Public and Secret Reserve Prices in ebay Auctions

Transcription

1 Public and Secret Reserve Prices in ebay Auctions Jafar Olimov AEDE OSU October, 2012 Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

2 Motivating example Need to sell a good with an unknown value Run a rst-price auction: expected revenue = expected second highest valuation Run a rst-price auction with a secret reserve price in stage one and posted price session in stage two: expected revenue = expected highest valuation - cost of relisting Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

3 Related Literature: Theory Public reserve prices Myerson (1981) and Riley and Samuelson (1981): independently distributed valuations - screening Milgrom and Weber (1982) and Cai, Riley, and Ye (2007): commonly distributed valuations - signalling Secret reserve prices No theory Vincent (1995): commonly distributed valuations - encourages entry (???) Rosenkrantz and Schmitz (2007): restrictive utility function of bidders (dependence on public reserve price and an outside option) Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

4 Related Literature: Empirics Secret vs Public Reserve Prices: Bajari and Hortacsu (2003) - eld data on collectible coins on ebay, small positive e ect of secret reserve prices on revenue is on average 1.5% of sale price (static auctions) Secret vs Public Reserve Prices: Katkar and Lucking-Riley (2006) experiments with 10 Pokemon cards on ebay, secret reserve prices lower revenue by 10% and the likelihood of sale by 34% (static auctions) Secret vs Public Reserve Prices: Lucking-Reiley et. al. (2007) - eld experiments with collectible pennies on ebay, positive e ect of public and secret reserve prices on sold items. Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

5 Related Literature: Conclusions No theory explaining secret reserve prices No testing of structural determinants of secret and public reserve prices Inconclusive price e ects of secret reserve prices Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

6 Empirical Evidence: Data on Used Tractors sold on ebay Auction sales of tractors on ebay between 11/17/04 and 5/30/07. Listing patterns Number Number Percent listed sold sold Single listing listings listings listings listings listings listings or more listings Total number of unique tractors Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

7 Empirical Evidence Times between relistings in two-stage auctions Duration between relistings Number of 2-stage auctions Percent less than 1 day days days days to 2 weeks weeks to 1 month from 1 month to 2 months more than 2 months Total Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

8 Empirical Evidence Parameters in ebay auctions. Auction parameter Observability ebay fee Public reserve price Fully observable $5 Secret reserve price Unobservable price, $5 observable indicator Buy-it-now price Observable prior to if listing 50/month, free, (BIN) auction, unobservable if listing >50/month, later $0.25/listing Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

9 Empirical Evidence The use of di erent auction features for tractors listed only once. Features used Number Percent Auctions with public reserve price (PRP) (>$100) Auctions with secret reserve price (SRP) Auctions with buy-it-now price (BIN) Auctions with PRP and SRP Auctions with PRP, SRP and BIN Total number of tractors listed once Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

10 Empirical Evidence The use of di erent auction features for tractors listed twice. Features used First listing Second listing Numbr. Percent Numbr. Percent Auctions with public reserve price (PRP) Auctions with secret reserve price (SRP) Auctions with buy-it-now price (BIN) Auctions with PRP and SRP Auctions with PRP, SRP and BIN Total number of tractors listed twice Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

11 Empirical Evidence Tractor characteristics in auctions with complete bidder information. Number Mean St.dev. Min Max of obs. Number of bidders Seller feedback score Tractor age Tractor horse power Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

12 Empirical Evidence Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

13 Empirical Evidence Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

14 Empirical Evidence: Conclusions Many items on ebay are relisted Many items are not successfully sold The sale rate does not increase with relistings Simultaneous use of public and secret reserve prices Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

15 Model Assumptions Bidders on ebay use "proxy bidding" - English auction Assumption 1. Bidders cost of participation is zero. Tractors are used and less likely to be resold Assumption 2. Bidders valuations are identically and independently distributed on a nite support [0, v]. Assumption 3. Bidders and a seller are risk-neutral. Assumption 4. Bidders participate only in one-stage auctions. Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

16 Proposition 1 Let [0, v] be a nite support of the distribution function of bidders valuations, r 0 be a public reserve price, s 0 be a secret reserve price, and b 0 be a buy-it-now price. Then under assumptions 1, 2, 3, and 4, the following holds: a) Conditional on a bidder s valuation exceeding the public reserve price r, it is a weakly dominant strategy for the bidder to enter an auction if the lower bound of the support of a secret reserve price is less than or equal v. b) The bidding strategies of participating bidders in an ebay auction with N bidders and with r,s,b coincide with the bidding strategies in an English auction with N+1 bidders and only with r. Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

17 Model assumptions Assumption 5. A seller does not have perfect knowledge about the distribution function of bidders valuations and its support. Assumption 6. A seller s cost of relisting is su ciently small. Proposition 2. Let [0, v] be an unknown support of the distribution function of bidders valuations, s 0 be a secret reserve price, and b 0 be a BIN price. Then under assumptions 1, 2, 3, 4, 5, and 6, the equilibrium strategy of an uninformed seller is to set a secret reserve price and a BIN equal to the maximum of the highest order statistic of the distribution function of bidders valuations. Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

18 Estimation Strategy Consider only unsuccessful auctions with public reserve $100 Split the sample into 18 groups based on age, horse power, brand Age: {<11,11-30,>30} Horse power: {<21,21-40,>41} Brand: {John Deere, non-john Deere} Estimate the distribution function for each category non-parametrically with normal kernel Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

19 Identi cation Assumptions Identi cation Assumption 1: Bidders valuations for tractors in each category come from the same distribution Identi cation Assumption 2: Bidders participate only in one-stage auctions Identi cation Assumption 3: Secret reserve prices do not restrict entry Identi cation Assumption 4: Bidders valuations are independently distributed Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

20 Test of Identi cation Assumptions Identi cation Assumption 2: Bidders participate only in one-stage auctions Type of repeated 2-stage 3-stage 4-stage 5-stage auctions auctions auctions auctions auctions 1 identical bidder in at most 2 stages (number) 1 identical bidder in 69.04% 46.34% 38.46% 23.81% at most 2 stages (percent) >1 identical bidders in at most 2 stages (number) >1 identical bidders in 30.96% 53.66% 61.54% 76.19% at most 2 stages (percent) Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

21 Test of Identi cation Assumptions Identi cation Assumption 3: Secret reserve prices do not restrict entry Regression of the number of bidders. Variable Poisson Standard Error Public reserce*secret reserve *** Public reserve*(1-secret reserve) *** BIN*(Secret reserve) *** BIN*(1-Secret reserve) *** Secret reserve -.206***.004 John Deere.08***.004 Age -.008***.0001 Engine HP.002*** ln(seller feedback).022***.0009 ln(buyer feedback).008***.0009 Constant 2.589***.007 Number of observations Dependent variable is the number of bidders; Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

22 Test of Identi cation Assumptions Identi cation Assumption 3: Secret reserve prices do not restrict entry OLS regression of the average bid on a secret reserve dummy. Variable Coe cient Robust Standard Error Number of bidders *** John Deere *** Age *** Engine HP *** Public reserve.785***.023 Secret reserve *** BIN.095***.012 Constant *** Number of observations R The dependent variable is the average bid; ***-stat. signif. at 1%; Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

23 Test of Identi cation Assumptions Identi cation Assumption 4: Bidders valuations are independently distributed IV regression of realized bids on the number of bidders Variable Coe cient Robust Std.Error Number of bidders *** John Deere *** Age *** Engine HP *** Secret reserve *** ln(seller feedback) *** ln(buyer feedback) Constant *** Number of observations The dependent variable is realized bids; *-statistical signi cance at 1%; Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

24 Test of Identi cation Assumptions: Conclusion Assumptions 3 and 4 are rejected Low-valuation bidders don t enter The highest observed bid in an unsuccessful auction > valuation (winner s curse) Estimated distribution of valuations is skewed to the right Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

25 Determinants of Public Reserve Prices Public reserve price r 1 = f (x 0, λ j (r ), b) x 0 - the seller s value of the used tractor, 1 - one over the estimated hazard rate for a tractor in category j and λ j (r ) evaluated at r b - the minimum bid. Hypothesis 1: Public reserve price is used for screening Hypothesis 2: Public reserve price is used for signalling Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

26 Determinants of Public Reserve Prices Variable OLS Fixed E ects John Deere (78.709) ( ) Age (9.555) (14.058) Engine HP (3.909) 6.942* (3.955) 1 Hazard rate j (r).021*** (.006).021*** (.008) Minimum bid.698*** (.114).528*** (.187) Constant ( ) ( ) Overall R Number of groups 5965 Number of observations The dependent variable is the public reserve price; ***-statistical signi cance at 1%,*-statistical signi cance at 10%; robust standard errors in parantheses; in FE model the observations and the errors are clustered by seller ID; Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

27 Determinants of Secret Reserve Prices Unobservable secret reserve - s : use BIN as a proxy Hypothesis 1: Secret reserve price is used for screening s should depend on 1 Hazard rate j (s) ; Hypothesis 2: Secret reserve price is used by informed patient sellers to sell at the highest price s should depend on v- the upper bound of the support of valuations; Hypothesis 3: Secret reserve price is used by uninformed patient sellers to learn and to sell at the highest price s should depend on the highest bid from previous unsuccessful auction; Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

28 Determinants of Secret Reserve Prices Determinants of a successful sale (pooled data from all auctions). Variable Logit Coe cient Sec. reserve*pub. reserve *** (.072) Sec. reserve*(1-pub. reserve) *** (.085) Public Reserve.678*** (.109) John Deere -.135*** (.051) Age.015*** (.002) Engine HP -.004*** (.001) BIN ( ) Seller feedback score.0002*** (.00006) Number of bidders.095*** (.006) Average bid.00002** ( ) Number of observations The dependent variable is Sale (Y/N); ***-statistical signi cance at 1%, **-statistical signi cance at 5%; robust standard errors in parantheses; Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

29 Determinants of Secret Reserve Prices Determinants of secret reserve prices in 2-stage auctions Variable OLS Coe cient OLS Coe cient Constant ( ) ( ) Highest Bid t *** (.045) 1.027*** (.048) Mean Highest Valuation j.147** (.058).152* (.089) John Deere ( ) Age (12.174) Engine HP ** (7.295) 1 Hazard rate j (BIN) (.099) Number of observations R The dependent variable is BIN t /secret reserve price t ; ***-statistical signi cance at 1%, **-statistical signi cance at 5%, *-statistical signi cance at 10%; robust standard errors in parantheses; Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

30 Determinants of Secret Reserve Prices: Hypothesis 2 vs 3 Informed versus uninformed sellers. Variable OLS Coe cient OLS Coe cient Constant *** ( ) *** ( Highest Bid t *** (.03) Highest Bid t 1.062*** (.053) Number of observations R The dependent variable is BIN t /secret reserve price t ; ***-statistical signi cance at 1%; robust standard errors in parantheses; Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

31 Determinants of Secret Reserve Prices Determinants of adjustments in BINs/Secret reserve prices Variable OLS Coe cient Robust Standard Error Constant *** BIN t 1 -Highest Bid t ***.038 BIN t 1 -Mean Bid t *.031 Number of observations 102 R The dependent variable is BIN t -BIN t 1 ; ***-statistical signi cance at 1%, *-statistical signi cance at 10%; Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

32 Determinants of Sale Prices Variable OLS Coe cient Robust Standard Error Number of Times a Secret Reserve Price is Used.107***.006 Number of Relistings -.094***.012 Public Reserve Price at Sale.00003*** Age at Sale -.012***.0003 Engine HP.004***.0001 Engine Hours *** Brand Category -.012***.001 Constant 3.851***.016 R Number of observations 8210 The dependent variable is log(sale price); ***-statistical signi cance at 1%; Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

33 Determinants of Sale Prices: Simulation Exercise Sell 37 year old John Deere tractor with a 95 HP Simulate CDF and inverse CDF from unsuccessful auctions with public reserve $100 Draw 5 valuations in each round up to 5 times Discount factor =0.99 Zero payo after 5th listing Initial secret reserve: $18988 Updating rule: S t = α S t 1 + (1 α) Yt 1 1, S t - secret reserve at time t, S t 1 - is the previous period secret reserve, Yt is the highest unsuccessful bid in the previous auction stage, α 2 [0, 1] - weight of S t 1 Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

34 Determinants of Sale Prices: Simulation Results Simulated mean price of a 37 year old John Deere tractor with 95 HP. Auction Format and Data Type Mean Price St. Dev. # of in dollars Relistings Actual data Simulated w/o Public or Secret Res Simulated with Secret Res. and α = Simulated with Secret Res. and α = Simulated with Secret Res. and α = Simulated with Secret Res. and α = >5 Simulated with Secret Res. and α = >5 Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

35 Conclusions Public reserve prices are used for screening and signalling Secret reserve prices are used for learning bidders valuations by uninformed sellers Secret reserve prices have a strong positive impact on sale prices Low success rate of ebay auctions is partly due to the use of secret reserve price High number of delisted items is due to departure of initially uninformed sellers to other platforms Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36

36 References Bajari, P. and Hortacsu, A. (2003). "The winner s curse, reserve prices, and endogenous entry: Empirical insights from ebay auctions." Rand Journal of Economics, Vol. 34(2), pp ; Cai, H., Riley, J., and Ye, L. (2007). "Reserve Price Signaling," Journal of Economic Theory, 135 (1), ; Katkar, R., and Reiley, D. (2006). "Public versus secret reserve prices in ebay auctions: Results from a pokémon eld experiment," Advances in Economic Analysis and Policy, 6(2), Article 7; Lucking-Reiley, D., Bryan, D., Prasad, N., and Reeves, D. (2007). "Pennies from ebay: The determinants of price in online auctions," Journal of Industrial Economics, Vol. 55(2), ; Milgrom, P., and Weber, R. J., (1982). A Theory of Auctions and Competitive Bidding, Econometrica, 50(5), ; Myerson, R. B., (1981), Optimal auction design, Mathematics of Operations Research, 6, 58 73; Riley, J., and Samuelson,W., (1981), Optimal auctions, American Economic Review, 71(3), ; Rosenkranz, S., and Schmitz, P. W., (2007), Reserve Prices in Auctions as Reference Points, The Economic Journal, 117, ; Vincent, D., (1995), Bidding o the Wall: Why Reserve Prices May be Kept Secret, Journal of Economic Theory, 65(2), ; Jafar Olimov (AEDE OSU) Public and Secret Reserve Prices in ebay Auctions October, / 36