Competition Between Sellers in Internet Auctions

Transcription

1 Competition Between Sellers in Internet Auctions Jeffrey A. Livingston Bentley College Abstract: A great deal of research using data from ebay auctions has been conducted to study a variety of issues. Almost all of these studies structure their research framework around a standard model of auctions which assumes that the number of bidders is exogenous and independent from auction to auction. However, auctions on ebay run concurrently and compete against each other for bidders. Peters and Severinov (2006) present a model of this situation that predicts that bidders should always choose to bid in the auction that offers the lowest standing bid. This paper evaluates this prediction empirically, and shows that bidders only choose this auction if it is also the next auction of the product that is scheduled to close, and if the seller has at least a few reports of honest behavior in past transactions. JEL classification codes: D44, L14 Keywords: ebay, Internet Auctions, competition Correspondence: Bentley College, Department of Economics, 175 Forest Street, Waltham, MA 02474, Phone , Fax , jlivingston@bentley.edu

2 I. Introduction Internet auctions sites, in particular ebay, have been used as a source of data to study many questions. Studies have used these data to examine the effect of a seller s reputation on bidder behavior; see, for example, Lucking-Reiley et. al. (2007), Melnik and Alm (2002), Resnick et. al. (2002) and Livingston (2005). Others have used ebay auctions to estimate the demand for various goods, such as Adams (2007) and Song (2005). Finally, these data have been used to test a variety of hypotheses from auction theory. For example, Katkar and Reiley (2007) investigate how public or secret reserve prices affect seller revenues, and Hussein and Morgan (2006) evaluate how higher shipping and handling charges affect the auction price and how many bidders place a bid in the auction. Each of these types of studies is typically based on a model of seller and/or bidder behavior that relies on a standard theoretical assumption in auction theory: that the number of bidders who participate in the auction is both known and exogenous. Unfortunately, this is likely not the case in Internet auctions, where there are frequently many auctions of the same item active at any given time that are in competition with each other. Buyers can choose which auctions they find the most attractive, forcing sellers to compete for bidders. The number of bidders in a given auction therefore is endogenous, not exogenous, and the number of bidders in each auction is not independent. This situation creates both theoretical and econometric issues that the literature has only just begun to take into consideration. Peters and Severinov (2006) develop a theoretical model of both bidder and seller behavior in a similar situation. The model studies an environment where sellers run English auctions that open at the same time and continue until no bidders wish to submit a new bid. Bidders enter sequentially, and are given an opportunity to submit a new 1

3 bid in turn. The authors show that in this environment, the bidders optimal strategy is to bid just enough to become the leading bidder in whichever auction currently has the lowest standing bid. However, this setting differs somewhat from how ebay auctions actually operate, where sellers can start auctions any time they wish, and the auctions have a set time when the auction closes. Anwar et al. (2006) offer an empirical test of this prediction. They focus attention on sets of auctions run by the same seller, that end at approximately the same time, and that have similar item descriptions, starting prices, and delivery methods. They find that bidders in these auctions frequently do in fact bid in the auction that currently has the lowest price. These results are interesting, but by focusing only on similar auctions run by the same seller, the strategy does not allow us to investigate how bidders are affected by differences in the auctions they have to choose from. Also, we cannot be sure that the bidder truly selected the auction with the lowest standing bid, since by design auctions by other sellers that the bidder could have selected, which may have had a lower standing bid, were eliminated from the data. The goal of this study is to test empirically whether bidders do in fact choose to bid in the auction that has the lowest standing bid, using data that includes all of the auctions of the good that bidders could choose from. Data were collected from auctions of Taylor Made Firesole Irons, a variety of golf clubs. A great deal of information is available about each auction regardless of whether the transaction results in a sale or not, including the complete bid history of the auction. The identity of every participating bidder, when they placed their bid, and the amount of the bid is available, as is the time when each auction is active. This makes it possible to identify each auction of the good that was active when a bidder placed a bid, and to examine the why bidders choose to bid in a particular auction, rather than other auctions of the same item that are going on at the same time. 2

4 The results are quite clear. The choices bidders make are largely consistent with the flavor of the prediction of Peters and Severinov, but there are differences because of the differences between the assumptions of the model and the actual institutional details of the ebay market. Bidders do not often select the auction with the lowest standing bid, but this is because the auctions do not end at the same time. Roth and Ockenfels (2002) argue clearly that rational bidders should wait until the final moments of an auction to place their bids. 1 Not surprisingly, bidders do not choose auctions with the lowest standing bid if that auction does not end for a substantial amount of time, and in particular if other auctions are scheduled to end sooner. However, if an auction is the next one scheduled to end among those the bidder has to choose from, and it also has the lowest standing bid, it is very likely to be chosen by the bidder. These results emphasize the point that future theoretical and econometric analyses of Internet auctions need to carefully account for how the competition between auctions affects both seller and bidder behavior. At the same time, they show that the central insight behind the Peters and Severinov model is correct, but the differences between the model and the trading environment in ebay lead to predictable differences in how bidders are predicted to behave and how they actually behave. The paper proceeds as follows. Section II presents the data. Section III reviews the empirical methodology and discusses the results. Section IV concludes. 1 Waiting until the closing moments can be a best response to several strategies. For example, Roth and Ockenfels (2002) note, inexperienced bidders might make an analogy with first-price English auctions, and be prepared to continually raise their bids to maintain their status as high bidder. Bidding very near the end of the auction would not give the incremental bidder sufficient time to respond, and so a sniper competing with an incremental bidder might win the auction at the incremental bidder s initial, low bid. In contrast, bidding one s true value early in the auction would win the auction only if one s true value were higher than the incremental bidder s, and in that case would have to pay the incremental bidder s true value. 3

5 II. Data For a period of 90 days after an auction has ended, ebay maintains web pages that describe the history of each auction. These pages are a very useful research tool because they provide the full bid history of each auction, including the ebay identity of each bidder, the amount of each bid, and the time that each bid was placed. Also, ebay s search engine makes it easy to find the web pages of all of the auctions of a specific kind of item. A search returns links to the pages of all auctions that were completed in the past two weeks. It is therefore possible to create a very thorough picture of who is shopping for a specific item. Such a dataset is used here. From April 16th 2001 through August 20th 2001, data were collected from 678 ebay auctions of Taylor Made Firesole irons. There are data from every auction that was completed during this interval. On the average day, there were 32 active auctions, so bidders usually had many auctions to choose from. Among these 678 auctions, 7735 bids were placed. For each bid, all of the auctions that were active at the moment the bid was placed are identified. These auctions are assumed to be the set of auctions in which the bidder could have placed the bid. This set of auctions constitutes a bid block. Some auctions offer clubs that are clearly of no interest to the relevant bidder, so they are dropped from the bid block. While the golf clubs are relatively homogenous, there are some major differences to account for: some clubs are left-handed, some are made for women, and some are made for seniors. If an auction within a bid block offers a set of clubs that does not have the same characteristics as the clubs in the auction that the bidder chose to bid in, then it is dropped from the bidder s choice set. For example, if a bidder places the bid in an auction for right-handed clubs, then all auctions of left-handed clubs are dropped from the bid block. These blocks are then stacked together to form a dataset where the unit of observation is an auction 4

6 which the bidder could have chosen to bid in. The average bid block contains auctions, yielding a total of 203,163 observations. The study examines which factors affect the auction that the bidder chose to bid in within each block. Summary statistics are presented in Table 1. The dependent variable is Bid Placed, a dummy variable that equals one if the bidder selected the auction, and zero otherwise. The independent variables measure relative differences between each auction. The first critical set of controls captures the relative levels of the standing bids. In one set of specifications, Lowest Price through 5 th Lowest Price are controlled for. They are dummy variables that indicate whether the auction in a bid block offered the lowest standing bid through the 5 th lowest standing bid among the auctions of the good that were active at the time the bid was placed, respectively. In another specification, the entire distribution of relative standing bids is examined by controlling for dummy variables indicating the decile of standing bid levels among the auctions in the bid block. The second critical variable captures how much time remains in the auction. Next to End is a dummy variable that equals one if the auction is the next one to end among all auctions in the bid block. The arguments of Roth anc Ockenfels (2002) support the conclusion that bidders should be more likely to choose to bid in the auction that is closest to ending. The third set of controls measures the relative reputations of the sellers. On ebay, after a transaction the buyer and seller can leave reports about each other that are classified as positive, neutral, or negative. 2 Livingston (2005) shows that bidders need to see only a few positive reports before they are convinced of a seller s honest intentions. They bid much more in the auctions of sellers who have just a handful of positive reports than they do in the auctions of sellers who have no reported history, but further reports beyond the first few do not result in 2 See Bajari and Hortacsu (2004) for a full description of the ebay marketplace and its reputation system. 5

7 much of an increase in bid amounts. To capture this affect, the sample distribution of the number of positive reports held by the seller in each auction is divided into within-bid block quartiles, and dummy variables are created that indicate whether an auction falls into each quartile. The first quartile is further divided by splitting off auctions where the seller has zero positive reports into a separate group. No Positives is a dichotomous variable that takes a value of one if the seller has zero positive reports. Positive Q1 takes a value of one if the auction is in the remainder of the first within-block quartile of the number of positive reports received. Auctions where Positive Q1 equals 1 will still be referred to as the first quartile, though the reader should keep in mind that this group is not the true first quartile, since it excludes auctions where the seller has no positive reports. Positive Q2 through Positive Q4 take a value of one if the auction is in the second through fourth within-block quartiles of positive reports held, respectively. The fourth set of covariates measures auction-specific characteristics that may affect the bidders decisions. Bidders may be attracted to auctions where the seller operates an identifiable and verifiable business outside of ebay. Business equals one if the seller provides a telephone number at which he can be contacted or a website address that promotes the seller s business, if the seller is an ebay power seller, or if the seller has an ebay store. Bidders may also be impressed by attractive presentations of the description of the gold clubs. Fancy Display equals one if the description of the golf clubs is displayed in a fancy manner. Most descriptions are simply black text that looks much like the text of this paper. The fancy descriptions are characterized by features such as different background and font colors, unusual fonts and font sizes, scrolling text, and the use of tables to display information about the clubs. 3 Finally, 3 This variable is somewhat subjective, but there are very few cases in the data where there was much question as to whether the presentation should be considered fancy or not. 6

8 bidders may be reassured that the seller actually possesses the clubs if the seller presents a picture of them. Shows Picture equals one if the seller shows at least one picture of the clubs being sold. Other differences may also impact decisions. The value of the clubs is directly measured by Retail Price, which is equal to the retail price of the clubs (which can vary with the type of shaft on the club, for example). Bidders may be turned off by high minimum-allowable bids, which act as publicly-known reserve prices. High Minimum Bid equals one if the auction ranks among the 5 highest minimum bids within a bid block. Sellers can run auctions that last either 3, 5, 7 or 10 days. Bidders may have a greater chance of observing and choosing to participate in auctions that run longer. 3 Days Long, 5 Days Long, 7 Days Long and 10 Days Long equal one if the auction lasts 3, 5, 7 or 10 days, respectively. Each of these variables is included in the specifications; the reference group is the small number of auctions that lasted less than 3 days because a bidder ended the auction early by selecting the buy it now option, which is discussed below. Bidders may also react to the use of a secret reserve price. 4 Secret Reserve Used takes a value of one if the seller uses a secret reserve price. Bidders may be more or less inclined to bid on new clubs. New Clubs takes a value of one if the clubs are new, not used. Finally, ebay recently started allowing sellers to give bidders the option to buy it now at a posted price specified by the seller. If a bidder selects this option, the auction ends immediately and the bidder wins the auction at the posted price. Buyitnow Used equals one if the seller uses the buy it now feature. 4 Sellers can set both publicly-known reserve prices (the minimum bid), and secret reserve prices. Bidders observe whether a secret reserve price is in use, but not the amount of the secret reserve price. 7

9 III. Methodology and Results To estimate the effect of different factors on the bidders decisions, the following equation is estimated as a probit model: y ij = X ij β 1 + ε ij, (1) where y ij = 1 if the relevant bidder i submits a bid in auction j, and 0 otherwise; X ij is a vector of variables including controls measuring the standing bid in auction j relative to the other auctions in the bid block, whether the auction is closest to ending among auctions in the bid block, the relative reputations of the sellers in the bid block, and various auction characteristics as outlined above; and ε ij is a robust error term that is clustered by bid block, because there should be massive negative covariance between the outcomes within a bid block if a bidder places a bid in one auction, she is by construction unable to place a bid in the other auctions within the block at that same time. The first set of specifications examines the main prediction about how bidders make their choice. They control for Lowest Price through 5 th Lowest Price. The results are presented in Table 2. Marginal effects are reported. Column 1 reports the results from estimating a specification that controls for only these variables, the seller reputation controls, and the auction characteristic controls. The results suggest that bidders in fact do not under all circumstances choose to bid in the auction that has the lowest standing bid. Bidders are actually 2.4 percentage points less likely to place their bid in auctions that have the lowest standing bid among the bid block than auctions that are outside the top five lowest bids in the bid block. However, once the time remaining in the auction is controlled for, the results support the conclusion that bidders choose the auction with the lowest standing bid. Column 2 reports a specification that adds Next to End, as well as interactions between this variable and Lowest 8

10 Price through 5 th Lowest Price. The probability that the auction with the lowest standing bid is chosen by the bidder increases by 40.2 percentage points relative to auctions outside the five cheapest if the auction is also the next to end. Similarly, the probability that the auction with the second lowest standing bid is chosen by the bidder increases by 29.3 percentage points if the auction is also the next to end. However, auctions with higher standing bids are allowed to pass even if they are the next to end. The probability that the auction with the third lowest standing bid is chosen by the bidder increases by only 2.3 percentage points relative to auctions outside the five cheapest if the auction is also the next to end, and there is no statistically significant change in the difference between the chance that a bidder selects the auction with the 4 th or 5 th lowest standing bid and auctions outside the top five even if that auction is the next to end. As a whole, these results clearly call for a new model of the ebay auction system that captures both the end time incentives described by Roth and Ockenfels as well as the incentives faced by bidders who can choose among several auctions of the same good. However, they are largely consistent with the flavor of the predictions of the Peters and Severinov model so long as the auction is about to end, bidders tend to select the auction with the lowest standing bid, and they do not bid in auctions that are about to end if there are better deals available elsewhere. A similar story emerges when looking at the entire distribution of relative standing bids. Table 3 reports a specification that replaces Lowest Price through 5 th Lowest Price with a set of dummy variables indicating the within-bid block decile of standing bid, and interactions between the decile indicators and Next to End. The highest decile of within-bid block standing bids is the reference group. The results show that auctions in the lowest decile are no more likely to be chosen by the bidder unless they are the next auction scheduled to end. Auctions in the lowest decile that are not scheduled to end soon are actually 1.7 percentage points less likely to be 9

11 chosen by the bidder than auctions in the highest standing bid decile. However, if the auction is scheduled to be the next to end, the chance that a bottom decile auction will be chosen over a top decile auction increases by 30.6 percentage points. There is no such increase for auctions in higher deciles however, even if they are the next auction to come to a close. There is one exception to this rule that bidders make, however, although it is difficult to see in the data. If the seller has no reported transaction history, then bidders are unlikely to choose that seller s auction even if it offers the lowest current available price and is the next auction that is scheduled to close. It is impossible to see this point in our regression format because among the 18 observations where the auction has a standing bid in the lowest decile, is the next to end, and the seller has zero positive reports, no bidders chose to bid in those auctions. However, some simple summary statistics tell the story. Table 4 shows the percentage of auctions that the bidder chose to bid in, broken down by whether the auction was in the cheapest ten percent among the auctions in its bid block, by whether the auction was the next to end among auctions in its bid block, and by whether the seller had zero positive reports. Not once did a bidder select an auction among the cheapest ten percent that was also the next to end if the seller had zero positive reports. However, if the seller had at least one positive report, bidders selected an auction among the cheapest ten percent that was also the next to end 42 percent of the time. Future models of the ebay bidding process should continue to account for the fact that bidders often do not trust sellers who have yet to establish any transaction history. IV. Conclusion The analysis presented here supports the central insight of the model of Peters and Severinov that auctions on ebay are not independent, and that bidders compare the prices available in various auctions of a good when determining which auction they want to bid in. As 10

12 the authors note, the goal of their model is not to model the ebay market specifically. Rather, they seek to show that when auctions compete against each other for bidders, a simple mechanism exists that results in an ex-post efficient outcome. However, there are differences between the setting studied by Peters and Severinov and the design on the ebay market, and these differences result in a divergence between the predictions of the model about how bidders will behave, and the choices that they are actually revealed to make in the data. The model predicts that bidders should always choose to bid in the auction that offers the lowest current price. The data, however, reveals that bidders only select this auction if it also is about to end, and if the seller has a suitably established reputation for honest behavior. 11

13 References Adams, Christopher. Estimating Demand from ebay Prices. International Journal of Industrial Organization, 25(6), 2007, Anwar, Sajid; McMillan, Robert and Zheng, Mingli. Bidding Behavior in Competing Auctions: Evidence from ebay. European Economic Review, 50, 2006, Bajari, P. and Ali Hortacsu. Economic Insights from Internet Auctions, Journal of Economic Literature, 42(2), 2004, Hossain, Tanjim and Morgan, John. "...Plus Shipping and Handling: Revenue (Non) Equivalence in Field Experiments on ebay." Advances in Economic Analysis & Policy, 6(2), Available at: Livingston, Jeffrey A. How Valuable is a Good Reputation? A Sample Selection Model of Internet Auctions. The Review of Economics and Statistics, 87(3), 2005, Lucking-Reiley, D., Doug Bryan, Naghi Prasad, and Daniel Reeves. Pennies from ebay: the Determinants of Price in Online Auctions. Journal of Industrial Economics, 55(2), 2007, Melnik, M.I. and James Alm. Does a Seller s ECommerce Reputation Matter? Evidence from EBay Auctions. Journal of Industrial Economics, 50(3), 2002, Peters, Michael and Severinov, Sergei. Internet Auctions with Many Traders. Journal of Economic Theory, 130, 2006, Resnick, P. and Richard Zeckhauser, Trust Among Strangers in Internet Transactions: Empirical Analysis of ebay s Reputation System. in The Economics of the Internet and E- Commerce (Advances in Applied Microeconomics, Vol. 11), edited by M. Baye. Oxford: JAI Press, Roth, A.E. and Axel Ockenfels, Last Minute Bidding and the Rules for Ending Second-Price Auctions: Theory and Evidence from a Natural Experiment on the Internet, American Economic Review, 92(4), 2002, Song, Unjy. Nonparametric Estimation of an ebay auction model with an unknown number of Bidders. Discussion Paper 05-14, University of British Columbia,

14 Variable Name Dependent variable: Bid Placed Price controls: Current Bid Table 1. Variable Definitions and Sample Characteristics Definition 0-1 dummy variable that equals one if the relevant bidder placed a bid in the auction Current price in the auction at the time the bid was placed Lowest Winning Bid 0-1 dummy variable that equals one if the winning bid was the lowest among all the bidder s choices 2 nd Lowest Winning Bid 0-1 dummy variable that equals one if the winning bid was the second lowest among all the bidder s choices 3 rd Lowest Winning Bid 0-1 dummy variable that equals one if the winning bid was the third lowest among all the bidder s choices 4 th Lowest Winning Bid 0-1 dummy variable that equals one if the winning bid was the fourth lowest among all the bidder s choices 5 th Lowest Winning Bid 0-1 dummy variable that equals one if the winning bid was the fifth lowest among all the bidder s choices Time left controls: Next to end 0-1 dummy variable that equals one if the auction is the next to end among the bidder s choices Mean and Standard Deviation 0.04 (0.19) (151.69) 0.05 (0.23) 0.03 (0.17) 0.04 (0.19) 0.04 (0.20) 0.04 (0.19) 0.04 (0.19) Reported history of seller: Positives Number of positive reports held by seller ( ) No Positives 0-1 dummy variable that equals one if the seller has 0 positive reports Positive Q1 0-1 dummy variable that equals one if the auction is in the first within-block quartile of positive reports received, less those with 0 reports Positive Q2 Positive Q3 Positive Q4 0-1 dummy variable that equals one if the auction is in the second within-block quartile of positive reports received 0-1 dummy variable that equals one if the auction is in the third within-block quartile of positive reports received 0-1 dummy variable that equals one if the seller is in the fourth within-block quartile of positive reports received 0.07 (0.26) 0.20 (0.40) 0.26 (0.44) 0.25 (0.43) 0.21 (0.41) Bad Report Ratio Percentage of reports that are neutral or negative 0.02 (0.06) 13

15 Table1. Variable Definitions and Sample Characteristics (cont.) Mean and Standard Variable Name Definition Deviation Auction characteristic controls: Business 0-1 dummy variable that equals one if the seller runs a business 0.30 (0.46) Fancy Display 0-1 dummy variable that equals one if the item description is fancy 0.47 (0.50) Shows Picture 0-1 dummy variable that equals one if at least one picture of the item is displayed 0.67 (0.47) Retail Price Retail price of the clubs (78.70) High Minimum Bid 0-1 dummy variable that equals one if the auction uses one of the five highest minimum bids, among 0.22 (0.41) those within the bidder block 3 Days Long 0-1 dummy variable that equals one if the auction lasts 3 days 0.09 (0.29) 5 Days Long 0-1 dummy variable that equals one if the auction lasts 5 days 0.18 (0.38) 7 Days Long 0-1 dummy variable that equals one if the auction lasts 7 days 0.60 (0.49) 10 Days Long 0-1 dummy variable that equals one if the auction lasts 10 days 0.07 (0.26) Secret Reserve Used 0-1 dummy variable that equals one if a secret reserve price is used 0.53 (0.50) New Clubs 0-1 dummy variable that equals one if the clubs being 0.36 Buyitnow Used auctioned are new 0-1 dummy variable that equals one if the seller allows the bidders to buy the clubs at a posted price (0.48) 0.07 (0.26) 14

16 Table 2. Do Bidders Choose to Bid in the Auction with the Lowest Current Price? a Dependent Variable: Pr(Bidder Bid in Auction) (1) (2) Lowest Winning Bid *** *** (0.000) (0.000) 2 nd Lowest Winning Bid *** *** (0.000) (0.000) 3 rd Lowest Winning Bid *** *** (0.000) (0.000) 4 th Lowest Winning Bid *** *** (0.000) (0.000) 5 th Lowest Winning Bid *** *** (0.000) (0.000) Next to end 0.101*** (0.004) Next to end Lowest Bid 0.402*** (0.030) Next to end 2 nd Lowest Bid 0.293*** (0.037) Next to end 3 rd Lowest Bid 0.023** (0.011) Next to end 4 th Lowest Bid (0.023) Next to end 5 th Lowest Bid (0.013) Positive Q *** 0.009*** (0.002) (0.002) Positive Q *** 0.014*** (0.002) (0.002) Positive Q *** 0.027*** (0.003) (0.002) Positive Q ** 0.005*** (0.002) (0.002) Bad Report Ratio *** (0.005) (0.008) Observations Pseudo R Robust standard errors in parentheses * significant at 10%; ** significant at 5%; *** significant at 1% a Specifications also include controls for auction characteristics listed in Table 1 15

17 Table 3. Do Bidders Choose to Bid in the Cheaper Auctions? a Dependent Variable: Pr(Bidder Bid in Auction) (1) Current Bid, cheapest decile *** (0.001) Current Bid, 2nd decile *** (0.000) Current Bid, 3rd decile *** (0.001) Current Bid, 4th decile *** (0.001) Current Bid, 5th decile *** (0.000) Current Bid, 6th decile *** (0.000) Current Bid, 7th decile *** (0.000) Current Bid, 8th decile *** (0.000) Current Bid, 9th decile *** (0.000) Next to end 0.024*** (0.003) Next to end cheapest bid decile 0.306*** (0.031) Next to end 2 nd bid decile (0.007) Next to end 3 rd Bid Decile (0.006) Next to end 4 th Bid Decile 0.014** (0.006) Next to end 5 th Bid Decile 0.017*** (0.006) Next to end 6 th Bid Decile 0.008*** (0.003) Next to end 7 th Bid Decile 0.008*** (0.003) Next to end 8 th Bid Decile (0.001) Next to end 9 th Bid Decile * (0.001) Observations Pseudo R * significant at 10%; ** significant at 5%; *** significant at 1% a Specification also includes seller reputation controls and auction characteristic controls listed in Table 1 16

18 Table 4. Percentage of Auctions Chosen by Bidder by Relative Price, Time Left, and Seller Reputation Characteristics: Mean (Standard Deviation) Auction is the next one to end 0.21 (0.40) Auction is in the lowest decile of standing bids 0.01 (0.12) Seller has 0 positive reports 0.02 (0.14) Next to end and in lowest decile of standing bids 0.41 (0.49) Next to end, in lowest decile, seller has zero positive reports 0 (0) N Next to end, in lowest decile, seller has at least one positive report 0.42 (0.49)