the market for picasso prints: an hybrid model...
TRANSCRIPT
The Market for Picasso Prints: An Hybrid Model Approach
Marilena Locatelli-Biey Department of Economics University of Torino - Italy E-mail: [email protected]
Roberto Zanola Department of Public Policy and Public Choice - Polis
Palazzo Borsalino - via Cavour, 84 – 15100 Alessandria - Italy E-mail: [email protected]
ABSTRACT: Two basic approaches have been used by the literature focusing on the return to holding artistic works: the hedonic price model and the repeat-sales model. This paper provides a procedure for jointly estimating the two models in a way that take advantages of the unique information contained in each. A semiannual price index for Picasso prints is estimated by using a model derived from the basic framework of the hybrid models. The empirical results suggest that the hybrid model provides the most precisely estimated price index by reducing the level of price volatility.
JEL Classification Numbers: C5, Z1. Key Words: Prints, Picasso, Hedonic Prices, Repeat Sales, Rate of Return, Hybrid models.
1 Introduction
The literature on art auctions focusing on the return to holding artis-
tic works uses two basic approaches: the hedonic price model and the
repeat-sales model.1 The hedonic price model attributes an implicit
price to each of the time-invariant and time-varying characteristics of
the item. As dependent variable the logarithm of price is used which
is regressed on those time-variant and time-invariant variables and on
a vector of time dummies-equal to one if the asset is sold in period t
and zero otherwise - that capture the pure effect of price changes over
time. Using the hedonic price model, however, it is difficult to control
for variable selection, functional form, instability of item characteris-
tics over time and sample selection [Knight et al., 1995; Wolverton and
Senteza, 2000].
The repeat sales model, first advanced by M.J.Bailey et al. (1963),
estimates all pairs of consecutive transactions of a single item trans-
acting more than once during the study period. Using ordinary least
squares, this technique estimates an index for price of art items by re-
gressing the change in the log of price of each object on a set of dummy
variables, one dummy for each period in the sample, with the exception
of the first value of the log price index, which is set to zero to normal-
ization. The dummy variables are +1 if the second sale of the asset
1See Ashenfelter and Graddy (2002) for a survey.
2
is in period t, and −1 if the first sale of the asset is in period t; the
dummy variables are zero otherwise. Using the repeat sales model there
is the difficulty to control for a typical market trend during the period
between a sale and resale of a given item, as well as sample selection
bias.
Case and Quigley (1991), focusing on the market for houses, go be-
yond these two approaches, by jointly estimating conventional hedonic
and repeat sales models. This methodology represents an improvement
over the previous techniques since it combines information on repeat
sales with hedonic approach, which allows to capture either the increase
and/or the depreciation of prices within the repeat sales model and
the serial correlation in hedonic data. They apply a generalised least-
squares estimation procedure. In particular, the estimator is a two-step
iterative maximum-likelihood procedure for models with grouped het-
eroschedasticity.
Carter Hill et al. (1997) extend this approach by assuming that even
if it is plausible that in the hedonic model errors are serially correlated,
nevertheless market forces tend to eliminate the systematic error over
time. This hypothesis about the first-order autoregressive properties of
errors in the hedonic model combined with the stochastic properties of
errors in the repeat sales model, allows to define log-likelihood functions
for auctioned items and repeat sales, which are maximised numerically
3
to obtain maximum-likelihood parameter estimates.
Although this last approach appears to be interesting, it is focused
on the market for houses, and until now no applications exist on the
market for arts due to the difficulty to identify time-varying variables
[Chanel et al., 1996]. The purpose of this study is to provide a partial
answer to this difficulty by considering the effect of boom period on
prices as a time-varying variable. To this aim three different models
have been estimated by focusing on the market for Picasso prints: the
hedonic price model; the repeat sales model; and the hybrid model.
The rest of the paper is organised as follows. Section 2 presents the
model which draws from Carter Hill et al. (1997). Section 3 describes
dataset. Results are analysed in Section 4. Section 5 concludes.
4
2 The Model
Define Pit as the logarithm of print value (i.e., selling price) at time t, Xi
as the set of relevant time-invariant characteristics, Bit as the set of rel-
evant time-varying characteristics, Dit as a set of dummy variables with
a value of one if a transaction on print i occurs in year t and zero oth-
erwise, and εit as a well-behaved error term. The hedonic specification
of the price may be expressed as:
Pit = Xiα+Bitβ +Ditδ + εit (1)
where α, β and δ are the shadow prices of the print-i characteristics.
However, since the only time-varying characteristic of the dataset is
represented by a boom period from 1987 to 1991,2 Bit may be defined
as a dummy variable with a value of one for the boom-period and zero
otherwise.
Since there are a number of observations within the dataset that are
observed to sell more than one, the repeat sales method can be used.
Define Pit+s as the logarithm of the print value at time t+ s. The price
difference between two sales of the same print may be expressed as:
Pit+s − Pit = ∆Piτ = Aiτβ + Tiτδ + νiτ (2)
2A potential time-varying characteristic is print depreciation, which is not regis-
tered in the dataset. However, due to the short period covered by the dataset, we
can assume that time does not cause any demage to the prints.
5
where: Aiτ = Bit+s −Bit, νiτ = εit+s − εit, and
Tiτ =
1
−10
if τ = t+ s
if τ = t
otherwise
(3)
Econometric problems preclude estimation of the parameter β in
equation (2). In fact, the effect of non-boom period cannot be distin-
guished econometrically without using additional data to provide an in-
dependent estimate of the parameter β [Bailey, 1963; Palmquist, 1979,
1980]. Hence, following Case and Quigley (1991), and Carter et al.
(1997), we impose cross equation equality constraints on β and δ in
order to obtain smaller standard deviations observations. The matrix
form for the system of the two equations is equal to:
Pit
∆Piτ
= X B D
0 A T
α
β
δ
+ ε
ν
(4)
6
3 Data
The empirical analysis utilises data collected during the period 1988-
1995 from the 1995 edition of the Mayer International Auction Records
on CD-Rom. The publication contains records of prints sold at the
world’s major auctions, providing information on a number of variables
(artist’s name, nationality, title of the work, year of production, mate-
rials, date and city of sales, prices, pre-sale estimate (when available),
dimensions, whether or not it is signed, and a number of further infor-
mation). Prices are gross of the buyers and sellers’ transaction fees paid
to auction houses and are recorded in four different currencies. No in-
formation is provided on the provenence of the prints and exhibitions of
the prints. As noted by Pesando and Shum (1996), due to the homoge-
neous quality and condition of the impressions we only focus on Picasso
prints, which also closely resemble price movements in the market for
modern prints as a whole.
The explanatory variables included in the study are:
• Dimension: the variable defines the surface of the print, dim.
• Number of prints: the variable defines the total number of copiesproduced of the same print, n_print.
• Signature: a dummy variable is introduced to take into account ifprints are signed, with sign =1 if prints are signed, and sign = 0
7
otherwise.
• Colour: a dummy variable is introduced to take into account ifprints are colored, with color = 1 if prints have more than one
color, and color = 0 otherwise.
• Salerooms: Sotheby’s and Christie’s are known to be the leading
auction houses in this kind of transaction while the most impor-
tant art auction markets are New York and London. In order
to avoid overlaps between auction houses and cities of sale, we
add some interaction dummies between salerooms and cities, as
follows: sothny, for Sotheby’s New York; sothlon, for Sotheby’s
London; chriny, for Christie’s New York; chrilon, for Christie’s
London; francall, for print sold in France; germany, for prints
sold in Germany; otherus, for prints sold in US but not in New
York; othereu, for prints sold in the European countries not men-
tioned before; world, all other salerooms and cities of sales; swiss,
for prints sold in Switzerland (excluded variable).
• Media: a set of dummy variables, reflecting the technique adopted,is used: etching, etching; litho, litho (excluded variable); drypoint,
dry point; aquatint, aquatint or eau-forte; linocut, linocut; and
maeother, all other media.
• Boom: a dummy variable is introduced to take into account if
8
prints are sold in the boom years or not, with dboom = 1 if prints
are sold between 1988 and 1990, and dboom = 0 otherwise.
• Period : a set of dummy variables, Dt, with t = 1988, ......, 1995,
are introduced for each semester between 1988:I and 1995:II (with
1995:II excluded).
Table 1 summarises the main findings of the sample.
[TABLE 1]
9
4 Results
In this section the results of three different models are compared:
• the hedonic price model, which involves the estimate of the implicitprices for each characteristic included in the equation by making
it possible to control for any non-temporal determinants of price
variations;
• the repeat sales model, which estimates a price index for arts byregressing the change in the log of price of each prints on a set
of dummy variables, one dummy for each period in the sample
(with the exception of the first value) which is set equal to +1 at
the time of second sale, -1 at the time of the initial sale, and 0
otherwise;
• the hybrid model, which jointly estimates the hedonic regressionequation and the repeat sales regression with cross-equation equal-
ity constraints on the common parameters.
Table 2 displays the coefficient estimates and standard errors obtained.
[TABLE 2]
The hedonic regression results are reported in columns (1) and (2).
Standard errors and variance-covariance matrices of the coefficients have
10
been computed by using theWhite (1980) heteroskedasticity-robust pro-
cedure due to heteroskedasticity. The coefficients associated with each
kind of independent variable can be used to rank prints according to
the price of a ‘normalised’ print, that is, the price of a print when all
the other variables are assumed to be at a standard level. The values of
coefficients are those expected. An F-test run for each group of dummy
variables shows that coefficients are significantly different from zero at
5 per cent probability level.3
Columns (3) and (4) show the results of the repeat sales method.
We compare the prices of identical prints that were sold twice or more
during the analysed period of time.4 For simplicity, we assume that all
sales occur at the end of each period. These estimates are substantially
different from the previous ones due to the impossibility to distinguish
econometrically the effect of non-boom period without using additional
data to provide an independent estimate of the parameter β in eq. (2).
To this aim, columns (5) and (6) display the set of coefficients from
joint estimation of the two equations. Due to the existence of con-
temporaneous correlation between equation errors,5 the hybrid model is
3Results are available on request by the authors.4The potential effect of outliners on the final results cannot be isolated due to
the few number of repeat sales.5The value of the χ2(1) = 0.460 (Breusch and Pagan, 1980) suggests to refuse
the null hypothesis of no contemporaneous correlation.
11
estimated using the seemingly unrelated regression methodology. The
hybrid model yields a smaller estimated standard deviation of the dis-
turbance term than the corresponding hedonic price model. In fact, the
hybrid model is estimated more precisely than the hedonic price model
since data on repeat sales are not ignored [Case and Szymanoski, 1995].
The set of dummy variables introduced for each semester between
1988 and 1995 is used to build a semiannual price index for Picasso
prints.6 The estimated values of the price index are presented in Table
3 and depicted in Figures 1.
[TABLE 3]
[FIGURE 1]
Although the period under scrutiny is characterized by price fluctu-
ations, the trend of price indexes shows the existence of a boom period
until 1990.7 Figure 1 suggests that the hybrid model provides the most
precisely estimated price index of the approaches considered. In fact,
the evidence based on this sample suggests that the hybrid model re-
duces the level of price volatility by capturing either the increase and/or
the depreciation of prices within the repeat sales model and the serial
correlation in hedonic data.
6The use of semiannual data are due to the characteristics of the international
auction market which concentrates sales in May/June and November/December of
each year [Pesando and Shum, 1999].7The trend corresponds to the least squares fitted through points.
12
5 Conclusions
This paper provides a procedure for combining the hedonic and repeat
sales approaches by analysing the performance of an investment in Pi-
casso prints during the period of time 1988-1995. In particular, we
jointly estimate the two models in a way that take advantages of the
unique information contained in each as developed by Carter Hill et al.
(1997). Although this last approach appears to be interesting, up to
now no applications exist on the market for arts due to the difficulty to
identify time-varying variables.
By considering the effect of boom period on prices as a time-varying
variable, this study represents a partial answer to this difficulty. The
empirical results suggest that the hybrid model provides the most pre-
cisely estimated price index of the approaches considered by reducing
the level of price volatility.
Given the limited sample used in this paper, it is difficult to de-
velop confident conclusions about the overall market for the visual arts.
However, the evidence presented here does help to clarify some issues
concerning the relative precision of different approaches to estimating
price indexes.
Acknowledgments
13
The authors are grateful to the participants of the12th International
Conference on Cultural Economics, Rotterdam, June 2002, for useful
comments to an early version of this paper. Usual disclaimers apply.
The research has been financially supported by CNR program on cul-
tural goods.
14
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Table 1. Descriptive Statistics
Variable Mean Std. Dev. Min. Max.
Price 21072.36 52478.52 200.00 1052630,00dim 1843.61 1627.52 0 31520.31n_print 89.50 102.90 0 1000,00sig 0.8379 0.37 0 1colour 0.2071 0.41 0 2sothny 0.2775 0.45 0 1sothlon 0.1651 0.37 0 1chriny 0.1278 0.33 0 1chrilon 0.1160 0,32 0 1francall 0.0751 0,26 0 1germany 0.0686 0,25 0 1otherus 0.0414 0,20 0 1othereu 0.0296 0,17 0 1world 0.0231 0,15 0 1swiss 0.0633 0,24 0 1etching 0.3834 0,49 0 1drypoint 0.0923 0,29 0 1aquatint 0.0675 0,25 0 1linocut 0.1734 0,38 0 1maeother 0.0178 0,13 0 1litho 0.2639 0,44 0 1dboom 0.4320 0,50 0 1D88:I 0.0568 0,23 0 1D88:II 0.0751 0,26 0 1D89:I 0.0899 0,29 0 1D89:II 0.0580 0,23 0 1D90:I 0.1148 0,32 0 1D90:II 0.0373 0,19 0 1D91:I 0.0450 0,21 0 1D91:II 0.0201 0,14 0 1D92:I 0.0538 0,23 0 1D92:II 0.0438 0,20 0 1D93:I 0.0746 0,26 0 1D93:II 0.0402 0,20 0 1
A. Single Sales (N = 1690)
APPENDICE
D94:I 0.0669 0,25 0 1D94:II 0.0769 0,27 0 1D95:I 0.1083 0,31 0 1D95:II 0.0385 0,19 0 1
Pricet 50523,46 67043,88 1600 378790Price(t+s) 45347,36 64910,00 2660 340000D88:I -0,10 0,30 -1 0D88:II -0,08 0,43 -1 1D89:I -0,12 0,39 -1 1D89:II -0,02 0,42 -1 1D90:I 0,01 0,53 -1 1D90:II 0,01 0,38 -1 1D91:I 0,04 0,49 -1 1D91:II 0,04 0,29 -1 1D92:I 0,12 0,39 -1 1D92:II 0,03 0,23 -1 1D93:I -0,07 0,29 -1 1D93:II -0,04 0,21 -1 0D94:I 0,02 0,15 0 1D94:II 0,00 0,21 -1 1D95:I 0,05 0,31 -1 1D95:II 0,09 0,28 0 1dboom 0,30 0,46 0 1
B.Repeat Sales (N R = 182 = 91 Pairs)
Table 2. Estimates of the different models
Variables Est. Std. Err. Est. Std. Err. Est. Std. Err.(1) (2) (3) (4) (5) (6)
constant 3,2897 0,28 3,8828 0,1252
dim 0,0002 0,00 0,0004 0,0000
n_print 0,0008 0,00 0,0010 0,0004
sig 0,8266 0,11 1,4336 0,0999
colour 0,3138 0,13 0,5708 0,1385
sothny 1,3572 0,19 2,4979 0,1343
sothlon 0,9795 0,20 2,2173 0,1487
chriny 1,0994 0,19 2,3752 0,1569
chrilon 1,3363 0,21 2,6321 0,1607
francall 0,7269 0,23 1,7417 0,1785
germany 1,3498 0,22 2,1521 0,1820
otherus 0,4325 0,20 1,6293 0,2174
othereu 1,4150 0,27 2,4688 0,2439
world 1,3749 0,28 2,7142 0,2687
etching 0,4923 0,18 1,0892 0,1061
drypoint 0,9346 0,20 1,6963 0,1507
aquatint 0,6609 0,18 1,1690 0,1627
linocut 0,6291 0,14 0,5861 0,1501
maeother 1,0474 0,37 1,7549 0,2894
dboom -1,7286 0,15 -0,3152 0,0340
D88:I 4,6653 0,27 -0,0149 0,0123 0,2869 0,0459
D88:II 4,9860 0,29 -0,0173 0,0105 0,3115 0,0430
D89:I 4,8681 0,29 -0,0060 0,0098 0,3238 0,0407
D89:II 5,1638 0,30 0,0476 .0117335 0,3866 0,0444
D90:I 5,0977 0,29 0,0215 .0085302 0,3555 0,0386
D90:II 4,8089 0,30 0,0424 .0143681 0,3410 0,0471
D91:I 3,5967 0,31 0,0271 .0128843 0,1286 0,0348
D91:II 3,0372 0,35 0,0169 .0195767 0,0415 0,0511
D92:I 3,3463 0,31 -0,0488 0,0122 0,0358 0,0322
D92:II 2,8661 0,31 -0,0182 0,0143 -0,0297 0,0371
D93:I 3,1441 0,29 -0,0081 0,0109 0,0354 0,0284
D93:II 3,1490 0,28 -0,0094 0,0148 0,0240 0,0386
D94:I 2,7130 0,29 0,0018 .0117666 -0,0054 0,0307
D94:II 3,2754 0,29 0,0018 .0108874 0,0466 0,0285
D95:I 2,8374 0,28 -0,0126 0,0091 -0,0123 0,0238
F(34,1721) = 748.74 F(15,1741) = 4.08 chi2 = 2056.75R-squared = 0.6532 R-squared = 0.034 "R-squared" = 0.496
Hedonic Model Repeat Sales Model Hybrid Model
Table 3. Prices Indexes
Period Hedonic Price Model
Repeat Sales Model
Hybrid Model
D88:I 100,00 100,00 100,00D88:II 137,80 99,76 102,49D89:I 122,48 100,88 103,76D89:II 164,61 106,42 110,49D90:I 154,08 103,66 107,11D90:II 115,43 105,89 105,56D91:I 193,46 104,20 116,99D91:II 110,56 103,16 107,22D92:I 150,61 96,65 106,62D92:II 93,18 99,71 99,86D93:I 123,04 100,69 106,58D93:II 123,64 100,55 105,36D94:I 79,95 101,66 102,31D94:II 140,30 101,68 107,77D95:I 90,54 100,22 101,60
Note: semi-annual period: D88:I=1, D88:II=2, ..., D95:I=15
Figure 1. Price Indexes
50
75
100
125
150
175
200
225
250
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Semi-annual Period
Hedonic Price ModelRepeat Sales ModelHybrid ModelTrend
23
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1999 n. 3* Mario Poma, Benefici economici e ambientali dei diritti di inquinamento: il caso della riduzione dell’acido cromico dai reflui industriali.
1999 n. 2* Guido Ortona, Una politica di emergenza contro la disoccupazione semplice, efficace equasi efficiente.
1998 n. 1* Fabio Privileggi, Carla Marchese and Alberto Cassone, Risk Attitudes and the Shift of Liability from the Principal to the Agent
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Department of Public Policy and Public Choice “Polis” The Department develops and encourages research in fields such as:
• theory of individual and collective choice; • economic approaches to political systems; • theory of public policy; • public policy analysis (with reference to environment, health care, work, family, culture,
etc.); • experiments in economics and the social sciences; • quantitative methods applied to economics and the social sciences; • game theory; • studies on social attitudes and preferences; • political philosophy and political theory; • history of political thought.
The Department has regular members and off-site collaborators from other private or public organizations.
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Instructions to Authors
Please ensure that the final version of your manuscript conforms to the requirements listed below:
The manuscript should be typewritten single-faced and double-spaced with wide margins.
Include an abstract of no more than 100 words. Classify your article according to the Journal of Economic Literature classification system. Keep footnotes to a minimum and number them consecutively throughout the manuscript with superscript Arabic numerals. Acknowledgements and information on grants received can be given in a first footnote (indicated by an asterisk, not included in the consecutive numbering). Ensure that references to publications appearing in the text are given as follows: COASE (1992a; 1992b, ch. 4) has also criticized this bias.... and “...the market has an even more shadowy role than the firm” (COASE 1988, 7). List the complete references alphabetically as follows:
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Periodicals: KLEIN, B. (1980), “Transaction Cost Determinants of ‘Unfair’ Contractual Arrangements,” American Economic Review, 70(2), 356-362. KLEIN, B., R. G. CRAWFORD and A. A. ALCHIAN (1978), “Vertical Integration, Appropriable Rents, and the Competitive Contracting Process,” Journal of Law and Economics, 21(2), 297-326. Monographs: NELSON, R. R. and S. G. WINTER (1982), An Evolutionary Theory of Economic Change, 2nd ed., Harvard University Press: Cambridge, MA. Contributions to collective works: STIGLITZ, J. E. (1989), “Imperfect Information in the Product Market,” pp. 769-847, in R. SCHMALENSEE and R. D. WILLIG (eds.), Handbook of Industrial Organization, Vol. I, North Holland: Amsterdam-London-New York-Tokyo. Working papers: WILLIAMSON, O. E. (1993), “Redistribution and Efficiency: The Remediableness Standard,”
Working paper, Center for the Study of Law and Society, University of California, Berkeley.