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The Quarterly Review of Economics and Finance 51 (2011) 212–224

Contents lists available at ScienceDirect

The Quarterly Review of Economics and Finance

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model for pricing Italian Contemporary Art paintings at auction�

icoletta Marinelli a,b, Giulio Palombaa,∗

Department of Economics, Università Politecnica delle Marche, Piazzale Martelli 8, Ancona 60121, ItalyDepartment of Management, Faculty of Economics, Università di Roma “La Sapienza”, via del Castro Laurenziano 9, Roma 00161, Italy

r t i c l e i n f o

rticle history:eceived 3 September 2009eceived in revised form 6 December 2010ccepted 23 February 2011vailable online 5 March 2011

a b s t r a c t

The aim of this paper is to model painting prices at auction. The novel aspects of our contribution areas follows: first, the set of regressors used as explanatory variables in the hedonic regression is widerthan those previously employed in the literature. Second, we consider the selection bias arising from thepossibility of unsold items. Finally, a model including pre sale evaluations by experts is also estimatedwhich allows us to evaluate their information content.

To do so, we use the Heckit model exploiting a unique dataset of 2817 Italian Contemporary Art painting

eywords:ainting pricesuctionseckit modelelection biasre sale evaluations

transactions which took place at auction worldwide between 1990 and 2006.Our results suggest that auction prices depend upon four sets of regressors (artist identity, physical,

artistic and sale characteristics of the painting); moreover, auction house, marketplace and year of saleseem to be crucial in getting artworks sold. Pre sale estimates seem to be a good predictor of painting pricesbut the hypothesis of their sufficiency is rejected and problems regarding the economic interpretation of

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the existing literature are as follows: first, we use a set of regressors

tatistical sufficiency the results arise.© 2011 The Board of Tru

. Introduction

The key objective of this paper is to model painting prices at auc-ion. Painting prices depend upon a set of variables related to theharacteristics of the works themselves as well as other aspectsore difficult to measure, such as the artist’s popularity or the

uction house’s prestige.Two main theories have been proposed in the literature regard-

ng art prices: on the one hand, Baumol (1986) claims that artworkrices float more or less aimlessly with unpredictable oscillationsmphasised by the activities of investors/speculators, so an equilib-ium price for artworks may not exist; on the other hand, Frey andommerehne (1991) maintain that supply and demand determinertwork prices, as for any other economic good, although a “nat-ral price” does not exist for paintings. From the empirical pointf view, the pricing of paintings is generally discussed within the

ramework of market price indices with the aim of evaluating theireturns. In this context, the most important indices are those basedn expert judgement, such as the Sotheby’s Art Index, the averageainting methodology (Stein, 1977) or its improved version known

� We are very grateful, without implicating them for errors, to Lloyd Blenman,aterina Lucarelli, Riccardo Lucchetti, Alberto Niccoli and GianMario Raggetti forheir helpful comments and suggestions.∗ Corresponding author. Tel.: +39 071 2207112; fax: +39 071 2207153.

E-mail addresses: nicoletta.marinelli@uniroma1.it (N. Marinelli),.palomba@univpm.it (G. Palomba).

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062-9769/$ – see front matter © 2011 The Board of Trustees of the University of Illinoisoi:10.1016/j.qref.2011.02.001

of the University of Illinois. Published by Elsevier B.V. All rights reserved.

s the representative painting (Candela & Scorcu, 1997), the repeatales regression (Goetzmann, 1993; Locatelli-Biey & Zanola, 1999;ei & Moses, 2002; Pesando & Shum, 1999), the hedonic regres-

ion (from Anderson, 1974 onwards)1 and the hybrid approach (seeocatelli-Biey & Zanola, 2005).

Of the methods developed to evaluate the rate of return ofn artwork investment, the hedonic regression approach makest possible to identify the most relevant explanatory variables foretermining art prices. Essentially, the approach is to gather priceata on art sales across time (generally from auction sales) and toegress the price of each work on some observable characteristicsf the painting, such as the artist identity, the size of the painting, itsedium and support. The estimated coefficients can be interpreted

s the “shadow prices” of each attribute.From this perspective, the novel contributions of our paper to

hat is wider than those previously employed in hedonic regres-ion. Considering that the explanatory variables used in previoustudies have generally referred to physical attributes of paintings,2

1 See also Frey and Pommerehne (1991), Buelens and Ginsburg (1993), Chanel1995), Ginsburgh and Jeanfils (1995), Agnello and Pierce (1996), Chanel, Gérard-aret, and Ginsburgh (1996), Czujack (1997), Agnello (2002), Renneboog and Vanoutte (2002), Hodgson and Vorkink (2004), Figini and Onofri (2005), Higgs andorthington (2005) and Worthington and Higgs (2006).2 Only a few studies have considered variables other than physical charac-

eristics: for example, Czujack (1997), Wieand, Donaldson, and Quintero (1998)

. Published by Elsevier B.V. All rights reserved.

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e extend the analysis to different categories of regressors thatre artist identity, physical characteristics of the paintings, artisticharacteristics and characteristics of the specific sale (see Sec-ion 2.1). Second, we improve the traditional hedonic regressionpproach by taking into account the possibility that an item mighto unsold. In the standard auction procedure, the seller indicates aeserve price that corresponds to the minimum price at which thetem can be sold; if the highest bid is lower than the reserve price,hen the painting goes unsold or bought-in: in this case, the price ofaintings may be affected in the future (see Beggs & Graddy, 2006).inally, we try to enhance our analysis by including pre auctionstimates in the price model. Specifically, we propose a functionf such pre sale estimates in order to evaluate their impact uponrices and information content.

To do so, we use a unique dataset relative to Italian Contempo-ary Art paintings thus providing an empirical contribution for aector that the literature has often neglected, despite the globalelevance of Italian Contemporary Art.3 This is also useful foromparing the Italian market to others, especially those with aomparable cultural ancestry and market structure.

The remainder of the paper is organised as follows: in Section 2e discuss the sample selection and our proposed function of pre

ale evaluations; the empirical analysis is carried out in Section 3,hile in Section 4 the information content of pre sale evaluations

y experts is discussed. Section 5 concludes. Finally, Appendices And B include all the estimates and the complete list of the availableariables.

. The sample

The dataset consists of 2817 painting transactions that tooklace between 1990 and 2006 in 19 different auction houses world-ide (see Appendix B for the complete list of artists, marketplaces

nd auction houses). All information is taken from “Artindex Plus”,detailed database which contains catalogue information about

everal artworks.4

The artists to be included in the sample were specificallyelected: this was crucial in order to avoid problems in the inter-retation of the results. Strictly speaking, no piece of artwork isomparable with another. As a consequence, a comparison cannly yield valid results when made between (unique) items thatre considered as being as homogeneous as possible. Discussionsith various art experts led us to conclude that an economic anal-

sis of auction prices best represents the real situation of the artarket when it focuses upon a selected group of artists, whoseorks may be considered as comparable. In particular, the main

uggestion proposed by experts was to concentrate upon a spe-

ific artistic period and upon a specific country; the reason is that,ven if the main factors affecting price are the same for the differ-nt segments of the art market, each one has its own specific ruleshat differentially affect the price. Here, we focus upon a sample of

nd Figini and Onofri (2005) take the previous ownership of the painting andts presence in exhibitions into consideration, while Wieand et al. (1998) andigini and Onofri (2005) use the work’s citations within the artistic literature.3 From 1990 to 2006 the percentage of Italian Contemporary Art paintings traded

n foreign markets is 59.14% (source: Artindex Plus - Gabrius S.p.A.). Neverthe-ess, only Candela and Scorcu (1997) use data about the Italian market of Modernnd Contemporary oil paintings; in their contribution, however, foreign paintersere also considered since the dataset included transactions of Modern and Con-

emporary Art paintings auctioned in Italy by “Casa d’Aste Finarte” in Rome andilan.4 Artindex Plus is provided by Gabrius S.p.A. operating in Milan and belonging to

he Munus Culture Holding (AMB network). The data on auction sales before 1990re very poor and incomplete, so they are excluded from our analysis. For moreetails see http://www.munusartinvest.com.

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Economics and Finance 51 (2011) 212–224 213

talian contemporary artists, and the other markets (“Old Master”,XIX Century”, “Modern Art”) will not be analysed.

Nevertheless, according to art experts, Italian Contemporary Arts not a homogeneous sample at all: in practice, there are differ-nces between “emerging” and “historical” contemporary Italianainters. The inclusion of “emerging” contemporary artists in theample could have produced ambiguous results;5 moreover, itould have increased the overall bias due to buy-in because theaintings made by this category of artists are, on average, more

ikely to go unsold at auction (the buy-in rate for “emerging” con-emporary artists is generally higher at auction). As a consequence,e considered the 21 Italian contemporary artists who, accord-

ng to Sacco, Santagata, and Trimarchi (2005), showed the biggesturnover at the most important international auctions during theeriod 1998–2002.6 Homogeneity in our sample is also preservedy the exclusion of prints and drawings because these items haveheir own specific price dynamics, as examined by Holub, Hutter,nd Tappeiner (1993), and are often traded in separate sessions atuction.

A second problem encountered in studying art prices stemsrom the fact that the auction data samples can suffer from someroblems of selection bias, as already underlined by Wieand et al.1998). It is well known that the art market is divided into “pri-

ary”, “secondary” and “auction” markets: in the primary markethe artist personally sells her works, while in the secondary marketalleries and art dealers trade paintings with private or institutionalollectors. The primary and secondary markets are the channelsenerally preferred by young/emerging artists; on the other hand,aintings with “extreme” prices, generally bought by museums,xit the market and are not traded at auction anymore. Therefore,ome paintings are less likely than others to be traded at auction.evertheless, in this case public information exists and this over-omes most of the typical problems that arise due to incompletend asymmetric availability of information about the art market.oreover, auction prices affect the art market because collectors

nd professional art dealers take these prices as guidelines, as it haseen convincingly argued by Frey and Pommerehne (1989). Finally,e also consider auction prices as adequate approximations of true

quilibrium prices, as suggested by Candela and Scorcu (1997).

.1. The variables

The dependent variable of our model is the auction price of eachainting. In our dataset the hammer price (ph

i) and the total pur-

hase price (pti) are available: the latter differs from the former

ecause it includes the auction house’s transaction fees. Even if fouralues of total purchase price are missing, the two variables are in

ractice identical to each other because the correlation betweenhi

and pti

is 0.9997; hence, in Sections 3 and 4 only the results forammer prices (in logarithms, yh

i) will be presented.

5 For example, catalogues play a promotional role for “emerging” art painters,hereas they provide a guarantee of authenticity with respect to “historical” con-

emporary painters; this implies that only with regard to “historical” contemporaryainters can catalogues lead to an increase in the prestige of a painting and, conse-uently, affect auction price.6 Sacco et al. (2005) define the “turnover” as the number of sold works multiplied

y their mean price. Moreover, they conventionally define Italian contemporaryrtists as those Italian painters who carried out their activities after 1960. However,his selection criterion was not strictly applied: a few Italian painters who weretill working after 1960 were not included because they are widely considered aselonging to Futurism art or to other artistic groups that preceded the 1960s. Thisas the case, for example, for Carlo Carrà. According to Sacco et al. (2005), the

talian Contemporary Art conventionally starts with the contributions of Fontana1899–1968), Burri (1915–1995), Marini (1901–1980) and Manzoni (1933–1963).

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rhis larger than that of the buyers F (F ⊂ I) and that the experts aimto minimise the expected value of a cost (loss) function L( · ). It is

14 N. Marinelli, G. Palomba / The Quarterly Rev

The explanatory variables for the price of Italian Contemporaryrt paintings are organised into four categories (see Appendix B foretails). Given the qualitative nature of most of the available data,everal variables are dichotomic.

.1.1. PaintersWe include the name of the artist, their living status and the

ear of birth. According to Grampp (1989), the name of the painters an essential attribute since it provides information about theainting itself, such as style and subject (also see WorthingtonHiggs, 2006). Moreover, Higgs and Worthington (2005) suggest

hat, all else being equal, the price of an artwork is often expectedo increase once an artist has died.

.1.2. Physical characteristicsThis includes different aspects related to the execution of the

rtwork. The characteristics can be divided into three categories:edium, support and size. Size is expressed as the surface area in2 and squared surface area, as in Czujack (1997), Renneboog andan Houtte (2002), Higgs and Worthington (2005) and recently inanola (2007). Table B.2 contains the complete list of artwork phys-cal characteristics. By following Czujack (1997), who describesainting prices as a concave function of their physical dimensions,e would expect to find a positive relationship between the price

f a painting and its area and a negative sign for the coefficientf its squared surface area. Furthermore, it has been suggested byhe literature that oil paintings are more expensive than artworksreated using other media.

.1.3. Artistic characteristicsThese variables can be considered as proxies for the prestige

nd the popularity of an artwork (see Table B.3). This category haseceived little attention so far in the literature, as recently pointedut by Campos and Barbosa (2008), and is thus particular to ourample.

Some variables are qualitative: authentication by the artistauthentic), publication in catalogues or monographs (catalogue)nd recognition by experts (expertise) are all of interest to theotential buyer as they help them establish the authenticity of theork and, in turn, reduce the risk of buying a fake;7further pieces of

nformation could be citations in literature (literature), artwork titlend date and whether the artist’s signature is present or not. Twoiscrete variables are also included: the first variable is the numberf exhibitions the painting has taken part in (exhibitions). Unfortu-ately, the available data do not allow us to distinguish betweenifferent types of exhibitions (such as permanent or temporary,olo or group exhibitions). The effect of the number of exhibitionsn the eventual auction price is hard to establish a priori. On thene hand, works that have been exhibited often are likely to com-and a higher price. On the other hand, a painting belonging to a

rivate collection, which has not been seen for a long time, couldlso be attractive to collectors and reach a very high price. The sec-nd variable is the number of previous owners (owners), which isommonly believed to affect the price of a painting. The datasetoes not allow us to classify all previous owners according to their

nstitutional nature (for example, museum, gallery or private col-

ector) because it only provides the names of previous owners. Wese this variable in order to test whether a painting that has rarelyeen traded in the auction market reaches a higher price than aainting that has often been put on sale (see Fiz, 1995).

7 For example, Alighiero Boetti’s works have no market value if they are notccompanied by an authentication since the number of fakes is high for this artist.

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Economics and Finance 51 (2011) 212–224

.1.4. Sale characteristicsThis set of explanatory variables (see Table B.4) includes sev-

ral dummies for auction house, marketplace, year and monthf sale. As regards auction houses, the law of one price dic-ates that, in the absence of transaction costs, no significant priceifference should exist between paintings of similar quality. How-ver, Pesando (1993), De la Barre, Docclo, and Ginsburgh (1994),enneboog and Van Houtte (2002), Hodgson and Vorkink (2004),iggs and Worthington (2005), among others, show that Christie’snd Sotheby’s systematically obtain higher hammer prices as a con-equence of the leading role played by both institutions in thisusiness. Since some auction houses have offices worldwide, weccount for 18 different marketplaces (see, among others, Czujack,997; Figini & Onofri, 2005; Renneboog & Van Houtte, 2002). Con-idering sale year and month, we aim to catch some possible timeffects in the price formation of paintings (see Agnello & Pierce,996; Worthington & Higgs, 2006).

The use of pre sale evaluations as explanatory variables deservespecific discussion. Before an auction takes place, experts usu-lly estimate the potential market value of the painting. Sincealesrooms provide pre sale estimates as a range, the maximumnd minimum potential prices are known in advance. These datarovide information on the expected hammer price and on theeller’s reserve price,8 so it is conceivable that their availabilityay affect the transaction. We define Mi and mi as the logarithmic

ransformations of these potential prices to make them compa-able with the dependent variables. The relationship betweenrt prices and pre sale estimates is discussed in the followingection.

.2. Auction prices and pre sale estimates

One branch of art research focuses upon the relationshipetween art prices and pre sale estimates provided by auctionouses. Most of the research has been concerned with the biasf these estimates and opinions differ widely. Ashenfelter (1989),ouargand and McDaniel (1991) and Abowd and Ashenfelter2002), among others, show that pre sale estimates are usuallyood predictors of hammer prices. In contrast, many authors haverovided empirical evidence of a systematic bias of pre sale esti-ates (see, for example, Bauwens & Ginsburgh, 2000; Beggs &raddy, 1997; Ekelund, Ressler, & Watson, 1998; Mei & Moses,005; Sproule & Valsan, 2006). Most of the above cited contri-utions use the midpoint as a proxy for pre sale evaluations. Anxception is Bauwens and Ginsburgh (2000), where the value ofhe range is specified as a weighted average of the low and highre auction estimates. Sproule and Valsan (2006) provide a dif-erent perspective: they investigated the predictive power of preuction estimates compared to that of the hedonic model by usinghem as instrumental variables for the hedonic regression in whichhe hammer price is the independent variable.

Obviously, the mental process by which experts provide theange [mi, Mi] cannot be observed; therefore, some hypothesesave to be made. We suppose that the experts’ information set I

easonable to assume that the loss function depends on the seller’seserve price and on the Mi − mi difference, which would under-ine the experts’ credibility if too large. Forming more detailed

8 In particular, it is well recognised that the seller’s reserve price is related to theinimum potential price as pointed out, for example, by Ashenfelter and Graddy

2003).

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ypotheses on the loss function would be essentially arbitrary,9

hus we need to specify a functional form for fi = arg min {E[L( · )]}hich has to be reasonably general and easy to estimate; more-

ver, fi could be a sufficient predictor of auction prices if it capturesll the available information, that is L(yh

i|F, fi) = L(yh

i|I).

In this setup it follows that if experts have rational expec-ations and a quadratic L( · ) the conditional mean E(yh

i|I) is the

est predictor for minimising E[L(yhi

− fi|I)]. Obviously, it is alsosufficient predictor if, using the law of iterated expectations,

(yhi|F, fi) = E(yh

i|I).

As the statistical properties of the experts’ loss function are alsonknown, we suppose that fi depends upon the first and secondoment which can be approximated by the midpoint (�i) and by

he spread (di) of the pre sale estimates respectively. By defining Ris

i =[

0.5 0.5−1 1

][mi

Mi

]=

[�i

di

], (1)

e can use a third-order Taylor expansion

i = f ′i � = [ R′

i(Ri ⊗ Ri)

′+ (Ri ⊗ Ri ⊗ Ri)

′+ ]

⎡⎢⎢⎣

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�s(3×1)

�c(4×1)

⎤⎥⎥⎦ , (2)

here ⊗ indicates the Kronecker product and the ()+ operator isnderstood to remove all duplicate elements.10

. The model

Our aim is to model the auction prices of Italian Contempo-ary Art paintings by considering the possibility of unobserved finalrices; in other words, we take into account the “buying risk” affect-

ng each transaction, thus a distinction between sold and unsoldaintings will be considered in our analysis. In Section 4, we addunction (2) to the set of regressors in order to evaluate the rele-ance of pre sale estimates and their information content.

.1. The Heckit model

From the statistical point of view, the possibility that items gonsold at auction implies a problem of selection bias which canrise from censoring. In order to address this problem, we usehe so-called Heckit model (Heckman, 1979); this method wasntroduced to correct the selection bias occurring in nonrandomlyelected samples and provides consistent estimates which elimi-ate the specification error in the case of censored data. Recently,anola (2007) used this method on a sample of Picasso prints cen-

ored for repeat sales, as did Collins, Scorcu, and Zanola (2007,009) on a sample of Symbolist paintings.

9 For example, the loss function may be asymmetric: in our sample, yhi

< mi 498imes (25%) and yh

i> Mi 684 times (34.4%).

10 For example, for the second-order term

Ri ⊗ Ri)+ = D+N

(Ri ⊗ Ri),

here

+N

=[

1 0 0 00 0.5 0.5 00 0 0 1

].

s the Moore–Penrose inverse of the duplication matrix for N = 2. See Magnus andeudecker (1988) for details.

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Economics and Finance 51 (2011) 212–224 215

Analytically, our Heckit model is

s∗i

= z′i� + ui i = 1, 2, . . . , N

yhi

= x′iˇ + εi ⇔ s∗

i> 0,

(3)

here N is the sample size. The first equation is the “selection equa-ion”, where s∗

iis a latent variable which is positive if the auction

rice is greater than the reserve price. Moreover, the 1 × K vector z′i

ontains the individual characteristics that determine whether theainting is sold or not, � is a vector of unknown parameters and ui

s a random disturbance. The latent variable s∗i

is not observed; aichotomic variable si for sold/unsold paintings is observed instead.

The second equation of the system (3) represents the “pricequation” which is the linear model of interest; yh

iis the dependent

ariable, xi is an M-dimensional vector of exogenous variables, ˇ isvector of unknown parameters and εi is a random error term. Thexplanatory variables in xi could also be included in zi and vicev-rsa. Moreover, we assume that the random disturbances are i.i.d.nd jointly distributed as

ui

εi

]∼N

([00

],

[�2

u �uε

�uε �2ε

]). (4)

In our model, selection bias arises because the price yhi

is onlybserved when the i-th painting is sold (therefore si = 1); if �uε ison-zero, Heckman (1979) shows that OLS estimation yields biasednd inconsistent estimates of ˇ. Model (3) is estimated by Maxi-um Likelihood (ML), which jointly returns the estimates of both

he selection and the price equation and guarantees consistencynd asymptotic normal efficiency (see for example Greene, 1981).n this context, the price equation can be thought of as a sort ofedonic regression in which the potential sample selection biasas been corrected by inserting an additional regressor providedy the Inverse Mills Ratio �i = (z′

i�)/(z′

i�), where ( · ) and ( · )

re respectively the density and the cumulative density of the stan-ardised Gaussian.

.2. Model specification

As shown by Pagan and Vella (1989), the Heckit estimator isenerally inconsistent if the normality assumption fails. Follow-ng Davidson and MacKinnon (1993), we carried out a conditional

oment (CM) test for normality, based on the Outer Product Gra-ients (OPG) Regression, as follows:

= ı1Z + ı2G + residuals, (5)

here � is a vector of ones, Z is the matrix whose each row is z′iand

ˆ1, ı2 are ML estimates from the probit Pr(si = 1) = (z′iı1). The

-th row of the matrix G is

′i =

[[(z′

i�)2 + 2]ui z′

i�[(z′

i�)2 + 3]ui

], (6)

here ûi are the model generalised residuals (see for exampleagan & Vella, 1989). For each observation, it can be shown that′i

contains the sample counterparts of the orthogonality condi-ions about skewness and kurtosis, that is the conditional moments(uk

i|ui < −z′

i�), when k is 3 and 4 respectively (see Skeels & Vella,

999).The basic idea is that if G′

iis not statistically relevant in the

PG regression, then the above probit model is correctly speci-ed. Hence, the null hypothesis of the CM test is H0 : ı2 = 0 and theest statistic is given by N times the R2 of regression (5). As G has

wo columns, the asymptotic distribution is the standard �2

2. For-ally, the normality assumption should be sufficient to identify

he above model because of the nonlinearity of the Inverse Millsatio, as discussed in Leung and Li (1996) and Puhani (2000); how-ver, when xi and zi have many variables in common, �i may show

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16 N. Marinelli, G. Palomba / The Quarterly Rev

n approximately linear dependency with respect to both of them,o the model will be under-identified for all practical purposes. Inhis case, the Heckit estimation is not credible because the modeluffers from some problems of collinearity (see Puhani, 2000, for aetailed list of the drawbacks of the Heckit model in finite samples).he generally adopted solution is to set some exclusion restrictionsn the price equation by dropping from the price equation a subsetf the variables that show good predicting power in the selectionquation.

Given these premises, different measures are employed to checkor collinearity in our model: the first is simply R2(�i, xi), the coef-cient of multiple correlations obtained via an OLS regression ofhe estimated Inverse Mills Ratio on the explanatory variablesf price equation. The second measure is the standard variancenflation factor VIF(j) = (1 − R2

j)−1

, where R2j

represents the coeffi-ient of multiple correlation between variable j and those includedn xi. Finally, we calculate the condition number (CN) via therocedure provided in Puhani’s (2000) appendix. According toelsley, Kuh, and Welsch (1980), a CN > 30 indicates problems ofollinearity.

.3. Empirical results

The estimation results for yhi

are provided in Table A.1, whileable A.3 contains the regression statistics; all the results are con-rmed by a battery of preliminary estimates that were conductedo check the robustness of the model. Some of the explanatoryariables among those presented in Section 2.1 are dropped tovoid collinearity, while other variables are excluded to reach theaximum possible reduction of parameters, without losing of any

elevant information.11 The sample size reduction is due to 5 miss-ng in surface values, and hence in squares too. All the preliminarystimates and results are omitted for brevity, but are available uponequest from the authors.

The t-statistic for ˆ� indicates that a sample selection mech-

nism is indeed operating and thus that the Heckit model isuperior to OLS. The fact that this coefficient is negative indi-ates that �uε < 0: paintings that go sold are traded for a pricehich is lower than that implied by their characteristics. Theull hypothesis of the CM test is accepted in both cases, whichakes us confident that the selection problem was satisfactorily

ealt with. The reference artist for the “Painters” set of dummyariables is Fontana (VIFFontana=9.631), while the variable dead isxcluded because it is strongly collinear with the variables relatedo painters. Finally, we can conclude that our estimates do not suf-er from any problems of collinearity as VIFs are less than 10 andN < 30.

.3.1. Selection equationOnly the dummy related to the painter Boetti positively con-

ributes to the outcome of artwork transactions. This suggests thathe paintings made by this artist are, on average, less likely to gonsold at auction, thus showing a strong tendency to be easilyraded. Clemente and Gnoli show a relevant negative effect uponales; Burri, Chia, Paladino and Pomodoro produce a feeble andegative effect.

The media and support of a painting do not seem to play a rele-ant role in determining the probability that paintings go sold; onlyhe medium other augments this probability, while the variablenamel has an opposite effect. None of the artistic characteristics

11 Specifically, we observed that collinearity occurs when a high number of phys-cal characteristics are inserted together with all the artistic characteristics.

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Economics and Finance 51 (2011) 212–224

eem to be relevant either (literature, even if significant, has a p-alue very close to the reject region).

On the contrary, the outcome of the sale, in terms of sold/unsoldork, is heavily influenced by the auction house where the sale is

rranged. The findings about Christie’s and Sotheby’s are consistentith those of De la Barre et al. (1994) who argued that some auctionouses are able to systematically influence the successful outcomef the sale since they often attract artistic works of higher value. Theesult of Finarte could be interpreted as a consequence of the “homeias effect”, that is the general preference of buyers for domesticrt production, as pointed out by Candela and Scorcu (2004).

Moreover, the marketplace seems to be relevant because itemsuctioned in London, New York or Milan (over 87% of the sam-le) are more likely to be sold. Preliminary estimates proved thatther auction houses or marketplaces and month of sale do notave any additional effect on the probability of going sold/unsold.ome years affect the outcome of the sale more than others: in par-icular, 1993, 1997, 2001 and 2002 show negative and statisticallyignificant relationships, while 1992 and 2004 have a positive andignificant parameter.

.3.2. Price equationIt is evident from Table A.1 that almost all variables play a signif-

cant role in determining auction prices. The impact caused by theajority of painters seems to be decisive: the negative parameters

uggest that their works generally achieve lower prices than thosechieved by Fontana.

The effect of painting support is heterogeneous because canvaseems to have a significant and positive influence upon paintingrices, while paper has the opposite effect. The variable media wasropped since preliminary analyses found that it did not have anytatistically significant effect. The signs of the coefficients for theariables regarding painting size are as expected and consistentith the findings of Czujack (1997): in particular, the artwork prices

an be described as a concave function in which the surface area andhe squared surface area exhibit positive and negative relationshipsespectively.

With regard to artistic characteristics, authentication by thertist, publication in catalogues, date, number of exhibitions, cita-ions in the literature and the number of previous owners all havepositive effect, while the variable expertise seems, surprisingly,

o have a negative impact. The variable title is dropped to preventollinearity. Finally, signature does not have any effect upon thestimation.

As in the selection equation, the principal marketplaces play aery important role: specifically, london and NY result in increasesn painting prices, while milan does not have a significant effect.uction houses are not included for parsimony as preliminary anal-ses showed that they did not have a significant impact.

Finally, the sale year substantially affects the final purchaserice of Italian Contemporary Art paintings, especially for the yearsetween 1991 and 2004. From the economic perspective, the seriesf these coefficients can be used to build the yearly price index

t, with all other characteristics being equal. This index shows theffect of year of sale upon auction price dynamics; the equations It = 100 · exp{ ˆ t}, where t = 1991, 1992, . . ., 2006. The base years 1990 in which It = 100; the index declines in the first years ofhe sample, it starts to grow in 1994 and only in 2006 does itvertake the base year value (see Fig. 1). This is consistent withhe evidence that the art market experienced a downturn in the

arly ninetees (see, among others, Mei & Moses, 2002) followedy an upturn lasting until June 2008. Various reasons have beenuggested that could explain this cycle, including macroeconomicactors, such as the dependence of the art market upon per capitancome (Frey & Pommerehne, 1991), financial factors, such as the

N. Marinelli, G. Palomba / The Quarterly Review of

Fw

cmt1

4

iahaaiAta

ea

iffikfa

aItTt

ltfspaeficnaiv

(patiafitpmarketable.

ig. 1. Price index for the Italian Contemporary Art paintings (It). The index is plottedith a confidence interval given by 100 · exp {ˇt ± 1.96 · se(ˇt)}.

orrelation between art market cycles and bullish/bearish financialarkets (Chanel, 1995) or simply art fads such as the changing atti-

udes of collectors towards Contemporary Art (Buelens & Ginsburg,993).

. Sufficiency of pre sale estimates

In this section, we insert pre sale evaluations made by expertsnto our analysis in order to test their sufficiency in determininguction prices. Thus, the model estimated in Section 3.3 will beere augmented by including the function fi which takes the preuction range into account. This model can no longer be interpreteds a hedonic regression, but it makes it possible to investigate thenteresting issue of the information content of pre sale estimates.

hedonic regression is no use for this purpose even if modified to

ake the sample selection into account, as it was done in Section 3nd by Collins et al. (2007, 2009).

The function we use is provided by Eq. (2) whose specificationxploits the second and the third power of the variables involved;s already argued in Section 2.2, if the third-order Taylor expansion

cof

0 2

4 6

8 1

-800

-600

-400

-200

0

d i

Fig. 2. Estimated pre sale evaluations fu

Economics and Finance 51 (2011) 212–224 217

s adequate and our hypothesis on the information sets is true, theni should be a sufficient predictor for painting prices. The word “suf-cient” in this context means that, when the pre sale estimates arenown, all other information becomes irrelevant. Furthermore, thisunction is easy to estimate because it is linear in the parametersnd allows us to carry out some hypothesis testing.

Table A.2 reports the Heckit estimates for yhi

taking Eq. (2) intoccount, while the regression statistics are provided in Table A.3.n this case, there are 40 missing values from series mi and Mi plushe 5 unavailable data values in the series surface and squares (seeables B.2 and B.4), hence 45 observations have been dropped fromhe sample.

In the price equation, we found that second and third-order Tay-or expansion terms generate serious problems of collinearity, sohey are dropped from the specification; the function we obtainedrom Eq. (2) is fi ≡ Ri = [ �i di ]′. Our results reveal that average preale estimates play a decisive role in determining the final price,robably due to the positive correlation between painting pricesnd the minimum potential price mi, as recently conjectured, forxample, by Valsan and Sproule (2008). This evidence was also con-rmed by the improvement of the Loglikelihood, the informationriteria and the McFadden R2. On the contrary, the difference di isot statistically relevant. The CM test accepts the null hypothesisgain, while there is no evidence of any other problem of collinear-ty occurring, even if the condition number is around the criticalalue of 30.

Focussing upon the selection equation, the use of the entire Eq.2) can be justified from two points of view: from the statisticalerspective, function fi seems to represent essential informationnd this is also confirmed by a battery of Likelihood Ratio (LR)ests presented in Table A.4. From the economic perspective, paint-ngs that sell easily seem to be those with lower values of �ind di: this evidence, plotted in Fig. 2, is consistent with thendings of Ashenfelter, Graddy, and Stevens (2002) who arguehat a large difference between mi and Mi would signal a highrice variance which, consequently, renders the painting less

It is difficult to give an economic interpretation of the modeloefficients in Table A.2, since they are not comparable with thosef Section 3.3; this problem arises from the possible sufficiency of

i, which has to be discussed and checked.

0 2

4 6

8 100

µi

nction (fi) in selection equation.

2 iew of

h

•

•

•

•

•

•

t2othspbi

prvatbepmba

5

it

egtdimeiFeesistrn

oqacprcaepeest

mwtFtetni

A

18 N. Marinelli, G. Palomba / The Quarterly Rev

Table A.4 also provides several Wald tests in which the nullypotheses are:

� = 0: auction prices do not depend upon pre sale estimates. Inthis context � is a two-dimensional vector;� = �, where � = [ 1 1 ]′: auction prices strictly depend upon boththe average pre sale estimates and the spread di. In this case, fi isan unbiased predictor and ˇ is the impact of xi upon the difference(yh

i− fi);

� = [ 1 0 ]′ ⇒ fi = �i: auction prices strictly depend upon aver-age pre sale estimates only. Vector ˇ provides the impact of xiupon the difference (yh

i− �i);

ˇ = 0: none of the explanatory variables in xi contain any rele-vant information when pre sale evaluations are considered in themodel;� = � and ˇ = 0: auction prices only depend upon �i and di, hencexi does not have any effect upon the difference (yh

i− fi). In this

case, fi is unbiased, efficient and also contains all the availableinformation;fi = �i and ˇ = 0: auction prices only depend upon average pre saleevaluations, as in Beggs and Graddy (1997), Ekelund et al. (1998)and Mei and Moses (2005).

It is also possible to test the “block sufficiency” by simply parti-ioning vector ˇ according to the categories introduced in Section.1; provided that ˇ = [ ˇpainter ˇphysical ˇartistic ˇsale ]′, we carryut 4 separate tests whereby the null hypothesis sets one parti-ion to zero. The main result for the price equation is that all theypotheses are rejected. This supports the idea that even if preale estimates are relevant for pricing Italian Contemporary Artaintings at auction, fi = f(mi, Mi) is not a sufficient statistic. Thelock sufficiency tests suggest that �i and di do not contain all the

nformation included in each subset of variables.There are three possible reasons for E(yh

i|F, fi) /= E(yh

i|I). First,

re sale estimates can suffer from some market inefficiency (nonational expectations) for which the hypothesis E(yh

i|I) = fi is

iolated; an example could be when new information becomesvailable in the time between the evaluation made by experts andhe actual sale. Second, the loss function of the experts may note quadratic; some asymmetries could arise especially becausexperts tend to reduce the difference di by adjusting the minimumotential price to a higher reserve price. Third, the log transfor-ation of auction prices can induce some distortion especially

ecause, according to Jensen’s Lemma, the expectations of the log-rithms are different from the logarithms of the expectations.

. Concluding remarks

This paper aims to improve the traditional hedonic regressionn order to model painting prices. First, while the existing litera-ure generally focusses on the physical attributes of paintings, we

AG

Economics and Finance 51 (2011) 212–224

mploy a broader set of explanatory variables represented by fourroups of regressors: artist identity, the physical, the artistic andhe sale characteristics of the paintings. Next, special attention isevoted to the problem of selection bias, arising from unsold paint-

ngs. In order to address this problem, we use the Heckman (1979)odel for final purchase prices. This method allows us to jointly

stimate two separate equations: one for the price of the paint-ng and one for the probability of the painting actually being sold.inally, since pre sale evaluations provided by experts present rel-vant information for determining art prices at auction, we try tonhance our analysis by exploiting their information content. To doo, we define a function of their midpoint and spread to be includedn our model as an additional regressor. The whole empirical analy-is is carried out using a unique and homogeneous sample of 2817ransactions of paintings made by 21 different Italian contempo-ary painters sold at auction during the period 1990–2006, hithertoever used in the applied literature.

On the one hand, our results highlight that some mechanismf selection bias is occurring, thus the Heckit method seems ade-uate for modelling the “buying risk” which affects transactionst auction. On the other hand, we found that all four groups ofharacteristics exert an influence upon auction prices, while therobability of sale is determined by a much narrower group ofegressors. To be specific, the marketplace and year of sale (saleharacteristics) play an important role in both equations, while theuction house prestige seems to be relevant only in the selectionquation. Moreover, we find medium, support and conventionalroxies of a painting’s artistic qualities to be less important inxplaining its marketability, although they were found to influ-nce the price equation. Overall, our results suggest that in ourample the characteristics of the specific sale seem to prevail overhe intrinsic characteristics of the paintings.

Finally, we found pre sale evaluations to play a crucial role in ourodel: in the selection equation, they serve as a deterrent to buyershen their midpoint and difference are high and, at the same time,

hey act as important predictors of prices when paintings are sold.rom the statistical point of view, our empirical results suggest thathe proposed function of pre sale estimates enhances the model’sfficiency, but it is not a sufficient statistic for auction prices; fromhe economic perspective, this implies that pre sale evaluations doot contain all the relevant information, thus making it difficult to

nterpret the results from the economical point of view.

ppendix A. Estimates

See Tables A.1–A.4

ppendix B. List of variables (source: Artindex Plus -abrius S.p.A.)

See Tables B.1–B.4

N. Marinelli, G. Palomba / The Quarterly Review of Economics and Finance 51 (2011) 212–224 219

Table A.1Heckit estimation.

Variable Price equation Selection equation

Coeff. s.e. t-Stat. Coeff. s.e. t-Stat.

Const 4.4263 0.1266 34.9559 −0.2926 0.1932 −1.5140�i −0.4676 0.0855 −5.4661

PaintersAdami −1.9055 0.0958 −19.8844 −0.2457 0.1535 −1.6010Beecroft −3.2983 0.3455 −9.5464 −0.4427 0.4504 −0.9830Boetti −1.6723 0.0880 −19.0100 0.3985 0.1531 2.6030Burri 0.0304 0.0960 0.3167 −0.2510 0.1406 −1.7860Campigli 0.1017 0.0814 1.2493 0.0333 0.1433 0.2321Castellani −1.2539 0.1012 −12.3892 0.1151 0.1626 0.7079Cattelan −0.3955 0.2798 −1.4133 0.0136 0.4680 0.0291Chia −1.7407 0.0998 −17.4432 −0.2506 0.1518 −1.6510Clemente −1.2172 0.1220 −9.9809 −0.4775 0.1697 −2.8130Cucchi −1.6888 0.1235 −13.6767 0.0379 0.2045 0.1853Gnoli −1.0910 0.1280 −8.5255 −0.4043 0.1871 −2.1600Kounellis −0.8751 0.1401 −6.2465 0.1145 0.2252 0.5084Magnelli −0.9758 0.0984 −9.9164 0.1037 0.1626 0.6376Manzoni 0.1390 0.0912 1.5246 −0.0688 0.1379 −0.4989Marini −0.2491 0.1262 −1.9742 −0.0683 0.1945 −0.3511Melotti −2.0412 0.3756 −5.4342 −0.4845 0.4605 −1.0520Merz −1.6802 0.1640 −10.2455 −0.2117 0.2321 −0.9121Music −0.7933 0.0838 −9.4640 −0.1400 0.1409 −0.9934Paladino −1.6882 0.0999 −16.9009 −0.2568 0.1493 −1.7210Pomodoro −1.7626 0.7323 −2.4069 −1.4051 0.7549 −1.8610

Physical characteristicssurface 0.6168 0.0284 21.7128squared −0.0492 0.0031 −16.0025oil 0.1310 0.0879 1.4900tempera 0.1034 0.1145 0.9025other 0.2160 0.0904 2.3910enamel −0.6827 0.2444 −2.7940mixed 0.0448 0.1148 0.3898canvas 0.1880 0.0529 3.5508 0.0997 0.0789 1.2640paper −0.4566 0.0661 −6.9117 −0.0615 0.1008 −0.6106

Artistic characteristicsauthentic 0.1674 0.0755 2.2173 −0.0963 0.1069 −0.9009catalogue 0.2255 0.0552 4.0859 −0.0353 0.0824 −0.4288date 0.1856 0.0540 3.4367 0.0253 0.0820 0.3080exhibit 0.0248 0.0099 2.4976 0.0244 0.0213 1.1480expertise −0.2628 0.0898 −2.9259 −0.1028 0.1380 −0.7453literature 0.2789 0.0588 4.7413 −0.1643 0.0868 −1.8930signature −0.0901 0.0583 −1.5453 0.0424 0.0890 0.4762owners 0.0907 0.0181 5.0187

Sale characteristicschristies 0.3993 0.1125 3.5500sothebys 0.5567 0.1141 4.8780finarte 0.3358 0.1135 2.9570london 0.2869 0.0733 3.9125 0.4175 0.1058 3.9450milan −0.0432 0.0681 −0.6344 0.2996 0.0934 3.2070NY 0.2863 0.0858 3.3363 0.6608 0.1239 5.3350d 1991 −0.4714 0.1044 −4.5139 0.1940 0.1702 1.1400d 1992 −0.6542 0.0949 −6.8932 0.2939 0.1542 1.9060d 1993 −0.7185 0.1124 −6.3911 −0.4028 0.1525 −2.6420d 1994 −0.9337 0.1003 −9.3128 −0.1485 0.1447 −1.0260d 1995 −0.7951 0.0974 −8.1665 0.0149 0.1494 0.1000d 1996 −0.8322 0.0955 −8.7096 −0.1029 0.1425 −0.7219d 1997 −0.8081 0.1076 −7.5078 −0.4566 0.1447 −3.1550d 1998 −0.6975 0.1068 −6.5283 −0.2463 0.1528 −1.6110d 1999 −0.5884 0.0877 −6.7081 0.1031 0.1386 0.7438d 2000 −0.5817 0.0969 −6.0038 −0.1229 0.1413 −0.8703d 2001 −0.7265 0.0949 −7.6561 −0.2269 0.1379 −1.6460d 2002 −0.5951 0.0949 −6.2678 −0.2590 0.1356 −1.9100d 2003 −0.5398 0.0932 −5.7942 −0.0839 0.1385 −0.6060d 2004 −0.3591 0.0904 −3.9741 0.4430 0.1521 2.9130d 2005 −0.0899 0.0883 −1.0176 0.1437 0.1355 1.0610d 2006 0.1200 0.0898 1.3371 0.1664 0.1369 1.2150

220 N. Marinelli, G. Palomba / The Quarterly Review of Economics and Finance 51 (2011) 212–224

Table A.2Heckit estimation with pre sale estimates.

Variable Price equation Selection equation

Coeff. s.e. t-Stat. Coeff. s.e. t-Stat.

Const 0.5830 0.0683 8.5350 2.3891 0.8116 2.9440�i −0.1233 0.0319 −3.8690�i 0.9090 0.0110 82.3800 −0.5202 0.4810 −1.0810di 0.1117 0.0790 1.4150 −10.2944 3.8442 −2.6780�2

i−0.1358 0.1078 −1.2600

�idi 4.3517 1.3989 3.1110d2

i4.9862 5.9135 0.8432

�3i

0.0227 0.0088 2.5810�2

idi −0.3894 0.1421 −2.7410

�id2i

−0.9469 1.5436 −0.6135d3

i−0.3230 1.4345 −0.2251

PaintersAdami −0.2334 0.0483 −4.8340 −0.6046 0.1645 −3.6750Beecroft −0.6392 0.1595 −4.0070 −0.8800 0.4696 −1.8740Boetti −0.1793 0.0428 −4.1930 0.1364 0.1614 0.8453Burri 0.0258 0.0438 0.5892 −0.3285 0.1470 −2.2350Campigli 0.0170 0.0369 0.4614 0.0322 0.1485 0.2172Castellani −0.1310 0.0471 −2.7830 −0.0604 0.1679 −0.3599Cattelan 0.1494 0.1244 1.2010 −0.1120 0.4777 −0.2344Chia −0.2153 0.0487 −4.4200 −0.4409 0.1579 −2.7920Clemente −0.2420 0.0561 −4.3140 −0.5560 0.1725 −3.2240Cucchi −0.0397 0.0583 −0.6808 −0.1244 0.2153 −0.5779Gnoli −0.2426 0.0584 −4.1540 −0.5890 0.1934 −3.0450Kounellis −0.1635 0.0631 −2.5930 0.1034 0.2297 0.4500Magnelli −0.2120 0.0452 −4.6880 −0.1150 0.1690 −0.6804Manzoni 0.0078 0.0405 0.1928 −0.2280 0.1394 −1.6360Marini 0.0098 0.0565 0.1739 −0.0093 0.2014 −0.0463Melotti −0.0972 0.1724 −0.5642 −0.8360 0.4824 −1.7330Merz −0.3035 0.0755 −4.0200 −0.3355 0.2355 −1.4250Music −0.0630 0.0389 −1.6190 −0.3431 0.1469 −2.3370Paladino −0.1404 0.0487 −2.8800 −0.4353 0.1562 −2.7860Pomodoro 0.2097 0.3388 0.6189 −1.6969 0.7694 −2.2060

Physical characteristicssurface 0.0420 0.0149 2.8210squared −0.0039 0.0015 −2.5210oil 0.0579 0.0938 0.6169tempera 0.0039 0.1220 0.0318enamel −0.8309 0.2562 −3.2430mixed −0.0541 0.1211 −0.4470other 0.1581 0.0961 1.6450canvas 0.0022 0.0239 0.0914 0.1733 0.0813 2.1330paper −0.0750 0.0301 −2.4930 −0.1914 0.1037 −1.8460

Artistic characteristicsauthentic −0.0248 0.0343 −0.7215 −0.0681 0.1106 −0.6152catalogue −0.0053 0.0250 −0.2119 −0.0275 0.0851 −0.3236date 0.0290 0.0243 1.1920 0.0548 0.0840 0.6527exhibit 0.0110 0.0044 2.4940 0.0393 0.0222 1.7650expertise −0.0789 0.0402 −1.9650 −0.0990 0.1430 −0.6926literature 0.0223 0.0266 0.8389 −0.0616 0.0900 −0.6841signature −0.0362 0.0262 −1.3800 0.0087 0.0909 0.0960owners −0.0050 0.0084 −0.5973

Sale characteristicschristies 0.4332 0.1215 3.5650sothebys 0.6091 0.1214 5.0190finarte 0.3484 0.1242 2.8040london −0.0009 0.0335 −0.0254 0.3779 0.1167 3.2390milan −0.0292 0.0298 −0.9802 0.2886 0.0999 2.8890NY −0.0092 0.0384 −0.2397 0.6378 0.1339 4.7630d 1991 −0.1423 0.0472 −3.0140 0.1207 0.1761 0.6852d 1992 −0.1922 0.0434 −4.4280 0.1256 0.1619 0.7761d 1993 −0.1370 0.0513 −2.6720 −0.5618 0.1587 −3.5400d 1994 −0.1417 0.0461 −3.0710 −0.3592 0.1536 −2.3390d 1995 −0.1268 0.0445 −2.8460 −0.1716 0.1574 −1.0900d 1996 −0.2133 0.0437 −4.8780 −0.2817 0.1497 −1.8820d 1997 −0.1742 0.0494 −3.5270 −0.6479 0.1529 −4.2380d 1998 −0.1097 0.0486 −2.2550 −0.4226 0.1610 −2.6250d 1999 −0.0440 0.0399 −1.1010 −0.0664 0.1459 −0.4553d 2000 −0.0419 0.0444 −0.9449 −0.2852 0.1478 −1.9300d 2001 −0.0740 0.0439 −1.6840 −0.4187 0.1454 −2.8790

N. Marinelli, G. Palomba / The Quarterly Review of Economics and Finance 51 (2011) 212–224 221

Table A.2 (Continued)

Variable Price equation Selection equation

Coeff. s.e. t-Stat. Coeff. s.e. t-Stat.

d 2002 −0.1083 0.0437 −2.4820 −0.4305 0.1422 −3.0270d 2003 0.0068 0.0428 0.1592 −0.2552 0.1458 −1.7500d 2004 0.0525 0.0407 1.2890 0.2826 0.1594 1.7730d 2005 0.0704 0.0403 1.7480 0.0552 0.1435 0.3847d 2006 0.1281 0.0409 3.1280 0.1001 0.1438 0.6961

Table A.3Regression statistics.

No pre sales With pre sales

Mean of dependent variable 4.0932 4.0762Std. dev. of dependent variable 1.2911 1.2871Total observations 2812 2772Censored observations 801 784Censored observations (%) 28.49 28.28�2

ε 0.7845 0.3421�uε −0.5960 −0.3605Loglikelihood −3741.333 −2123.692Akaike Information Criterion 7588.666 4357.384Bayesian Information Criterion 7885.805 4665.103Hannan–Quinn Information Criterion 7697.739 4357.384Jarque–Bera normality test 224.387 2689.78p-value (�2

2) 0.0000 0.0000No. of cases correctly predicted 2029 2050No. of cases correctly predicted (%) 72.16 73.95McFadden R2 (probit) 0.0739 0.0933LR test (probit) 248.487 308.134p-value (�2

n) 0.0000 0.0000g.d.f. (n) 56 65CM test for the normality of ui 1.0901 1.2726p-value (�2

2) 0.5798 0.5293R2(�i, xi) 0.8487 0.7397VIF(�i) 6.6074 3.8417Variables for which VIF(xj) > 10 None NoneMaximum VIF (var. surface) 7.679 9.711Condition number (CN) 20.2626 32.6027

Table A.4Tests for parameter restrictions.

Wald tests for sufficiency Wald tests for block sufficiency

H0 Test stat. p-Value d.o.f. H0 Test stat. p-Value d.o.f.

� = 0 6846.15 0.0000 2 ˇpainter = 0 97.1506 0.0000 20� = � 175.831 0.0000 2 ˇphysical = 0 13.9467 0.0075 4fi = �i 73.3521 0.0000 2 ˇartistic = 0 14.4691 0.0434 7ˇ = 0 235.836 0.0000 51 ˇsale = 0 123.85 0.0000 19� = �, ˇ = 0 395.555 0.0000 53fi = �i , ˇ = 0 255.777 0.0000 53

LR tests for selection equation a

H0 Test stat. p-Value d.o.f.

Model in Table A.1 3235.282 0.0000 11� = 0 105.606 0.0000 9�c = 0 13.124 0.0107 4�s = 0, �c = 0 32.918 0.0000 7�s = 0, �c = 0, �l,1 = 0 61.758 0.0000 8�s = 0, �c = 0, �l,2 = 0 37.740 0.0000 8fi = �l,1�i + �s,1�2

i+ �c,1�3

i28.162 0.0001 6

fi = �l,2di + �s,3d2i

+ �c,4d3i

59.158 0.0000 6

a General specification of fi = f(mi , Mi) derived from Eq. (2):

fi = �l,1�i + �l,2di + �s,1�2i

+ �s,2�idi + �s,3d2i

+ �c,1�3i

+ �c,2�2idi + �c,3�id

2i

+ �c,4d3i

222 N. Marinelli, G. Palomba / The Quarterly Review of Economics and Finance 51 (2011) 212–224

Table B.1Painters (N = 2817)

Variable Obs.

birth (year of birth) 2817

Dichotomic variables:

Variable Birth Dead Obs. Variable Birth Dead Obs. Variable Birth Dead Obs.

Adami 1935 – 170 Chia 1946 – 155 Manzoni 1933 1963 137Beecroft 1966 – 9 Clemente 1952 – 101 Marini 1901 1980 68Boetti 1940 1994 212 Cucchi 1950 – 65 Melotti 1901 1986 8Burri 1915 1995 126 Fontana 1899 1968 720 Merz 1925 – 41Campigli 1895 1971 268 Gnoli 1933 1970 64 Music 1909 2005 241Castellani 1930 – 114 Kounellis 1936 – 51 Paladino 1948 – 150Cattelan 1960 – 10 Magnelli 1888 1971 105 Pomodoro 1926 – 2dead (the painter is dead at the moment of selling) 1705

Table B.2Physical characteristics (N = 2817).

Size

Variable Obs.

surface (painting surface area, in m2) 2812squared (painting squared surface area) 2812

Dichotomic variables:

Medium Support

Variable Obs. Variable Obs.

collage 5 board 185enamel 29 canvas 2254gouache 1 cartoon 173mixed 385 fabric 75pencil 2 marble 5oil 1429 masonite 26tempera 320 panel 166other 1037 paper 275

wood 7support 146

Note: for some paintings, different media or different supports are jointly used.

Table B.3Artistic characteristics (N = 2817).

Variable Obs.

exhibit (number of exhibitions) 2817owners (number of previous owners) 2817

Dichotomic variables:

Variable Obs. Variable Obs.

authentic 187 literature 1049catalogue 680 signature 2071date 1700 title 1722expertise 132

N. Marinelli, G. Palomba / The Quarterly Review of Economics and Finance 51 (2011) 212–224 223

Table B.4Sale characteristics (N = 2817).

Pre sale evaluation

Variable Obs.

mi (minimum estimation) 2777Mi (maximum estimation) 2777

Dichotomic variables:

Auction houses Marketplace Sale date

Variable Obs. Variable Obs. Variable Obs. Variable Obs.

Curial 36 Amsterdam 4 d 1990 242 jan 1Bonhams 4 NY 363 d 1991 100 feb 161Bruun 2 Berlin 8 d 1992 140 mar 245Bukowskis 2 Paris 88 d 1993 109 apr 134Camels 2 Cologne 39 d 1994 133 may 564Christies 914 Copenhagen 2 d 1995 135 jun 466Dorotheum 9 London 1109 d 1996 148 jul 38Doyle 2 LA 4 d 1997 127 aug 5Finarte 536 Lugano 17 d 1998 116 sep 4Grisebach 8 Milan 994 d 1999 190 oct 433Koller 5 Montecarlo 3 d 2000 158 nov 519Lempertz 39 Munich 3 d 2001 182 dec 347Neumeister 3 Rome 140 d 2002 201Pandolfini 1 Stockholm 11 d 2003 206Phillips 37 Sidney 1 d 2004 187

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