The Market for Sculptures: an Adjacent Year Regression Index Marilena Locatelli-Biey Department of Economics University of Torino - Italy E-mail: locatell@cisi.unito.it Roberto Zanola Department of Public Policy and Public Choice - Polis Corso Borsalino, 50 – 15100 Alessandria - Italy E-mail: zanola@sp.unipmn.it ABSTRACT: This paper analyses the performance of an investment in sculptures during the period 1987-1995 by applying the hedonic price technique with time dummy variables to a sample of over 27,000 sales occured at auctions. The main finding is that the trend of the rate of return on an investment in sculptures is more stable than those associated to alternative forms of investment during the analysed period. JEL Classification Numbers: C5, Z1. Key Words: Auction; Hedonic Price; Sculpture; Return. 1 Introduction Sculpture is the art of producing in three dimensions representations of natural or imagined forms and it embraces a variety of construction-techniques as well as a variety of materials 1 . The most important classi…cation of sculpture is based on the raw material used, but it is also important the size, the function, and the period of the production. The market for sculptures has characteristics that make it di¤erent from other markets for collectibles. Although similar to the market for paintings, the market for sculptures is smaller than it, with about 3-5 per-cent of total collectibles sold at auctions. A number of reasons explain this, such as technical di¢culties and the high costs of production as well as the fact that sculptures need appropriatespaces to be placed or because of the lower number of sculpture collectors than painting collectors [Locatelli-Biey and Zanola, 1999a]. The purpose of this paper is to examine the investment value of sculptures. Although there are a number of studies that have investigated the investment valueof collectibles, such aspaintings [Anderson, 1974; Stein, 1977; Buelens and Ginsburgh, 1993; de la Barre et al., 1994; Chanel, 1995; Chanel et al., 1996; Mossetto and Lazzaro, 1996; Agnello and Pierce, 1996; Candela and Scorcu, 1997; Renneboog and Van Houtte, 1998; Agnello and Pierce, 1998; Locatelli- Biey and Zanola, 1999b], prints [Pesando, 1993], violins [Ross and Zondervan, 1989], wine [Nerlove, 1995; Combis et al., 1997], antique furniture [Graeser, 1 The raw material depends on the construction technique. Hand modelling uses terracotta, or raw material that allows to produce glazed ceramics. Casting is an ancient technique which uses bronze. Carving is performed by using a number of di¤erent materials, such as marble, stone, wood, ivory, bone, and, more recently, plaster and resin. 1 1993], photos [Pompe, 1996], to our knowledge this it is the …rst time that the performance of sculptures as …nancial assets is studied. This study applies the hedonic price technique 2 with time dummy variables which allows price indexes for sculptures and shadow values for characteristics to be simultaneously estimated. Data are drawn from auctions hold during the period 1987-1995, as compiled by Mayer International Auction Record on CD-Rom. The remainder of this paper is organised as follows. Section 2 brie‡y outlines the methodology of the hedonic technique. Section 3 de…nes the empirical speci…cation of the model. Section 4 describes the data set used, which is compiled from Mayer International Auction Records on CD-Rom. Section 5 summarises the basic …ndings. Conclusions are drawn in Section 6. 2 See Gordon (1990); Griliches (1990); and Triplett (1990). 2 2 Methodology The approach used to estimate a price index for sculptures is the hedonic price technique as developed in similar studies analysing the investment value of collectibles. The hedonic approach involves the estimate of the implicit prices to each characteristic included in the equation by allowing to control for possible non-temporal determinants of price variations. A set of j-characteristics, x jkt, with j = 1;:::n; are identi…ed for a regression of the price of the sculpture k, with k = 1;:::;m, sold in year t, with t = 1;:::;T; on its j-characteristics, such that: lnp kt = ¯ 0 + T¡1 X t=1 ¯ t z t + n X j=1 ° j x jkt + " kt (1) where lnp kt is the logarithm of the price of sculptures sold in year t; z t is a dummy equal to 1 when a sale occurs in year t, 0 otherwise; ¯ 0 ;¯ t and ° j are coe¢cients to be estimated, where ° j is the implicit price; " kt is the random error term, with " s N (0; P k -I T ). Two observations are necessary. First, an implicit assumption in (1) is that the social valuation of sculpture characteristics does not change over time given the shortness of the analysed period. Secondly, the model is speci…ed in semi-log transformations in order to handle the severe skewness in auction prices. Transforming the dependent variable, enables us to use ordinary least squares estimators without having to worry about the sensitivity of the results to skewness. Based on hedonic regression equation (1), a number of price indexes can be computed 3 . In this study we adopt the adjacent year regressions index, which implicitly weights each observation equally [Berndt et al., 1995]. 3 In this respect, we are only considering sculptures as …nancial assets, without any refer- 3 By subtracting from the logarithm of the auction price the implicit prices given to speci…c characteristics, the characteristic-free price of sculpture k in year t is equal to: z kt = lnp kt ¡ n X j=1 ° j x jkt (2) Given the functional form of equation (1), the annual return on a ‘standardised sculpture’ [Buelens and Ginsburg, 1993] may be written as: ¯ t = 1 m t X z kt (3) Setting the price index at time t equal to 1, the price index at time t+1 is given by exponentiating the coe¢cient associated to the time dummy variable from adjacent year regressions. De…ne I t the price index at time t, the adjacent year regression index is: I t+1 = I t (1 + ³) (4) where » is equal to e ( b ¯ t+1 ¡ b ¯ t ) ¡1: ence to their psychic returns [Baumol, 1986; Frey and Eichnberger, 1995; Santagata, 1998; Czujack, 1997]. 4 3 Functional Form The hedonic regression framework takes into account the e¤ect of heterogeneity on prices by controlling for a number of di¤erences in characteristics among sculptures. The dependent variable is the logarithm of sale price, de‡ated and reduced by 15% to correct for transaction fees charged by auction houses to sellers. The independent variables are classi…ed as follows: ² Production Available data do not allow us to distinguish between di¤erent schools. However, as suggested by some auction experts contacted by us, three di¤erent periods of production may be identi…ed: old, for sculptures produced before 1800; mod, for sculptures produced between 1801 and 1930; and cont, for sculptures produced after 1931. ² Nationality Using the frequency with which the sculptors’ nationalities appear in the data set, the following dummy variables are introduced: France, natf; Usa, natus; Germany, natd; Italy, natit; and Great Britain, natgb: ² Size There is no standard measure of size due the variety of construction techniques 4 . In what follows, for each observation we use the highest dimension value (width, length, thickness), size, as a proxy for volume. ² Media A set of dummy variables is used: bronze, bro, and marble, mar, are the traditional raw materials used, expecially for old and modern sculptures, while resin and plaster, res, are used in contemporary sculp- tures. Finally, given the high number of sculptures of this kind, also ivory, ivo, and terra-cotta, ter, are considered. 4 For instance, there are sculptures in the round, which can be viewed from any direction, as well as incised relief, in which the lines are cut into a ‡at surface. 5 ² Salerooms and Cities of Sale Sotheby’s, soth, and Christie’s, chr; are known to be the leading auction houses in this kind of transactions. Their overall performances di¤er only slightly. The most important sculptures auction’ markets are New York, ny, London, lon, and Paris, par. A further city is introduced, Rome and Milan, rom, given the importance of the Italian market for arts. ² Masterpieces In order to take into account the most valued sculptors, fol- lowing Pesando (1993), dummy variables proxy the masterpiece portfolio of the top 20 percent of sculptures by prices, top20, as well as the inex- pensive portfolio, low20; the remainder is assigned to the middle market, mid20. ² Period: a set of dummies, d, is introduced for each year between 1987 and 1995. Formally, our speci…cation is given by: lnp = ¯ 0 + ¯ 1 old + ¯ 2 mod+¯ 3 natf +¯ 4 natus+¯ 5 natd+ ¯ 6 natit + ¯ 7 natgb +¯ 8 size + ¯ 9 bro +¯ 10 mar + ¯ 11 res + ¯ 12 pla + ¯ 13 ter + ¯ 14 ivo +¯ 15 soth + ¯ 16 chr +¯ 17 ny +¯ 18 lon + ¯ 19 par +¯ 20 rom + ¯ 21 top20 + ¯ 22 low20 + 30 X j=23 ¯ j d j + " (5) 6 4 Data The data used in this paper are drawn from auctions hold during the period of time 1987-1995. The source of this data is the 1995 edition of the Mayer International Auction Records (MIAR) on CD-Rom, which contains records of 27119 sculptures sold at the world’s major auctions 5 . For each sculpture in the data set, a number of informations are provided. Prices are gross of the buyers’ and sellers’ transaction fees paid to auction houses and are recorded in four di¤erent currencies. No informations is provided on the origin of the sculptures and exhibitions of the sculptures. For the sake of simplicity, we assume that all sales occur at the end of each period. All sculptures are priced in US. dollars, de‡ated by using the US. consumer price index (1990 = 100) 6 to remove the general trend of in‡ation. Prices are 15% less to correct for transaction fees charged by auction houses to sellers, but as in most studies, we do not take into account storage and insurance costs. Summary statistics of the sample are displayed in Table 1. [TABLE 1] 5 Even if auction records alone do not re‡ect the entire market - since auction houses have little incentive to sell out of fashion sculptures and, besides, ‘bought in’ works may in‡ate prices [Goetzmann, 1993] - it is not clear whether prices are biased upwards or downwards [Agnello and Pierce, 1998]. 6 Source: The Fedaral Reserve Bank. 7 5 Results Following Berndt et al. (1995), since heteroscedasticity may be present, stan- dard errors and variance-covariance matrices of the coe¢cients have been com- puted by using the White (1980) heteroscedasticity-robust procedure. Table 2 displays the main results obtained in the hedonic regression. [TABLE 2] In almost all cases the coe¢cients are signi…cantly di¤erent from zero at 5 per cent or even at 1 per cent probability level. The coe¢cients associated to each kind of independent variable can be used to rank sculptures according to the price of a ‘normalised’ sculpture, that is, the price of a sculpture when all the other variables are assumed to be at a standard level. Sculptures produced before 1800 are the most pro…table due to the scarcity of oldest sculptures, while those produced after 1930 performs worse than sculp- tures produced between 1801 and 1930. As to nationality, the German, the En- glish and the Italian sculptors secure the highest prices. Prices are increasing in size, as in the case of paintings [Buelens and Ginsburg, 1993; Chanel et al., 1996; Agnello and Pierce, 1996; Candela and Scorcu, 1997; Renneboog and Van Houtte, 1998; Agnello and Pierce, 1998]. The most expensive media is marble due to the high cost of production, as well as technical di¢culties in producing sculptures by using this media. By contrast, other media display negative coe¢cients, even if bronze and resin are not statistically signi…cant. Prices recorded at Sotheby’s are higher than those at Christie’s, and New York is the city where prices of sculptures are the highest. By generalising Pesando’s analysis of the market for prints, a possible reason for this is due to New York’s capacity to attract high quality sculptures because the bidder 8 audience is truly international. Finally, masterpieces perform better than mid- dle market artists; by contrast, inexpensive portfolio works perform worse than middle market portfolio. The set of dummy variables introduced for each year between 1988 and 1995 is used in equation (4) to build the adjacent year regressions index for sculptures, which is reproduced in Table 3. [TABLE 3] A market shock characterises the period 1987-1995 covered by the data-set, since after a boom period until 1990, the market for collectibles registers a non-boom period from 1991 to 1994. The rate of return of an investment on sculptures seems to follow the trend of the rate of return on paintings during the same period of time [Candela and Scorcu, 1997; Locatelli-Biey and Zanola, 1999b]. Rates of return arepositive until 1990, followed by a negative trend from 1991 to 1994, with a positive sign in 1995, but still lower than the price index 1987. However, the trend of the performance of an investment in sculptures is lower than those associated to alternative forms of investment. Figure 1 compares the de‡ated index for sculptures with the de‡ated indexes of real returns on US stocks, US 30 year government bonds and gold. [ FIGURE 1] During the boom period investments in sculptures earned lower real returns than US stocks, US 30 year government bonds, and gold, forms of investment characterised by a comparable degree of risk. However, starting from 1991, re- turns on sculptures decrease, but at a lower rate than other kinds of investment. This result may be due to the characteristics of the market for sculptures, as illustrated in Section 1. In fact, the demand for this kind of collectibles is ex- pected to be rather inelastic, so that the returns on sculptures are not so much a¤ected by boom and non-boom periods. 9 [...]... price indexes 200,00 175,00 150,00 125,00 100,00 75,00 50,00 25,00 0,00 1987 1988 1989 Sculptures 1990 Gold 1991 1992 D.J Stocks 17 1993 U.S 30Y Bonds 1994 1995 Working Papers The full text of the working papers is downloadable at http://polis.unipmn.it/ * Economics Series **Political Theory Series 2000 n 15* Marilena Locatelli-Biey and Roberto Zanola, The Market for Sculptures: An Adjacent Year Regression. .. economics and the social sciences; • quantitative methods applied to economics and the social sciences; • game theory; • studies on social attitudes and preferences; • political philosophy and political theory; • history of political thought The Department has regular members and off-site collaborators from other private or public organizations 19 Instructions to Authors Please ensure that the final... numerals Acknowledgements and information on grants received can be given in a first footnote (indicated by an asterisk, not included in the consecutive numbering) Ensure that references to publications appearing in the text are given as follows: COASE (1992a; 1992b, ch 4) has also criticized this bias and “ the market has an even more shadowy role than the firm” (COASE 1988, 7) List the complete references... 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