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ANALYSES
198
Hedonic Price Methods
and Real Estate Price Index:
an Explanatory Study
for Apartments Market
in Belo Horizonte, Brazil,
from 2004 to 2015
1 Brazilian Institute of Geography and Statistics (IBGE), Avenida República do Chile 500, 5o andar Rio de Janeiro, Brazil.
E-mail: luiz.paixao@ibge.gov.br, phone: (+55)2121420194.
Abstract
Brazil does not have an ocial real estate price index yet. A 2011 presidential decree stipulated for the Brazilian
Institute of Geography and Statistics (IBGE) the assignment to create and spread a real estate price index
for Brazil. In this paper, we test some dierent hedonic model methods to estimate quarterly price indices
for apartments in Belo Horizonte, Brazil, from January 2005 to December 2015. Our goals are: i) to measure
and compare the dierent hedonic methods; ii) to present some results that will contribute to the discussion
about the development of an ocial real estate price index in Brazil. e empirical results corroborate the idea
of intense apartment prices valuation in Belo Horizonte, mainly between 2007 and 2011, when the annual price
index growth remained above 20%. ese results cast light on the potential use of both hedonic methods
and administrative data base to construct an ocial real estate price index for Brazil.
Keywords
Price indices, hedonic price model, housing market
JEL code
C43, E31, R31
INTRODUCTION
Subprime crises turned attention around the world to the real estate price dynamics question. In Brazil
the recent large valuation of real estate price adds more attention to the subject. Academics, news, real
estate agents, Brazilians government agencies and statistical institutes started to discuss the importance
Luiz Andrés Ribeiro Paixão1 | Brazilian Institute of Geography and Statistics, Rio de Janeiro, Brazil
DOI
https://doi.org/10.54694/stat.2022.46
Received 30.9.2022, Accepted (reviewed) 16.11.2022, Published 16.6.2023
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of having an adequate measure of real estate price over time. e Federal Government Decree number
7 565, dated 21 September, 2015, established IBGE (Brazilian Institute of Geography and Statistics)
as the responsible entity to create and disseminate an ocial real estate price index for Brazil. Since
then, IBGE and others governmental agencies have implemented studies regarding the database
and methodology to construct a future Brazilian ocial real estate price index (Nadalin and Furtado,
2011; Santos and Salazar, 2011).
e Brazilian academy has been studying real estate price index and its application in Brazilian
context. In recent years, Rozenbaum (2009), Paixão (2015), and Simões (2017) are examples of doctoral
thesis related to this subject. Rozenbaum (2009) used administrative data to construct a hedonic
quality adjusted price index for the city of Rio de Janeiro. Simões (2017) also measured the hedonic
quality adjusted price index for Rio de Janeiro, using real estate agencies data, while Paixão (2015),
also used administrative data to construct a hedonic quality adjusted price index for Belo Horizonte’s
ci ty.
Some researches in this eld published in Brazilian academic journals. Gonzalez (1997) estimated
a simple time-dummy hedonic model to construct price index for apartments rents in Porto Alegre.
e same approach was applied by Rozenbaum and Macedo-Soares (2007), to estimated real estate
valuation in Rio de Janeiro’s district of Barra da Tijuca, and by Paixão (2015a), to estimate real estate
price indices for Belo Horizonte. Albuquerque et al. (2018) used repeated sales method to construct
an index for the city of Brasilia, the capital of Brazil.
Some University’s agencies like the Institute of Economic Research Foundation (FIPE), from University
of São Paulo (USP), and the Institute of Economic, Administrative and Accounting Research (IPEAD),
from Federal University of Minas Gerais (UFMG), released real estate price indices using stratied median
methods. e widespread FIPE-ZAP real estate index is calculated by FIPE from the real estate advertised
data collected in ZAP’s web site platform. e Brazilian Central Bank also estimated and published
a monthly stratied median real estate price index, constructed from the real estate loans data, called
Financed Residential Properties index (IVG-R). Despite the importance and relevance of those indices
for the society, government, academics and real estate agencies some gaps remain. None of those indices
used the hedonic quality adjustment methodology, recognized as the best to deal with the nature of real
estate’s market data (Diewert, 2009; Hill et al., 2018). Besides that, only IPEAD uses administrative data
which cover the whole transacted market.
In this paper we try to construct quarterly hedonics quality adjusted real estate prices indices for Belo
Horizonte city using administrative data. For this task we will use the hedonic methods proposed by Hill’s
(2013), and Hill’s et al. (2018). We will use the same methods used by Hill et al. (2018) in their analysis
of Sidney and Tokyo markets, to produce comparable results.
e last part of the paper is structured as follows. e next section explains the dierent hedonic
price methods used to measure the quality adjusted housing price indices. e second section is focused
on the database and introduces the Brazilian city of Belo Horizonte. e objective of the third section
is to test the several hedonic methods in Belo Horizonte’s real estate market database. Finally, our main
results are summarized in the conclusion.
1 HEDONIC QUALITY ADJUSTED REAL ESTATE PRICE METHODS
1.1 The hedonic price model
Estimating housing price indices is a complex task. Housing is a type of complex good (or service),
that is, a good where each unit or model diers from the others in qualitative terms. A complex good
can be described as a bundle of many characteristics (or attributes), so each unit or model is a peculiar
bundle of attributes. Computing index prices for complex good necessarily means controlling the change
in the good price by the change in composition of its characteristics.
ANALYSES
200
The hedonic price model establishes a functional relationship between the price of the good
and its characteristics. In a hedonic perspective a good is a basket of characteristics Z, as represented below:
1, 2
,,
n
ZZ
zz z
. (1)
e price of a good follows a hedonic function as describes in Formula (2):
1, 2
,,
n
PP
zz z
. (2)
Although only the price of the good can be observed in the market, the hedonic function establishes
that the price of a good is determined by the composition of basket of characteristics. Therefore,
each attribute (i) has an unobserved price (implicit price) that is represented by the rst derivative
of the hedonic function with respect to i.
. (3)
i
i
P
px
e seminal paper of Rosen (1974) validated the hedonic price model in theoretical terms. Empirically,
Waugh (1928) was pioneer in apply hedonic regression in vegetables market study. Court (1939) used
hedonic price regression to construct automobile price indices. Griliches (1958, 1961) constructed
hedonic quality adjusted price indices for fertilizers and automobile markets respectively. From Griliches
contributions, the application of hedonic model widespread in the academic world, covering many
types of dierent goods and services like computers, refrigerators, fruits, musical instruments, paints
etc. However, it was in the real estate market that the hedonic approach achieved its largest projection.
1.2 The hedonic quality adjusted price indexes: the real estate case
Griliches (1971) argues that a complex good’s price change can be divided in two dimensions. e rst
is the observed price change of the good in the market. e second is the unobserved price change
of the basket of characteristics. To estimate the unobserved price change, it is necessary to use the hedonic
model regression as a quality adjusted factor. Discounting the price change of the attributes bundle from
the observed price of the good results in a “pure” estimate of a complex good price change.
ere are several ways how to construct a quality adjusted price index from the hedonic methodology.
Court (1939) and Griliches (1961) already advanced some questions, like the possibility of using both
cross-section regressions or time-dummy approaches. Tripllet (2004) created a taxonomy of the several
hedonic methods used to compute quality adjusted price indices for technological goods. Hill (2013)
applied this Tripllet’s taxonomy to the housing market case.
Hill et al. (2018) using a Hill (2013) approach compiled the hedonic methods used by the European
national statistics institutes. e rst category embraces all indices which requires cross-section regressions
models and, as a result, involves data imputation. e second category is based on time-dummy regressions.
1.2.1 Imputation approach
1.2.1.1 Repricing model
e rst imputation method described by Hill et al. (2018) is the repricing method. Like Hill et al. (2018)
in this study we adopted quarterly price indices as default and hedonic quality adjusted price indices
could be constructed for any period. Dening the base period is the rst task in the repricing model.
en, a hedonic regression is estimated for this period. e price implicit estimated in hedonic regression
is used to impute prices for each subsequent quarterly. e base period can be xed or be updated
at regular time intervals.
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Hill et al. (2018) recommends estimating one regression for the whole base year:
, (4)
where ln(p) is the natural logarithmic of housing price in the base year (1), q is the quarterly of the sale,
h is the dwelling sold and c is each characteristic of the dwelling.
en, the implicit prices estimated (
ˆ
) are used to estimated prices for each subsequent quarterly.
e repricing method is, therefore, a sort of Laspeyres index. e quality adjustment factor
,1,,
tq tq
QAF
is dened as the ratio of the imputed prices for adjacent quarters, q and q –1 for example.
. (5)
1, ,,
1
,1,,
1, ,1,
1
exp
exp
ˆ
ˆ
C
ctq c
c
tq tq C
ctq c
c
z
QA
F
z
To construct the repricing method price index (RP) a quality unadjusted price index (
,, 1
tq tq
QUPI
)
dened as a ratio between geometric mean prices (
p
) of adjacent quarters is calculated as follows:
. (6)
,
,, 1
,1
tq
tq tq
tq
p
QUPI
p
Finally, RP is the ratio between quality unadjusted price factor and quality adjusted price factor.
. (7)
,,
,, 1
,1 ,,,1
tq tq tq
tq tq tq
PQUPI
PQAF
e main attractive feature of RP relies on the fact that it is not regression intensive. In the end,
it requires only one regression (Hill et al., 2018). However, to achieve good results, Hill et al. (2018: 224)
suggested that “the base year under the repricing method should be updated at regular time intervals”.
Italy and Luxembourg national statistics institutes are benchmark examples since both updated the base
every year (Hill et al., 2018).
1.2.1.2 Average characteristic method
e average characteristic method (AC) requires, as any method, a denition of a base period. Aer that,
the average characteristic of the dwellings sold in the base period are computed. e next step consists
in estimating hedonic regressions for each subsequent period, quarterly in our case. en the imputed
prices are calculated, applying the estimated quarterly implicit prices on the average characteristics
of the base period.
Following Hill et al. (2018), the European national statistical institutes calculated the basket of average
characteristics for a whole year (base year), . In this line, the European national statistical institutes
adopted a Laspeyres version of AC1. e base is updated every year. en, a hedonic regression is estimated
for each quarter (q) of the following year (t):
. (8)
,
,, ,,
,,
,
1
ln
()
C
tc
tq htqhctqh
c
pz
e quality adjusted price index estimated by AC is given as follows:
. (9)
1,
,,
,
1
,1 1,
,1,
1
exp( )
expˆ
()
ˆ
C
tc
tq tq c
c
C
tq tc
tq c
c
Pz
Pz
ANALYSES
202
1.2.1.3 Hedonic imputation method
Real estate is a threshold situation of complex goods. Each unity of real estate diers from the other.
Added to this, the set of dwellings sale in one period diers from the set of dwellings sale in other periods.
erefore, it is not possible to construct a basket of dwellings to follow over time. e hedonic imputation
method is a way to estimate the price of each dwelling sold in t would have in another period, t + 1
for example. According to Hill et al. (2018: 225–6): once a hedonic model has been estimated, it allows
one to ask counterfactual questions such as what a particular dwelling actually sold in say period t would
have sold for instead in period t + 1.
Like the AC, one regression as (8) is estimated for each period. The regression in t + 1 is used
to impute the price in t + 1 for each observed transacted dwelling in t. Likewise, the regression
in t is used to impute the price in t for each observed transacted dwelling in t + 1. To construct
the index, Hill (2013) recommended to use the regression estimated price in t instead of the observed
price for each observed transacted dwelling in t. Such procedure is known as double imputation. From
the hedonic imputation method geometric Laspeyres (GL), geometric Paasche (GP) and Tornqvist prices
indices can be extracted.
Few European national statistical institutes use hedonic imputation methods. Hill et al. (2018) follow
the German version of double imputation Tornqvist (DIT). From a set of regressions like (8) the GL,
GP and DIT are estimated as follows:
, (10)
,1
,
1
,1 1,
1
ˆ
ˆ
C
tq tc
c
C
tq tc
c
GL
ex
pz
, (11)
,,
1
,1 ,
1
ˆ
ˆ
C
tq tc
c
C
tq tc
c
GP
ex
pz
*
DITGLGP
. (12)
1.2.2 Time-dummy approach
1.2.2.1 Simple time-dummy
The time-dummy approach consists in constructing price indices from the estimated parameter
of a dummy time variable in a hedonic regression. Usually, the rst period in the series is used as the base.
e simple time-dummy model (TD) requires only one regression and it is the simples and most intuitive
hedonic method. e typical TD regression is illustrated as follows:
, (13)
where is a time dummy for each period and is the prince index estimated for the period .
Despite its simplicity, there are some pitfalls in using TD (Hill, 2013). First, the TD does not allow
the implicit price changes over time. As a result, the longer the series, the worst will the TD prince index
estimations be. For national statistical institutes, TD is not recommended because it does not follow
the temporal xity criterium, as dened by Hill (2004). According to this criterium, once an index has
already been disseminated by the national statistical institute it should remain unchanged when new data
becomes available. Using the single regression TD approach, when new data is added, a new estimation
of (13) changes all parameters previously disseminated.
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1.2.2.2 Rolling time-dummy method
e hedonic rolling time dummy method (RTD) consists in estimated hedonics time-dummy regressions
for subperiods instead of only one regression for the whole period. e limiting case occurs when
a regression is estimated for each pair of adjacent periods. Although when data points are scarce
it is recommended to estimate a regression including more than one subperiod.
France and Portugal, for example, estimated price index from RTD with 2 quarter windows. In other
words, both countries are using an adjacent period RTD. Other countries like Cyprus and Croatia
estimated a 4 quarter windows RTD. e RTD price index is calculated from an RTD regression like
(13) as showed below:
. (14)
1
1
eˆ
x
ˆ
p
exp
q
q
q
q
P
P
2 THE DATA
2.1 Belo Horizonte, Brazil: an overview
Belo Horizonte, the capital of the State of Minas Gerais, is an important economic, politic and cultural
center in Brazil. According to 2010 Brazilian Census (IBGE, 2010), Belo Horizonte had a population
of almost 2.4 million and was the 6th most populous city in Brazil. e Metropolitan Area (MA) of Belo
Horizonte, in turn, had a population of 5.4 million and was the 3th most populous MA in Brazil.
Belo Horizonte was a planned city, conceived to replace Ouro Preto as the capital of Minas Gerais,
and was founded in 1897. Nowadays, the planned area corresponds to downtown and its nearby
districts bounded by Contorno Avenue. Like Aguiar et al. (2014, 119) resumes: this planning created
a center-periphery radial model for the city, which concentrated urban services and urban infrastructure
in particular areas, and reinforced social disparities.
From an administrative point of view, the space of Belo Horizonte is divided into Districts (487),
Planning Units (82), and Regionals (9). Following Villaça (1998), historically, the Central-South city’s
Regional (Regional Centro-Sul) concentrated the elite’s neighborhoods. Nowadays, some bordering Central-
South Regional districts in the West Regional (Regional Oeste) are also occupied by Belo Horizonte’s
elite. Nonetheless, a few elite’s districts are in Pampulha Regional (Regional Pampulha), in the north
of the city, surrounding Pampulha’s lagoon.
2.2 Database
In Brazil all real estate transactions are subjected to the Real Estate Transfer Tax2 (RETT) and its collection
is in charge of municipalities. We used Belo Horizonte municipality’s RETT as our dataset, covering
the period from 2004 to 2015, collected by IPEAD/UFMG. The RETT dataset contains the value
of transaction, type of building, area, age, quality of building nishing material, zoning and location
(district). e type of building includes apartments, houses and commercial real estate. In this paper
we analyzed only apartments market. Further we shall expand the analysis for house and commercial
real estate markets.
Tables 1, 2 and 3 resume the data. ere were 266 529 observations in our dataset for the whole period.
e mean apartment price was around R$ 218 149 (approximately U$ 57 000) and the standard deviation
was 235 011, indicating a high dispersion of this variable. Apartments sold in Belo Horizonte were fairly
big and new, the mean area and age was 120 m2 and 13 years, respectively. Most of apartments were
2 Imposto de Transmissão Imobiliária Inter-Vivos (ITBI).
ANALYSES
204
classied as normal in terms of quality of building nishing material and this variable classied the quality
into 5 categories. Ordering from the top there were the following categories: luxury, high, normal, low
and popular. Most observations where located in the Center-South (Centro-Sul) and West (Oeste) Regionals.
Table 2 Distribution of quality building nishing materials: Belo Horizonte, 2004 –2015
Source: IPEAD/UFMG, author's calculation
Year Observation
Value (reais) Area (m2) Age (years)
Mean Median Standard
deviation Mean Median Standard
deviation Mean Median Standard
deviation
2004 17767 90682 60122 91427 122.0 102.9 70.6 12.4 8.0 11.7
2005 39606 93363 61746 99219 118.7 99.1 68.9 13.7 10.0 12.0
2006 37614 107572 70196 117326 120.4 102.1 69.2 14.3 10.0 12.2
2007 19664 125848 83000 129249 120.9 103.2 68.4 14.3 10.0 12.2
2008 19224 155117 100000 156457 121.4 101.7 70.6 14.5 10.0 12.5
2009 18272 186106 130000 172571 118.4 98.9 69.8 14.0 10.0 12.8
2010 21177 227110 160764 201441 114.4 94.4 68.5 12.1 8.0 13.1
2011 19257 297875 220000 247637 118.9 98.3 70.3 11.7 7.0 13.3
2012 18408 362735 274412 284955 123.8 107.0 70.9 11.8 6.0 13.5
2013 20364 389815 303982 283168 120.5 104.4 67.9 11.1 4.0 13.7
2014 19516 418895 330000 291744 120.6 105.7 66.9 10.1 2.0 13.3
2015 15727 420250 334000 290847 117.0 102.1 64.9 10.9 3.0 13.8
2004–2015 266596 218149 140000 235011 119.7 101.4 69.0 12.8 8.0 12.8
Table 1 Descriptive statistics for apartments in municipality of Belo Horizonte: 2004 –2015
Table 3 Apartments transactions – mean for regional – Belo Horizonte: 2004–2015
Source: IPEAD/UFMG, author's calculation
Source: IPEAD/UFMG, author's calculation
Quality of building nishing materials Mean Standard deviation
Popular 0.02 0.15
Low 0.21 0.41
Normal 0.59 0.49
High 0.16 0.37
Luxury 0.02 0.13
Regional Mean Standard deviation
Centro-Sul 0.21 0.31
Leste 0.09 0.28
Nordeste 0.10 0.29
Noroeste 0.11 0.31
Oeste 0.21 0.40
Pampulha 0.15 0.35
Venda Nova 0.05 0.21
Barreiro 0.04 0.18
Norte 0.04 0.18
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3 QUALITY ADJUSTED PRICE INDICES FOR BELO HORIZONTE, BRAZIL
3.1 Hedonic prices indices for Belo Horizonte, Brazil
We estimated quarterly housing price indices for Belo Horizonte using the various methods discussed
in Sections 1.2.1 and 1.2.2 and an UP’s stratied median method (MIX-UP).3 Since some methods were
based on previous regression or mean characteristics, the 2004 data was used to compute reference
baskets used in 2005. For this reason, results are represented for years 2005–2015. Following Hill et al.
(2018) we estimated three forms of repricing model (RP): i) (RP-X, which uses shadow price from 2004
(no updating base year); ii) RP-5, which updates the shadows prices every ve years; iii) RP-1, which
updates the shadows prices annually.
e average characteristic indices (AC) were estimated with a base update every year. In AC case,
the base is the one year lagged average characteristics. e double imputation indexes were calculated
estimating, for some quarter set of observations, counterfactual housing’s basket for previous and posterior
periods. e double imputation Laspeyres (DIL), Paasche (DIP) and Tornqvist (DIT) were estimated
as presented in Section 1.2.1.3. e rolling time dummy indices were estimated for 2 (RTD2) and 4
(RTD4) quarters window. Finally, we estimated an UP stratied median (MIX-UP) index, to compare
the quality adjusted hedonic housing price index with a simpler and more intuitive price index. Table 6
resumes the quarter housing price indices estimated.
From the chosen period (2005–2015), the large appreciation of housing prices in Brazil was supported
by estimated indices. Even so, the magnitude of the appreciation diers between methods. Using the DIP
index, Belo Horizonte’s house prices rose 383.6% in contrast with DIL which shows an increase of 435.7%.
RIP-X, which uses the shadow price from 2004, was apartheid from RP-5, which changes the base
every ve years, and RP-1, which updates shadow prices every year (Figure 1). From our Belo Horizonte’s
3 e control variables of hedonic price regression are resumed in Tables A1, A2, A3 and A4 in the Annex. We illustrated
the results for control variables using a time-dummy regression (Formula 13) for the whole period in Table A5, also
in the Annex. e results for the other regressions are available from the author.
Figure 1 Repricing Indices for apartments in Belo Horizonte (2005Q1 = 100)
Source: IPEAD/UFMG, author's calculation
0
1
2
3
4
5
6
2005Q1
2005Q2
2005Q3
2005Q4
2006Q1
2006Q2
2006Q3
2006Q4
2007Q1
2007Q2
2007Q3
2007Q4
2008Q1
2008Q2
2008Q3
2008Q4
2009Q1
2009Q2
2009Q3
2009Q4
2010Q1
2010Q2
2010Q3
2010Q4
2011Q1
2011Q2
2011Q3
2011Q4
2012Q1
2012Q2
2012Q3
2012Q4
2013Q1
2013Q2
2013Q3
2013Q4
2014Q1
2014Q2
2014Q3
2014Q4
2015Q1
2015Q2
2015Q3
2015Q4
RP-X RP-5 RP-1
ANALYSES
206
database, the RIP-X seems not be an appropriate index due to its failure to control shadow prices
change over time. RP-5 and RP-1 lines were close each other, highlighting the importance to update
the base year from time to time. Since RP-1 is the more exible RP index it will be used in the remainder
of the paper.
e double imputation Laspeyres (DIL) and double imputation Paasche (DIP) showed evidence
of dri (Figure 2), as Hill el al. (2018) also have noted for the Sydney data. For Belo Horizonte apartment’s
market, DIP estimated the smallest price variation while DIL estimated the biggest. In agreement with
price index theory, DIL, as a Laspeyres index, tends to overestimate the price change and DIP, as a Paasche
index, tends to underestimate it. Double imputation Tornqvist (DIT), in any case, does not exhibit
a dri. DIT, as a Tornqvist-Geometric index, is a geometric mean of DIP and DIL. Bearing in mind that
the Tornqvist indices are recognized as superlatives, the DIT becomes an attractive alternative method
to compute housing index prices. Since DIP a DIL exhibited a dri behavior, the imputation methods
will be reduced to DIT in the following analysis.
e rolling time dummies (RT) were estimated for 4 quarter window (RT4) and 2 quarter window
(RT2) from our database. On the RT4 index the quarter base changes once a year, and on RT2 the base
changes every quarter. RTs methods are attractive because the index corresponds to the estimated
regression time dummy parameter. RT2 indices stayed above RT4 for the whole period. Both RT indices
will be kept in the following analyses.
e Figure 3 compares the Belo Horizonte’s housing price indices estimated by dierent hedonic
methods and by stratied median.
DIT, RP1 and RT4 exhibited a very close behavior. AC and RT2 do the same, although the latter
stayed above the former in the most recent quarters. Partly, the dierent behavior between AC and DIT
is expected, since the rst is a Laspeyres type of index and the second is a Tornqvist type. e MIX-UP
line was more volatile than the other index lines due to the lack of characteristics control related to this
method.
Figure 2 Double Imputation Indices for apartments in Belo Horizonte (2005Q1 = 100)
Source: IPEAD/UFMG, author's calculation
0.0000
1.0000
2.0000
3.0000
4.0000
5.0000
6.0000
2005Q1
2005Q2
2005Q3
2005Q4
2006Q1
2006Q2
2006Q3
2006Q4
2007Q1
2007Q2
2007Q3
2007Q4
2008Q1
2008Q2
2008Q3
2008Q4
2009Q1
2009Q2
2009Q3
2009Q4
2010Q1
2010Q2
2010Q3
2010Q4
2011Q1
2011Q2
2011Q3
2011Q4
2012Q1
2012Q2
2012Q3
2012Q4
2013Q1
2013Q2
2013Q3
2013Q4
2014Q1
2014Q2
2014Q3
2014Q4
2015Q1
2015Q2
2015Q3
2015Q4
DILDIPDIT
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Hill et al. (2018) recommended analyzing the volatility of indices in more detail. e authors present
two volatility measures: the root mean squared error (RMSE) and mean absolute deviation (MAD). Also,
they calculated the minimum (MIN) and maximum (MAX) value for each index. All these indicators
are computed both on a year-by-year and quarter-by-quarter basis. e indicators volatility formulas
are specied below:
, (15)
, (16)
, (17)
. (18)
e results are summarized in Table 4.
Figure 3 Estimate of Price Indices for apartments in Belo Horizonte (2005Q1 = 100)
Source: IPEAD/UFMG, author's calculation
0.0000
1.0000
2.0000
3.0000
4.0000
5.0000
6.0000
2005Q1
2005Q2
2005Q3
2005Q4
2006Q1
2006Q2
2006Q3
2006Q4
2007Q1
2007Q2
2007Q3
2007Q4
2008Q1
2008Q2
2008Q3
2008Q4
2009Q1
2009Q2
2009Q3
2009Q4
2010Q1
2010Q2
2010Q3
2010Q4
2011Q1
2011Q2
2011Q3
2011Q4
2012Q1
2012Q2
2012Q3
2012Q4
2013Q1
2013Q2
2013Q3
2013Q4
2014Q1
2014Q2
2014Q3
2014Q4
2015Q1
2015Q2
2015Q3
2015Q4
RP-1 AC DITRTD4 RTD2 MIX -UP
ANALYSES
208
MIX-UP is more volatile than the other indices. As Hill et al. (2018) pointed out, it is expected
for stratified median indices (like MIX-UP) to exhibit more volatility since they are not adjusted
for changes in the quality of median over time. e hedonics quality adjusted indices exhibited relative
low volatility, the magnitudes were between those which were estimated for Sidney and Tokyo by Hill
et al. (2018). From volatility indicators perspectives our results suggest, for Belo Horizonte’s housing
market in 2005–2015, that the hedonic quality adjusted housing price indices were accurate, except for
the MIX-UP cases.
3.2 Apartment price valuation in Belo Horizonte, Brazil: 2005–2015
We will illustrate the previous results measuring quarterly apartments prices rate of appreciation for Belo
Horizonte. Table 5 summarizes the results for dierent methodologies.
Table 4 Volatility of the House Price Indices in Belo Horizonte
Source: IPEAD/UFMG, author's calculation
RP-X RP-5 RP-1 AC DIL DIP DIT RTD4 RTD2 MIX-UP
Year-on-Year (Q1)
RMSE 0.072 0.064 0.063 0.068 0.064 0.065 0.064 0.063 0.067 0.103
MAD 0.063 0.057 0.055 0.058 0.052 0.056 0.054 0.054 0.056 0.087
MIN 2.478 3.666 4.081 3.653 4.714 2.438 3.570 3.396 3.516 –5.605
MAX 31.089 28.572 29.046 32.496 32.032 29.225 30.621 29.619 30.013 32.880
Year-on-Year (Q2)
RMSE 0.072 0.066 0.065 0.068 0.065 0.066 0.065 0.065 0.068 0.078
MAD 0.056 0.053 0.053 0.056 0.051 0.055 0.053 0.052 0.054 0.063
MIN 2.478 3.666 4.081 3.653 4.714 2.438 3.570 3.396 3.516 –5.605
MAX 31.089 28.572 29.046 32.496 32.032 29.225 30.621 29.619 30.013 32.880
Year-on-Year (Q3)
RMSE 0.077 0.074 0.076 0.075 0.072 0.074 0.073 0.072 0.075 0.085
MAD 0.067 0.065 0.066 0.064 0.059 0.063 0.061 0.061 0.064 0.077
MIN 3.601 2.651 3.459 3.391 4.018 2.578 3.295 3.230 3.273 2.861
MAX 33.371 29.050 31.020 30.412 30.474 29.011 29.740 30.045 30.609 32.779
Year-on-Year (Q4)
RMSE 0.075 0.075 0.076 0.077 0.075 0.077 0.076 0.075 0.078 0.090
MAD 0.065 0.065 0.066 0.065 0.062 0.065 0.064 0.062 0.065 0.080
MIN 3.961 1.250 1.535 2.799 2.847 1.961 2.403 2.360 2.115 1.320
MAX 29.141 28.151 28.631 29.721 29.755 29.023 29.388 30.185 30.102 30.513
Quater-on-Quarter
RMSE 0.033 0.029 0.029 0.031 0.029 0.029 0.029 0.028 0.029 0.047
MAD 0.028 0.025 0.024 0.024 0.023 0.024 0.024 0.024 0.024 0.039
MIN –2.665 –1.703 –1.703 –1.779 –1.531 –1.581 –1.556 –1.567 –1.661 –5.867
MAX 11.985 10.658 10.658 13.308 11.875 10.498 11.184 10.440 11.070 13.229
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STATISTIKA
Table 5 Rate of appreciation (%) of apartment prices in Belo Horizonte: 2005–2015
Year Quarter RP-1 AC DIP RTD4 RTD2 MIX -UP
2005 Q2 1.59 1.22 1.32 1.51 1.48 1.60
2005 Q3 1.39 1.50 1.52 1.31 1.30 1.32
2005 Q4 0.59 0.85 0.92 0.88 0.97 –3.70
2006 Q1 7.86 7.86 7.65 7.73 7.75 8.52
2006 Q2 1.43 1.16 0.95 1.16 1.10 5.40
2006 Q3 1.84 2.04 2.03 1.98 1.90 1.53
2006 Q4 2.00 2.00 2.09 1.99 2.06 8.09
2007 Q1 8.33 8.25 8.25 8.30 8.24 –3.55
2007 Q2 5.14 5.23 4.95 5.08 5.07 12.59
2007 Q3 2.66 2.63 2.63 2.71 2.74 5.59
2007 Q4 4.33 4.27 4.37 4.24 4.15 1.49
2008 Q1 7.19 7.07 7.16 7.09 6.96 10.12
2008 Q2 6.64 6.65 6.44 6.28 6.56 8.50
2008 Q3 3.24 3.65 3.19 3.35 3.26 4.09
2008 Q4 4.34 2.71 3.33 3.57 3.12 2.53
2009 Q1 8.39 10.94 10.32 10.44 10.44 4.73
2009 Q2 5.66 5.59 5.80 5.57 5.49 7.02
2009 Q3 3.55 5.00 4.57 5.37 5.20 4.25
2009 Q4 7.31 5.47 5.70 5.97 6.15 11.70
2010 Q1 9.91 13.31 10.50 9.96 10.36 0.09
2010 Q2 3.68 3.87 4.53 5.45 5.62 4.89
2010 Q3 7.14 5.05 5.66 5.84 5.56 13.23
2010 Q4 2.46 4.13 2.29 2.38 3.85 5.38
2011 Q1 10.66 10.37 10.12 8.78 11.07 5.86
2011 Q2 6.45 4.35 5.27 4.87 4.76 6.13
2011 Q3 6.80 6.87 5.53 6.01 6.06 9.26
2011 Q4 2.25 2.63 2.69 2.38 2.34 0.02
2012 Q1 5.61 6.92 6.47 6.85 6.73 11.67
2012 Q2 1.19 2.40 1.88 1.70 2.04 –0.25
2012 Q3 2.75 2.21 1.68 2.66 2.49 1.97
2012 Q4 2.95 3.31 3.53 3.78 3.79 9.78
2013 Q1 7.30 7.24 6.97 6.67 6.96 –1.59
2013 Q2 2.44 2.46 1.63 2.32 2.01 0.02
2013 Q3 2.10 2.70 2.74 2.94 2.88 –1.91
2013 Q4 2.85 2.56 2.59 2.61 2.56 10.75
2014 Q1 5.39 5.14 5.16 5.38 5.61 6.94
2014 Q2 –0.92 –0.73 –1.23 –1.08 –0.95 –3.14
2014 Q3 –1.46 –1.12 –1.48 –1.14 –1.13 –5.87
2014 Q4 2.57 0.96 0.69 1.09 1.15 3.91
2015 Q1 3.93 4.60 4.55 4.59 4.50 –0.37
2015 Q2 –1.27 –1.78 –1.58 –1.57 –1.66 3.38
2015 Q3 –1.70 –0.32 –1.00 –0.81 –0.64 –3.90
2015 Q4 0.67 0.38 0.09 0.24 0.01 3.91
Source: IPEAD/UFMG, author's calculation
ANALYSES
210
Figure 4 shows the quarterly variation of Belo Horizonte’s apartment prices. It’s clear in the gure
the great volatility of the median index (MIX-UP), as we have seen in the previous section. From 2005
to 2011 there was a signicant housing prices growth path, from then there was a decline tendency.
Aer the second quarter of 2014, the decline was more intense due to the Brazil’s economic crises which
began in this period.
CONCLUSION
Brazil does not have an ocial price index yet. In this paper we used a database from Belo Horizonte,
a big Brazilian city, to test some hedonic quality adjusted price indices. e indices constructed were
the same used by European Statistical Institutes as described by Hill et al. (2018). Our results suggested
that the hedonic quality adjusted indices exhibited a good performance in volatility terms. However, some
dri in double imputation Laspeyres and Paasche indices was detected. e former with a strong upper-
ward bias relative to the other hedonic indices and the latter with a strong down-ward bias.
According to our analyses, the double imputation Tornqvis (DIT) and the repricing with an annual
base update (RP-1) produced very similar magnitude’s indices. e same could be said about the average
characteristics (AC) and the 2-quarter rolling time dummy (RT2). However, the index price lines
of the latter stayed above the former. The 4-quarter rolling time window, in its turn, exhibited
an intermediate behavior, as compared with the previously listed indices.
From the rst quarter of 2007 to the rst quarter of 2014 there was an intense apartment’s price
appreciation in Belo Horizonte. is situation is in line with Brazilian real estate outlook. is appreciation
was contemporary with the expansion rate of housing credit in Brazil. Some institutional improvements
like duciary alienation law’s renement in 2004 agreed with income growth and the decline interest rates
helped the housing credit’s growth (Aguiar, 2014). Cardoso and Leal (2009) highlighted the government
politics and the restructuring (more market concentration) of real estate development’s firm role
in the real estate market expansion.
Figure 4 Apartment annual valuation rate (%) – triennial moving geometric average – Belo Horizonte: 2005–2015
Source: IPEAD/UFMG, author's calculation
RP-1 AC DIPRTD4 RTD2 MIX -UP
–4.0
–2.0
0.0
2.0
4.0
6.0
8.0
10.0
2005 2006 2007 2008 2009 2010 2011 2012 2013 20142015
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103 (2)
STATISTIKA
In contrast to Hill et al. (2018) estimation for Sydney and Tokyo’s evidence, the repricing method
with no base update (RP-X) had an upper-ward bias relative to the other hedonic indices. e ve years
update base repricing method, as well as Hill et al. (2018) empirical evidence, exhibited a down-ward
bias. Finally, our models result suggested that median indices are not the most appropriate to estimate
housing price indices. e stratied median index (MIX-UP) used was more volatile than the hedonic
indices. is is because this kind of index is imperfect in control for housing quality variation over time.
is paper emphasized the potentiality for constructed housing price indices in Brazil using hedonic
quality adjusted price methods and for administrative data. e Real Estate Transfer Tax (RETT) emerges
as a hopeful database once this tax is collected in the whole country. Further analysis could extend
the hedonic price models to estimate price indices for the Brazilian smaller city context and its less
frequent housing sales reality. e smaller number of observations imposes new challenges to estimated
housing prices hedonic quality adjusted indices. In addition, future analysis could extend the types
of real estate units, including houses and dierent types of commercial real estates.
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ANNEX
Table A1 Belo Horizonte's apartment numeric variables
Table A2 Belo Horizonte's apartment quality building nishing material dummy variable
Source: Own construction
Source: Own construction
Variable Description Expected signal Meaning
Area Apartment’s internal area + Consumers tend to prefer living in higher apartments
Age Apartment’s age – Proxy of depreciation
Age^2 Apar tment’s squared age +
Repair and improvements reduce the depreciation’s age eect.
Also there is the vintage eect (Goodman and Thibodeau, 1995),
when some old apartments are valued in the real estate market
Variable Description Expected signal
Luxury Apartment’s with the best kind of quality building nishing material classication +
High Apartment’s with the second best kind of quality building nishing material classication +
Normal Apartment’s with the mean kind of quality building nishing material classication Basical category
Low Apartment’s with the second worst kind of quality building nishing material classication –
Popular Apar tment’s with the worst kind of quality nishing material classication –
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STATISTIKA
Table A3 Belo Horizonte's zoning dummy variables
Source: Own construction
Variable Description Expected
signal Meaning
ZAP Zona de Adensamento Preferencial
(preferential density zone)
Basic
Category Areas where the municipality encourages new bulding
ZPA Zona de Proteção Ambiental
(environmental protection zone) –Areas where new buildings are not allowed or encoraged
due to natural or topographic conditions. Despite
the new buildings restrictions, these areas are not valued
in housing markets because of its lack of aordable
natural conditions
ZAR Zona de Adensamento Restrito
(restricted density zone) –
ZA Zona Adensada (dense zone) +
High density areas where the municipality discourages
new buildings. Commonly ZA’s are in the most valuated
Belo Horizonte’s districts and it represents supply
restrictions in a high demand context
ZE
Zona de Infraestrutura e Equipamentos
Urbanos (urban’s infrastructure equipment
zone)
–
Areas with great urban equipment (like bus stations,
cemeteries, waste treatment etc.). ZE represents poorly
valued areas by the real estate’s agents
ZEIS Zona de Especial de Interesse Social
(special social interest zone) –
Original spontaneously occupations’s areas (like informal
slums), which were formalized by municipality. ZEIS
represents poorly valued areas by the real estate’s agents
ZHIP Zona Hiper Central (over central zone) +
Belo Horizonte’s downtown. ZHIP represents valued
land’s location – where rms and families wish to be
located
ZCBH Zona Central de Belo Horizonte
(Belo Horizonte’s central zone) +
ZCBH corresponds the districts besides Belo Horizonte
downtown, into Contorno Avenue boundary. As ZHIP
Its represents a valued land’s location – where rms
and families wish to be located
ZCVN Zona Central de Venda Nova
(Venda Nova’s central zone) +
Central area of Venda Nova’s distanst suburb. ZCVN
represents, in a minor magnitude, valued land’s location
on Belo Horizonte’s extremely north location
ZCBA Zona Central do Barreiro
(Barreiro’s central zone) +
Central area of Barreiros’s distant suburb. ZCBA
represents, in a minor magnitude, valued land’s location
on Belo Horizonte’s extremely west location
ANALYSES
214
Table A4 Belo Horizonte's Planning Units (UP) dummy variables*
Note: * Savassi is the basical category
Source: Own construction
UP Belo Horizonte’s Regional
Sagrada Família East
Floresta East
Pompéia East
Santa Egênia East
Santa Inês East
Cabana West
Jardim América West
Barroca West
Betânia West
Buritis West
Barro Preto South-Center
Centro South-Center
Savassi South-Center
Prudente de Morais South-Center
Serra South-Center
São Bento South-Center
Belvedere South-Center
Anchieta South-Center
Glória Northwest
Padre Eustáquio Northwest
Camargos Northwest
PUC Northwest
Abílio Machado Northwest
Caiçara Northwest
Pampulha Pampulha
Santa Amélia Pampulha
Ouro Preto Pampulha
Jaraguá Pampulha
Castelo Pampulha
Cachoerinha Northeast
Concórdia Northeast
Cristiano Machado Northeast
São Paulo Northeast
Planalto North
São Bernardo North
Primeiro de Maio North
Jaqueline/Tupi North
Barreiro de Baixo Barreiro
Cardoso Barreiro
Europa Venda Nova
Venda Nova Venda Nova
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STATISTIKA
Table A5 Hedonic price model for Belo Horizonte's apartment market: 2004–2015
TD regression
Variable Estimated parameter Standard deviation t P-value
Constant 10.496 0.005 2 042.01 0.000
Area 0.007 0.000 705.04 0.000
Age –0.018 0.000 –151.19 0.000
Age^2 0.000 0.000 53.89 0.000
Luxury 0.101 0.004 24.39 0.000
High 0.051 0.001 34.59 0.000
Low –0.067 0.001 –50.69 0.000
Popular –0.095 0.004 –25.79 0.000
ZPA –0.054 0.009 –6.21 0.000
ZAR –0.055 0.002 –33.83 0.000
ZA 0.139 0.002 60.23 0.000
ZHIP 0.072 0.006 12.74 0.000
ZCBH 0.443 0.004 123.34 0.000
ZCVN 0.062 0.020 3.18 0.002
ZCBA 0.200 0.013 15.62 0.000
ZE –0.178 0.007 –25.5 0.000
ZEIS –0.232 0.029 –10.61 0.000
Sagrada Família –0.026 0.004 –6.367 0.000
Floresta 0.017 0.004 4.271 0.000
Pompéia –0.130 0.007 –18.241 0.000
Santa Egênia –0.069 0.005 –14.192 0.000
Santa Inês –0.090 0.007 –13.025 0.000
Cabana –0.310 0.007 –47.263 0.000
Jardim América –0.133 0.004 –35.616 0.000
Barroca 0.020 0.003 6.137 0.000
Betânia –0.249 0.005 –46.833 0.000
Buritis 0.008 0.003 2.382 0.017
Barro Preto –0.503 0.006 –81.412 0.000
Centro –0.154 0.005 –30.452 0.000
Prudente de Morais 0.151 0.004 34.750 0.000
Serra 0.039 0.004 9.146 0.000
São Bento 0.205 0.008 26.220 0.000
Belvedere 0.450 0.010 43.427 0.000
Anchieta 0.141 0.003 41.652 0.000
Glória –0.364 0.006 –64.096 0.000
Padre Eustáquio –0.081 0.004 –20.465 0.000
Camargos –0.323 0.005 –66.197 0.000
PUC –0.117 0.005 –23.256 0.000
Abílio Machado –0.244 0.006 –43.292 0.000
Caiçara –0.062 0.004 –14.130 0.000
Pampulha –0.186 0.009 –21.060 0.000
Santa Amélia –0.189 0.004 –43.934 0.000
Ouro Preto –0.093 0.004 –21.629 0.000
Jaraguá –0.108 0.004 –26.144 0.000
Castelo –0.139 0.004 –38.273 0.000
Cachoerinha –0.233 0.005 –44.255 0.000
Concórdia –0.202 0.008 –24.445 0.000
Cristiano Machado –0.022 0.003 –6.313 0.000
São Paulo –0.301 0.005 –62.567 0.000
Planalto –0.279 0.005 –51.841 0.000
São Bernardo –0.302 0.007 –46.206 0.000
Primeiro de Maio –0.298 0.009 –32.703 0.000
Jaqueline/Tupi –0.459 0.006 –82.517 0.000
Barreiro de Baixo –0.348 0.004 –77.391 0.000
Cardoso –0.498 0.006 –87.897 0.000
Europa –0.309 0.006 –52.310 0.000
Venda Nova –0.274 0.004 –63.328 0.000
Time xed eect = yes
Ajusted R2 0.924
F 30 399.1 0.000
Source: IPEAD/UFMG, authors calculation
