be identified by the agency's inspector are also disclosed on the sticker. While the vehicles are locked prior to the auction, each car is driven into the auction area just before it is sold. At that time, prospective buyers have an opportunity to listen to the engine and can read the window sticker.

Most of the vehicles offered for sale are domestic four-door sedans that are 4- to 5-years old, with an average mileage of about 90,000 miles. All of the vehicles examined in this study are 1988 Chevrolet (Caprice sedans that have been used as state police cars. The sale of these cars began in January 1990 and continued through May 1991. These vehicles differ in two important ways from the other vehicles being sold at the auction. First, the cars are sold after only 2 years of use, by which time they have accumulated an average of 88,000 miles. Second, police cars are equipped with a special package of manufacturer-installed options, including a heavy-duty radiator and transmission, a reinforced frame and body, and a special suspension. As a result of these special options and the late vintage, used police cars are often convened to taxcabs.

B. Role of the taxicab industry and impact on auction prices

While the auction is open to the public, many of the buyers at the auction are used-car dealers, brokers, and buyers for taxicab companies. For example, out of 340 vehicles examined in this study, I could identify only a few nonprofessional buyers. Professional buyers regularly compete against one another for used police cars and other used vehicles that are sold throughout the eastern half of the U.S. This repeated aspect of used vehicle sales can facilitate collusion, especially in an oral auction where bidders' behavior is easily monitored.(8)

While repeat sales has received much attention in the theoretical literature on collusion, even more important for this study is a peculiar New York City regulation on taxicab conversions. The so-called hack-up policy of the Taxi and Limousine Commission (TLC) is as follows:

Hack-up Policy. (a) Basic policy. Vehicles may be hacked-up (outfit

a vehicle as a taxicab and approval by TLC) within two model years of

the vehicle's manufacture. [e.g.], Model year 1987 vehicles may be

hacked-up until September 30, 1989. The vehicle may remain in use as

a taxi, using the medallion as long as the vehicle passes inspection

(this has been and remains our basic policy).(9)

In other words, 1988 Caprice sedans were eligible for conversion from police cars to taxicabs up to September 30, 1990. This condition led to high winning bids in January and February 1990 relative to the "book values" of like-model used vehicles (non-police cars).(10) The winning bid for the used police cars sold at the auction averaged $5,900 per vehicle in January 1990 and $6,042 per vehicle in February 1990. These prices were 86%-91% of the book values. However, average prices dropped to $4,398 in March 1990 and $%585 in May 1990, or roughly 67%-74% of the book values. in order to demonstrate that these price changes may have been due to bid rigging, it is necessary to examine the economic conditions that existed at the several auctions. That is the objective of the empirical section of the article.

The ring members apparently set a target price of $4,500 per vehicle, but the bids (valuations) of nonring members had to be taken into account. At the March 29th auction, the ring purchased 15 vehicles and all but two of these were bought for less than $4,500. The average price for the ring was $4,410 per vehicle compared to $4,360 for nonmembers' purchases. At the May 10th auction, the ring was successful in purchasing 18 vehicles and paid an average price of $4,608 per vehicle. The average price for the nonmembers was $4,550. The next auction was not held until August 2d and at that time the alleged bidding ring broke down. Only six police cars were offered for sale and this was the last opportunity to purchase 1988 model cars that were eligible for conversion in New York City.(11) The average price for the six cars sold in August 1990 was $5,233 per vehicle, an increase of $648 compared to May. The August price was 90% of We book value, so that in relative terms the January-February and August 1990 prices were about equal.

Additional insight into these events can be obtained by recognizing that several so-called facilitating conditions can aid the formation of bidding rings.(12) First, the English auction mechanism allows for easy detection of cheating by ring members and for fast and low-cost retaliation. Second, collusion is facilitated if bidders are professional buyers who share a long-term relationship with each other. Third, the vehicles were of like-model, with some relatively minor quality variations due to differences in mileage and mechanical condition. Fourth, the vehicles were sold individually rather than as larger lots of multiple vehicles. Fifth, there were easily recognizable "focal points" based on the book values that can be obtained from used car valuation guides or from the bids of nonmembers. Sixth, the New York City hack-up policy created an asymmetry of payoffs among the bidders that meant that the valuation of the vehicles was sharply different for one group of buyers relative to others, i.e., a comparison of the average prices in February and March or May and August is indicative of these differences in valuations. However, these simple comparisons are not accurate measures of damages because they ignore vehicle, auction, and time-specific differences in the sales. Lastly, the effect of the hack-up policy on valuations meant that the ring members could be likened to a "dominant firm," except that the ring is a buyer rather than the usual textbook case of a dominant seller.(13) Although the market supply curve at any given auction is vertical, the ring faces an upward sloping supply curve that depends on the valuations of the vehicles by nonmembers. And the higher the bids of the ring, the more winning bids they could be expected to make.(14)

With this background, I next describe the data for the measurement of damages and present some descriptive statistics summarizing these data.

III. Description of the data and variables

The objective in this and the next section is to construct estimates of what the winning bids would have been if competitive bidding for vehicles had occurred in March and May 1990. Damages for a given vehicle are measured by the difference between the actual bid and the estimated competitive value.(15) The competitive bids are estimated in three different ways and the damage estimates are compared. The basic data consist of winning bids on 1988 Chevrolet Caprice sedans for the 340 vehicles sold at 13 auctions held between January 1990 and May 1991. In addition, the data set contains the window sticker for each car. It is thus possible to measure several quality dimensions for each vehicle. I also know the number of vehicles offered for sale (including cars sold, forfeitures and rejects) and the number of winning bidders for each auction. The former variable is a measure of the supply available at the auction, while the latter variable is a proxy for potential competition.(16) both variables are important on theoretical grounds for price formation in an English auction.(17)

Because the 13 auctions took place over an extended period of time, it is important to control for external changes in the broader market for used cars. In Howard and Kaserman's study, they had to control for both the heterogeneity of construction jobs and for cost changes, and they used the engineer's estimate of the cost of each individual job as an explanatory variable.(18) Similarly, in addition to the vehicle quality measures, I employ book value estimates of the market resale value for reconditioned like-model (nonpolice) used vehicles sold at various auctions held in the previous month. The book value is a control variable for price differences due purely to time and other general changes taking place in the market for used vehicles. If this control was not used, the estimates of damages would be biased because time-specific factors substantially affect the actual bids.(19)

Table 1 shows the definitions of the variables. The dependent variable is PRICE, the winning bid for each of the 340 vehicles. The book value is VALUE and the ratio of the winning bid over the book value is denoted by (P/V). This is the ratio used below in the so-called ratio approach to damage determination. Four explanatory variables capture dimensions of vehicle quality: MILE, DMECH, DMECH2, and DCOND. The number of vehicles offered for sale is CARS and the number of potential competitors is BIDS. Because these latter two variables are measured at the auction level, they each have only 13 different values. Consequently, CARS and BIDS are highly correlated, and I also report some results for a combined measure of auction size called MULTI (= CARS/BIDS).


The remaining variables are all binary (or "dummy") variables for different time periods. HACK captures the effect of the New York City hack-up policy on winning bids. It equals one for all sales between January and August 1990 and zero for all other sales. MAR and MAY are equal to one for sales in March and May 1990 respectively, while MAR-MAY combines the sales in these 2 months into a single dummy variable. In the regression analysis, these are alternative measures of the effect of the bidding ring on PRICE. A dummy variable OCT is also defined for the auction that took place in October 1990. This variable is discussed below. Lastly, K denotes the size of the several different samples used in the analyses, where k = 1, . . . , K is the number of completed vehicle sales in a given sample.(20)

Table 2 displays descriptive statistics for several measures of auction size and vehicle valuation. Auction size can be measured by either the number of cars auctioned (CARS), the number of winning bidders (BIDS), or by a combination of these variables called MULTI. For example, BIDS varies from a minimum of three in August 1990 to a maximum of 33 in February 1991. More active bidders at an auction of a given number of vehicles should result in higher prices, but more vehicles should result in lower prices. However, CARS and BIDS are not perfectly correlated because of multi-unit purchases by some bidders. The average number of cars purchased per winning bidder (MULTI) is shown in the fourth column of the table. High values for MULTI indicate more concentrated purchases (e.g., February and March), while lower values indicate greater diversity of winning bidders. The net effects of these three variables on winning bids will be determined empirically in the next section.


The fifth column shows the average winning bid (PRICE) for the 13 auctions and the next column is the book value (VALUE) of a reconditioned like-model used car. The book value estimate declines progressively from $6,840 per vehicle in January 1990 to $4,752 in May 1991. However, the average winning bid does not decline progressively; instead it exhibits significant increases in both August and November 1990. The August increase corresponds to the breakdown of the bidding ring, and the November increase follows the October auction. The latter auction has the lowest average winning bid of all 13 auctions. The exact circumstances surrounding the October auction are unclear. However, in order to insure that unbiased damage estimates are derived for March and May, an OCT dummy variable is included in the regression analyses.(21) This variable controls for any peculiar aspects of the October auction, including the possibility of explicit or implicit collusion among bidders.

The last column in table 2 shows the average ratio of the winning bid over the book value, or (P/V). This relative measure of winning bids has a maximum in February and August and a minimum in October. in the next section, I use these ratios to calculate damages by the ratio approach.

IV. Comparative damage estimates

This section presents damage estimates or average price reductions using three alternative approaches. As illustrated in the figure, the basic problem addressed in this study is to estimate the gap in the level of winning bids between January-February and March-May. Average damage estimates are presented in tabular form for each method, and summary statistics are given for damages calculated for individual vehicles.

The first method is the ratio approach; it is expected that winning bids, on average, will be systematically lower in relation to the book value estimate for rigged auctions. The second method is the dummy variable approach, which uses an econometric model of price formation and a pooled sample of rigged and unrigged bids. I estimate the model for two different samples of 340 and 76 observations respectively. The third approach is the forecasting method. For this method, the econometric model is first estimated using a sample of 2S9 unrigged bids. Predicted values are then obtained for those vehicles sold at rigged auctions, and these values are compared to the actual winning bids. The advantages and disadvantages of each of the three methods are discussed at some length in Howard and Kaserman, and only summary statements are given here.(22)

A. The ratio approach

This method is based on the relationship between the average winning bid and the book value for both the rigged and unrigged auctions.(23) Let [(P/V).sub.cj] be the ratio of the winning bid to book value for a sample of j = 1, . . . , J competitive bids and let [V.sub.ri] be the book value estimate for a sample of i = 1, . . ., I rigged bids. The product [[(P/V).sub.cj] * [V.sub.ri]] = [] is the predicted competitive winning bid for the [] sale. The average damage estimate is calculated in the following manner

(1) [D.sub.r] = [P.sub.r] - [P.sub.c] = [P.sub.r] - [[(P/V).sub.c] * [V.sub.r]] for all i = 1, ... where [D.sub.r] is the estimated reduction in the average winning bid due to the conspiracy, [P.sub.r] is the actual average winning bid at the rigged auction, [(P/V).sub.c] the average relative bid for the unrigged sales, and V, is the average book value of the rigged sales.

In order to apply the ratio method, three choices must be made: (1) selection of book value estimates; (2) selection of the sample of unrigged sales; and (3) selection of a significance level for statistical support for this method. The book value estimates are discussed above in note 19. For damage estimation, two unrigged samples are examined. The first sample uses the relative-bid ratio for all sales made at the January, February and August 1990 auctions. The sample size is [K.sub.1] = 26. The average value, [(P/V).sub.c1], from this sample is applied to the March and May sales. The second sample uses the relative bids from seven auctions: September, November, and December 1990 plus the four auctions held in 1991. The sample size is [K.sub.2] = 233. The average value, [(P/V).sub.c2], from this sample is applied to the October sales.

The calculated average values for the (P/V) ratios for both the rigged and unrigged auctions are reported in table 3. Note that only the sales made prior to September were affected by the New York City hack-up policy. In order to establish a statistical basis for the ratio approach, a t-test is conducted for a significant difference between the average ratios, [(P/V).sub.r] less [(P/V).sub.c]. A negative and significant t-value supports the hypothesis that bid rigging suppressed the average level of winning bids. The calculated t-values are shown in the fifth column of table 3. All of the comparisons are statistically significant at the 1% level of significance; the hypothesis that bid rigging had no effect on the (P/V) ratio is rejected with a 99% level of confidence.


Applying equation (1) to the actual average winning bids yields the damage estimates given in the first column of table 4. For example, the March entry is obtained from the calculation of $4,398 - [(O.893) * $6,572] = -$1,471 per vehicle. Note that the damage estimate for March-May is based on weighted average values for [P.sub.c] and [V.sub.r] for the pooled March-May sales; the weights are the proportions of vehicle sales.


The main advantage of the ratio approach is its simplicity--both the method of estimation and for presentation to a judge or jury. A potential disadvantage is that the ratio method ignores many factors that can influence winning bids other than the book value estimate and whether bids were rigged.(24) For example, the ratio method does not account for variation in winning bids due to differences in vehicle quality or the number of vehicles offered for sale at a given auction.(25) These shortcomings are addressed using either of the next two approaches.

B. The dummy variable approach

The most common econometric technique used to deal with categorical data is the binary or dummy variable method.(26) In this approach, an econometric model is first specified for price formation at an English auction, and the observations on winning bids are then categorized as either rigged or unrigged. The effect of bid rigging is obtained by estimating the parameters of the model by one or more of several possible regression techniques, such as the ordinary least-squares (OLS) technique. A representation of the econometric model estimated in the present study is(27)

(2) [Mathematical Expression Omitted] where QUALITY is a vector of variables for quality (MILE, DMECH, DMECH2, DCOND), R is the vector of dummy variables for rigged bids (e.g., MAR, MAY, OCT), and & is a random disturbance term.28 The regression coefficients or model parameters are denoted by the terms [a.sub.0], [a.sub.1], . . . , [a.sub.6], where [a.sub.2] and [a.sub.6] are interpreted as vectors of coefficients for variables measuring vehicle quality and collusion respectively.

Moreover, equation (2) is equivalent to two equations, one for rigged bids and one for unrigged bids, with the following forms

(3) [Mathematical Expression Omitted] for i = 1, . . ., I rigged bids

(4) [Mathematical Expression Omitted] for i = 1, . . ., J unrigged bids

These equations differ only in the intercept terms, which equals [a.sub.0] + [a.sub.6] for the first expression and [a.sub.0] for the second expression. The hypothesis is that the coefficients for all dummy variables in the vector R are negative; that is, bid rigging at any given auction leads to a lower overall level of winning bids. Average damages are measured directly by the magnitude of the estimated coefficient. All other influences on winning bids, such as vehicle quality or the number of bidders, are netted out of the damage estimate through the explanatory variables and their estimated coefficients.

One possible shortcoming of the dummy variable approach is the assumption that the price functions for the rigged and unrigged auctions differ only in the intercept terms; that is, the regression or slope coefficients are the same for both the rigged and unrigged sales.(29) This can be a strong assumption, and a procedure to determine if this is a problem is to estimate the model parameters using different pooled samples of rigged and unrigged bids or to estimate the model using only unrigged bids in the forecasting approach. As a check on the model's robustness, I follow both of these procedures. The first sample uses 340 winning bids, including 81 vehicles affected by bid rigging. The second sample uses 76 winning bids, including 50 rigged bids. The third sample, which is employed in the forecasting approach, uses 259 unrigged bids.

Regression estimates for equation (2) are displayed in table 5 for all three samples.(30) Regressions (1)-(3) are estimated using the full sample of 340 bids, while regressions (5)-(6) employ the smallest sample of 76 observations. Regression (4) uses a sample of 259 unrigged winning bids. Focusing on the first set of results, all of the quality variables have the correct signs and are statistically significant at conventional confidence levels. The coefficient for the book value is positive and significant, but the magnitude of the coefficient is less than one. This means that winning bids for used police cars do not mimic, on a dollar for dollar basis, the price changes taking place in the broader market for used cars. Further, an increase in the number of vehicles sold at a given auction reduces winning bids, but more bidders raises winning bids. The effect of the New York City hack-up policy is reflected in the coefficient for HACK. The parameter estimates range from $1,672 per vehicle to $2,020 per vehicle. These values represent estimates of the elevation of bids in January-February 1990 that was the impetus for the formation of the bidding ring in March. Summarizing, the damage estimates using regression (1) are respectively -$1,402 per vehicle for March, -$981 for May, and -$717 for October. Bid rigging significantly lowered prices in this market.(31)


Regressions (2) and (3) show the effects of different specifications of the bid-rigging dummies and auction size. The damage estimates for MAR-MAY are -$1,176 per vehicle in regression (2) and -$1,232 in regression (3). The damage estimates for October are, respectively, -$676 and -$614 per vehicle. All of the other coefficients have the correct signs and are statistically significant. The coefficient for MULTI shows that an increase in the average number of cars per winning bidder tends, on balance, to reduce winning bids.

Regressions (5) and (6) are estimated with the smallest sample and covers only the time period January to August 1990. Consequently, HACK and OCT are omitted. The results for several variables are disappointing, especially when the MAR-MAY dummy is used. The main reason for this outcome is multicollinearity due to the more restricted variation in the data.(32) However, the damage estimates are statistically significant and are comparable in magnitude to the estimates in regressions (1) and (3).

In table 4 above the damage estimates for both samples are summarized. Reading across a row gives a comparison of different methods, while reading down a column gives a comparison of different model specifications.

C. The forecasting approach

The forecasting method uses only unrigged bids to estimate the model. The dummy variables for the rigged auctions are therefore omitted. The results of this estimation are shown in regression (4) in table 5. The results for this sample specification are very similar to the results obtained using the pooled sample.(33) Consequently, it can be expected that the dummy variable and forecasting approaches will yield similar damage estimates.

The damage estimates for the forecasting approach are obtained by plugging the data points for each rigged bid into regression (4), which represents the model of competitive price formation. This produces an estimated competitive bid, [], for each rigged sale. The damage estimate is then calculated as

(5) [D.sub.r] = [P.sub.ri] - [] i = 1, . . ., I where [D.sub.r] is the damage estimate and [P.sub.ri] is the actual (rigged) winning bid. The damage estimates are summarized in table 4 above. Average damages are calculated for several different time periods by summing across the estimates for the individual vehicles and then dividing by the number of vehicles.

D. Summary of the damage estimates

The lower part of table 4 shows the mean damages for March and May combined and descriptive statistics for damages on individual vehicles. The largest mean damage is obtained using the dummy variable approach with sample size K = 76. This is also the estimate with the smallest standard deviation relative to the mean and the smallest range of values. The estimate with the largest standard deviation and the largest range is the ratio approach. This outcome reflects the fact that the ratio approach fails to account for other economic aspects of the auctions and vehicles. However, all of the damage estimates are within 10% of the value of $1,259 per vehicle.(34)

V. Conclusions

The empirical findings in this study establish that winning bids were significantly lower at three auctions of used state police cars. The impetus for the alleged bidding ring was a legal constraint on vehicle conversions imposed by the City of New York's Taxi and Limousine Commission. This constraint elevated winning bids by $1,600 to $2,000 per vehicle during January and February 1990. Several professional buyers are believed to have entered into a market sharing agreement in March and May 1990. The stability of the agreement was facilitated by several market conditions such as the ease of monitoring bids in an oral auction and the sequential aspect of the sale of the vehicles.

Following procedures outlined by Howard and Kaserman, I developed comparative damage estimates using three different statistical methods: the ratio approach, the dummy variable approach, and the forecasting approach. These estimates are summarized above in table 4. In general the damage estimates for comparable samples are within approximately 10% of each other, regardless of the method of estimation. For example, the range for the MAR-MAY damages is $120 per vehicle or 9.5% of $1,259. Since the usual bidding increment at this auction is $100, this is an acceptable degree of accuracy. One reason for the small degree of variation may be that, on average, the vehicles are fairly homogeneous, despite some obvious differences in the auction-specific variables. However, it is reassuring to know that the damage estimates produced by the simple ratio approach are supported by the more complex dummy variable and forecasting approaches. Thus, one conclusion that emerges from this study is that all three statistical approaches can be viable methods, provided the objects are not too heterogeneous or that it is possible to control for heterogeneity. This study therefore reaffirms Howard and Kaserman's findings that reliable damage estimates can be prepared and the methods to do so should be of interest to all parties involved with the adjudication of bid-rigging cases.(35)

A second conclusion is that the English auction mechanism for selling objects can facilitate collusion, especially when bidders face asymmetric payoffs. The ?Yew York City hack-up policy produced a sharp division among the bidders, resulting in a relatively small number of high-valuation bidders. Moreover, unlike the conditions at a sealed-bid auction, ring members at an English auction can easily monitor each others' actions during the process that determines the winning bids. In contrast, at sealed-bid auctions, monitoring is only possible at the bid opening, at which time price is already determined, or by elaborate means of bid rotations and determination of bid specifications. Further, the ceiling on bids in an English auction can easily be determined by the bids of lower-valuation nonmembers and identical bidding, a common outcome in sealed-bid auctions, is not necessary. The conditions of sale at an English auction thus complicate the problem of detection of bid ringing on the part of antitrust officials. (1) Surveys of the Economics literature are found in McAfee & McMillan, Auctions and Bidding, 25 J. Econ. Lit. 699 (1987); Hendricks & Porter, Collusion in Auctions, 15/16 Annales D'Economie et de Statistique 217 (1989); and Wilson, Strategic Analysis of Auctions, in The Handbook of Game Theory (R. Auman & S. Hart eds. 1992). (2) See Timberlake, The Legal Injury Requirements and Proof of Damages in Treble Damage Actions Under the Antitrust Laws, 30 George Wash. L. Rev. 231 (1961); Guifoil, Damage Determination in Private Antitrust Suits, 42 Notre Dame Law. 647 (1967); Kuhlman, Theoretical Issues in the Estimation of Damages in a Private Antitrust Action, 32 S. Econ. J. 548 (1967); Parker, Measuring Damages in Federal Treble Damage Actions, 17 Antitrust Bull. 497 (1972); Davidow, Proof of Purchases and Damages by Public Buyers of Price-Fixed Goods, 17 Antitrust Bull. 363 (1972); and Adams & Bock, Damages in Horizontal Price-Fixing Cases, 49 Antitrust L. J. 141 (1980). (3) L. Froeb, Auctions and Antitrust 21 (Economic Analysis Group Discussion Paper 88-8, U.S. Department of Justice, Antitrust Division, 1988). (4) Howard & Kaserman, Proof of Damages in Construction Industry Bid-Rigging Cases, 34 Antitrust Bull. 359 (1989). (5) Id. at 391. The two nonstatistical approaches considered by Howard & Kaserman--the direct evidence and engineering analysis methods--are not applicable in the present study. (6) The author was a consultant in the case. The data used in this article were provided by the agency conducting the auction and by the state attorney general's office. Ml interpretations of the data are my own and do not necessarily reflect the views of any other individual or agency. (7) Each auction is announced by a brochure that is mailed to prospective buyers. The brochure lists each vehicle by item number, year and model of the car, and it describes acceptable methods of payment and other conditions of the sale. The auction is a traditional English auction; there is a secret reserve price and a minimum bid increment of $50. The vehicles are sold individually and sequentially at a rate of about one car per minute. (8) It is well known that, in a repeated oligopolistic game, a collusive or cooperative strategy is the dominant strategy. This solution is known as the "folk theorem" of repeated games; see D. Kreps, Game Theory and Economic Modelling (1990). (9) 13441 RCNY tit. 35-Taxi and Limousine Commission: ch. 3, Taxicab Specifications, 3-01 (a) Basic Policy. I have been informed by the TLC that the two model-year rule under the "hack-up" policy has been in effect since the 1970s. (10) The following statement from a staff report of the Taxi and Limousine Commission also helps to set the stage for the bidding ring: "Vehicle issues concern the quality of taxi vehicles and the levels of insurance coverage. Many taxi owners have taken cost-cutting steps in these two areas. One result is that the taxi fleet as a whole is aging. Taxi owners are using existing vehicles longer, postponing the cost of a new vehicle. When replacing their car, vehicle owners are relying more heavily on used cars than on new cars. This yields an immediate savings of roughly $8,000 to $11,000. . . . Aging of the fleet reflects higher prices for new cars and, to a lesser degree, problems with the redesigned Chevrolet Caprice, the industry's workhorse." NYC Taxi and Limousine Commission, The Taxi Industry, 1991: A Report on the Taxi Industry's Financial Condition and the Quality of Service 15 (1991). (11) It takes approximately a month to convert a car to a taxicab. The September auction was not held until September 27, 1990, making it too late to meet the deadline of the "hack-up" policy. (12) See F. Scherer & D. Ross, Industrial Market Structure and Economic Performance 277 (3d ed. 1990); and Hay & Kelley, An Empirical Survey of Price Fixing Conspiracies, 17 J. Law & Econ. 13 (1974). (13) F. Scherer & D. Ross, supra note 12, at 221. (14) To see this point, let S be the total available supply and let [D.sub.r](P) and [D.sub.n](P) be the demand schedules of ring members and nonmembers respectively. The elasticity of the supply schedule faced by the ring will be given by

nr = [-e.sub.n] [Q.sub.n]/[Q.sub.r] where [e.sub.n] is the demand elasticity of the nonmembers and Q, and Q,, are quantities purchased. The facts of be case suggest that a reasonable condition for the demand functions would be that the reservation price of the nonmembers was below all competitive-bid prices of the ring. These demand conditions mean that the ring could have bid so as to limit nonmember purchases to zero, but this might have facilitated detection of collusion. See generally Blair & Harrison, Antitrust Policy and Monopsony, 76 Cornell L. Rev. 297 (1991); The Measurement of Monopsony Power, 37 Antitrust Bull. 133 (1992). (15) This is the conventional measure of damages in price-fixing cases. The damage estimates are relate to economic welfare if (1) the government's revenue target is fixed and additional revenue must be raised by means of distortionary taxation; (2) the ring fails to allocate vehicles to the members with the highest valuation; or (3) the ring incurs real costs in the process of bid rigging. See K. Elzinga & W. Breit, The Antitrust Penalties: A Study in Law and Economics (1 976); Page, Antitrust Damages and Economic Efficiency: An Approach to Antitrust Injury, 47 U. Chi. L. Rev. 467 (1980); and Blair & Harrison, Rethinking Antitrust Injury, 42 Vand. L. Rev. 1539 (1989). (16) The total number of bidders is a poor measure of competition because it includes many nonprofessional buyers and dealers interested in only certain vehicles. I did experiment with another proxy that included buyers of 1984 and 1985 model vehicles that had been used by state police administrative personnel. Although the findings do not differ much, I believe that the number of winning bidders is the best proxy for potential competition, given the way the auction is conducted. On the importance of the number of bidders, see Brannman, Klein & Weiss, The Price Effects of Increased Competition in Auction Markets, 69 Rev. Econ. & Stat. 24 (1987). For discussion of the number of units, see Burns, Market Structure and Buyer Behavior: Price Adjustment in a Multi-Object Progressive Oral Auction, 6 J. Econ. Behaviour & Organ. 275 (1985). (18) Howard & Kaserman, supra note 4, at 374. (19) Book value estimates for used vehicles are available from three reports: (1) N.A.D.A. UseD Car Guide Co., N.A.D.A. Official Used Car Guide--The Market Report of Used Car Values (Eastern Edition, McLean, VA); (2) N.A.D.A. Used Car Guide CO., N.A.D.A. Official Whole-Sale Used Car Trade-In Guide (McLean, VA); and (3)Maclean Hunter Market Reports, INC., Automobile Redbook--Official Used Car Valuations (Region A Edition, Chicago, IL). The main differences among these reports are the frequency of publication and the amount of detail available on value by vehicle condition. However, it is important to recognize that for a given vehicle model the book values in these reports differ by level, and the changes over time are almost identical in absolute terms. Consequently, the choice of one report over another does not have a significant impact on the damage estimates. Because the information in reports (1) and (3) is more widely disseminated, I have chosen to measure the book value as a simple average of the values given in these two reports. The model numbers used are BL5 and BL5-H respectively. Some additional damage estimates based on the wholesale book values in (2) will also be given for comparison purposes.

The reports also contain several different value estimates, including average loan values, avenge retail values, and average wholesale values, The latter is also available by condition of the car at time of sale (rough, average, clean). Examination of these data reveals that they are constant proportions of each other For example, the avenge finance value is 90% of be avenge retail value. For this reason, the results reported below for the ratio method are unaffected by the choice of the average loan value as the measure of the book value. In equation (1), the mean values of [(P/V).sub.c] and [V.sub.r] are affected to the same degree if, for example, I had used the average retail value for V. The same is true for the average wholesale values, and I have estimated the regressions in table S using a variety of different book value estimates. The basic results and conclusions are unaffected (see also note 34 below). (20) Because of forfeitures and rejects, the number of vehicles auctioned can be more than the number of completed sales. A forfeiture occurs when, after paying the $100 security deposit, a winning bidder fails to pay the balance within five working days. A reject occurs when the winning bid is below the reserve price. (21) Failure to include this variable could result in an errors-in-variable problem for the dummies MAR, MAY, and MAR-MAY. For discussion of errors-in-variable bias in the context of dummy variables, see Aigner, Regression with a Binary Independent Variable Subject to Errors of Observation, 1 J. Econometrics 49 (1973). (22) See also Rubinfeld & Steiner, Quantitative Methods in Antitrust Litigation, 46 Law & Contemp. Prob. 69 (1983); and Fisher, Multiple Regression in Legal Proceedings, 80 Colum. L. Rev. 702 (1980). (23) The ratio approach is also discussed in Kuhlman & Johnson, Estimating Damages on Highway Construction Contracts, 29 Antitrust Bull. 719 (1984). (24) Howard & Kaserman, supra note 4, at 377. (25) Data on auctions held prior to January 1990 are irrelevant because only wrecked 1988 Caprices were sold prior to that date. Some data were available for the sample period on other cars sold at the auction, including 1986 Ford LTD/Crown Victoria police cars and 1985 Dodge Diplomat police cars. These cars had been used by detectives and administrative officers, but neither model was eligible for conversion under the NYC hack-up policy nor was there any evidence that bid rigging took place for these vehicles. Consequently, it is expected that the relative winning bids for these vehicles will follow a different pattern than the 1988 Caprices unless there is some unobserved conditions that had affected all police car sales. Since the damage results depend importantly on the observed fall in winning bids relative to book value in March-May 1990, I have calculated the relative winning bids for these other models for the six auctions held between January 1990 and August 1990 (the two models are combined due to the small number of observations):
            Ford - Dodge               Caprice
  Auction   Aver. P/V (s. d)   No. of Obs.   Aver. PIV (s.d)
  1-11-90    0.546 (.102)          18         0.863 (.056)
  2-15-90    0.637 (.122)          18         0.906 (.039)
  3-29-90    0.667 (137)           12         0.669 (.050)
  5-10-90    0.790 (139)            8         0.742 (.044)
  8-02-90    0.540 (221)           12         0.902 (.057)

For these models, be rho of be winning bid to the book value increases through May and then declines in August. This is exactly the opposite of the pattern observed for the 1988 Caprices. The differences are consistent with bid rigging in March and May 1990 for the 1988 Caprices and with enhanced demand due to the hack-up policy in January, February, and August 1990. (26) This method is discussed in any econometric text; see, for example, D. Gujarati, Basic Econometrics (2d ed. 1988). (27) The model specification follows Hansen, Sealed-Bid Versus Open Auctions: The Evidence, 24 Econ. Inquiry 125 (1986); see also J. Nelson, Price Formation in a Repeated Multi-Unit English Auction of Used Police Cars (unpublished paper, Pennsylvania State University, 1992). (28) The disturbance term captures purely random elements of bidding behavior as well as the net effects of random measurement errors and any omitted explanatory variables that are uncorrelated with the included explanatory variables. (29) This point is emphasized in Finkelstein & Levenbach, Regression Estimates of Damages in Price-Fixing Cases, 46 Law & Contemp. Prob. 145,161 (1983). (30) All regression estimates have been obtained by ordinary least squares. Three summary statistics are given. The R-SQ is the multiple coefficient of determination; a value of 0.91 indicates that 91% of the variation in the dependent variable is explained by the set of regressors. The ADJ-RSQ is the R-SQ adjusted for the number of regressors and can be used to select a parsimonious model specification (see below). The SEE is the standard error of estimate of the regression; it measures how far, on average, the actual prices deviate from the prices predicted by the estimated regression equation. Rubinfeld & Steiner, supra note 22, at 103, suggest that a model fits the data well if the SEE is less than 20% of the mean value of the dependent variable. The SEE values in table 5 are all about 7% of their respective means. (31) Omitting the dummy variables for bid rigging from equation (1) reduced the ADJ-RSQ from 0.908 to 0.756. Unless there is some other omitted variable that explains the low prices in March, May, and October, this result supports the model specifications presented in table 5 and the hypothesis of a significant overall effect due to the bid-rigging conspiracy; see J. Kmenta, Elements of Econometrics 594 (2d ed. 1986). (32) Multicollinearity occurs when two or more explanatory variables move together in some pattern. This makes it difficult to establish independent influences on the dependent variable. The effect of multicollinearity shows up in unstable coefficient estimates and inflated values for the coefficient standard errors. However, while some estimates tend to be imprecise, they are unbiased. Thus, multicollinearity is not an impossible problem if attention is focused on the overall regression and those coefficients that are always statistically significant. (33) Because of severe multicollinearity, it was not even possible to estimate the full model using only the rigged bids. However, from one perspective, it is not clear what is gained by estimating the proposed model using only the rigged bids. Instead, it must be shown that there is some omitted variable that explains the gap in the level of bids between January-February and March-May. My hypothesis is that this gap is due to the conspiracy, and the statistical results support this hypothesis. (34) Estimating regressions (2)-(4) and (6) using a wholesale book value yielded damage estimates for March-May of -$1192, -$1258, -$1179, and -$1243 respectively. Estimating these equations after deleting two possible outlier observations yielded damage estimates for March-May of -$1181, -$1232, -$1144, and -$1352. These results show that the damage estimates are robust with regard to changes in the book value or sample specifications. The outlier analysis used the procedures described in D. Belsley, E. Kuh & R. Welsch, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity (1980). (35) Howard & Kaserman, supra note 4, at 393.

AUTHOR'S NOTE: I have benefited from the helpful comments of James Donahue, David Kaserman, and two anonymous referees.

JON P. NELSON Department of Economics, Pennsylvania State University, University Park, PA.
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Author:Nelson, Jon P.
Publication:Antitrust Bulletin
Date:Jun 22, 1993
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