Paintings
Pricing the priceless
An econometric approach on art
Art and money. An apparent contradiction according to a lot of art and culture lovers.
Nonetheless a great deal of money hides behind the world of beautiful masterpieces.
The turnover of auction houses like Chistie's and Sotheby's alone runs into billions of
dollars. When we also notice that art pieces like Mondriaan's Victory Boogie Woogie
are sold for tens of millions of dollars, we cannot conclude differently than there is
indeed a relationship between money and the world of art. On this relationship, and
especially the price setting of individual paintings, we've done an econometric
research. It proved to be a precarious but learning endeavour.
The art market
The market for art pieces is constructed differently than most other markets
economists and econometrics analyse. One of the big differences is the fact that the
supply -in most cases- is made of unique products. Still, unique products have
characteristics that can be measured or mapped. In an econometric model it is even
possible to do this all at the same time. We've 'explained' the proceeds of 4950
paintings, auctioned at Christie's. And because numbers say more than words, we'd
like to refer to the estimation results, stated in table 1.
Table 1. Estimation results of the log-linear regression model
Variable
Coefficient
Constant
6.398
Log Surface
0.309
Classification in periods
18th century
-0.036
19th century
-0.171
Impressionism
-0.071
20th century (before 1945)
-0.094
20th century (after 1945)
-0.366
Origin and attribution of a work of art
Dated
0.402
Origin Known
0.375
Land of Auction = Origin
-0.529
Signed
-0.011
In Literature
0.716
Is Exhibited
0.705
Technical characteristics
Paper
-0.514
Chalk
0.341
Pen
0.031
Tempera
0.721
Not Oil paint
-0.099
Fame of artist
Author
0.934
In Janson
0.898
Log Internet Hits
-9.7E-5
Standard error
0.017
t-value
17.7
0.083
0.072
0.076
0.076
0.079
-0.4
-2.4
-0.9
-1.2
-4.6
0.041
0.107
0.039
0.048
0.156
0.162
9.8
3.5
-13.7
-0.2
4.6
4.3
0.117
0.136
0.118
0.245
0.135
-4.4
2.5
0.3
2.9
-0.7
0.073
0.079
8.4E-4
12.9
11.4
0.9
Auction Year:
1990
1991
1992
1993
1994
1995
1996
1997
1998
Performance: adjusted R2 = 0.32
0,448
0,0537
0,0192
0,059
0,0253
0,0552
-0,1298
0,0545
-0,1012
0,0537
-0,0525
0,0511
0,0367
0,0491
-0,0395
0,0491
-0,2062
0,0644
model standard error = 1.27
8,34
0,33
0,46
-2,38
-1,88
-1,03
0,75
-0,81
-3,2
The performance is not at all great. The adjusted R2 tells us that 32% of the variance
in the price is explained by the variables above. Or: we are unable to explain 68% of
the 'movement' in the price. The model standard error (1.27) tells us that the 95% of
the confidence interval is from 12.71) times as cheap to 12.7 times as expensive as the
estimated price! We owe it to the large quantity of data, that we still get significant
results.
In the table above are two kinds of variables. Dummy-variables and variables in the
logarithm. The coefficient of a dummy-variable must be interpreted as follows: small
coefficients are almost proportional differences, but a coefficient of 0.7 means that a
work of art becomes ceteris paribus twice as expensive (e0.7 = 2.01). The coefficients
matching the logarithms are elasticity's: when a painting gets 10% bigger, the price
rises with approximately 3% (1.100.309 = 1.03). And in case of a larger change like two
times as big as the standard work, the price is 1.24 times as high (20.309 = 1.24).
Classification in periods
We've made distinctions in the works of Old Masters (17th century and before), art out
of the 18th century, the 19th century, works of art by (Post-)Impressionists, art out of
the first half of the 20th century and out of the second part. To avoid econometric
pitfalls like dummytraps, we've taken the Old Masters group as the reference group which technically means leaving it out of the picture. All period dummy's coefficients
have values smaller than 0. This implies that the multiplication factor is somewhere
between 0 and 1. For clarification we've shown the correction factors in the next
figure.
Figure 1. Correction factors of the different periods
1.1
1
0.9
0.8
0.7
0.6
Old Masters
th
18
th
19
Impress
th
20
I
th
20
II
After the correction for differences in material and size -one of the advantages of
multiple regression- it shows that, in reference to the works of art made by Old
Masters, the paintings made in the other periods are in general worth less. The figure
shows that works out of the 18th century and out of the Impressionism period are the
runners up. The 19th century appears to be a less valuable period, according to our
model.
It's interesting to see that works out of the Impressionism period and out of the first
half of the 20th century are not worth much less than the works of art by Old Masters
such as Rembrandt, Rubens and Michelangelo. This shows the significance of
'pricepushers' like Monet, Van Gogh and Picasso. It's remarkable that modern art has
a significant2) lesser value. Artists like Appel, Corneille and Warhol must cope with a
lot less than their colleagues of before the wars. This has to do with two reasons. First
of all the supply is bigger, and second it is the question if the art evaluation of today
will last.
The authenticity and history of the work of art
We've also taken a look at the influences of the fame and history that the painting has
and whether the attribution is certain on the value of the work of art. First we'd like to
discuss the factors concerning the authenticity of the attribution of a painting to a
certain artist. When it is found out that a painting is not made by the master -which
was originally thought- but by a lesser painter, the price of the work would probably
drop. If the work of art is dated or the origin is known, then its value would be
significantly higher. A remarkable fact is that a signed work doesn't yield more. The
coefficient is even -neglectable- negative.
Besides the big differences in value between different painters, there is also a big
difference in value between several works of art made by the same painter. To catch
those differences, there are some variables in the model which could tell something
about the quality of the work of art. It shows that when a painting has been in a
exhibition of some kind about the artist the value will be twice as much as when it
wasn't in an exhibition. When a painting can be found in art historical literature, it
also yields c.p. twice as much.
When a painting is auctioned in the same country in which the artist is born it shows
that it yields 70% less. So it would seem that auctioning a work of art in your own
country isn't the smartest thing to do. But here lies the danger of non-experimental
data: paintings of higher quality are more likely sold abroad. It takes a more subtle
investigation to correct this.
Trend in de art market
The trend in the art market in the period 1990-1998 is modelled here with a second
degree equation. It's better done with dummy's, but this somewhat abstract -and
especially not usable to forecast- description give us a nice insight into the considered
period. The negative value of the coefficient of the year of auction states that the
equation is a dalparabool. This is in agreement with the reality. In 1990 the art market
was ready to pop. Encouraged by the threatening recession, the market collapsed. At
about 1993 it had hit rock bottom and afterwards it steadily increased. However the
high level of 1990 has not been reached since.
Technical characteristics
Because a sketch in general yields less than an oil painting, there is also a difference
made in the canvas and the drawing or painting material. The results are noteworthy.
De reference point is a painting made on canvas and oil as painting material. It shows
that works made with chalk render significantly more. This coefficient should
however be viewed together with the paper coefficient, because 96% of the chalk
works are made on paper. Then it shows that chalk on paper works yield less than oil
on canvas. When an art work is painted with paint but not with oil paint -like gouache
or acrylic paint- the work is worth slightly less than if it had been made with oil paint.
Tempera -paint with yolk instead of oil as a binder- works render more than twice as
much as oil paintings. Tempera is a technique used frequently by the Old Masters. So
once again we'd have see the coefficients in combination with each other.
But we don't understand what is really going on, and neither do the appraisers as will
be shown.
Artistic performance
Lastly we've tried to model the artistic performance of an artist. To do so, we've
defined three explaining variables. These are Author -does the author of this article
know the artist-, Janson -is the artist stated in the standard art historical literature
"History of Art" of H. W. Janson- and the on our own gathered indicator of the
modern world: the logarithm of the exact number of internet hits on the name of the
artist by the 'search engine' AltaVista. If the author of this article is familiar with the
name of the artist, the worth of the work rises with 250%. If the artist is listed in
Janson's work, it almost yields twice and a half as much. The real big ones, which are
stated in Janson and known to the author, are more than six times worth as much. The
high t-values also state the importance of such variables for the model. Only the
internet hits doesn't work. This is remarkable: the world of high priced art and the
internet differ apparently.
The opinion of the art connoisseur
In the art market there are persons who can give an estimate of what the work of art is
worth. During auctions there opinions are frequently sought after. Estimates of the
values that those art connoisseurs have given to a work of art are known in a part of
our data. We've taken these opinions in consideration in our analysis.
First we've looked at the next question: 'Is the art connoisseur right?'. For that we've
taken the logarithm of the rendered value of a work of art and regressed that on the
logarithm of the mean value the art connoisseur has attached to the work. The results
are encouraging. The performance improve significantly: an adjusted R2 of 0.89 and a
standard error of 0.49.
We are encouraged by these improvements to further investigate. For that we've put
together the powers of our examined model and the estimates of the art connoisseur.
We've put together the first model and the opinion of the art connoisseur. This
improved the performance a little: the adjusted R2 rose to 0.90 and a standard error
declined to 0.48. The estimation results are shown in table 2. All non significant
deviates are left out, so what is left are the significant deviates of the opinion of the art
connoisseur.
Table 2. Estimation results of the regression model with the estimation the art connoisseur.
Variable
Coefficient
Standard error
Constant
0.887
Log estimation
0.931
0.011
Classification in periods
20th century (before 1945)
-0.067
0.040
20th century (after 1945)
-0.138
0.037
Origin and attribution of a work of art
In Literature
0.130
0.057
Trend in the art market
Auction year
-0.143
0.083
(Auction year)2
0.023
0.018
Technical characteristics
Tempera
0.605
0.181
Fame of the artist
In Janson
0.173
0.044
Log Internet hits
-1.2E-3
6.0E-4
Performance: adjusted R2 = 0.90 model standard error = 0.48
t-value
84.4
-1.7
-3.6
2.3
-1.7
1.3
3.3
3.9
-2.2
This model is a slight improvement in comparison to the model in which the art
connoisseur stood alone with an adjusted R2 of 0.89 . However the standard error
means that still one in twenty paintings is sold 2.6 times higher or lower than
expected. The number of significant variables is noticeable lower, which shows that
the art connoisseur estimates most of the price influences correctly. Still, objections
can be made here.
A constant term and coefficient matching the estimates of the art connoisseur of 0.931
remain, significantly different from one. It shows that art appraisers in general
underestimate the paintings and the real expensive ones even more than the more
normal works. With the model their opinion can be systematically adjusted. The
variable Log Surface has disappeared out of the results table. This means that in
general the art connoisseur estimates the value of the surface remarkably well.
However, there are enough points on which the opinion of the art connoisseur must be
corrected. For instance: there has to be a constant correction for the Old Masters who
are listed in Janson's standard work, or if the painting itself is stated in the art
historical literature. The internet hits correction might even be relevant: surprisingly
the variable has become significant. But, to say it ones more, more research is needed
here.
Conclusion
Even though the construction of a model which explains the prises of works of art is
difficult, it creates a lot of insight. Especially when the appraisal of the art
connoisseur is used besides the econometric techniques. With a model these appraises
can be corrected and supplemented. And with models there are a lot more possibility's
than is discussed here. We would get a much better estimates of trends in the art
market than we get now, should we make a nice model type analysis for all the
available data -about 6.5 million. Which will not take away that buying art is a
financial risky business. But with a model we could at least figure out how risky.
1)
A 95% confidence interval is calculated by adding twice the standard error to the
estimation. Because we are working with a log linear model, we have to take the
exponent of two times the standard error, e2*1.27 = 12.7.
2)
A variable has a significant influence on the price setting when the t-value of the
coefficient is bigger than 2.