Bidding and prices for online art auctions: sofa art or investment
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- Highfill, J. & O’Brien, K. J Cult Econ (2007) 31: 279. doi:10.1007/s10824-007-9054-7
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The article uses auction data collected from the eBay internet site to examine the effect of various parameters on number of bids and selling price of art. The article further uses an insight from the auction literature to gather evidence about whether art on eBay is purchased for consumption or investment purposes. The article argues that the evidence found of a positive relationship between the number of bids and the final price suggests that art sold on eBay is not, in general, investment art.
Ashenfelter and Graddy (2003) in their important survey “Auctions and the Price of Art” make the argument that “the value of most important works of art is established by public auction” (2003, 763) and go on to summarize the rates of return on art as an investment from a number of empirical studies (2003, 769). Singer and Lynch (1997, 215) test the relative value of three categories of art, differentiated by the artist who created the painting or other work of art. Their conclusion is that Category 1 art (by such artists as Picasso, Matisse, and Manet) “is a quasi substitute for financial instruments, whereas average-priced art is a consumer good” (1997, 215). The value of art sold on eBay, the subject of this article, is largely determined by auction, but again the question remains of whether such art is investment art or a consumer good (sofa art—proverbially chosen to match the living room furniture). The strategy of the present article is to use some insights from auction theory to gather evidence about the effect of bidding behavior on selling price, and whether art sold on eBay is investment or consumer art. Briefly, evidence of a positive relationship between the number of bids and the final sales price suggests that art sold on eBay is not, in general, investment art. The article will also examine the effect of various parameters on the number of bids and selling price. Finally, the analysis will be repeated for a restricted data set which does not include auctions with the “buy-it-now” option offered by some sellers on eBay.
In addition to the traditional art auction literature cited above, there are papers that examine other questions in the art market (e.g. Beckmann 2004) and papers that examine the art market using non-auction data (e.g., Rengers and Velthuis 2002). But, to our knowledge, this is the first article to examine online art auctions, specifically using data from eBay. There are certainly papers which examine eBay auctions of other valuables, Lucking-Reiley et al. (2006), and Melnik and Alm (2005) for coins, Eaton (2005) for guitars, Dewally and Erdington (2004) for comic books. The present article uses a censored dependent variable approach something like Lucking-Reiley et al. (2006) and Melnik and Alm (2005). Of these papers, only Dewally and Erdington (2004) address the question of the relationship between the number of bids and final sales price that is the focus of the present article, and their emphasis is on confirming auction theory; they do not try to distinguish between investment and consumption goods. More generally, a number of studies have examined the phenomena of e-commerce with a mention of eBay (Bakos 2001; Borenstein and Saloner, 2001). Lucking-Reiley (2000) summarized basic eBay data such as auction format, revenues, and fees. In addition to Dewally and Erdington (2004), studies that have used eBay auction outcomes to empirically investigate auction theory are List and Lucking-Reiley (2002), Roth and Ockenfels (2002), and Bajari and Hortacsu (2003). Another strand of the online auction literature has examined the effect of reputation on auction prices (Resnick et al. 2006; Bajari and Hortacsu 2003; Houser and Wooders 2006; Melnik and Alm 2002; McDonald and Slawson 2002).
The subsequent section will briefly review the contributions of auction theory to an analysis of the relationship between number of bids and final sales price. The third section will describe the sample data. The fourth section will present the empirical model. Two sets of regressions will be run with the dependent variable being the number of bids in the first set and final sales price being the dependent variable in the second set of regressions. In the bidding equations, two different regression techniques are employed to determine which is the superior means of estimating bidding behavior. In the final sales price regressions, three different specifications are employed to determine the effect of the number of bids on the final sales price for an item. The fifth section presents the empirical results and the final section will offer the major conclusion of the study.
2 Some implications of auction theory for bidding and prices
The goal of the present article is to gather evidence about whether the art sold on eBay, (i.e., anything listed by the seller in the eBay category “Art”) is investment or consumer art. In auction theory parlance, an auction of a consumer good is a “private value” auction because each potential buyer has his or her own reservation price for the item, which is assumed to be independent of other bidder’s reservation prices. In this case, there should be a positive relationship between the number of bids and the final selling price because an increase in the number of bidders—whether predicted or not—increases the range of reservation prices from which the bids are drawn.
An auction for any investment is a “common value” auction in that, ex post, some time after the auction is held, observers would agree that the item has some given value, say 20,000 dollars for a work of art. The problem is that, ex ante, this value is unknown to potential bidders, and each must estimate the value of the investment, and plan their bid accordingly. Suppose, for example, there are three potential bidders; one estimates the value of the work of art at 18,000 dollars, the second at 20,000 dollars, and the third at 22,000 dollars. If each simply bids his or her estimate, the third bidder will win the auction—only to find ex post that he or she had bid too much for it—the “winner’s curse.”
Bidders can avoid the winner’s curse by shading their bids based on the number of bids, but the problem is that the number of bidders is also often uncertain. Thus to avoid the winner’s curse, bidders (1) need to accurately predict the number of bidders, and then (2) shade their bids correctly. Focusing on the first of these, if bidders predict the number of bids substantially correctly, then the final sales price is not a function of the number of unexpected bids because the number of unexpected bids would be quite small. (In the extreme case of predicting the numbers of bids exactly right, there would be no unexpected bids.) In this case, the final sales price is not a function of the (correct) predicted number of bids if and only if bidders shade their bids appropriately. On the other hand, if bidders fail to predict the number of bids correctly, then final sales price should increase with the expected number of bidders. And if bidders fail to predict the number of bidders, then in some sense any mistakes in shading the bids becomes a moot point.
Notice that for the three cases outlined above—(1) private value auction, (2) common value auctions when the number of bidders is correctly predicted, and (3) common value auctions when the number of bidders is not correctly predicted—there is only one case where the theory signs the relationship between the predicted number of bids and the final sale. For private value auctions, an increase in the number of bids should increase the final sales price, but it makes no difference whether that increase is predicted or unpredicted. That is, for private value auctions the coefficients for predicted bids and unexpected bids should be non-negative with at least one being positive. For common value auctions with insignificant unexpected bids, the sign of the predicted bid coefficient is positive if bidders fail to shade their bids correctly, and insignificant otherwise. For common value auctions with significant unexpected bids, the theory makes no prediction about the sign of the predicted bid coefficient.
Final sales price
Shipping and handling
Of the independent variables, the first is the minimum bid set by the seller for each auction. The minimum bid for an auction can also be interpreted as the reserve price of an item and the mean vale of this variable was 592.17 dollars. Given the mean final sales price for the entire sample was 599.79 dollars, the mean minimum bid was 98.7% of the final sales price. Thus, it appears, sellers were setting the minimum bid essentially at the final sales price. However, if auctions where items did not sell are omitted, the mean for the minimum bid was 445.85 dollars and the mean for the final sales price was 1,059.43 dollars. The ratio of the minimum bid to the final sales price for auctions where the item sold was 42%. Thus, for auctions where the item sold, the minimum bid was significantly lower than the final sales price.
The next three variables measured different characteristics of the auction. The buy-it-now (BIN) variable is a binary variable that had a value of one if this purchase option was available for an auction and was zero, otherwise. This feature allows the buyer to terminate the bidding process by paying a set price determined by the seller. Relatively few sellers offered this purchase option as only 13% of the auctions in the sample had this feature. The next two variables reflect time characteristics of the particular auction. The first is also a binary variable and it indicates whether the auction ended on a weekend or on a weekday. If the auction ended on a weekend, the value of the variable was one and took a value of zero for weekdays. Table 1 indicates that 37% of the auctions ended on a weekend. The second variable measures the length of the auction and the mean length was 6.12 days.
The next variable measured the shipping and handling fees charged by the seller. The mean for the shipping and handling fees was almost 11 dollars. Given that the mean final sales price was 599.79 dollars for the entire sample and 1,059 dollars for auctions where the item sold, shipping and handling fees were a small portion of the overall cost of purchasing an art item. One method of payment variable was included in the sample–whether a seller accepted Paypal. If a seller accepted Paypal as a method of payment, the variable had a value of one and was zero, otherwise. Paypal is an electronic, online, form of payment and was very popular with sellers. About 78% of the sellers accepted this form of payment. The next variable was a feedback measure for sellers. Seller feedback was constructed as a binary variable that took a value of one if the seller had a feedback score greater than 500. The variable took a value of zero if the seller had a feedback value less than or equal to 500. The seller feedback score is calculated as the number of positive feedbacks minus the number of negative feedbacks. Higher values of this variable mean a seller, on net, has received a greater number of positive feedbacks which should enhance the reputation of a seller. In this sample, 37% of the sellers had a feedback score of greater than 500. This statistic demonstrates that over a third of the sellers had high feedback values and had sold many items on eBay.
The last two variables are designed to control for artist heterogeneity in lieu of controlling for item-specific heterogeneity. Unlike such items as coins (Lucking-Reiley et al. 2006; Melnik and Alm 2005) and baseball cards (Highfill and O’Brien 2007), something like “book values” cannot be obtained for much of the art sold on eBay. Thus, the next two variables are designed to measure the popularity and reputation for a particular artist in the sample. Each item was identified by artist. Then a search was done on eBay for all auctions of art by the same artist. The first variable is the average price for items sold on eBay (completed auctions) for the given artist. If the number of completed auctions for an artist was 50 or less, then all completed sales were used to calculate this average. If the number of completed auctions was greater than 50, then the 50 most recent auctions were used to construct the average price for an artist. (About 16% of auctions fell in the latter category.) The average price for an artist in this sample was 643.93 dollars. The second variable is the number of an artist’s completed auctions that had a positive number of bids. The mean number of auctions with at least one bid for a given artist was 173.42.
4 Empirical Model
Two different sets of regressions were specified with the dependent variable being the number of bids in the first set and the (censored) final sales price in the second set. In the first set of regressions where the number of bids is the dependent variable, two regressions are employed. Both of these regressions use the same independent variables. Minimum bid is the first independent variable. In the case of common value auctions when different potential bidders have different ex ante estimates of the item’s ex post value, the higher the minimum bid the fewer the number of potential bidders whose adjusted ex ante bid will be greater than the minimum bid. For private auctions, higher values for the minimum bid should also decrease the number of bids by reducing the range of reservation prices bidders are drawn from. The buy-it-now variable should cause a decrease in the number of bids since it allows a bidder to preempt the bidding process. A weekend closing should increase the number of bids since potentially weekends allow greater participation in bidding on eBay. Auction length should also increase the number of bids since it allows more opportunities for bidding. Increased fees for shipping and handling should decrease bidding since higher fees increase the total cost of a transaction. On the other hand, availability of Paypal should increase bids since it speeds up the process of completing a transaction. Greater values for seller feedback should increase bids as an enhanced reputation for sellers ought to induce more bidding. The final two variables measuring the popularity of an artist, average artist price, and proportion of completed sales for an artist, should each increase the number of bids for an artist. The regressions also include 38 dummies representing different eBay art categories. These measure the effect of a given category relative to the most common category “Paintings, Contemporary, American.”
Two versions of the bids regressions were estimated with the first regression using OLS and the second using the Poisson model for count data. The Poisson model is best suited for discrete variables that tend to be limited to small values. This is an apt description of the bid data in the sample and, as will be seen shortly, the Poisson model appears to be an appropriate technique for this data.
For the second set of regressions, the final sales price is the dependent variable. All of these regressions are estimated using a censored Tobit. As noted above, 131 auctions in the sample ended with no sale. This implies that the minimum bid exceeded the willingness-to-pay for these 131 no sale auctions. To handle these left-censored observations, a Tobit maximum likelihood estimation technique with variable cut-offs is used. These variable cut-offs are the minimum bid specified for each auction in the sample. In the discussion that follows “final sales price” will be understood to mean the censored variable. Each of the final sales price regressions is corrected for possible heteroscedasticity by using the technique described in Greene (2000).
Though each regression uses the same estimation technique, they differ by how the bid variable is specified. Before the discussion of the bid variable, the independent variables common to all three regressions are described. Some of the predicted effects of these variables are the same as in the bid regressions but some differ. In the absence of a book value, the effect of a higher minimum bid on the final sales price should be positive to the extent that a higher minimum bid reflects an item with a higher value. The exception would be if a seller sets an excessive bid which prohibits entry, for example, a bid which is greater than any bidder’s estimate of the value of a common value auction item. The effect of the buy-it now option is usually negative. If the buy-it-now price is set low, a buyer may quickly use this option and preempt entry by other buyers, decreasing the final sale price. On the other hand, if the buy-it-now price is set high then the item may well remain unsold.
Of the remaining variables, a weekend closing date may increase bidding activity and so increase the final sales price. The effect of auction length is ambiguous because it is unclear if an extended auction will increase bidder participation (positive effect) or if it is an indication of an item which has been difficult to sell (negative effect). Similar to the bid regressions, a higher amount for shipping and handling should have a negative effect as bidders will attempt to offset shipping and handling cost by offering a lower final bid for an item. The use of Paypal as a payment option should increase the final sales price for an item as buyers should be willing to pay a premium for an item in order to facilitate the transaction. For the feedback dummy, increased positive feedback for sellers should have a positive effect on the final sales price for an item. In the studies reviewed by Resnick et al. (2006) and Bajari and Hortacsu (2003), higher positive feedback did increase the final sales price for an item. However, this premium decreased as the number of feedbacks became large. The last two variables, average artist price and proportion of an artist’s auctions completed, should both increase the final sales price in an auction as both indicate the popularity or reputation of a given artist.
In terms of how the number of bids affects the final sales price, each regression has a different specification of the bid variable. For the first regression, the bid variable is simply the number of bids for a particular item. However, especially in the case of common value auctions, it is important to distinguish between expected bids and unexpected bids. The expected bids variable is taken from the predicted number of bids derived from the Poisson count regression. The unexpected number of bidders is calculated as the actual number of bidders minus the expected number of bidders. In the third regression, no bid variable is included in the regression but the remaining independent variables are retained. In this regression, the coefficients of the independent variables represent the total effect of the variable on the final sale price including the variable’s indirect effect via its influence on the number of bidders. Another way to interpret the coefficients in this third regression is that they measure the effect of the variables on the bidder’s willingness to pay.
5 Empirical Results
Bids regressions-full sample
Shipping and handling
For the Poisson count regression, seven of the nine explanatory variables were significant. For the first explanatory variable, an increase in the minimum bid had a significant, negative effect on the number of bids. However, the effect was quite small. The buy-it-now option seems to preempt bidding and so decreased the number of bids. Like the OLS regression, an increase in the auction length led to a higher number of bids. Thus, longer auctions do allow for increased bidding activity. Though the effect was small, an increase in shipping and handling decreased the number of bids. Contrary to expectations, the availability of Paypal had a negative, significant effect on bids. An increase in average price of a given artist’s work, indicating higher regard for the artist, increased the number of bids. In addition, an increase in the number of completed sale increased the number of bids. However, the effect of both these demand variables was small. Neither a weekend closing day nor the amount of positive seller feedback had a significant effect on bids: weekend closing day and the amount of positive seller feedback. Lastly, the pseudo-R2 for the Poisson was 0.2575. Overall, in terms of the number of significant variables, the level of significance of these variables and the coefficient of determination, the Poisson specification performed better than the OLS equation. In the latter portion of the article, the results for the Poisson regression will be the source of predicted bids in the final sale price regressions.
Final sales price regressions-full sample
Shipping and handling
Moving to the important bid variable, its coefficient was positive, significant, and relatively large. At the mean final sale price, an extra bid increased the final sale price by 5.61% for the entire sample and 12.6% for sold items. As noted above, this positive effect can be the result of three factors: the art items have private values, bidders do not adjust their bid values for the winner’s curse or bidders do not correctly estimate the number of competing bidders. However, it is not possible to ascertain from this specification of the bid variable the relative importance of these three possibilities.
For the second regression, the bid variable was divided into predicted and unexpected portions. In this regression, the minimum bid variable had similar effect as in the first regression. As in the first regression, a higher minimum bid had a positive, significant effect but the effect was small. Similar to the first regression, an increase in shipping and handling fees significantly decreased the final sale price. Also, similar to the first regression and contrary to expectations, the availability of Paypal significantly decreased the final sale price and the effect was large. As expected, the two artist demand variables, average sales price and number of completed sales, significantly increased the final sales price but in both cases the effect was small. Although not shown in the table, of the eBay art category dummies only “Drawings, Modern,” “Paintings, Antique, American,” and “Paintings, Antique, European,” were significant, the latter barely. For all three of these categories the effect was positive, meaning that they tended to get a higher price than the comparison category “Paintings, Modern, American.” None of the other independent variables, including the average price of a given artist’s work, significantly affected the final sale price.
Examination of the bid variables shows that a higher number of expected bids significantly increased the final sales price and this effect was relatively large. An increase in the number of expected bids increased the final sales price by 8.3% for the entire sample and 14.6% for sold items. An increase in the number of unexpected bids also significantly increased the final sales price and this effect was larger than the effect of predicted bids. For the entire sample, an increase in the number of unexpected bids increased the final sales price by 12.8%. For sold items only, the increase was 22.7%. Thus, unexpected bids had an effect almost 65% larger than the effect of predicted bids. Also, while the coefficient for predicted bids was significant at the 10% level, the coefficient for unexpected bids was significant at the 1% level.
The last regression in Table 3 omits any bid variable and so measures both the direct effect of each independent variable on the final sales price and its indirect effect on the final sales price via its effect on bids. As noted above, the coefficients now measure the effect of each independent variable on the bidder’s willingness-to-pay. Five of the variables in this regression had significant effects on the final sales price. A higher minimum bid increased the final sales price and this coefficient was somewhat smaller than the coefficients in the other regressions. This would imply that a higher minimum bid increases willingness-to-pay but the effect is not large. An increase in shipping and handling decreased the final sales price and this effect was larger (in absolute terms) compared to the first regression. This outcome implies that higher amounts for shipping and handling decrease the willingness-to-pay of bidders. Again, Paypal had a significant negative effect on the final sales price and so the willingness-to-pay for an item. Moreover, similar to the first two regressions, the effect was very large. The two artist demand variables, average price and completed sales, both significantly increased the final sales price and so increased the willingness-to-pay. However, the positive effect of both of these variables was small.
There were a number of findings common to all three final sales price regressions. Two common findings were the positive effects of the minimum bid and the average price for a given artist’s work. Also, common to all three regressions was the large negative effect of Paypal. Compared to Paypal, the positive effects of the first two variables were quite small. Shipping and handling fees had a negative effect in two of the regressions and the effect was moderate. Also, significant in two of the regressions was the completed sale variable for artists but the positive effect was quite small.
Recalling the large coefficients on unexpected bids, the results so far suggest that bidders have difficulty predicting the number of bids. The next section removes all the auctions with the buy-it-now (BIN) option from the dataset to see if that feature explains the difficulty bidders have in predicting bids. When the BIN observations are removed, the sample size is reduced to 265. Of these auctions, 140 of resulted in a sale and 125 did not. (That is, buy-it-now was an option offered by the seller but no bidder chose to bid on the item nor use the buy-it-now feature.) The regression specifications are the same as previously except for the BIN variable.
Bids regressions without BIN observations
Shipping and handling
Final sales price regressions without BIN observations
Shipping and handling
Again the results in Table 5 of the regressions are very similar to the results of the entire sample. However, there are some differences. For example, auction length is significant and negative in the first regression in Table 5, which implies that a longer auction length may indicate an item that is difficult to sell. The key difference is in the second regression which contains the predicted and unexpected bids variables. Similar to the result for Table 3, the coefficient on unexpected bids is positive, significant, and of similar magnitude. But, while the predicted bid coefficient is positive and similar in size compared to the coefficient in Table 3, the variable is now insignificant. Recall that with the unpredicted bid variable being significant, the theory makes no predictions about the effect of predicted bids. The fact that the magnitude of the unexpected bid coefficient in Table 5 is in the same order of magnitude as that in Table 3 suggests that it is not more difficult to predict the number of bids in BIN auctions.
One purpose of this article was to examine the determinants of bidding for online art auctions. For the full sample, two regressions were specified for the bid equations and the Poisson count model performed better than OLS model. In the Poisson regressions, a number of variables significantly affected the number of bids. As predicted, a higher minimum bid decreased the number of bids and the effect was small. Also as predicted, availability of the buy-it-now option decreased the number of bids. A longer auction length increased bids by allowing more opportunities for bidding. Increased shipping and handling fees decreased bids by adding to the overall cost of an item. However, the effect was small. Both artist demand variables, average price and completed sales, increased the number of bids but both effects were quite small. Thus, when significant, the variables had the expected effects.
Also using the full sample, the second set of regressions explored the determinants of the final sales price for the art items being auctioned. Three regressions were estimated with the bid variable being specified differently in each regression. In the first regression, the bid variable was simply specified as the number of bids on an item. The results showed that an increase in the number of bids significantly increased the final sales price. At the mean final sales price, an extra bid increased the final sales price by 5.61% for the entire sample and 12.6% for sold items. By dividing bids into predicted and unexpected bids, the second regression showed that an extra predicted bid increased the final sales price by 8.3% for the entire sample and 14.6% for sold items. However, an extra unexpected bid increased the finals sale price by a considerably larger amount: 12.8% for the entire sample and 22.7% for sold item.
In addition to the full sample, the same bid and final sales price regressions were run for a reduced sample that did not include auctions with the buy-it-now option. The results for both the bids and final sales price regressions were very similar to the results for the full sample. In the bids regressions, similar to the full sample, the Poisson performed noticeably better. For the final sales price regressions, there was one main difference with the full sample results. In the second regression, the effect of predicted bids was insignificant. However, given the significant effect of unexpected bids, no inference can be drawn about the predicted bid.
Finally, although the primary result is that an increase in unexpected bids has a large positive effect on the final sales price does not logically exclude the possibility that the art sold on eBay is investment art (i.e., in a common value auction); we would argue that the size of these effects probably suggests the art sold on eBay is consumption art. It seems unlikely that bidders buying art for investment purposes would make mistakes in their bidding that result in them paying substantially more for the work of art than if they had not bid. The very size of the mistakes involved suggests that an investor would not make them. On the other hand, it is perfectly appropriate to bid more for a piece of art that exactly matches the living room décor, even if you are the “unexpected bidder,” so to speak. (It goes without saying that a work of art that is not of investment status is still art.) The fact that the coefficients on final price of the average price of a given artist’s work and completed sales are quite small (although sometimes significant), we would argue, also suggests this is not investment art—for investment art, the reputation of the artist is not everything, but its important. Finally, supposing for a moment that art must have a selling price of $5000 or more before it is a candidate to be an investment piece, in this data only seven sales were in that range, and of these only two were by artists (Gauguin, and Chagall) in Singer and Lynch’s (1997, 215–6) “Category 1” of investment quality art.
The authors would like to thank Linda Ficht and Pavel Chladek for their invaluable assistance with this research.