iBusiness, 2010, 2, 354-362
doi:10.4236/ib.2010.24046 Published Online December 2010 (http://www.scirp.org/journal/ib)
Double Perspective Data Envelopment Analysis:
One Approach to Estimate the “LOOP” Arbitrage
Luiz Fernando de Lyra Novaes, Sérgio Antâo Paiva
1D Sc Production Engineering, Avalsoft, Brazil; 2M Sc Regional & Urban Planning, Caixa Economica Federal, Federal Savings Bank,
Brazil.
Received July 17th, 2010; revised August 18th, 2010; accepted October 2nd, 2010.
ABSTRACT
This paper introduces the application of real estate pricing DP DEA - Double Perspective Data - Envelopment Analysis
to solve the LOOP (Law of One Price) arbitrage. A general equilibrium model of real estate values was developed to
analyze price variation over digital map, and applied to the urban area of the city of Joinville. The power of real estate
locational value assessment using DP-DEA is then compared with the usual MRA - Multiple Regression Analysis using
a real case of land data. All computational generated results and data were subsequently geocoded on a GIS - Geo-
graphic Information System. The computational generated Price line Map is easily visualized in a real estate value
chart that can enhance accuracy when compared to a conventional methodology, also a tool for immediate updates and
testing the effects of new developments over urban areas.
Keywords: Double-Perspective Data Envelopment Analysis, Law of One Price, Spatial Model and GIS
1. Introduction
In this paper, the DP-DEA (Double Perspective – Data
Envelopment Analysis) [1] is applied in order to estab-
lish the LOOP (Law of One Price) [2] arbitrage for esti-
mating property taxes value.
Kuosmanen et al. [3] approached an application with
LOOP-based weight restrictions incorporated in Data
Envelopment Analysis, utilizing the relation between the
industry level and the firm level cost efficiency measures,
they propose to apply a set of input prices that is com-
mon for all firms and that maximizes cost efficiency of
the industry. The proposed methodology was utilized to
the evaluation of the research efficiency of economics
departments of Dutch Universities.
The LOOP’s main principle states that when assets are
identical in all aspects of value or characteristics, they
must have the same price under market equilibrium. If
two identical assets have different prices, there will exist
an arbitrage opportunity and exploring this opportunity
will help ensuring that prices of the two assets converge.
An asset’s fundamental value is the price that well-
informed investors must pay in a free and competitive
market. By the Law of One Price investors would assess
values such that equivalent assets have the same price.
There can be a temporary difference between the market
price of an asset and its fundamental value. Likewise,
security analysts make their living by researching the
prospects of various firms and recommending which
stocks to buy, because their price appears low relative to
fundamental value, and which to sell, because their price
seems high relative to fundamental value.
Baye et al. [4] says: although, simple textbook models
of competitive markets for homogeneous products sug-
gest that all-out competition among firms will lead to the
law of one price. Yet, empirical studies spanning more
than four decades reveal that price dispersion is the rule
rather than the exception in many homogeneous product
markets.
More clearly, this occurs to the heterogeneous real es-
tate market. At despite of this to investment decisions,
there are many other situations in which you may need to
determine the value of an asset. Suppose that the tax as-
sessor in your town has assessed your house at $490,000
for property tax purposes. Is this value too high or too
low?
In the real estate market it is stated that no two distinct
assets are identical in all aspects. Always, some differ-
ence of characteristics exists, maybe the localization,
configuration or the size of the lot and the house or
something else. The process of valuation requires that we

Double Perspective Data Envelopment Analysis: One Approach to Estimate the “LOOP” Arbitrage 355
find assets comparable to the one whose value we want
to estimate, and make judgments about which differences
are important on their value to investors. This specific
market equilibrium point is achievable when buyer and
seller engaged in a dispute have attended their own in-
terests of all kinds on the value of a specific real estate.
Valuation information is fundamental to financial de-
cision-making. Our goal in real estate assessment is to
estimate a value of a spread range between the maximum
value and the minimum value offered or bided in an effi-
cient property market.
2. Tax Assessment
The Direct Capital Comparison (DCC) is the most con-
ventional method used in real estate value appraisal (see
Mackmin (1994), for instance). DCC requires an “al-
lowance in money terms” (Lewis (1999)) for any differ-
ences between the subject property and the comparable
properties, for which the appraiser can employ either
multiple regression analysis (MRA), expert systems (ES)
or artificial neural networks (ANN). The most usual me-
thod established is the MRA that’s diffused between the
professional’s experts.
The tax assessment problem consists in establishing a
mean value of tax that will apply over different proper-
ties. Nowadays, in spatial models DCC and GIS data
basis are used.
The question is to consider valuing a house using the
observed prices of comparable houses. Suppose that you
own a house and that each year you pay property taxes to
the local town council, which are computed as a propor-
tion of the house estimated market value. You have just
received a notice from the town’s real estate assessor
notifying you that the estimated market value of your
house this year is $ 490,000.
Suppose that your next-door neighbors just sold a
house identical to yours for $ 330,000. You could justi-
fiably appeal the town’s assessment of $ 490,000 for the
value of your house being too high, on the grounds that a
house virtually identical to yours was just sold for a price
$ 160,000 less than your assessed value.
In the valuation of your house, you are applying the
Law of One Price, considering that if you were to put the
house up for sale, you are implying that your expectation
is that it would fetch a price of $330,000 because a com-
parable house just sold for that amount.
Of course, the house next door is not exactly identical
to yours because it is not located on your lot but on the
one next to it. And you probably cannot prove that if you
actually put your house up for sale it would fetch only $
330,000 rather than the $ 490,000 that the town’s asses-
sor says it is worth. Nonetheless, unless the town’s as-
sessor can point to some economically relevant feature of
your house that would make it worth $ 160,000 more
than your neighbor’s house (such as more land or floor
space), you would have a strong logical case (and proba-
bly a strong legal case, too) for appealing the town’s as-
sessment.
The point is that even when the force of arbitrage
cannot be relied on to enforce the Law of One Price, we
still rely on its logic to value assets.
But how did the assessor place a value on your house?
Because you will have to pay taxes based on his assess-
ment, the assessor must choose a valuation method that
is perceived as fair and accurate. Valuation models used
in real estate assessment vary significantly in their level
of complexity and mathematical sophistication.
Property tax, or millage tax, is an ad valorem tax that
an owner is required to pay on the value of the property
being taxed. Property tax can be defined as generally, tax
imposed by municipalities upon owners of property
within their jurisdiction based on the value of such prop-
erty. There are three species or types of property: Land,
Improvements to Land (immovable manmade objects;
i.e., buildings), and Personal (movable manmade objects).
Real estate, real property or realty is all terms for the
combination of land and improvements. The taxing au-
thority requires and/or performs an appraisal of the mon-
etary value of the property, and tax is assessed in propor-
tion to that value. Forms of property tax used vary be-
tween countries and jurisdictions.
The property tax (ad valorem tax) relies upon the fair
market value of the property being taxed for justification.
In Brazil, it's often given to property tax a value per
square meter. To calculate the property tax for a lot, the
authority will multiply the assessed unit tax value of the
property by its area.
We developed a LOOP DP DEA on a Spatial Model to
a housing data set from Joinville, Santa Catarina, Brazil.
The County Department is responsible for complying
with Brazilian fiscal responsibility law that improves
public finance rules while enforcing responsibility in
fiscal management. That presumes well-planned and
transparent actions to prevent social risk and correct de-
viations that may affect the equilibrium of public ac-
counts. This law is a major obligation to be achieved. In
that way, the town’s assessors have to establish equitable
and fair values to different real estates.
3. LOOP/DP-DEA
A new approach is being proposed to solve LOOP arbi-
trage, where the uncertainty in the unit’s value resulting
from market transactions was taken into account by ex-
plicitly representing the economic agents involved in a
transaction, namely buyer and seller, whose actions es-
tablish a set of transactions. Because of its non-linear

Double Perspective Data Envelopment Analysis: One Approach to Estimate the “LOOP” Arbitrage 356
structure, the proposed method performs better than re-
gression analysis, in terms of adhering to data informa-
tion, as shown in Subsection 3.2. Concerning ES and
ANN, the new method overcomes an important weak-
ness, as it offers model parameters, i.e., the weights as-
signed to each input, thus facilitating the cognitive rea-
soning process. However, the major advantage of this
method consists in supplying a reference set for com-
parison with the assessed property, a characteristic di-
rectly linked to DCC philosophy and which is not pro-
vided by any other method so far.
The methodology to achieve this was named Law of
One Price by Double Perspective-Data Envelopment
Analysis (LOOP/DP-DEA). The DP-DEA makes use of
two encapsulating surfaces that enfold, in an n-dimen-
sional space, all the observed data. Real estate units
which, from the point of view of either the seller or the
buyer, present an “efficient” price, define those surfaces.
The remaining units can have their value assessed by
taking the envelopments as frameworks, under an out-
put-oriented or an input-oriented DEA model. The
LOOP/DP-DEA is the market value estimated between
the two encapsulating surfaces, which minimize the me-
dian absolute deviation of the whole distribution.
This methodology intends to make a contribution to
the real estate community in three different ways: firstly,
by introducing the concept of the LOOP/DP-DEA used
to estimate the fundamental value; secondly, by showing
how this concept can be applied in real terms, namely the
real estate value assessment problem; and thirdly by
suggesting that the idea of the two enveloping surfaces
can be brought to the more general context of economic/
financial transactions, taxation, urban planning or even
auctions.
The specific application of DP-DEA to real estate tax
assessment can have wide impact in county public insti-
tutions involved on regulation and taxation, dealing with
many daily decisions concerning county administration.
If a more precise tool is available, these institutions
would be able to achieve a much more reliable portfolio
of taxation and, therefore, attending a well-planned pub-
lic administration.
In recent years, GIS has established itself as an inte-
gral component of business improvement programs at
government agencies and utilities, it has sparked flashes
of interest from the utility of visualizing the analysis re-
sults. In that way, assuring for the analyst a powerful
instrument to better understood. New emphasis on reen-
gineering bodes well for commercial GIS, however, and
this trend could trigger GIS’ ascent to a more prominent
spot in corporate decision-making tools in Brazil. On this
propose we apply the value estimation made by MRA,
DP-DEA and real estate data over a geographic data ba-
sis of Joinville and analyze them comparatively. The
comparison of each estimated isolines formed by the
regions with the same taxes value per square meter. The
isolines join points of equal value on a surface geo-
graphic map. The shading defines bands between two
succeeding isolines. In our study case, they decrease of
value on the inside to the outside of the map.
3.1. Double Perspective DEA Model – DP-DEA
The DEA method is used to accomplish comparative
analyses of a set of observations. For each observed unit,
either a State in a national economy or a simple piece of
equipment, it provides a measure of efficiency or pro-
ductivity. DEA is a generalization of the nonparametric
method of productivity measurement originally devel-
oped by Farrell [5].
The first classical DEA model was the CCR proposed
by Charnes, Cooper and Rhodes [6], also known as CRS
because it assumes Constant Returns to Scale. The sec-
ond one was the BCC introduced by Banker, Charnes
and Cooper [7], or VRS, as it postulates Variable Returns
to Scale. Shortly, the method works as follows [8]. Some
applications and integration perspectives in Decision
Support Theory may be seen in Lins et Meza [9].
The DP-DEA is an extension of Data Envelopment
Analysis [10]. This approach has been able to assess a
particular real estate, or for a general assessment, esti-
mated by market’s data. The mathematical formulation
of the DP-DEA method makes it possible to obtain an
interval for a property’s value as a function of its physi-
cal features and location, as proposed by Novaes [1].
In this paper the DP-DEA method was applied to a
database consisting of the market values of lots that were
established in real estate transactions or offers, and
which have occurred in several neighborhoods in the city
of Joinville. This data basis was been performed by the
Joinville Municipal Treasurer Department. The buy and
sell bids for the different units define the supply and de-
mand possibilities as a function of the commodities’ at-
tributes [11].
Double Perspective DEA (DP-DEA) uses as an objec-
tive measure of the observed units the normalized dis-
tance to the two simultaneous perspectives: the hyper
planes by maximization of outputs and by the minimiza-
tion of inputs, in such a way that inputs under a buyer’s
perspective are the outputs under the seller’s perspective
and vice-versa. Property value is the dependent variable
estimated by the MRA method when applied to real es-
tate assessment. Analogously, in LOOP DP-DEA we will
estimate the dependent variable, which is the property
value: the monetary amount received (output of the
transaction on a seller’s perspective) and the monetary
amount paid (input of the transaction on a buyer’s per-

Double Perspective Data Envelopment Analysis: One Approach to Estimate the “LOOP” Arbitrage 357
spective). The property’s physical features are the input
of the transaction on seller’s perspective and the output
of the transaction on buyer’s perspective. In LOOP
DP-DEA, like in MRA method, they are the independent
variables.
The method employs both classical CRS and VRS
DEA models. Starting from the selection of n observed
real estate data, with m independents variables like lo-
calization and s dependent variable, a DP-DEA model
determines a subset composed of k data that belongs to
the perspective’s enveloping surface. These data are
considered the best to attend one or other perspective
and define the segments of the enveloping surface, thus
motivating the envelope form of DEA CCR or BCC
models. The contained subset, not belonging to this
surface, is formed by the remaining n - k inefficient
data to each perspective. The computation of the nor-
malized distance of each observed unit requires the so-
lution of a linear programming problem. To estimate
the value of the dependent variable, we have to multiply
the observed value by the result Z of equation 28 which
minimizes the median absolute deviation of the whole
distribution.
The formulation of DP-DEA in their dual multipli-
ers/envelope output-oriented is the same of the both clas-
sical CCR and BCC DEA models, shown in Table 1. In
the multipliers model, the optimal values of the decision
variables: v, u and u0* are the parameters of the frontier
hyper plane defined by the constraints (3). They are
finding such that the distance measure for observed data
Table 1. Output-oriented CCR and BCC models.
Multipliers (Primal)
*
000
1
m
ii
i
Min Lxu 


 (1)
0
1
1
s
rr
r
Subject toy 



 (2)
*
0
11
01,...,
sm
rrj iij
ri
yxu jn 


 (3)
,1,......, ,1,....,
ri
rs im     (4)
,0,,
ir ir
  (5)
**
00
:0 :
F
orCCR uForBCC u unconstrained (6)
Envelopment (Dual)
11
sr
SSy x
yx
M
ax Hhss 


 

(7)
0
1
0, 1,......,
n
Srjrj r
j
Subject tohyysrs 



 (8)
0
1
0, 1,......,
n
iJiji
j
x
xs im 


 
 (9)
,,0, ,,
jri
s
skji 

 (10)
1
:1 



n
j
j
For BCC (11)
“O” is minimized. This distance can be defined as a pro-
gramming problem that minimize the linear combination
of its independents variables (1) subject to the constraints:
the normalized linear combination of its dependents
variables (2) and that all distance measures must be plus
than or equal to one (3). Non-Archimedean constrained
multipliers (4) can be a substitute for classical positive
constrained multipliers (5), where is an infinitesimal
(non-Archimedean) amount.
According to the envelope form, the problem consists
of maximizing the objective function (7) on the decision
variable h S (1/h S represents the normalized distance to
the hyper-plane) subject to constraints (8) to (11). These
constraints guarantee that the projected efficient unit in
seller’s perspective will be located inside the production
or demand possibilities set, which is defined as a linear
combination of the outputs (and inputs) vectors, using
the coefficient vector. In accordance to the BCC assump-
tions, this linear combination should be subjected to a
convex constraint (11), which does not hold in the CCR
model. The inclusion of this latter constraint in BCC
corresponds to an unconstrained dual variable (6) in the
multipliers model.
Analogously, to the classical input-oriented dual mul-
tipliers/envelope CCR and BCC models the variables and
constraints are quite similar; the main difference being
that in the multipliers model the objective is to maximize
the linear combination of the outputs of the observed
data, keeping the independent variables normalization
constraint. As for the envelope form, the variable h is to
be reduced, and multiplied by the input of the assessed
(observed) unit [6,7].
As Figures 1 and 2 illustrate, considering only one
input and one output (either the maximum or the mini-
mum values of the units’ sale and only one attribute, i.e.,
their areas).
In order to simultaneously use both input and output
oriented models, we will transpose the graph of the input-
Figure 1. Output-oriented model.

Double Perspective Data Envelopment Analysis: One Approach to Estimate the “LOOP” Arbitrage 358
oriented model in Figure 2 to obtain, in Figure 3, the
same axes as in the output-oriented model of Figure 1.
The input-oriented model transposed is resulted of the
transposition of the classical input-oriented dual multi-
pliers/envelope CCR and BCC model demonstrated in
Table 2.
The formulation of DP-DEA in their dual multipli-
ers/envelope input-oriented shown in Table 2 is result of
the transposition of the both classical CCR and BCC
DEA models. In the multipliers model, the optimal val-
ues of the decision variables: v, u and w0* are the pa-
rameters of the frontier hyper plane defined by the con-
straints (14). They are finding such that the observed
DATA “0” is maximized. This distance can be defined as
a programming problem that maximizes the linear com-
bination of its independents variables (12) subject to the
constraints: the normalized linear combination of its de-
pendents variables (13) and that all distance measures
must be less than or equal to one (14). Non-Archimedean
constrained multipliers (15) can be a substitute for clas-
sical positive constrained multipliers (16), where is an
infinitesimal (non-Archimedean) amount.
According to the envelope form, the problem consists
of minimizing the objective function (18) on the decision
variable hB, subject to constraints (19) to (22). These
constraints guarantee that the projected efficient unit in
Buyer’s perspective will be located inside the demand
possibilities set, which is defined as a linear combination
of the outputs (and inputs) vectors, using the coefficient
vector. In accordance to the BCC assumptions, this linear
combination should be subjected to a convex constraint
(22), which does not hold in the CCR model. The inclu-
sion of this latter constraint in BCC corresponds to an
unconstrained dual variable (17) in the multipliers mod-
el.
Figure 4 shows the two graphs put together. The
space defined by the enveloping surfaces corresponds to
a set of accomplished transactions [10]. It results from
the intersection of the set of supply possibilities [12,13]
Shephard [14], and the set of demand possibilities. In
other words, the DP-DEA defines supply and demand
frontiers. Formally, it is possible to devise the DP-DEA
model as a classic DEA output-oriented model together
with an input-oriented model with the transposition of an
axis, as shown in Figure 4.
The software EDODEA [15] assesses the projected ef-
ficient unit on buyer’s and seller’s perspective envelop-
ing surfaces.
3.2. Law of One Price by Double Perspective
Data Envelopment Analysis –
LOOP/DP-DEA
The software EDODEA assesses the dependent variables
Figure 2. Input-oriented model.
Figure 3. Input-oriented model (transposed).
Table 2. Input-oriented CCR and BCC models transposed.
Multipliers (Primal)
*
000
1
m
ii
i
MaxZv xw


 (12)
0
1
1
s
rr
r
Subjecttou y


 (13)
*
0
11
01,...,
ms
iijr rj
ir
vxuywjn

 
 (14)
,1,......, ,1,....,
ri
ursvi m    (15)
,0, ,
ri
uv ir (16)
**
00
:0 :
F
orCCRwForBCCw unconstrained (17)
Envelopment (Dual)
11
sr
BBy x
yx
M
inH hss 


 

 (18)
0
1
0, 1,......,
n
Brjrj r
j
Subject tohyysrs 



 (19)
0
1
0, 1,......,
n
iJiji
j
x
xs im 



 (12)
,,0, ,,
jri
s
skji 

 (21)
1
:1
n
j
j
ForBCC 


 (22)

Double Perspective Data Envelopment Analysis: One Approach to Estimate the “LOOP” Arbitrage 359
Figure 4. Double perspective DEA method.
Фj by the minimization of the median absolute deviation
of the whole distribution determined by the escalate Z,
the formulation is:
1
()0
n
jj
j
y 


 (23)
()
j
Sj BjBj
Z
yy y

 (24)
00
jZ

 (25)
By Seller’s Perspective j
Sj Sj
y
yh  (26)
By Buyer’s Perspective
B
jjBj
yyh

 (27)
11
1
1
nn
j
Bj j
jj
n
Sj j
jSj
yhy
Z
hy
h










(28)
Notation
j

Real estate j price assessable
Sj
y Projected value of data j on the enveloping surface
on seller’s perspective
B
j
y Projected value of data j on the enveloping surface
on buyer’s perspective
j
y Real estate j price observed
Z
escalate
Sj
h Real estate assessed j deviations to the enveloping
surface on seller’s perspective
B
j
h Real estate assessed j deviations to the enveloping
surface on buyer’s perspective
The LOOP/DP-DEA piece-wise line on R2 is illus-
trated in Figure 5, applying all possible variation of
j

by Equation (24).
4. Conclusions
Applying on the software EDODEA, the data basis of
two papers Novaes et Paiva [1] and [16], we obtain re-
spectively:


2004 0,41045Z and

2006 0,2739Z
The results of MRA and DP-DEA medium value ob-
tained in Novaes et Paiva [16] paper are related on Table
3 and compared with the news results obtained by the
applying to LOOP/DP-DEA.
The results obtained in Novaes et Paiva [1] paper are
related on Table 4 and compared with the new results
obtained by the applying to LOOP/DP-DEA.
Comparison of results on Tables 3 and 4 indicates de-
viations with best results on estimating with LOOP/DP-
DEA method.
Figure 5.
J

The piece-wise line-LOOP DP-DEA.
Table 3. The results of MRA and DP-DEA medium value in
Novaes et Paiva [1].
Statistical Analysis
of deviations
Multiple
Regression
Analysis
DP-DEA
medium value
LOOP/DP-D
EA
Medium deviations0,00 −105,27 0,01
Total sum of
deviations 1,14 −26.633,65 1,57
Total sum of squares
of deviations 54.794.462,34 17.965.031,42 7.534.440,88
Table 4. The results of MRA and DP-DEA medium value in
Novaes et Paiva [16].
Statistical
Analysis
of deviations
Multiple
Regression
Analysis
DP-DEA
medium value LOOP/DP-DEA
Medium
deviations 0,01 −1.372,30 0,00
Total sum of
deviations 1,31 −351.309,63 −0,01
Total sum of
squared
deviations
13.699.082.578,10 8.905.893.694,13 8.139.847.100,39

Double Perspective Data Envelopment Analysis: One Approach to Estimate the “LOOP” Arbitrage 360
The software ArcGIS Desktop lets perform full range
from a geodatabase design and management to editing
from map query to cartographic production and sophisti-
cated geographic visualization and analysis. When you
add a dataset to a map, a layer is created. In the course of
making your maps, you’ll add and remove layers, turn
them on and off, changing the draw order, and so on, to
display exactly the data you need to see and work with.
When you add a dataset to a map, the software draws
all the features using the same symbol. Often you’ll want
to draw the data symbolized by an attribute value (almost
the case for continuous areas). The symbol used to draw
each feature (the marker size, continuous line, or area
color fill, for example) is determined by the value of a
feature for a particular attribute.
Our case study, applied in the Arcview architecture,
over a geographic data set on Joinville map, the land
value per square meter of a property tax estimated by
each method: MRA and both DP-DEA methods are
geocoded in coordinate system UTM-Universal Trans-
verse Mercator SAD 69. In an easy view, we compared
then with the observed data. The technical named ordi-
nary kriging produce from each point geocoded with the
same value a linkage and an interpolation in a continue
surface by the variance between of the estimated or ob-
served values [17,18].
These applications result on four cartographic layers,
Figures 6 to 9, that possibility an analysis of the accu-
racy on estimation of each method. It possibility the
comparative overview analysis, on how the isolines sur-
face seems more adjustable with the Figure 6, that is the
performed by a collection of a County cartographic lot
tax rates geocoded data basis. The defined isolines de-
limit areas with the same estimated value, which in prac-
tice represents the land value per square meter for a
block. The geographic Figure 6 represents the variations
of real estate value observed; Figure 7 represents the
variations of land value estimated by MRA; Figure 8
represents the variations of lands by DP-DEA medium
value, and; Figure 9 represents the variations of lands by
LOOP/DP-DEA. The outside isolines to inside have the
range variations of lands value per square meter of $0 to
$25,00; $25,00 to $50,00; $50,00 to $100,00; $100,00 to
$200,00; $200,00 to $400,00; $400,00 to $800,00, and
more than $800,00.
Visualizing the Figure 9 we conclude that the map
with the isolines estimated by LOOP/DP-DEA is closer
to the real estate original value isolines represented in
Figure 6. In conclusion, LOOP/DP-DEA method in this
case is more accurate to estimate real estate value than
MRA method.
Figure 6. Real estate value.
Figure 7. Real Estate Value estimated by MRA (Multiple
Regression Analysis).

Double Perspective Data Envelopment Analysis: One Approach to Estimate the “LOOP” Arbitrage 361
Figure 8. Real estate value estimated by DP-DEA medium
value.
Figure 9. Real estate value estimated by LOOP/DP-DEA.
REFERENCES
[1] L. F. L. Novaes, “Double Perspective DEA in Real Estate
Assessment with GIS,” D.Sc. Thesis, Coppe/UFRJ, 2002,
pp. 20-26.
[2] E. W. Eckard, “The Law of One Price in 1901,” Eco-
nomic Inquiry, Vol. 42, No. 1, 2004, pp. 101-110.
[3] T. K. Kuosmanen, L. Cherchye and T. Sipiläinen, “The
Law of One Price in Data Envelopment Analysis: Re-
stricting Weight Flexibility across Firms,” European
Journal of Operational Research, Vol. 170, No. 3, 2006,
pp. 735-757.
[4] M. Baye, J. Morgan and P. Scholten, “Information,
Search, and Price Dispersion,” In: T. Hendershott, Ed.,
Handbook on Economics and Information Systems, El-
sevier, Forthcoming, 2006.
[5] M. J. Farrell, “The Measurement of Productive Effi-
ciency,” Journal of the Royal Statistical Society, Series A,
General, Part 3, Vol. 120, No. 3, 1957, pp. 253-281.
[6] A. Charnes, W. W. Cooper and Rhodes, “Measuring the
Efficiency of Decision-Making Units,” European Journal
of Operational Research, Vol. 2, No. 6, 1978, pp. 429-
444.
[7] R. D. Banker, A. Charnes and W. W. Cooper, “Some
Models for Estimating Technical and Scale Inefficiencies
in Data Envelopment Analysis,” Management Science,
Vol. 30, No. 9, 1984, pp.1078-1092.
[8] R. Färe and G. Grosskopf, “Estimation of Returns to
Scale Using Data Envelopment Analysis a Comment,”
European Journal of Operation Research, Vol.79, No. 2,
1994, pp. 379-382.
[9] M. E. Lins and L. A. Meza, “Data Envelopment Analysis
and Integration Perspectives Decision Support Theory,”
Coppe/UFRJ, 2006, pp. 7-53.
[10] M. E. Lins, L. F. L. Novaes and L. F. L. Legey, “Real
Estate Appraisal: A Double Perspective Data Envelop-
ment Analysis Approach,” Journal of Operational Re-
search, Vol. 138, No. 1, 2005, pp. 79-96.
[11] G. Debreu, “Theory of Value: An Axiomatic Analysis of
Economic Equilibrium,” In: Cowles Foundation for Re-
search in Economics of Yale University, 1959, pp. 28-79.
[12] Färe, R., G. Grosskopf and C. A. K. Lovell, “Production
Frontiers,” Cambridge University Press, Cambridge,
1996.
[13] R. Färe, C. A. K. Lovell and K. Zieschang, “Measuring
the Technical Efficiency of Multiple Output Technolo-
gies”, W. Eichhorn, R. Henn, K. Neumann, Eds., 1983.
[14] R. W. Shephard, “Cost and Production Function,” Prince-
ton University Press, New Jersey, 1953.
[15] Software: EDODEA. http:www.avalsoft.com.br
[16] L. F. L.Novaes, M. E.Lins, S. A. Paiva and L. F. e
Pinheiro Jr., “Avaliação Imobiliária Pelo Método da
Envoltória sob Dupla Óptica,” 3º Simpósio Brasileiro de
Engenharia de Avaliações, Curitiba, 2002.
[17] N. Cressie, “Statistics for Spatial Data,” 1st Edition,
Wiley InterScience, New York, 1991.

Double Perspective Data Envelopment Analysis: One Approach to Estimate the “LOOP” Arbitrage 362
[18] E. H. Isaaks and R. M. Shrivastava, “Applied Geostatis-
tics,” 1th Edition, Oxford University Press, New York,
1989.