Trends in prices for Flemish-Dutch, French and Italian drawings over the last twelve years are described here, with an attempt at evaluating how the technique used, the subject of the drawing, its dimensions, its provenance and other objective characteristics may influence prices. The results are based on prices obtained in public auctions between 1980 and 1991 in almost all Christie’s and Sotheby’s sales; this includes drawings by sixty-eight representative artists for whom drawings turn up frequently, including Cambiaso, Rosa, the two Tiepolos, Rubens, Van Goyen, De Wit, Verdier and Boucher. This makes for 2,375 drawings (707 Flemish-Dutch, 513 French and 1,155 Italian).
Constructing price indices
The methods used to construct price indices for commodities (wheat, gold, oil) or stocks and bonds can hardly be used for art. There are two obvious reasons for this. First, commodities and stocks are homogeneous goods; paintings, drawings and works of art in general are not; a bushel of wheat sold in Chicago in 1947 is almost identical to a bushel sold in London twenty-five years later, while even two Picassos may be very different goods (a fortiori, a Picasso is different from a Chagall). Second, commodities and stocks are quoted almost continuously (once a day or once a week); art works are not.
Therefore, it is straightforward to devise a price index for a specific commodity by merely observing the prices quoted every day or week. It is a little more difficult for stocks, since one needs to aggregate (add) the prices of various stocks; to do this, one uses weighted averages (the weight for stock X can be any observed characteristic of the firm; for instance, the value of its assets).
It is precisely this weighting which cannot be observed for art works. Therefore, indexes for art are often constructed by mere addition of the values of sales. That this may lead to strange results can be illustrated as follows. Assume there are only two artists and two years; the first sells five drawings for £1,000 each in year one, and two drawings at the same price in year two. The second sells three drawings at £200 in year one, and eight at £300 in year two. The number of drawings sold has increased from eight to ten, but the total value has decreased from £5,600 to £4,400. What is the value of the price index in year two with respect to year one? The usual (but wrong) method of calculation would simply compare the value of an average sale in the two years, viz £700 in year one and £440 in year two, and conclude that the index dropped. Obviously though, prices have increased, and a properly defined index should reflect this, by taking into account the qualitative change in the drawings sold over the two years. Note that the mix of qualities did not change, average values would give the correct index.
This quality weighting, missing in the previous calculation, can precisely be computed by using a technique inspired by what econometricians have come to call hedonic regression. Roughly speaking, the technique starts from the assumption that an object (here a drawing) consists of a bundle of observable characteristics (true attributes such as technique used, subject, dimensions, artist, year of sale, etc) and aims at inferring statistically the non-observable “price” of each such characteristic. The observed price of the object can then be decomposed and thought of as a weighted sum of the prices of each characteristic; since one does not observe all the attributes, a part of the price of each drawing will remain unexplained, and contain the influence of time (the trend, if any), as well as random elements; this is the “characteristic free” (i.e. corrected for quality) price of a drawing; these prices can now be added and by taking annual averages, one obtains the “average price of the year”. Clearly, the method does more than that, by allowing us to infer how the various attributes affect the price of a drawing: could the subject change the price of a drawing; how does provenance or technique used affect prices, etc. As characteristics, we have included:
• eight drawing techniques: pen and ink, black chalk, red chalk, wash, oil, pastel, watercolour or gouache, white heightening
• seven types of subjects: religious drawings, one-person studies, landscapes, animals or flowers, historical or mythological drawings, several-person studies, heads or portraits
• provenance of the drawing: this is represented by the number of prestigious collection stamps
• dimensions: height and width
• other characteristics: such as signature, and the fact that the drawing is reproduced in the catalogue of the auction
• the auction house
• the artist.
Pricing of characteristics
Table 1 and Figures 1 and 2 illustrate our results and call for the following comments.
Technique Often the most decorative techniques, such as red chalk or watercolour are the most expensive, while pen and ink, black chalk or slight pastels tend to be cheaper. Differences can account for prices varying between one and four: Flemish-Dutch pastels are about three times cheaper than watercolours; French pastels are four times cheaper than oils; the differences are less important for the Italian School, since Italian drawings in general are more sought after and collected than others. Clearly, however, the fame of the artist overrides all these statements: a pen and ink Rembrandt is vastly more expensive than an eighteenth-century watercolour.
Subject matter Here again, the most common subjects (religious, “academies”) are the cheapest, while landscapes and mythological drawings can be twice as expensive as religious. Again, the differences are less pronounced for Italian art, for the same reason as before. The fact that French academies are relatively expensive should come as no surprise: this style was much more developed in eighteenth-century France than elsewhere, namely by Boucher and Greuze.
Provenance It is not rare to see a mediocre drawing reach a relatively high price, just because it was owned, three hundred years ago, by a prestigious collector. Needless to say, though, drawings which bear a good provenance are usually of good quality: the drawings collected by such a fine connoisseur as the seventeenth-century English painter Peter Lely are now the pride of the world’s greatest museums.
A prestigious provenance is amongst the best proof of quality. Therefore, we estimated the price of the characteristic “provenance”, for those drawings bearing stamps from important collections. As can be seen, this may very significantly increase the price; two stamps make the price six times higher for Flemish-Dutch drawings and may multiply the price by as much as twenty for French drawings.
Dimensions The effect of size is marginal; an additional centimetre in height or width adds approximately 0.2% to the price.
Signature A signature, rather than a characteristic of a drawing, is more a characteristic of an artist. Some artists used to sign; most, in particular the Italians, did not. A signature may, however, if present as on seventeenth- and eighteenth-century Low Countries drawings, add as much as 40% to the price.
Reproduction Most drawings are reproduced in the catalogues published before the auction. Christie’s and Sotheby’s obviously reproduce only quality drawings, and these appear, on average, to be 2 to 2.6 times more expensive than non-reproduced ones. Note that the price may also be driven up as a consequence of being reproduced; it is well known, for example, that drawings reproduced on a catalogue’s cover fetch a higher price.
Saleroom Drawings sold by Sotheby’s seem to be some 5 to 10% more expensive than those sold by Christie’s. This effect is however statistically not very significant.
Price indices 1980-91
The price indices (in current prices, i.e. with no correction for inflation) for 1980-1991 appear in Table 2 and in Figure 3. The French School is obviously the one for which prices have increased most (14% per year), while Italian and Flemish-Dutch drawings have increased with 10.5% and 9% per year respectively. Though after eleven years the differences are not very large, the detailed profiles over time may well be so. In particular, prices for drawings from the Low Countries were stagnant (and thus decreased in real terms) until 1986, they soared in 1987 but not enough to catch up with French and Italian. The jump in 1984 for French and Italian artists obviously reflects the prestigious Chatsworth sale and the entry into the market of the Getty Museum.
Robin Duthy’s calculations for Italian artists (see The Art Newspaper No. 15, February 1992, p. 19) roughly lead to the same profile as ours. However, his average price still increases by 18% in 1991, while we have a very significant downturn for Italians, while the decreases are of the order of 10%, 18% and 35% for the Flemish, French and Italian drawings respectively. Though drawings were not part of the dramatic price increases of art during the late 1980s, it does not seem justified to claim that they went untouched by the general downturn of 1991.
The last point worth discussing is whether we are capable of predicting prices. To test this, we computed our equations on sales between 1980 and 1990, thus excluding 1991; also, to make our life more comparable to that of experts who see the drawing before estimating its value, we have awarded marks to the drawings reproduced in the catalogues, classifying them as outstanding, good or fair. Then, using our equations, we predicted the prices for the first four sales of the year 1991: Sotheby’s 8 January and 18 February 1991, Christie’s 9 January and 16 April 1991. The results are summarised in Table 3; there, we compare the mean error made by Christie’s and Sotheby’s experts (on the basis of their pre-sale estimation) with ours (on the basis of the econometric equation).
Estimating prices for four 1991 sales
Mean square errors
Mean absolute error
Sale House Ours
Sotheby’s 8 Jan 1991 29 39
Christie’s 9 Jan 1991 238 56
Sotheby’s 18 Feb 1991 113 28
Christie’s 16 Apr 1991 79 29
As is apparent from the results, and with the exception of Sotheby’s 8 January sale, we seem to do at least as well as the experts. Clearly, however, we do not take this as a decisive proof that econometrics can do as well as experts, and a lot more experimentation is needed.
List of artists included in the sample
Flemish and Dutch artists
Flanders 16th century: H. Bol, A. Bloemart, P. Bril, J. De Gheyn II, Toeput
Flanders 17th century: J. Jordaens, P.P. Rubens, A. Van Diepenbeek, A. Van Dyck
Holland 17th century: J. De Bisschop, L. Bramer, C. Saftleven, H. Saftleven, J. Van Der Ulft, W. Van De Velde I, W. Van De Velde II, J. Van Goyen, I. Van Ostade, A. Waterloo
Holland 18th century: A. Andriessen, P. Barbiers, J. Cats, D. Langendijk, I. De Moucheron, D. Verrijk, J. De Wit
17th century: J. Callot, R. Lafage, C. Gellée, F. Verdier
18th century: E. Bouchardon, F. Boucher, J.-H. Fragonard, J.-B. Greuze, N. Lancret, C. Natoire, J.-B. Oudry, J.-B. Pillement, H. Robert, A. Watteau
Sixteenth century: B. Bandinelli, L. Cambiaso, Il Parmigianino, Palma il Giovane, G. Romano, J. Tintoretto, F. Zuccaro, T. Zuccaro
17th century: S. Della Bella, A. Carracci, P. Da Cortona, G.-B. Castiglione, L. Giordano, Il Guercino, C. Maratta, P.-F. Mola, G. Passeri, D. Piola, S. Rosa, Volterrano
18th century: G.-B. Bison, D. Creti, G. Diziani, G. Gandolfi, P.-L. Ghezzi, F. Guardi, G.-B. Piazzetta, G.-B. Tiepolo, G.-D. Tiepolo
Originally appeared in The Art Newspaper as 'Of course every work of art is unique—but enter the technique of “hedonic regression”'