Table 2 Hedonic regression of natural log of hammer price on the natural log of scrap value and other characteristics. Variable Predicted sign Full sample Coeff. (1) Bonhams Coeff. (3) 0.485 -0.239 0.317** -0.100 0.187 In (scrap) Spread In (age) Order QI 02 prov assay off Constant Observations Description dummies Place dummies Year dummies Quarter dummies Adj. R-squared See Table 1 for variable ove v eve 7 eve eve eve NA Table 3 Identifying arbitrage opportunities Arbitrage category P.Draper et al/Economics Letters 162 (2018) 45-48 Price Scrap Price Scrap Price & buyer's premium Scrap No lots sold 9924 690 56 0.457** -0.248- 0.411*** 0.129** 0.240 0.056*** definitions.p<0.01,"p<0.05,"p<0.1. 0.602*** 0.050*** 05 M -0.071 1.850 10,614 (11) (3) (5) (3) 0.547 regression: In(Price),= d+a, In(Scrap),+Characteristics, Std. err (2) (0.008) (0.046) (0.018) (0.033) (0.029) (0.016) (0.061) (0.014) (0.015) (0.115) Total weight (oz.) 245,311 29,877 1.608 + Controls + e, (1) Where In Price), is the natural log of the auction lot's hammer price. and In(Scrap), is our main variable of interest, the natural log of the lot's scrap value, for which we expect a significant positive coefficient if buyers' consider the scrap value of a lot an important feature when bidding Characteristics, include characteristics found in the auction catalogues that may explain the auction price. Specifically, we control for uncertainty as the spread between the high and low pre-sale estimate, age as the natural log of the lot age, the lot position in the auction, two binary quality variables to indicate if the lot was made by a notable silversmith working in the twentieth century (Q1) or earlier (Q2), and three binary variables to indicate provenance, the presence of an armorial or other inscription, and whether the assay office was other than London. Finally, we include binary variables (Controls) to control for the lot description (e.g. flatware), place of sale, year of sale, and quarter within the year in which the lot was sold. 4. Empirical analysis and results Table 2 reports the hedonic regression results of Eq. (1) for the full sample, lots sold by Bonhams, and lots sold by Woolley and Wallis. In all three regressions, we use unreported dummy variables to control for the lot description, place of sale, year of sale and quarter within the year in which the lot was sold. We report robust standard errors using the White heteroskedasticity-robust procedure. For all three regressions, the scrap value of silver has a 2 The lot's scrap value is calculated as the product of the lot's weight in ounces and the corresponding non-trade scrap price of silver on the auction day from Cookson Precious Metals Ltd at http://www.cooksongold.com/. This represents the price at which they are prepared to trade on that day. Over our sample period the non-trade scrap price of silver per ounce ranges from £5.26 on 15 January 2009 to (21.38 on 28 April 2011, has a mean (standard deviation) of £11.03 (C353), and an average (standard deviation) daily change of 0.002 (0.295) 0.058*** 0.268** 0.047** 0.018 2.255*** 5.179 (11) (2) (5) (3) 0.638 Total price (K) 8.976,321 371,875 14,490 Std. err (4) (0.010) (0.055) (0.022) (0.043) (0034) (0.020) (0.092) (0018) (0.019) (0.134) Woolley and Wallis Coeff (5) 0.399 -0.061 0512** 0.421*** 0.240** 0.052 0772 0.061*** -0.104 LIO 5.435 (11) NA (5) (3) Total price-bp (0) 10,900,000 454229 17,679 47 Std. err. (6) (0.011) (0.074) (0.029) (0.052) (0.046) (0.025) (0.074) (0.021) (0.021) (0.180) Total scrap ( 2,734,583 398,286 20,792 significant positive effect on the hammer price and the remaining variables, where significant, are all of the predicted sign. In an auction environment, this implies that bidders are partly setting their bids based on the lot's scrap value. The evidence does not, however, confirm whether profitable arbitrage opportunities exist between the silver auctions and scrap value of the lots sold and purchased. If arbitrage opportunities exist, then there is prima facie ev- idence of market inefficiency. While this is a weak-form test of market efficiency, since it only uses price information, the absence of arbitrage is a very important characteristic of financial markets, which we test for in the physical silver market. Purchasers of silver goods are faced with a variety of costs, notably the buyer's premium. Therefore, we expect profitable arbitrage may be pos- sible before allowing for the buyer's premium but is most likely impossible once it is added into the price of the good. To test this, we identify and report summary statistics in Table 3 of all lots sold above and below their scrap value based on the hammer price paid to the seller, and all lots sold below the scrap value based on the hammer price and buyer's premium paid by the bidder. Our findings in Table 3 show that arbitrage opportunities are available if the only cost imposed on buyers is the hammer price. However, once the buyer's premium is included, arbitrage oppor- tunities almost completely disappear. Specifically, less than one percent of our sample would yield a profit of, on average, less than £60 per transaction, ignoring any physical costs of collection and resale. 5. Conclusions The absence of arbitrage opportunities after costs, particularly the buyer's premium, suggests that bidders are sensitive to the total price. Moreover, although scrap silver can be sold for cash at 3 The buyer's premium is a fee set by the auction house, and paid to the auction- eer by the buyer. This is constant for each auction, but varies between houses and over the sample period from 19.5-25% of the hammer price. 4 Analysis of the 56 lots for which arbitrage is possible indicates that 91% were sold by Bonhams and more than half in the fourth quarter. 46 Table 1 Descriptive statistics and sample distribution Panel A: Pooled sample statistics Variable Price Price bp Scrap Weight Spread Age Order Q1 02 prov arm assay off 2009 2010 2011 2012 2013 Mean 880.74 1073.17 295.16 25.93 0.39 166.06 2014 Quarter 1st 2nd 3rd 0.67 0.08 0.19 0.02 0.40 0.62 Std.dev. 1906.84 231157 441.80 37.03 0.13 Pape 77.75 0.25 0.26 0.39 0.15 0.49 0.48 Knightsbridge Obs. Price 551 667 Scrap 708.85 220.07 696.21 278.90 899.24 538.90 539 1089.38 645.23 447 1062.86 41761 332 1386.42 485.82 671 ART P. Draper et al/Economics Letters 162 (2018) 45-48 892.68 391.53 1134 928.36 424.30 393.99 895.67 959.65 452.56 424 1160 Min 20.00 2440 0.89 0.10 0.05 1.00 0.00 Panel B: Sample distribution of lots sold, average lot hammer price (C), and average lot scrap value (E) Year Bonhams Max. 85,00000 101,5790 6.211.80 553.00 1.00 $10.00 1.00 1.00 1.00 1.00 1.00 1.00 Knowle Obs. Price Scrap 402 382.44 179.87 298.34 476 458.25 472 596.60 459.47 291 465.10 275.94 394 488.48 324.64 296 487.53 306.71 369 358.25 49145 the bullion dealer at the prices quoted and with speedy or even immediate payment. The possibility, therefore, of selling for scrap provides a minimum guaranteed price, allowing sellers to realise cash with a minimum of restrictions. Both sales for scrap, and to antique dealers provide immediacy to the seller. They also provide certainty and low transaction costs. They do not however provide exposure to a wide range of buyers. The significant transactions costs associated with selling by auction suggests that sellers of silver goods that are of low quality and plentiful supply should sell direct to bullion or antique dealers to maximise their receipts from sale. Despite this, low quality silver is sold at auction. Selling for scrap removes any chance of receiving a premium for artistic merit or scarcity and there may be some sellers of low quality items who prefer, perhaps through ignorance. to sell by auction. High quality items should not be scrapped but sold to dealers or by auction. Many silver goods have some worth relating to their scarcity. usefulness, artistic merit and quality of workmanship. A number of items, however, have no such merit. They may have been mass produced and of poor quality originally, or may be battered and broken. The demand for such items is slight. They are of limited interest to collectors or dealers. They do however retain value, a value that depends on their silver content. They may be easily melted and reduced to pure silver. In an efficient market, we would expect any silver item to have a minimum value directly related to its scrap value. Description Hammer price of lot (C) Hammer price of lot including the buyer's premium (E) Scrap value of lot(C) Weight of lot (ounces) 2. Sample and data To examine the role that the scrap value plays in determining the price of silver items sold at auction, along with any possible opportunities for riskless arbitrage, we construct a unique database from the catalogues of 88 silver auctions from two major En- glish auction houses, Bonhams, and Woolley and Wallis, between Auctioneer's spread (High estimate-Low estimate)Low estimate) Age of lot (years) Order of lot in the auction Dummy (1 if notable 20th century maker: 0 otherwise) Dummy (= 1 if notable pre-20th century makers: O otherwise) Dummy (1if provenance: 0 otherwise) Dummy (1 if armorial; 0 otherwise) Dummy (1if London assay office: 0 otherwise) New Bond Street Obs. Price Scrap 148 3245.54 281.95 377.16 132 361477 146 3987.33 741.78 61 3179.48 67479 407473 798.47 5035.71 685.61 93 274 3748.17 635.91 72 2750.69 285.49 276 398184 541.78 Woolley and Wallis Salisbury Obs Price 567 828 478.66 920.42 986 684.69 1018 580.38 1080 559.84 956 506.69 1180.00 549.56 1376.00 691.92 1415.00 60724 1464.00 634.33 Scrap 81.93 192.16 288.25 211.68 162.78 116.80 170.31 186.19 186.37 185.68 January 2009 and December 2014. Although no statistics are available for the proportion of antique silver sold by dealers in the UK, informed sources have suggested that, while dealers are responsible for about half of annual sales, auction houses have become more dominant in the market. Bonhams is the third major international UK auction house and the largest seller of UK antique silver by volume over our sample period, and Woolley and Wallis is the UK's largest regional auction house and the second largest seller of UK antique silver by volume. Since it is common for auctioneers to exclude some of the available pre-sale information from the online data (Campos and Barbosa, 2009), copies of the physical catalogues are used. Whilst attempting to be as comprehensive as possible we exclude unsold lots, mixed collections (since it is impossible to assign detailed information to the individual pieces), and lots without a pre- sale estimate. Our final sample contains information on 10,614 sold lots spread across three Bonhams locations, Knightsbridge (30%), Knowle (13%), New Bond Street (6%), and Woolley and Wallis house in Salisbury (51%). In terms of the timing of the silver auctions, Woolley and Wallis hold auctions quarterly, while Bonhams have departed from a fixed schedule in recent years, and closed their knowle salesroom in 2011. Table 1 reports the main descriptive statistics and sample distribution of the dataset described above. 3. A hedonic price model for silver goods To examine the relation between the hammer price and the scrap value of the auction lot, we use the following hedonic pricing 1 Unlike other studies, we do not concentrate on the international auction houses, Christies and Sotheby's, since both rarely hold specialist silver auctions in London over the sample period.