Addressing methodological challenges in the mass real estate valuation
process, specifically within the context of the Republic of Moldova.
ALEXANDRU PALADI
Department of Real Estate Economy and Management
Technical University of Moldova
Bld. Pacii, 1, Mun. Straseni
THE REPUBLIC OF MOLDOVA
Abstract: This research investigates the precision of mass real estate valuation models, particularly focusing on
the methodology of mathematical value modeling. The discussed challenges are particularly relevant to nations
employing an ad-valorem taxation system. The Republic of Moldova's mass appraisal system for real estate
serves as an illustrative case. Through a comparative analysis of the performance metrics between existing
models and those refined based on the proposed recommendations, the study illustrates the improved efficiency
of the advocated methodology.
Key-Words: - real estate, assessment, mass evaluation system, mathematical models, real property taxation, log-
linear regression, ratio study, law of diminishing returns
Received: April 14, 2023. Revised: April 19, 2024. Accepted: May 14, 2024. Published: June 10, 2024.
1. Introduction
In both advanced and emerging market economies,
the mass real estate assessment system assumes a
pivotal role across various dimensions of social and
economic domains. It serves as the foundational
framework for computing local taxes and
establishing a system for calculating economic
indicators that gauge the dynamics of national
economic development. Accurate assessment is
imperative to ensure equitable taxation and
streamline the effective collection of tax revenues
required for the provision of governmental services
[1]. Sound property valuation guarantees that
taxpayers contribute taxes commensurate with the
actual value of their property, thereby fostering an
equitable distribution of the tax burden.
Precision in the extensive valuation of real estate
holds crucial significance for urban planning and
economic advancement. Local administrations
leverage these valuations to identify burgeoning
areas, allocate resources, and foster sustainable
development. A transparent and well-managed
mass evaluation system enhances public trust in the
fairness and impartiality of the process, mitigating
concerns of corruption or preferential treatment.
Additionally, precise valuation is indispensable for
the seamless operation of the real estate market,
furnishing accurate property value information and
facilitating real estate transactions. These
valuations cultivate a competitive market
environment, offering essential data for banks and
financial institutions to assess risks associated with
mortgages and secured loans.
Regular updates to the massive appraisal system are
imperative to reflect contemporary changes in the
economy and real estate market, ensuring accurate
and relevant property valuations. Maintaining the
accuracy of evaluation results hinges on the type
and methodology of mathematical modeling
employed. The evolution of legal and economic
relations within the real estate market necessitates
the adaptation of market value calculation
mechanisms. The incorporation of sophisticated
contemporary econometric functions in modeling
can circumvent certain methodological challenges
and enhance the precision of obtained values.
Following their declaration of independence and
the transition towards market economies, countries
in Central and Eastern Europe embarked on
extensive tax system reforms, which included the
restructuring of real property taxation. This
transformative endeavor has been scrutinized by
researchers in several nations, such as Slovenia, the
Russian Federation, Belarus, and Lithuania [2].
This case study serves as an illustration for the
residential real estate valuation model in the
Republic of Moldova. The objective of this
research is to pinpoint the primary factors
contributing to the inefficiency of the mass
assessment models in Moldova, estimate the losses
incurred due to their inadequacy, and propose
effective strategies for enhancing these models.
The article provides a comparison between linear
and nonlinear regressions, focusing on the primary
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factors affecting real estate value: its size and the
age of the building's construction.
2. Problem Formulation
Owing to the heightened dynamics of
contemporary methodologies, the existing mass
evaluation models established from the ages 2003-
2010 for calculating the taxable value in the
Republic of Moldova are deemed oversimplified.
This is attributed to a limited number of factors
utilized in determining property value and the
application of simplistic techniques of linear
regressions that inadequately capture intricate
dependencies influencing market value formation
[3]. In most cases, the models represent the linear
mathematical equation where the dependent factor
(V - Value) is determined by the middle value
(VM) and independent factors such as surface area
(S), location factor, level, materials, etc., which are
introduced as straightforward adjustment
multiplication coefficients.

  (1)
These models fail to comprehensively represent the
many cost factors that influence a property's market
value, resulting in frequent changes. Consequently,
there is a need to revise real estate valuation
methods in accordance with the principles of taking
into account various factors and taking into account
the nuances of constructing the real estate market.
It is extremely important to recognize that the
market value of a subject property is not simply the
arithmetic sum of its constituent elements, such as
the land and associated improvements. In addition
to this shortcoming, the mass assessment system in
the Republic of Moldova faces various
methodological problems that are typical for other
regions of Eastern Europe.
2.1. The method of obtaining the data
used
The prevailing expert-analytical method, upon
which the current models in the Republic of
Moldova are constructed, revolves around
formalizing expert opinions on the interdependence
of land market value and various influencing
factors. Widely acknowledged at both national and
local levels in the Republic of Moldova and the
broader Eastern European region, this method is
primarily employed for individual evaluations to
determine adjustment coefficients for value factors.
It is predominantly utilized for assessing real estate
in small and medium-sized cities exhibiting
standard urban planning characteristics.
However, when applied to large cities or small and
medium-sized cities with nonstandard urban
planning features (such as satellite cities of district
centers/municipalities, settlements with enterprises
forming cities, resort cities, etc.), the use of this
evaluation model template may lead to significant
distortions compared to the actual cost of specific
sections of the urban area. This is particularly
attributed to the inherent heterogeneity of these
assessed cities, necessitating a pre-division into
territorial areas that align more closely in terms of
cost characteristics. Subsequently, appropriate sub-
areas within these cities should be allocated based
on their functional purpose. In this methodology,
the unit of comparison should not be a hypothetical
rated residential area with average city
characteristics for key price drivers but specific
typical test areas within each selected sub-area with
the corresponding functional purpose.
As an alternative to the expert-analytical method,
the statistical method does not serve as a universal
remedy for the addressed issues. Practical
application of the statistical method reveals that the
results of statistical analysis do not automatically
yield an ideal regression for modeling real estate
value. Additional efforts are required to calibrate
the model using alternative information sources,
including the empirical practices of individual
valuation specialists.
2.2. Low linear model elasticity
The employment of simple linear regressions in the
model is marked by the model's lack of elasticity.
Specifically, the value factors are represented in a
linear form within the models and lack the
flexibility to accommodate nonlinear functions
when manipulating these factors. An illustrative
instance is the examination of the surface factor
(S), interpreted as a linear function with the value
(V) denoted as V=F(S) in current models. The
diagrams in Fig. 1 depict both linear and nonlinear
functions for the V=F(S) regression. The trend for
nonlinear function is presented with log-equation
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Fig. 1Diagrams of value estimated using
linear and log- linear regressions
To address errors arising when the compared
functions intersect, transaction prices from the
observations in the studied sample were adjusted
based on market conditions (sale date: 01.06.2023),
location within the region (city and value zone:
Chisinau, Center), year of construction (2020), and
other technical parameters consistent with a
predefined standard object.
The departure of the linear function from the
market data, depicted by a nonlinear function, is
ascribed to the principle of diminishing returns,
initially postulated by Anne Robert Turgot in 1767
[4]. This phenomenon is alternatively recognized
as diminishing marginal returns, suggesting that in
a production system with fixed and variable inputs,
while keeping the fixed input constant, each
additional unit of the variable input yields
increasingly smaller additional effects [5]. This
concept is manifested in the nonlinear correlation
between value and the independent variable,
notably in terms of measurements derived from
statistical analysis of market data. As illustrated in
Fig. 1, the parabolic impact of increasing value in
relation to the surface area of the object is
established, revealing a notable disparity in higher
surface values.
The difference between linear and nonlinear
regression reflects the undervaluation of small
properties (segment A-B in Fig. 1) and the
overvaluation of large properties (segment B-C in
Fig. 1) by the existent models.
Regarding 1 squire meter (1m2) Value, the
difference of model’s results is displayed in Fig. 2
Fig. 2 Diagrams for linear and log-linear
regression values per 1 square meter (1 m2)
Using statistical data on apartments as an example,
we can calculate approximate losses in the
assessment due to a lack of linear functions. It's
worth noting that the biased valuation results in the
undervaluation of small properties, representing
98% of the total housing stock, and the
overvaluation of large properties, accounting for
2%.
Table 1 The discrepancy in value estimation
between linear and nonlinear regression
estimation for the apartment example.
Surface
m2
Number
of units
Share
Difference
per group,
Euro
<20
19547
4.3%
-39094000
20-30
32191
7.0%
-96573000
30-40
73267
16.0%
-366335000
40-50
104293
22.7%
-625758000
50-60
80397
17.5%
-401985000
60-70
90221
19.7%
-451105000
70-80
27882
6.1%
-139410000
80-90
13641
3.0%
-40923000
90-100
7238
1.6%
0
100-110
3683
0.8%
18415000
110-120
2434
0.5%
24340000
120-130
1441
0.3%
24497000
130-140
858
0.2%
19734000
>140
1831
0.4%
54930000
Total
458924
100%
-489522000
The data from Table 1 indicates that the residential
stock value for apartments in multi-storey buildings
is underestimated by approximately 490 billion
euros. Consequently, tax revenue losses are
estimated based on minimum (0.05%) and
maximum (0.4%) tax rates [1], ranging from 0.25
to 2.0 million Euros annually.
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2.3. Grouping of value factors
An additional limitation is evident in the utilization
of multipliers for value adjustment, which has been
addressed by aggregating and clustering
quantitative variables into segments. This approach
resulted in the creation of a value scale that lacks
precision in determining fair values between two
contiguous quantities. As an illustration, the value
function is articulated in relation to the year of
construction. Table 1 displays the adjustment
coefficients for real estate value based on the year
of construction, as per the existing models and
alternative coefficients obtained as a result of
statistical calculations.
Table. 2 Coefficient of adjustment for building
age
Year of
construction
KAge,
(2003)
KAge,
(2023)
(2023)-
(2003)
Units
rate
WR
1900<>1955
0.65
0,874
-22%
1%
-0,23%
1956<>1965
0.76
0,949
-19%
9%
-1,70%
1966<>1975
0.85
0,988
-14%
20%
-2,82%
1976<>1985
1.00
1,037
-4%
25%
-0,95%
1986<>1995
1.03
1,100
-7%
21%
-1,45%
1996<>2005
1.06
1,179
-12%
3%
-0,33%
2006<>2015
1.08
1,280
-20%
10%
-2,02%
2016<>2022
1.08
1,435
-20%
11%
-3,76%
Total
-133%
100%
-13,2%
Kage, (2003) – represents the adjusted coefficient
for age factor used in the current models [6]. The
discrepancy in adjusting for the year of
construction becomes evident when factors are
grouped, as illustrated in Fig. 3. The inconsistency
in applying correction factors across these groups
results in a disparity between limit values. For
instance, in the given example, a property
constructed in 1975 is appraised at 15% lower than
a property built in 1976, akin to the valuation of a
property built in 1985. This calculation approach
introduces abrupt jumps between neighboring
values and deviates from real market trends. The
smoothed trend line is depicted in a logarithmic
function for a more accurate representation.
WR - weighted average percentage of cost
reduction in accordance with the number of
objects in the group (Units rate).
Fig. 3 Diagrams of the current grouped
Age coefficient Kage(2003) and the actual
adjustment for this factor Kage (2023)
Kage, (2023) – represents the real adjustment
coefficient derived from current market data using
nonlinear polynomial regression techniques.
K=Exp*(Int+AxKage+A2xKage2+A3xKage3); (2)
Where Int - denotes the intercept of the regression,
A - signifies the age of construction, and Kage -
represents the polynomial regression value
indicators for A, A2 and A3.
The financial losses incurred due to the utilization
of an incorrect grouping system, using the age
coefficient of buildings as an illustration, are
computed and displayed in Table 2. As per the
statistics, the adjustment for age results in the loss
of over 13,2 % of the tax value.
2.4. Ratio Study
As a part of the statistical analysis, the author
performed the ratio study for the values generated
by the existing models for some of the previously
evaluated residential urban categories and the
accumulated market data. The results of the rate
study are presented in Table 3
Table. 3 Current models ratio study
Indicator
Apartments
Family
houses
Num. of
observations
1710
7693
RM
0.41
0.24
COD
108.26
128.32
PRD
1.78
1.69
R2
0.14
0.07
The interpretation of the quality indicators on the
existing models indicates a series of problems
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related to the compatibility of the old methodology
with the prices on the current market real estate:
Median Rate (RM) – this value is the middle rate
when arranged from low to high. Confidence
intervals are calculated around the RM. According
to the International IAAO, the RM confidence
interval should overlap with the suggested
assessment level range (0.90 – 1.10) [7]. RM is
preferred over the mean (or average) rate because it
is less likely to give misleading results if extreme
outliers (i.e., very high or very low) are in the
sample. The low level of the medians on the
studied categories indicates the underestimation of
the values obtained according to existing models.
Coefficient of Dispersion (COD) – this value
provides an estimate of how much rates spread or
disperse around the RM. Lower CODs are desirable
over higher ones as they indicate less variation and
greater precision/consistency. The IAAO
recommends COD thresholds based on property
type, jurisdiction size and market activity, which
range from 5-20% for residential properties [7], as
well as local standards [8]. COD values above
100.5% for the old models notify about the
enormous dispersion of the results as a result of the
low prediction of the old models.
Price Related Differential (PRD) – this value
provides an estimate of how much rates fluctuate
between lower, mid and higher priced properties.
PRD is centered on 1.0, with values above 1.0
suggesting regressive vertical inequity (higher
priced properties enjoy lower rates) and values
below 1.0 indicating progressive vertical inequity
(lower priced properties enjoy lower rates) [9].
The IAAO rate study standard recommends PRD
values to be between 0.98 and 1.03 [7]. When the
sample size is small or the weighted average is
heavily influenced by several extreme values of
selling prices, the PRD may become an
insufficiently reliable measure of vertical
disparities. Under the representativeness
hypothesis, high PRDs generally indicate low
valuations for high-priced properties. In case of
insufficient representativeness, extreme selling
prices may be excluded from the PRD calculation.
Similarly, for very large samples, the PRD may
become too insensitive to highlight small areas
where there is significant vertical inhomogeneity.
Price related injury (PRB) and coefficient of
variation (COV) are additional values not used in
this report. PRB is not included because
unpublished research has shown it to be a highly
flawed and misleading measure of vertical inequity
[10] COV is not included because COD is viewed
as a more appropriate measure of dispersion, which
is less likely to give misleading results if there are
extreme outliers in the sample.
3. Problem Solution
Combining the statistical and expert-analytical
methods in the development of mass real estate
valuation models is an effective approach, as both
methods have their advantages and can
complement each other. In the same vein, combined
methods rectify mutual shortcomings caused by
external and internal factors. Thus, the errors
caused by the application of the expert-analytical
method in the development of primary models are
solved by the application of complex regressions,
deduced from the statistical processing of market
data. At the same time, the errors caused by the
lack of data, the reduced level of data transparency,
as well as the invalidity of some existing statistics,
are brilliantly rectified by applying the
methodology based on empirical practice through
the expert-analytical approach. A series of measures
is proposed below by the author in order to solve
the problems addressed.
3.1. Implementation of log-linear models
Following research and examination of market
data, for residential real estate (Apartments in
multi-storey blocks, Individual houses in urban and
rural localities in the municipalities of Chisinau,
Balti, Individual garages, Orchard lots with/without
constructions and Apartments on the ground) by the
author the type of log-linear model is proposed:
󰇛󰇜
 ; (3)
Where:
Ln(V) – The natural logarithm of the estimated
value of the real estate (lei);
Int – Intercept of the math function. It presents the
free (constant) term of the model;
i – value factor indicator;
n – the number of value factors in the model;
Ki – the constant coefficient of the value factor;
aix – value factor (independent variable) to the x
power (for nonlinear regression).
The advantages of the optimized model consist in
raising the elasticity of the nonlinear regression
between the dependent variable (V) and the value
factors. Log-transforming the variables in a
regression model is a very common way to handle
situations where there is a nonlinear relationship
between the independent and dependent variables.
Using the logarithm of one or more variables
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instead of the equation of the line makes the
effective relationship nonlinear while keeping the
model linear.
Logarithmic transformations are also a convenient
means of transforming a highly skewed variable
into one that is more approximately normal. In fact,
there is a distribution called log-normal distribution
defined as a distribution whose logarithm is
normally distributed but whose untransformed scale
is skewed [11]. Log-linear models have several
advantages in real estate valuation:
• Log-linear models take into account the
logarithmic relationship: In most cases, real estate
prices have a logarithmic (nonlinear) relationship
with various factors such as area, number of
bedrooms, distance from the center, etc. Using
logarithms allows taking into account this
dependence in an equation, making the model more
accurate.
• Increasing regression elasticity: Thanks to the use
of the logarithmic equation, regressions between
dependent and independent variables become
sensitive and can be predictable for situations of
extreme values, which is very important for
massive evaluation with a wide range of specific
objects.
• Scale clustering inference for numerical
independent variables: This fact reduces the
distortion of marginal factor evaluation results from
group-based classifiers.
• Stability of estimates: Using logarithms of the
data makes them less sensitive to outliers and
skewed distributions. This reduces the influence of
unusual observations and can improve the stability
of the estimates.
• Interpretability: Logarithms can make the
interpretation of model coefficients more intuitive.
For example, in the case of a linear model, a one-
unit increase in one of the factors can be interpreted
as an increase in the percentage or proportion of
change in the dependent variable.
• Improving hypothesis fit: Many statistical
methods, including regression, assume normal error
distributions. Taking logarithms can make the
distribution closer to normal, which improves the
fit of the model to the established assumptions.
• Reducing multicollinearity: Using logarithmic
equations in the model reduces multicollinearity
between factors, making the estimate more stable.
3.2. Quality effect
In order to analyze the level of optimization of the
methodological framework regarding the effect of
raising the quality of the models, the quality
indicators of the modified models were calculated
by the author. This made it possible to compare the
degree of efficiency of the new methodology
proposed by the author. International best practices
recommend evaluating model accuracy, uniformity,
and equity through ratio studies. Extreme
observations were adjusted based on the IAAO
Standard on Ratio Studies using the IQRx1.5
methodology. In this approach, the model
calculates a valuation estimate for each sale,
dividing it by the sale price to determine an
assessment-to-sale price ratio. These ratios are then
categorized into quartiles, ranging from lowest to
highest. The "interquartile range" or "IQR" is
computed by subtracting the first quartile from the
third quartile. Ratios beyond the third quartile
ratio+(1.5IQR) or below the first quartile ratio-
(1.5IQR) are considered "extreme observations" or
"outliers" and are recommended to be trimmed
following IAAO standards. The Fig. 4 below
illustrates the distribution of ratios.
Fig. 4 Distribution of ratios for log linear
regression
Table 4 shows comparison reports of quality
indicators for old and new models, formed
according to the new methodology.
Table 4 Quality effect of proposals
Indicat
or
Apart
ments
Rate
Family
Houses
Rate
RM
1.03
56%
1.03
73%
COD
37.28%
70.98%
42.45%
85.87%
PRD
1.19
59%
1.28
41%
R2
89%
75%
84%
77%
Explanation of the data from the comparison table
of indicators from Table 4:
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Median rate (RM): Compared to the median of the
old models, the given indicator is improved () for
the studied examples by 56% in the category of
apartments and by 73% for urban houses.
Coefficient of Dispersion (COD): The dispersion
indicator improved () by 70.98% for apartments
and by 85.87% for townhouses.
Price Related Difference (PRD): PRD is centered
on 1.0, with values above 1.0 suggesting regressive
vertical inequity (higher priced properties benefit
from lower rates) and values below 1.0 indicating
progressive vertical inequity (lower priced
properties get lower rates). Although the indicator
of price differentiation remains with regressive
inequity, optimization () qualifies with 59% for
apartments and 41% for urban houses. The
coefficient of determination R2 has improved for
both categories, indicating a heightened level of
predictability for the new models.
4. Discussions
The results of the study were integrated into project
reports and are intended to develop new models for
mass valuation of real property for tax purposes in
the Republic of Moldova. These recommendations
go beyond the Moldovan valuation system and
provide targeted solutions consistent with modern
mass real estate valuation systems, especially for
former socialist countries, which adapt to market
dynamics and ensure accurate valuation.
The practice of mass assessment has long been
focused on complex mathematical algorithms and
does not refer to primitive linear regressions based
only on the area of the assessed object. Moreover,
not only qualitative assessment factors are carefully
considered, but also the psychology of real estate
market participants. Governments of countries with
developed real estate markets use modern theories
such as triangular theory of fuzzy numbers
(VIKOR), rough set theory [12], cost tolerance
ratio, fuzzy logic [13] and genetic algorithms [14].
Significant attention is also paid to the use of
artificial intelligence in the development of new
mass assessment models.
However, modern technology is based on accurate
information about real estate transactions, extensive
investment in scientific research and a wide range
of guarantees. Thus, the critical demands facing
developing countries require the application of
cutting-edge science, supported by a reliable
financial infrastructure, information security and
insurance guarantees.
Moreover, mass valuation of real estate for tax
purposes entails certain social reactions and
necessitates simplifying the model for discussion
with taxpayers and reducing its complexity.
However, future research will focus on improving
valuation methodology and increasing the accuracy
of mass real estate valuation results by
incorporating modern mathematical modeling
theories while maintaining reasonable restrictions
on their applicability and effectiveness.
5. Conclusion
Implementation of recommendations based on
these studies can lead to significant improvements
in the quality of real estate market data, the
methodology used in mass valuations, and the
accuracy of the results obtained. Compliance with
the proposed recommendations in the real estate
value modeling methodology will contribute to the
development of operational processes and
optimization of efficiency in the field of mass real
estate valuation. Refining the quality indicators of
models developed in accordance with the proposed
methodology emphasizes the real goal of
developing the field of mass real estate valuation. A
comparative analysis of the quality indicators of
existing models and the models proposed by the
author of the study highlights the effectiveness of
the proposals, reinforcing the hypothesis that the
use of mathematical tools developed to formulate
methodologies for mass calculation of real estate
values increases the accuracy and predictability of
calculation models.
The identified shortcomings of the current system
of mass valuation of real estate for tax purposes in
the Republic of Moldova can be quickly eliminated
by improving the regulatory and methodological
framework governing the calculation of the
cadastral value of real estate with relatively small
resources.
Declaration of Generative AI and AI-
assisted technologies in the writing process
I hereby confirm that all ideas and innovations in
this article belong to the author and not to other
persons or to AI engines
References:
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Volume 2, 2024
[1]. Law no. 1163, Fiscal Code, Chisinau:
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Sources of Funding for Research Presented
in a Scientific Article or Scientific Article
Itself
In the research, author used the date, presented
by The Project of Land registration and
Assessment from the Republic of Moldova
(2018-2024), Implemented by the Department
of Cadaster from the Public Services Agency.
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Conflict of Interest
The author has no conflict of interest to declare that
is relevant to the content of this article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The author contributed in the present research, at all
stages from the formulation of the problem to the
final findings and solution.
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