Quality, uncertainty and the internet: the market for cyber lemons *.

Huston, John H. ; Spencer, Roger W.

I. Introduction

The Internet has opened the door to development of an enormous number of innovative markets that could not have existed as little as a decade ago. Some function to auction industrial purchasing contracts from business to business. Others, termed buyer-biding auctions, serve to facilitate the sale of pre-owned consumer items such as art, collector cards, antiques, or rare coins. The firm eBay popularized the latter category, altering permanently the way millions of individuals buy or sell numerous commodities. (1)

Internet markets differ from traditional markets in that reduced transactions costs make it possible for a large number of buyers and sellers to interact over long distances. However, that distance between market participants is not fully bridged by technology. Buyers cannot hold the merchandise, and they are less likely to be familiar with the vendor. The resulting asymmetry of information may lead to sub-optimal market performance. These markets, which have contributed to a more competitive, entrepreneurial environment across the country, provide economists new opportunities to assess fundamental principles associated with market activity. Surprisingly, few analysts to date have published articles in mainstream economics journals about the workings of the new internet markets.

This paper takes a fresh look at the issues of quality, asymmetric information, and uncertainty in the context of the market for lemons, as labeled by George Akerlof (1970) in a classic article three decades ago. Akerlof developed a small, theoretical model that led him to conclude that bad cars ("lemons") drive good cars out of the market and that in certain situations, there is no price at which trades will take place. Also, in similar markets such as medical insurance, there may be no insurance sales at any price to cover older, unhealthy ("lemons") individuals in part because of the related principle of adverse selection. This paper builds on the work of Akerlof and others to study the internet trading of rare coins. Coins are a particularly good market for study because of the high volume of trades, multiple levels of quality, the potential for improved information to reduce uncertainty, asymmetric information and existence of dual markets--internet and dealer--for similar products.

The use of auction markets to study the various issues associated with the lemons problem is somewhat novel. Akerlof for example, observed that quality variance, asymmetric information, and/or dishonest behavior accounted for the lemons problem in the auto, medical insurance, and minority labor markets, as well as credit markets in underdeveloped countries, none of which could be identified as auction markets. Kim (1985) and Wilson (1980) extended Akerlof's study of used cars. Cooper and Ross (1984) examined the degree to which prices convey information about product quality while Landon and Smith (1998) provided estimates of the impact of current quality (and reputation) on price. Both studies took wine markets, a non-auction market, as a point of reference (Landon and Smith (1998) in considerable detail).

An exception is Feinstein, Block, and Nold (1985) who studied the impact of asymmetric information on the collusive behavior of highway construction contractors submitting rigged auction bids to governmental purchasers of their services. More typical of auction papers is the recent work of Lucking-Reiley (1999) who examined Vickrey's (1961) revenue equivalence theorem across English, Dutch first-price, and second-price auctions. Lucking-Reiley's article, which does not focus on lemons quality or informational issues, is an important antecedent of the current paper because of its expansive use of the internet to study collector card auctions. In conjunction with the internet, Lucking-Reiley (p. 1067) noted that his approach differed from previous laboratory experiments "by auctioning real goods on a real market."

Our results are also based on the auctioning of real goods on a real market. As with Akerlof, it is determined that bad goods (or "lemon" coins, in this case) drive out good. Additionally, the study of quality as a continuum demonstrates that of the coins which do trade, higher quality coins trade at lower prices relative to their market value, a result which could be termed a "lemons" corollary. A third finding is that the internet market shrinks dealer spreads, with similar coins selling on the internet for only 78 percent of the dealer selling price. The lower internet price results from a combination of reduced transactions costs and the lemons problem.

This introduction is followed by the development of a small, theoretical model. The coin market and related data are discussed in section III. Section IV presents the empirical results, and the concluding remarks are found in section V.

II. Model

Sellers are assumed to know the quality of the good they offer. Buyers are unable to differentiate between the quality of items less than R units apart. Thus sellers can offer goods with quality ranging from [q.sub.m], the maximum quality, to ([q.sub.m] - R), the minimum quality, without buyers being able to distinguish between them. To create the potential for exchange, buyers value the product more than sellers. We assume that while sellers value a product of quality q at q dollars, buyers would be willing to pay dq dollars, where d > 1. (Akerlof uses a similar linear utility to motivate his argument. In his model sellers value a product at x and buyers at 1.5x.)

Quality (measured in dollars) is assumed to be uniformly distributed between [q.sub.m] - R and [q.sub.m]. If all goods sold, then the average quality would be ([q.sub.m] - R + [q.sub.m])/2. However, sellers with a product of quality higher than the price, p, will choose not to sell. The expected quality of the goods sold is thus midway between [q.sub.m] - R and p: [q.sub.e] = (p + [q.sub.m] - R)/2. This "quality supplied" is shown in Figure 1. (At any price above [q.sub.m] all the goods are sold and the expected quality is [q.sub.m] - R/2; supply is vertical.) Buyers are willing to pay p = [dq.sub.e] for a product of average quality [q.sub.e]. Solving for q generates the "demand" for quality, [q.sub.e] p/d as shown in Figure 1. Setting demand equal to supply and solving for p gives an equilibrium price of

[p.sup.*] = [q.sub.m] - R / 2/d-1

provided that 1) d> 1

2) [q.sub.m] < R

3) R < 2 [q.sub.m] (1- 1/d)

This is an equilibrium in the rational expectations sense. At any price above [p.sup.*], the quality required by buyers to justify the price is greater than the average quality provided by sellers. At a price below [p.sup.*], the quality required by buyers to justify the price is less than the average quality provided by sellers.

The first inequality stipulates that buyers value the product more than sellers do. If d falls below 1 then the demand curve rotates downward and, as a result, does not intersect supply. Since in that case, buyers value the product less than sellers, no items are exchanged. The second inequality requires that R must be less than [q.sub.m], If R = [q.sub.m] then buyers can't distinguish between even the very worst and very best goods. In the model supply crosses demand at a price of zero. This is the extreme case of Akerlof's model in which the worst goods drive out all goods of higher quality.

The model predicts that as long as demand intersects supply in its upward sloping range, that is as long as the third inequality holds, price will be less than [q.sub.m]. This provision is violated if either R is too small or d is too large. A smaller R implies better informed consumers who can distinguish finer gradations of quality. If R < 2[q.sub.m] (1 - 1/d) then consumers are well enough informed to avoid the lemons problem, and a price above [q.sub.m] is generated. At the extreme, if R = 0 customers know precisely what quality is being offered. The second and third inequalities combined imply that [q.sub.m] > 2[q.sub.m] (1 - 1/d). Solving for d generates the constraint that d < 2. If d is above 2, buyers value the product so much more than sellers that even at p = [q.sub.m], the price where all the sellers are willing to sell their products, buyers are still willing to buy, and thus the lemons problem doesn't come into play. If either R is too small or d is too large, demand intersects supply along the vertical section above [q.sub.m] and the interesting aspects of informational asymmetry are assumed away. The alternative results discussed above are summarized in Appendix Table 1.

An extension of the model permits the inclusion of information as a continuous variable. The buyers' information set, I, enters the model through R, the range of quality. Sellers are able to market items with quality less than [q.sub.m] because buyers are unable to distinguish between [q.sub.m] and lower qualities. Increasing the amount of information available to consumers reduces the range of marketable qualities and increases the equilibrium price [[partial]R/[partial]I < 0, [partial]p/[partial]I > 0]. In the extreme, fully informed customers know precisely the quality of the good, and R goes to 0. In that case price rises above [q.sub.m] and only goods of quality [q.sub.m] are sold in this market. (Each quality level would have its own unique price and market.)

The empirical model will be estimated in two stages. First, it is necessary to model whether or not an item sells as a function of q and I. For those items that sell, a second set of relationships will be estimated modeling the sales price as a function of q and I.

III. Data

The data consist of the results from 225 Morgan Type (Liberty Head) dollar auctions carried out on eBay.com during mid-May 2000. (2) A single type of coin was chosen to minimize the variation in the product. Coins were chosen because their attributes can be well described with a small number of variables. Since the lemons principle concerns items omitted from the market, the auction format was selected because of the rare chance to observe items which do not sell due to an excessively high minimum bid set by the seller. (3)

[q.sub.m] is the maximum quality the buyer could obtain. In our sample this is the quality claimed by the seller. Sellers could be offering a lower quality but it is unlikely they would provide a product even better than advertised. Two measures of [q.sub.m] are tested;

1. MARKET is the retail price for the coin if it had the quality claimed by the seller. Since in the model [q.sub.m] is measured in dollars, market value is the logical gauge of quality. The data for this variable come from Coin Universe Price Guide for May 18, 2000 (http://www.coin-universe.com) They are the average dealer asking prices for coins of a specified year, mint and grade.

2. The grade of the coin, G__. Coin collectors and dealers place grades on their coins reflecting the quality of the coin. These grades vary from Poor-1 "worn so smooth it is barely identifiable as to type" up to MS-70, a "mint-state" coin-- an absolutely perfect uncirculated coin" (Ruddy 1995, pp. 8--9). (4) Mint state coins are graded from 60 to 70.

The very low quality coins are rarely collected or exchanged. The coins in our study ranged from VF, very fine," (lowest quality) to MS-67 (highest quality).

GEF = 1 if the coin is "extra fine" and 0 otherwise.

GAU = 1 if the coin is "about uncirculated" and 0 otherwise.

G60 = 1 if the coin is uncirculated of MS60 quality and 0 otherwise.

G62 = 1 if the coin is uncirculated of MS62 quality and 0 otherwise.

G63 = 1 if the coin is uncirculated of MS63 quality and 0 otherwise.

G64 = 1 if the coin is uncirculated of M564 quality and 0 otherwise.

G65 = I if the coin is uncirculated of M565 quality and 0 otherwise.

G66 = 1 if the coin is uncirculated of MS66 quality and 0 otherwise.

G67 = 1 if the coin is uncirculated of MS67 quality and 0 otherwise.

Coins with a zero for all of the above dummies an those graded VF, very fine, the lowest grade o those coins in this study.

The buyers' information set, I, contains:

CERT = 1 if the coin is certified by one of the major coin grading services. Because of the difficulty in determining a coin's grade, particularly for less experienced collectors, firms began offering grading services. For a fee these firms will have a team of expert graders establish the grade of the coin. The coin and a ticket specifying its grade are then sealed in a plastic "slab" to guarantee that the coin remains in the stated condition. This third party grading should be valuable information for buyers.

OTHER = 1 if the coin is graded by a less well known grading service. In addition to the well-known grading services such as NCG, ANACS and PCGS there are other less well-known grading services. It is anticipated that the information value of these services will be lower.

PICTURE = 1 if a picture is included with the description of the product.

EBay calculates a seller's rating based on the number of transactions the seller has had and the proportion of buyers who gave the seller a positive evaluation following a transaction. They then give sellers stars of various colors based on the seller's rating. A seller with a rating less than 10 has no star, 10-99 a yellow star, 100-499 a turquoise star etc. SELL = 0 if the seller is in the lowest range (no star), 1 if the seller is in the next highest range, 2 if the seller is in the category above that etc. (5)

IV. Results

A. Factors Affecting Sales

Results for the regression determining the factors affecting the likelihood of an item selling are presented in Table 1. The dependent variable is SOLD which equals one if the item sold and 0 otherwise. Prediction success is frequently used as a gauge of the fit of a probit model. (6) The model correctly predicts 70% of the outcomes.

The coefficient on MARKET is negative and significant at the 5% level. As expected, higher quality items are less likely to sell. The coefficient for the "about uncirculated," GAU, grade is negative and significant, implying that this grade is less likely to sell than the lower very fine grade. The coefficients on the "mint state" grades are negative and generally become larger and more significant as the grade rises. The coefficient on G66 is insignificant due to a very large standard error stemming from the small number of coins of this grade in our sample. Three of the four information variables are statistically significant at the 10% or better level. Only PICTURE fails to explain any variation in sales.

As expected, certified coins are more likely to sell. Oddly, the coefficient on OTHER is negative and barely significant at the 10% level. (7) Not only are the less well-known certifying firms not as valuable to buyers, they actually reduce the likelihood of a sale. However, this result is not very robust. In alternative specifications, the coefficient on OTHER slips below the threshold for statistical significance. Even more surprising is the negative coefficient on SELL, the level of the seller's experience. Apparently, the more experienced seller is less likely to have an item sell. Novice buyers may be wary of dealing with more experienced sellers. It is also likely that the more experienced sellers place higher minimum bids on their items, thus reducing the odds of a sale.

B. Factors Affecting Price

The model predicts that in a market with asymmetric information, price will be less than the [q.sub.m]. In this sample the mean ratio of price to market value is .775. Internet price and dealer asking price are highly correlated ([rho] = .86), but a dollar's increase in dealer price does not, on average, lead to a dollar's increase in internet price. A simple regression of price on MARKET, the dealer price, serves to demonstrate the point. Table 2 contains the results with price as the dependent variable. We confirm that price rises with quality, but as expected the coefficient is less than one. Sellers increasing the quality of a good by one dollar receive an increased price of 87 cents. This result is consistent with consumers who are not fully informed and thus discount the claim of increased quality.

To facilitate the comparison of prices charged by dealers and prices charged by internet sellers, the ratio of internet price to dealer price is regressed against our measures of quality and other information. Two changes were made to the set of explanatory variables before estimating the price-ratio equation. The coin grades were collapsed into two ranges; about uncirculated to MS62 (GAU62) and MS63 to MS67 (G6367), as the reduced number of observations made it difficult to get reliable results for the individual grades. Information concerning the experience of the buyer was also added. Other studies have found that the likelihood of a winner s curse is reduced for better informed and more experienced bidders. The variable BUY is a measure of the buyer's level of experience and is formed using the same methodology as for the variable SELL. (8)

The ratio of price/market is regressed against the other independent variables in Table 3. Once again certification is shown to have a positive effect on price. The variable PICTURE is now significant at the 10 percent level suggesting that the picture increases the sales price. (It is perhaps not surprising that picture has so little impact on price and ability to sell. The differences in characteristics of the mint-state coins are so minute that pictures are often incapable of capturing them (Ruddy 1995, p. 22).) The most highly graded coins have lower prices relative to their market value. This is consistent with information asymmetry leading to lower demand for high quality items.

The significant coefficient on CERT raises the question of whether the increased certainty in buyers minds leads certified coins to have a unique regression function. To examine this hypothesis we reestimate the function with distinct coefficients for certified coins. Each variable in the regression is multiplied times CERT and the products are added to the regression. (9)

Table 4 presents the results of this regression. Employing a Wald test of the hypothesis that the coefficients on the certified variables are all equal to zero generates a test statistic of 20.16. (10) Thus, we can reject at the 1 percent level the hypothesis that certified and uncertified coins share the same regression coefficients. PICTURE is positive and significant at the 10% level for uncertified coins but not for certified coins. (11) Finally, higher quality uncertified coins sell at a larger discount to market price while higher quality certified coins do not. (The positive coefficient on C6367*CERT nearly cancels out the negative coefficient for G6367.) Apparently the informational asymmetry for uncertified coins is greater, thus generating a larger lemons problem for this group.

The price spread in the retail coin market appears to be quite large. The prices at which dealers buy coins are less than half the prices at which they sell coins. (12) As noted above, the prices paid by the internet buyers in our sample were 78% of dealer prices. This suggests that if instead of selling directly to buyers, coins were sold by dealers in internet auctions, the price margin would be significantly reduced. While the above results imply the presence of an asymmetric information problem for the internet, the results do not fully explain the differences between retail and internet prices. For uncertified coins, those most likely to suffer from a lemons problem, the average price in our sample is 24.8% below dealer prices. For certified coins, those that customers should be most confident in, the average price is 20.0% below retail. (Certified coins with pictures were still 19.2% below retail.) These results suggest that while the information asymmetry which discourages buyers is an important explan ation for low internet prices relative to dealer prices, other factors such as the reduction in transactions costs for internet deals account for the bulk of the differential.

V. Conclusion

Rapid advances in internet commodity trading have not only fostered a renewed, competitive entrepreneurial sprit across multiple markets, but have also provided economists with fresh opportunities to examine basic tenets of market operation. One of these is the lemons principle as described by George Akerlof (1970). Akerlof's model showed that since firms cannot charge a premium for high quality products when consumers lack information about the product, only products of low quality ("lemons") will trade.

A small, theoretical model is developed in this paper following Ackerlof in relating quality or value to price in a setting of asymmetrical information. The model predicts that, as with Akerlof, higher quality goods above a certain value will not be sold in the market. Since buyers have difficulty distinguishing quality, sellers would have to accept lower prices for their higher quality items. Improved information is expected to increase the likelihood of a sale and the equilibrium price.

The empirical evidence indicates that higher quality coins, based on two measures of quality, are less likely to sell than lower quality coins. Buyers are clearly aware that sellers could be offering a lower quality coin than claimed. Certification by a major coin grading service enhances the likelihood of a sale by way of improved information to the potential buyers.

Of the coins which do sell, price rises with quality but only by 87 cents for each dollar of claimed quality improvement, suggesting that consumers discount seller claims of increased quality. Also, the more highly graded coins fetch lower prices relative to their market value, a result that could be termed a "lemons corollary." Display of coin pictures increases the price only slightly. Seller experience seems to enhance the value of uncertified coins but negatively affects the price of certified coins. The empirical evidence also suggests a greater informational asymmetry for uncertified than certified coins, resulting in a more substantial lemons problem for the uncertified coins.

Finally, the internet coin market appears to cut substantially into the wide profit margins enjoyed by coin dealers. Prices paid by internet buyers are only 78% of dealer prices. Both lower transactions costs (supply) and a "lemons sensitive" set of buyers (demand) probably contribute to lower internet prices.

APPENDIX TABLE 1

Alternative Equilibria and Disequilibria

Condition Result

Condition 1: d > 1, otherwise buyers [GRAPH OMITTED]
value product less than sellers. The
figure to the right shows the case
where d < 1; note that there is no
equilibrium.

Condition 2: [q.sub.m] > R. If [GRAPH OMITTED]
[q.sub.m] = R, buyers cannot distinguish
any quality differences between 0 and
[q.sub.m]. The figure to the right shows
the case when 1 < d < 2. If d > 2 then
a second equilibrium can be found on the
vertical portion of S. (See condition 4.)

Condition 3: R > 2[q.sub.m](1 - 1/d) [GRAPH OMITTED]
Otherwise, buyers are sufficiently well
informed to avoid the lemons problem
completely (i.e., equilibrium occurs on
the vertical part of S). The figure to
the right shows that this happens when the
kink in S occurs to the right of D so
that [q.sub.m] / d < ([q.sub.m] - (R/2)).

Condition 4: d < 2. Otherwise, buyers [GRAPH OMITTED]
value the product so much more than
sellers that the lemons problem does
not occur. The figure to the right
shows that d > 2 so that D is more
steeply sloped than S.

[FIGURE 1 OMITTED]

TABLE 1

Probit Results

Dependent Variable SOLD = 1 if the coin is sold, 0 otherwise SOLD =
[[beta].sub.1] + [[beta].sub.2]MARKET + [[beta].sub.3]CERT +
[[beta].sub.4]OTHER + [[beta].sub.5]PIC + [[beta].sub.6]SELL +
[[beta].sub.7]GEF + [[beta].sub.8]GAU + [[beta].sub.9]G60 +
[[beta].sub.10]G62 + [[beta].sub.11]G63 + [[beta].sub.12]G64 +
[[beta].sub.13]G65 + [[beta].sub.14]G66 + [epsilon]

VARIABLE ESTIMATED ASYMPTOTIC
NAMES COEFFICIENT T-RATIO

MARKET -0.002 -2.085 **
CERT 0.495 2.014 **
OTHER -0.775 -1.746 *
PICTURE -0.199 -0.819
SELL -0.317 -3.495 ***
GEF 0.005 0.010
GAU -1.306 -3.282 ***
G60 -0.372 -0.828
G62 -0.425 -0.801
G63 -0.771 -1.828 *
G64 -0.982 -2.387
G65 -1.130 -2.451 **
G66 -6.084 -0.0391
CONSTANT 1.923 4.210 ***

N = 225 OBSERVATIONS

LIKELIHOOD RATIO TEST = 53.7780

MADDALA R-SQUARE 0.2126

* = significance at 10% level

** = significance at 5% level

*** = significance at 1% level
TABLE 2

Price Equation Dependent Variable: Price

PRICE = [[beta].sub.1] + [[beta].sub.2]MARKET + [epislon]

VARIABLE ESTIMATED T-RATIO
NAME COEFFICIENT 124 DF

MARKET 0.866 19.11 ***
CONSTANT -57.32 -1.61

R-SQUARE 0.748

R-SQUARE ADJUSTED = 0.746

N = 125 OBSERVATIONS

* = significance at 10% level

** = significance at 5% level

*** = significance at 1% level
TABLE 3

Price Ratio Equation

Dependent Variable: (PR = Internet Price/ Dealer Price) PR =
[[beta].sub.1] + [[beta].sub.2]CERT + [[beta].sub.3]OTHER +
[[beta].sub.4]GAU62 + [[beta].sub.5]G6367 + [[beta].sub.6]PIC +
[[beta].sub.7]SELL + [[beta].sub.8]BUY + [epsilon]

VARIABLE ESTIMATED T-RATIO
NAME COEFFICIENT 118 DF

CERT 0.158 2.601 ***
OTHER -0.160 -1.290
GAU62 -0.008 -0.120
G6367 -0.302 -4.090 ***
PICTURE 0.095 1.671 *
SELL -0.018 -0.859
BUY 0.014 0.425
CONSTANT 0.814 9.325 ***

R-SQUARE = 0.247

R-SQUARE ADJUSTED = 0.201

N = 125 OBSERVATIONS

* = significance at 10$ level

** = significance at 5% level

*** = significance at 1% level
TABLE 4

Certified versus Uncertified Coins

Dependent Variable: (PR = Internet Price/Dealer Price)

PR = [[beta].sub.1] + [[beta].sub.2]G6367 + [[beta].sub.3]SELL +
[[beta].sub.4]BUY + [[beta].sub.5]PIC + [[delta].sub.6]CERT +
[[delta].sub.7]G6367*CERT + [[delta].sub.8]SELL*CERT +
[[delta].sub.9]BUY*CERT + [[delta].sub.10]PIC*CERT + [epsilon]

VARIABLE ESTIMATED T-RATIO
NAME COEFFICIENT 116 DF

G6367 -0.381 -6.353 ***
SELL 0.013 0.438
BUY 0.024 0.632
PICTURE 0.105 1.713 *
CERT 0.101 0.471
G6367*CERT 0.326 0.459 **
SELL*CERT -0.060 -1.354
BUY*CERT -0.052 -0.658
PIC*CERT 0.014 0.083
CONSTANT 0.736 7.536 ***

R-SQUARE = 0.293

R-SQUARE ADJUSTED = 0.238

N = 125 OBSERVATIONS

* = significant at 10% level

** = significant at 5% level

*** = significant at 1% level

Notes

(1.) The New York Times (June 2, 2000) reported that U.S. consumer online auction sales are expected to rise to $6.4 billion in 2000 from $3 billion in 1999. EBay, with 12.6 million registered users, controls more than 90% of the market.

(2.) EBay auctions are a form of Vickrey second-price auction. Bidders enter a maximum bid and eBay's software automatically out bids others up to that figure. Thus the winning buyer pays a price just above the second highest bid.

(3.) In some cases there is also a "reserve price" in addition to a minimum bid. If the high bidder does not bid over the reservation price, the seller does not have to sell.

(4.) There are "proof' coins prepared by the mint with collectors in mind. These were excluded from the study.

(5.) Experimentation with both the raw seller score and dummies for the various levels produced similar results.

(6.) The observation is predicted to be zero if the estimated probability is less than .5 and is predicted to be one if the probability is greater than or equal to .5. Hensher and Johnson (1981, p. 54) develop a related measure of predictive success.

(7.) The importance of certification by reputable firms with regard to internet activities was highlighted in a recent arrangement worked out between Saturn Auto and eBay. Saturn, the small GM car company with a reputation for honest dealing, plans to perform a 135-point inspection of a seller's vehicle for about $100, permitting the seller to link the inspection report to the vehicle's eBay auction site. The program, which should be available at all 433 Saturn locations by year-end 2000, is seen by eBay as a way to improve the quality of information available to potential used-car buyers, which in turn should increase eBay internet car sales (Williams, 2000, p. 20). Table 1 model results suggest that auto sales will indeed be enhanced by certification by a well known "grading" agency such as Saturn, but would be negatively affected by information provided by a lesser known firm such as a local garage. That eBay realizes the significance of quality information and honest dealings to its sales is revealed in the following: "But eBay's profit depends on people trusting the site--trusting that sellers are really offering what they claim to offer; trusting that buyers will pay up; and trusting that the bidding is really being done by legitimate bidders. General distrust of giving credit-card numbers online delayed the growth of electronic commerce in the first few years of the internet. However, sales have taken off after numerous security measures have been instituted, such as encrypting vital data like credit-card numbers so they can't fall easily into the wrong hands." (Carlton and Bensinger, 2000, pp. BI, B4).

(8.) Coins that did not sell were omitted. In addition five other observations were removed. In one case a negative buyer rating was reported. Four others were outliers with studentized residuals above 3.

(9.) OTHER and GAU62 were insignificant in Table 3 and were not included in this regression. SELL and BUY were included in the hopes that they had different effects for certified and uncertified coins.

(10.) Referring to the equation in Table 4, this is a test of [[delta].sub.6] = [[delta].sub.7] = [[delta].sub.8] = [[delta].sub.9] [[delta].sub.10] = 0.

(11.) For certified coins this is a test of the sum of the coefficients on PIG and PIC * CERT, [[beta].sub.10] + [[delta].sub.10] The large standard error on prevents the sum of the two from being significant.

(12.) By our calculations, the average dealer buying price is 46.2% of market value (dealer asking price) for Morgan Dollars. Data for the dealer's bid price come from the Official Blue Book of United States Coins 2000 Handbook of United States Coins.

References

Akerlof, George A., 1970. "The Market for "Lemons": Quality Uncertainty and the Market Mechanism." Quarterly Journal of Economics 84, 488-500.

Carlton, Jim and Ken Bensinger, 2000. "Phony Bids Put eBay on Defensive." Wall Street Journal 24, May, pp. B1 and B4.

Cooper, Russell, and Thomas W. Ross, 1984. "Prices, Product Qualities and Asymmetric Information: The Competitive Case." Review of Economic Studies 51, 197-207.

Feinstein, Jonathan S., Michael K. Block, and Frederic C. Nold, 1985. "Asymmetric Information and Collusive Behavior in Auction Markets." The American Economic Review 75, 441--60.

Hensher, D.A. and Johnson, L.W., 1981. Applied Discrete Choice Modeling, John Wiley & Sons, New York.

Kim, Jae-Cheol, 1985. "The Market for "Lemons" Reconsidered: A Model of the Used Car Market with Asymmetric Information." The American Economic Review 75, 836--43.

Landon, Stuart, and Constance E. Smith, 1998. "Quality Expectations, Reputation, and Prices." Southern Economic Journal 64, 628--47.

Lucking-Reiley, David, 1999. "Using Field Experiments to Test Equivalence Between Auction Formats: Magic on the Internet." American Economic Review 89, 1063--80.

Ruddy, James F., 1995. Photo grade: A Photo graphic Grading Encyclopedia for United States Coins 18th Edition, Bowers and Merena Galleries, Inc.

Vickrey, William, 1961. "Counterspeculation, Auction, and Competitive Sealed Tenders." Journal of Finance 16, 8--37.

Williams, G. Chambers, 2000. "Saturn Dealers, eBay to Link Used Car Checks." San Antonio Express News 17, June, pp. 20--21.

Wilson, Charles, 1980. "The Nature of Equilibrium in the Markets with. Adverse Selection." Bell Journal of Economics 11, 108--30.

Roger W. Spencer *

* Professors of Economics, Trinity University, San Antonio, TX 78212-7200, 210-999-8471, 210-999- 7255 (Fax); jhuston@trinity.edu

The authors gratefully acknowledge the helpful comments and suggestions of an anonymous referee.