XVIIIth International Conference on Cultural Economics,
Montreal, 2014
Decomposition analysis of returns from nonstandard investment markets:
Why selling Picasso in New York is different
A.M.Jones* and R.Zanola°
* University of York, Department of Economics, UK
° University of Eastern Piedmont, Institute of Public Policy and Public Choice, Italy
1
Outline of the presentation
 Motivation
 Method
 Beyond Oxaaca decomposition
 Unconditional RIF-regression
 RIF-based decomposition
 Decomposition results




Data
Total effects
Decomposition analysis: 1990-1999
Decomposition analysis: 2000-2010
 Conclusions
2
Motivation
Limits of the LOP
 The Law of One Price (LOP) say that identical assets must
have identical prices  arbitrage
 Serious doubts arise about the validity of the LOP in the
markets for non-standard investments:
 No identical goods
 Presence of risk
 It could be no possible to resale goods
 In the art market there is evidence that the arbitrage does not
necessarily equalize prices (Pesando, 1993; Renneboog and
Van Houtte, 2002; Forsund and Zanola, 2007; among the
others)
3
Motivation
Aim
 To analyze why the distribution of prices differ across New
York (NY) and the Rest of World (RoW). To this aim two
different questions arise:
 Does the distribution change because items sold in NY have different
characteristics than items sold in the RoW?
 Is the distributional change unrelated to item characteristics, and has
caused differences in the hedonic price functions across markets?
 Based on the unconditional Recentered Influence Function
(RIF) regression method based on Firpo et al. (2007, 2009),
we decompose price distribution across different markets
4
Method
Beyond Oaxaca decomposition
 The Oaxaca-Blinder decomposition is widely used to
decompose average price gap between two groups into an
effect explained by the differences in covariates and an
unexplained effect due to the different returns to covariates.
 However, the simple mean Oaxaca-Blinder comparisons are
not necessarily informative about developments in the upper
tail of the price distribution (Etilé, 2011; Johar et al.)


Conditional quantile regression: to assess the impact of a covariate on
quantile of the outcome conditional on a specific values of other
covariates  Cons: a change in the distribution of covariates may
change the interpretation of the coefficients estimates
Unconditional quantile regression: Firpo et al. (2007, 2009)
5
Method
Firpo et al. (2007, 2009)
 The Firpo et al. (2007, 2009) decomposition method is based
on two steps:
 First step: to estimate the unconditional Recentered Influence
Function (RIF) regression to primarly investigate the differences
across quantiles in the distribution of returns
 Second step: based on quantile RIF-regressions, we decompose
price distributions across different markets
6
Method
First step: RIF-regression
 The Firpo et al. (2009) replaces the original dependent variable of a
standard hedonic regression (Yij) with a simple transformation known
as RIF. The Recentered Inluence Function ( RIF) for the quantile qt is
RIF Y ; qt   qt 
t  I Y  qt 
fY qt 
where fY is the marginal density function of Y, and I is an indicator function.
 Since the RIF is unobserved in practice, we use its sample analog that
replace the unknown quantities by their estimators
RIF Y ; qˆt   qˆt 
where q̂t is the tth sample quantile and
t  I Y  qˆt 
fˆY qt 
fˆY is the kernel density estimator.
7
Method
Second step: RIF-based decomposition
 The distributional statistic of interest can be written in terms of
expectations of its conditional RIF


qg ,t   X  RIF Yg ; qˆg ,t  X g  X g ˆg ,t
where qg,t is the unconditional tth sample quantile for group g  NY , RoW; X is a vector of
covariates; and ˆg ,t is the coefficient of the unconditional quantile regression.
 From which it follows:

RIF Y , qˆ t   RIF Y , qˆ t  

NY
NY ,
R 0W
RoW ,
ˆ

NY ,t
X

X
 t     X t

 


NY
RoW
ˆ

X ,t
Explained (composition effect)
NY ,
NY
RoW
ˆ

 ,t
NY ,
Unexplained (structural effect)
8
Decomposition results
Data
 974 Picasso paintings sold at auction worldwide during the
period 1990-2010 (Art Price)
 List of variables: artist’s name, nationality, title of the work, year
of production, materials used, date and city of sale, auction
price, dimensions, signature, and a number of further
information that might vary from case to case.
 Dataset completed with a series of indicators about the artistic
styles of the painting
 Nominal USD prices are deflated using US CPI prices
(2000=100)
9
Decomposition results
Data
price
size
panel
canvas
mixed
other_med
ny
world
sotheby
christie
other_auc
style1
style2
style3
style4
style5
style6
style7
style8
Mean
2,732,559
.626
.085
.712
.039
.0249
.544
.456
.424
.442
.134
.050
.018
.050
.100
.094
.135
.133
.223
Description
price of paintings (Euros, 2000=100)
area (m2)
oil on panel
oil on canvas
mixed media
other media (omitted category)
sold in New York
sold in the rest of the world (omitted category)
sold at Sotheby's
sold at Christie's
sold at other auction houses (omitted category)
Childhood and Youth (1881-1901)
Blue and Rose Period (1902-1906)
Analytical and Synthetic Cubism (1907-1915)
Camera and Classicism (1916-1924)
Juggler of the Form (1925-1936)
Guernica and 'Style Picasso' (1937-1943)
Politics and Art (1944-1953)
The Old Picasso (1954-1973) (omitted category)
10
Decomposition results
Unconditional quantile RIF-regression results
25th quantile
size
panel
canvas
mixed
ny
sotheby
christie
style1
style2
style3
style4
style5
style6
style7
constant
Time d.
F
Prob > F
Adj R2
Coef.
.142*
1.199***
1.280***
-1.013***
.305***
.212
.240
.334
.767**
.495*
-.283
.495***
.307**
-.183
10.739***
Bootstrap
Std. Err.
.087
.265
.204
.381
.109
.245
.245
.302
.364
.276
.186
.178
.151
.170
.426
[incl.]
12.19
.000
.23
50th quantile
Bootstrap
Coef.
Std. Err.
.423***
.166
.765***
.275
1.132***
.180
-.378
.301
.256**
.125
.301
.192
.265
.204
1.206***
.287
.809**
.396
.819***
.310
-.181
.213
.774***
.212
.933***
.197
.078
.174
10.977***
.402
[incl.]
12.38
.000
.27
75th quantile
Coef.
.592***
.464*
.932***
.115
.411***
.411**
.201
1.182***
2.207***
1.117***
.093
1.122***
1.072***
.248
12.105***
Bootstrap
Std. Err.
.158
.253
.167
.287
.139
.175
.176
.363
.510
.336
.225
.261
.229
.196
.420
[incl.]
9.00
.000
.23
90th quantile
Coef.
.650***
.717***
.732***
.380*
.515***
-.260
.009
.718**
3.368***
1.382***
.389*
1.111***
.438**
-.067
13.799***
Bootstrap
Std. Err.
.142
.283
.175
.223
.137
.183
.177
.310
.930
.930
.238
.361
.215
1.69
.373
[incl.]
4.16
.000
.17 11
Decomposition results
Decomposition analysis: full sample
Std Oaxaca-Blinder

Std. Err.
25th quantile
Std.

Err.
RIF-based Oaxaca-Blinder
50th quantile
75th quantile
Std.

Err.

Std. Err.
90th quantile

Std. Err.
overall
difference
.647***
explained
.372***
unexplained
.275*
characteristics (explained)
size
.045*
media
.115***
auctions
.236*
style
.043
time
-.067
coefficients (unexplained)
size
.165***
media
-.353*
auctions
.106
style
.023
.111
.136
.149
.436***
.160
.275
.128
.145
.178
.350*** .127
.207
.192
.143
.211
.027
.038
.109
.034
.046
.023
.133***
.101
-.010
-.087*
.015
.039
.123
.028
.049
.060*
.098*
.131
.051
-.133**
.037
.041
.164
.044
.064
.065
.193
.351
.101
.147*
-.397*
-.165
-.092
.085
.245
.413
.131
.171**
-.042
.092
.123
-76
0,25
.515
.126
time
constant
.436
.687
.617
.166
0,544
.833
-.163
-.038
.585
.965
-.054
.388
.596***
.222
.374*
.143
.187
.218
.538***
.229
.309
.149
.215
.246
.061*
.028
.157
.067*
-.092*
.038
.032
.161
.041
.057
.067*
.053
.048
.101**
-.041
.042
.039
.187
.048
.061
.058
.080
.084
.050
.098
.308
.600
.158
-.545
.581
.709
12
1.146
-.063
.091
-.662** .279
.193
.521
-.023
.145
1.340** .635
2269** 1.009
Decomposition results
.6
.6
Kernel density
New York
New York
.2
0
0
.2
Density
.4
World
.4
World
5
10
15
Log(price)
1990-1999
20
5
10
15
Log(price)
2000-2010
The two-sample Kolmogorov-Smirnov test rejects the null hypothesis that the logarithmic prices for the
two groups (NY vs. RoW) come from the same distribution (the p value is 0.000) for both sub-samples.
13
20
Decomposition results
Decomposition analysis: NY vs. RoW (1990-1999)
Std. Oaxaca
Blinder

Std.
Err.
overall
difference
.526*** .145
explained
1.060*** .374
unexplained
-.534
.366
characteristics( explained)
size
.212*** .070
media
.030
.038
auctions
.831* .355
style
.062
.061
time
-.075
.058
coefficients (unexplained)
-.027
.086
Size
.111
.229
media
1.498** .698
auctions
-.051
.115
style
-.089
.331
time
-1.976 1.102
const
RIF-based Oaxaca-Blinder
25th quantile
Std.

Err.
50th quantile
Std.

Err.
75th quantile
Std.
Coef
Err.
90th quantile
Std.

Err.
.246
.833*
-.587
.155
.489
.496
.244
.392
-.148
.155
.485
.491
.683***
.076
.607
.196
.632
.639
.719*** .240
.078
.796
.641 .811
.163***
.097*
.562
.042
-.031
.057
.051
.481
.041
.059
.221***
.014
.177
.081
-.102
.074
.036
.474
.070
.074
.257***
-.048
-.082
.145
-.197**
.087
.045
.620
.093
.086
.279***
-.027
-.295
.180*
-.058
.048
-.066
.916
-.073
.044
-1.456
.124
.324
.961
.162
.468
1.531
.148
.024
.352
.061
.147
-.879
.117
.310
.950
.155
.451
1.508
-.021
-.004
-.093
.049
-.847
1.525
.147
.392
1.241
.195
.579
1.965
.097
.051
.784
.109
.104
-.207
.189
.412
.501
-.555
1.569
-.180
.253
-.770
.740
1.940 14
2.488
Decomposition results
Decomposition analysis: NY vs. RoW (1990-1999)
1
0,8
0,6
0,4
0,2
0
-0,2
25th
50th
75th
90th
-0,4
-0,6
-0,8
difference
composition effect
structural effect
 For higher quantiles differences in
characteristics explain a large
proportion of the difference between
two groups (lines closed and follow the
same direction)
 For lower quantiles structural effect
explain more of the differences
between two groups
15
Decomposition results
Decomposition analysis: NY vs. RoW (2000-2010)
Std. OaxacaBlinder

Std.
Err.
overall
difference
.842*** .166
explained
.367*** .128
unexplained .475*** .171
characteristics (explained)
size
.022
.030
media
.247*** .072
auctions
.117
.075
style
.015
.042
time
-.034
.051
coefficients (unexplained)
size
.257*** .099
media
-.314
.268
auction
-.674
.455
style
.093
.144
time
-.196 .561
const
1.309
.869
25th quantile
Std.

Err.
RIF-base Oaxaca-Blinder
50th quantile
75th quantile
Std.
Std.

Err.

Err.
90th quantile
Std.

Err.
.416**
.200
.217
.207
.152
.228
.648***
.285*
.363*
.186
.172
.225
.483**
.245
.237
.200
.165
.228
.651***
.191
.460*
.201
.185
.252
.013
.225***
.102
-.053
-.088
.019
.077
.095
.051
.066
.032
.232***
.037
-.011
-.005
.044
.084
.110
.050
.070
.036
.145*
.089
.054
-.078
.049
.067
.102
.061
.072
.017
.136*
-.015
.105
-.053
.025
.078
.122
.070
.077
.374***
-.638*
-.399
.169
-.440
1.151
.138
.364
.603
.198
.759
1.166
.094
-.053
-.582
.078
-.173
1.000
.111
.356
.655
.180
.745
1.203
-.018
-.311
-.261
.137
-.139
.829
.130
.369
.633
.198
.773
1.204
-.057
.191
-.364
.158
-.093
.626
.130
.405
.733
.207
.846
16
1.357
Decomposition results
Decomposition analysis: NY vs. RoW (2000-2010)
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
25th
difference
50th
75th
composition effect
90th
structural effect
 From 25° to 75th quantile both
composition and structural effects
explain the difference between two
groups
 For higher quantile structural effect
explain more of the differences
between two groups
17
Conclusions
 This study sheds light on the factors that contribute to
differences in price returns among markets
 Unconditional quantile RIF-regression show differences between
covariates along the entire distribution of log price.
 Differences between NY and RoW are decomposed into a part
explained by differences in the distribution of characteristics
(composition effect) and a part explained by differences in the
impact of these characteristics (structural effect).
 In the 2000-2010 the structural effect is important in explaining differences
between markets in the upper end of the distribution
 NY premium return for top paintings
 This method can be easily applied to other non-standard
investment markets.
18
Thank you!
19