Beauty or money? Statistical analysis

1. Introduction

The recent events on a top of the “monetary ladder” in art, where closest neighbors now are pieces by such different artists as Leonardo da Vinci ($452M) and Willem de Kooning ($300M), revitalized the question about relationship between aesthetics and economic value in art. What people do pay money for? For “beauty”? For a “big name”? “For investment purposes”? Can one estimate that relation numerically?

Questions like that have been long standing. In a thorough overview of the early history (Marchi, 2009) it is traced back to de Piles (1708), Richardson (1719), and then through different contributions by famous economist Smith, political thinker Bentham, and others, to works by one of the founders of mathematical economics Jevons and initiators of the conference “Aesthetics of Value” in 1870s.

The very first attempt by de Piles in 18th century was to estimate “56 of the best-known painters … for their performance in the four dimensions, composition, design, coloring, and expression” (Marchi, 2009, p. 98). Among the painters were: Romano, who on the 1–10 scale (10 is the best) had received 4 for coloring; Reni, with 1 for composition; Rembrandt with 6 for design; and Titian with 6 for expression. All the scores could be disputed but for that time it was a huge brave leap ahead.

Richardson, who considered the art estimation as a “Science of a Connoisseur”, extended the de Piles’ list to 8 attributes: Composition, coloring, handling, drawing, invention, expression, grace, and greatness. The novelty was in that he estimated not artists, but separate paintings (especially portraits), and that he gave some general characteristics of the works of art, like Advantage or Pleasure, together with eight more specific features. His notion of “Intrinsic Qualities of the thing itself” (Marchi, 2009, p. 100), was really the first concept of “objective quality of art,” strongly defended by Birkhoff (1933) more than two hundred years later.

Qualitatively, important aspects of “pleasure” and market value were considered by Adam Smith, who “pointed to all the causal factors …, but …did not develop a pleasure index, nor did he try to quantify the role of any one of the causal factors” (Marchi, 2009, p.105).

The pioneering works of the 18-th century did not spark a lot of interest among scholars in creating the “pleasure indexes” or similar indicators in measurable form. As late as in 1966, a famous art historian Gombrich treated de Piles’ numerical exercise as “notorious aberration” (Ginsburgh & Weyers, 2009, p. 112). But the relationship between aesthetic and economic values, touched in those works for the first time, were actively discussed, although mainly theoretically, among different researchers, especially philosophers. Complex questions about different values of art (economic, aesthetic, propaganda, theological, moral, therapeutic, prurient, and decorative) were considered in (Lopes, 2011), where the author, after taking into account many different opinions in philosophical literature, concludes that artistic and aesthetic values are actually the same. In (Spaenjers et al., 2015) even more aspects of the art value (especially related to economics) are considered.

Different aesthetic indicators have been the subject of many studies, both theoretical and empirical; a thorough overview can be found in (Markovi & Radonji, 2008). A lot have been said about relations between economic and aesthetic values in theoretical aspects – see many references in (Spaenjers et al., 2015). There were special studies about different relations between elements of art, like “angles” versus “rounds”, and other (Locher, 2012); “art consumers” (like behavior of visitors in museums – see in Mastandrea et al, 2009); titles and prices (Park et al, 2021); and a national identity as a factor (Mastandrea et al., 2019). However, when it comes to quantitative measurement of the relations between economics and aesthetics, the number of studies is surprisingly small.

In (Ginsburg & Weyers, 2009), the authors took de Piles’ estimates of the quality of 56 painters as four independent variables and used them for considering two dependent variables they calculated. The first one was the number of lines about a given painter in the most comprehensive art dictionary (Turner, 1996). The second one was a price estimate for all paintings of a given painter sold on auctions during 1977–1993 (525 transactions). The coefficients of multiple determination of the models by de Pile’s factors (dimensions, composition, design, coloring, and expression) were relatively high, over 30%.

In a similar study (Throasby & Zednik, 2014), the experiment was designed in another way. The authors asked visitors of the gallery in Sydney, Australia, to estimate the economic and aesthetic (cultural) values of six different paintings. After 3 days of the experiment, they gathered a comparatively high number of responses in 480 filled questionnaires and conducted regression analysis based on the answers. This study has a few advantages over the work by Ginsburg and Weyers (2009) with only a single person in the study. The people looked at real art objects, not photographs; however, there were a few potential flaws: the visitors of the gallery were not typical population representatives; the number of paintings was too small; Australian aboriginal works played disproportionally high role (2 out of 6). The key limitation was the fact that respondents were given the actual market prices of all works to create their own “economic value.” It inevitably created a bias, not only the anchoring effect, admitted by the authors (respondents’ price estimates were anchored to actual prices known to them), but of another type: if one knows that this is a very expensive painting, she could value it higher in aesthetic terms as well. And this bias was greatly amplified by the fact that paintings were extremely heterogeneous: prices varied from $6k to $2.5M, which is substantial range for such a small sample. It could be the main reason of the high value of the coefficient of multiple determination 66% for the market price. The model had many predictors, but the role of one variable of the aesthetics estimate was the most important.

In another study on art and persuasion, Mastandrea and Crano (2019) aimed to determine whether artworks, being presented as created by famous artists, will be appreciated higher than the same artworks, when they are attributed to non-famous artists. Findings showed that the works attributed to famous artists were more appreciated than the same works attributed to non-famous artists. In particular, participants were willing to pay more to see the artworks in a museum, if those were described as created by famous artists.

However, lack of models with aesthetic variables does not mean a shortage of general models for the art prices. Likely started by Anderson (1974), boosted by the influential work by Baumol (1986) about repeated sales, very carefully modeled on a huge number of paintings by several scholars (Goetzmann et al., 2013; Penasse et al., 2014), it culminated in the very important recent study (Korteweg et al., 2017), based on repeated sales of more than 30,000 pieces of art. These and other studies (for example, Marinelli & Palomba, 2008, about 2,800 pieces; Bocart & Hafner, 2012, about 550 pieces; Teti, et al., 2014, about 300 pieces) mainly employed a technique of the so called “hedonic regression” and did not use aesthetic value in their models. Characteristically, the scholars admitted the importance of the aesthetics’ value, and in (Teti et al., 2014) the authors stated that without it, any art price models would be “ephemeral” and “fruitless,” but they had not explored the problem further.

Let us look closer at, possibly, the most comprehensive study of this type (Renneboog & Spaenjers, 2013). The authors used the very reliable source of data – auction sales of 1957–2007, as opposite to galleries and other types of sales where data usually is not available. There were 10,442 various artists lived in different times from Medieval to present. The total number of transactions, including repeated ones, was 1,088,709 (about 60% oils, and the others split almost evenly between drawings and watercolors). It is a huge amount of data which could yield reliable conclusions for such problems as return on investment. What did it say about the aesthetic and art-historical value of the works? Out of around 50 independent variables used in regression, there was just one which could be related to the art-historic value – it occurred to be a binary variable with the value 1 if before sale an artist was included in the last edition of the catalogue (Tansev et al., 1995) and 0 otherwise. Therefore, it relies exclusively on just one source – the knowledge of the painter’s importance, which is strongly dependent on the source used, such as mentions in the art dictionaries and critics’ opinions. In addition, the aesthetics is not clearly presented within those 50 variables. Styles of paintings (impressionism, surrealism, etc.), or genre (landscape, portrait, etc.) have very remote relation to the aesthetics, if any.

The lack of aesthetic variables in modeling could be explained by the fact that aesthetic values are very hard to measure. One cannot collect data from the auction houses and make cumbersome aesthetic measurement for many thousands of paintings by multitudes of people. This problem, possibly, will never be solved in a satisfactory manner. The current proposed study is one of the ways to find an approximate solution.

In light of all discussed and other issues the situation looks quite puzzling. The world art market is huge; for the last 15 years it was fluctuating around $62B per year (with one exception, $40B, in 2009, after the financial crisis). What do people pay that money for? Which of the “values of art” play a decisive role “Rarity”? Beauty? “Cult-following”? If the relationship between the aesthetics and market value is not clearly and numerically understood – the whole area of the “art economics” (Heilbrun & Gray 2009; Amariglio et al., 2009; Spranzi, 2008) looks like a castle built on shifting sands. Art economics should address many very practical questions, like state’s funding of museums, creation of curriculum in colleges, sponsoring artists, etc., but without a clear understanding of relations between “money” and “beauty” it hardly could be done. Finally, what is art if it does not create an aesthetic value? And if it does, but no one pays for it – should such an art be discouraged? If it does not, but still gets the highest price tag, should it be encouraged? How does that fit a societal wellbeing? Should the art be reduced merely to its market value, as all quoted studies tried to model? Should one agree that “In practice, art is actually traded as an investment. This is empirically confirmed by activity from dealers, funds …who store artworks in warehouses, or bank vaults…where obviously the aesthetic return is null” (Bocart & Hafner, 2012, p. 3092), or is there anything else behind it? What do unbelievable prices of the past years mean? Is that just the market’s whim with a hope to sell it even higher soon, or are there other reasons?

All these and related questions motivated us to conduct an experiment to understand better the relations between the aesthetic and economic aspects of art in a more systematic way than it was done before.

On a different vein, the relationship between such different fields as statistics and art is not too often discussed in statistical journals (see Lipovetsky & Mandel, 2007, 2009; Mandel & Lipovetsky, 2007). In that sense the paper feels the gap, because it is not only describing the application, but also proposes some simple methods and models which help to deal with data of the specifical structured nature.

The rest of the paper is organized as follows. Section 2 describes different types of data used in the study, including a created website pollart1000.com and its design. Section 3 contains analysis of the collected data. Finally, Section 4 summarizes the findings.

2. Data and survey design

In this paper only a high-level description of the data and experiment are presented; more details could be found in (Mandel, 2020). A hundred painters were selected based on certain procedure from the list provided in Murray (2004). They all are outstanding painters who entered an exclusive list of 600 + “significant painters of Western tradition” out of potential hundreds of thousands of painters during last millennia. Each artist has the so-called Murrays’ Index (referred to later as MI), varied from 100 (the best painter; turned out to be Michelangelo) to 1. For each painter 10 works were presented: 5 most expensive and 5 randomly selected, totaling to 1,000 pieces, although much smaller number was actually used in the analysis.

Each painting had an estimated auction price (hammer plus premium) paid at the time of the latest auction for this piece, transformed into values comparable over time, in dollars as of the end of 2015. The most expensive work was Les femmes d’Alger by Pablo Picasso ($179,365,000) and the cheapest – Cavalier on horseback in a field by Giovanni Fattori ($1,059). The difference in about 170,000 times is a good illustration of what art prices are, considering that all those artists were by definition the “significant figures”. In addition, many other parameters were also collected and analyzed in (Mandel, 2020).

Following (Markovi & Radonji, 2008) and our own intuition and understanding, the following list of variables was used to measure aesthetical values, rated from 1 to 7 (1 – I don’t like it at all; 7 – magnificent, I like it a lot): General Aesthetic Impression, Harmony, Relaxation, Hedonic Value, Arousal, and Technical perfection. The presentation was supported by visual four examples for the best and worst scores with comments, helping respondents to understand what they are asked to focus on. Examples are presented in (Mandel, 2020, Annex 2).

Collecting estimates through an online survey was not an easy task. The key challenge was that one cannot expect a person to spend time rating all 1000 pieces in our database. Ideally, if each work could get at least 30 estimates (usually considered as sufficient for making a statistical inference) – but how to ensure for those desired 30,000 estimates to be evenly distributed among all pieces?