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Bargaining powers of buyers and sellers on the online diamond market: a double perspective non-parametric analysis

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Abstract

This paper investigates the relative efficiency of buyers and sellers on the online diamond market using a non-parametric double-frontier setting. Our data consists in a sample of more than 100,000 round cut diamonds offered for sale online. For a given quality defined by a combination of color and clarity grades, we turn to the free disposal hull model to estimate the sets of efficient diamonds respectively for buyers and sellers in the price-weight space. We find that the average bargaining power of buyers is lower than that of sellers. Regression estimates show that the relative efficiency of buyers is reduced for heavier diamonds and when there are many diamonds of the same quality offered for sale.

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Notes

  1. For recent evidence of geographic price dispersion in retail markets, see for instance Lee (2010).

  2. To explain the online price dispersion, Baylis and Perloff (2002) and Pan et al. (2004) suggest that there exist differences in e-tailer service quality, which may be part of product differentiation strategy.

  3. As emphasized in Lins et al. (2005, p. 95), the DP-DEA method “can possibly be applied to any situation—typically those encountered in auctions—in which there is a game situation where one player aims at maximizing an output which is the input that the other player would like to minimize”. Hadley and Ruggiero (2006) provide an application to final-offer arbitration in major league baseball.

  4. In the price-quality space, Wolff (2014) identifies the set of efficient decision making units using data on French ski resorts. Efficient resorts are located on the outer envelope where price is the lowest for any given quality.

  5. All diamonds have a certificate which is obtained following a professional examination in order to authenticate the diamond’s attributes. While certificates provide unbiased information on each diamond, the issue of biased information on the general state of the diamond market remains an open question.

  6. See the following url: http://www.info-diamond.com/diamonds/loose-diamonds.html. For more detailed information on the various characteristics of diamonds, see http://www.lumeradiamonds.com/diamond-education/glossary. Note that there is no specific information of the end-use of the diamonds. Everyone connecting to the website may buy one or several diamonds offered for sale, meaning that sales are not restricted to jewelry or industrial use.

  7. Several websites presents an average per carat price for different color and clarity combinations for a given shape. See for instance http://www.ajediam.com/diamond_price_calculator.html or http://www.pricescope.com/diamond-prices/round.

  8. Scott and Yelowitz (2010) and Vaillant and Wolff (2013) investigate the impact of diamonds’ characteristics on their prices using both OLS and quantile hedonic regressions.

  9. In our data set, there are less than 100 diamonds offered for sale per color in the P–Z range of colors (whatever clarity). Also, there are 40 color-clarity combinations with zero diamond offered for sale.

  10. For instance, a D-VVS1 diamond is of better quality compared to a E-VVS2 diamond (better color, better clarity), but we cannot rank a D-VVS2 diamond and a E-VVS1 diamond. Banker and Morey (1986) have investigated the use of categorical variables in DEA.

  11. Using a sample of digital cameras sold in Germany, Chumpitaz et al. (2010) find that test statistics lead to a rejection of the convexity assumption in their price hedonic frontier setting.

  12. As emphasized in Farrell (1959, pp. 378–379), “a glance at the world about us should be enough to convince commodities are to some extent indivisible and that many have large indivisibilities”.

  13. All calculations for this study were made using the Stata software. We use the orderalpha command proposed by Tauchmann (2012) to estimate the two sets of efficient units. Detailed codes are available upon request.

  14. Another interpretation is that these diamonds are poor sales that should be disregarded. For that purpose, we further investigate the characteristics of the efficient diamonds located on the lower frontier. For these 37 diamonds, 70.3 % have either excellent or very good cut grade, 78.4 % have either excellent or very good polish, 70.3 % have either excellent or very good symmetry, and 70.3 % have either no or light fluorescence. While these proportions tend to be slightly lower than those found for the 2729 inefficient diamonds (82.8 % for excellent/very good cut shape, 91.9 % for excellent/very good polish, 88.6 % for excellent/very good symmetry, 74.6 % for no/light fluorescence), this comparison shows that most diamonds offering the lowest price for a given weight are not necessarily bad features.

  15. When interpreting the vertical distance between the inferior and superior frontiers, one should consider both the imperfection of the market (in terms of incomplete information for instance) and the likely heterogeneity of the exogenous variables characterizing each observed transaction.

  16. On the one hand, the average bargaining power of buyers is below 35 % for diamonds with slight inclusions (clarity grade of SI3) and slightly tinted white (color grades of I and G). On the other hand, the bargaining power exceeds 0.6 for high-quality diamonds of the type exceptional white \(+\) (color grade of D) and no inclusion (clarity grade of IF) or very small inclusions invisible to the naked eye (clarity grade of VVS2).

  17. As a consequence, buyers will pay on average too much for their purchases and do not behave in an efficient way.

  18. However, the relative efficiency of buyers is also higher for diamonds characterized by color grades of L and M (tinted white or tinted color) and with very very small or very small inclusions (clarity grades of VVS1, VVS2, VS1, VS2). The range of diamonds available for sale in these categories is more restricted.

  19. We thank an anonymous reviewer for this insight. For the sake of robustness, we have also estimated a beta distribution with the mean and scale parameter as functions of carat weight and number of diamonds and reach similar conclusions.

  20. We obtain a very similar negative coefficient (equal to \(-\)0.163 and highly significant) when taking into account the log of price instead of the log of carat weight, which was expected given the very high correlation between price and weight.

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Authors and Affiliations

  1. LEMNA, Université de Nantes, BP 52231, Chemin de la Censive du Tertre, 44322, Nantes Cedex, France

    François-Charles Wolff

  2. INED, Paris, France

    François-Charles Wolff

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  1. François-Charles Wolff
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Correspondence to François-Charles Wolff.

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We are indebted to two anonymous reviewers for many insightful comments and valuable suggestions on previous drafts.

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Wolff, FC. Bargaining powers of buyers and sellers on the online diamond market: a double perspective non-parametric analysis. Ann Oper Res 244, 697–718 (2016). https://doi.org/10.1007/s10479-016-2160-1

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