Statistical models for generation of generic values plants in urban areas

Faria, Reynaldo Furtado; Brito, Jorge Luís Silva; Gonçalves, Rosiane Maria Lima

doi:10.1590/0104-530X2482-15

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Articles • Gest. Prod. 24 (2) • Apr-Jun 2017 • https://doi.org/10.1590/0104-530X2482-15 copy

Statistical models for generation of generic values plants in urban areas

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

The calculation of the Tax on Land and Urban Property (IPTU) is based on property market value, usually established in the city plant of general values (PVG). However, there are municipalities, especially small ones that do not collect IPTU taxes. This is due to outdated real state register, in addition to the lack of qualified personnel, financial resources and robust and easy methodology to determine real state market value. Therefore, this work aims to combine the spatial regression model and location factor modeling to determine the market value of each property in a small city for the generation of the table of general values (PVG). The study was conducted in the city of São Gotardo/MG. One hundred and eighty-four samples of residential real state assessments made by Caixa Econômica Federal in 2012 and 2013 were used. Aiming to analyze the application of spatial models, four multiple regression models were generated based on the logarithm dependent variables on the total and unit values, and the independent variables related to the construction characteristics of the constructions, according to previous studies. Additional variables related to the land characteristics were also tested. For the models with spatial error dependence, a spatial error model was generated to determine a new homogenized variable encompassing the location factor (VH), which was used as an independent variable on a new linear regression model. The best regression model was selected based on the compliance of assumptions of the linear regression model and the analysis of the lowest Dispersion Coefficient. The model with the logarithm dependent variable on the unit values and the homogenized variable as independent, showed the best results and observed all the assumptions. Thus, it was demonstrated that the homogenized variable improves the performance of the linear regression model, since it includes the property location factor in the independent variables.

Keywords:
Property market value; Small towns; Spatial model; IPTU; Table of general values

Category	Variable	Acronym	Description/definition of the variable	Unit
Price of the property	Total value of the property	VT	Total value of the property assessed	Real
Price of the property	Unit value of the property	VU	Total value of the property assessed / built-up area	Real/m²
Characteristics of the land	Form of the land	FO	Irregular or Triangular = 0 Rectangular or Trapezoidal = 1	-
	Share/Greide of the land	CT1, CT2	If CT1 = 0; CT2 = 0: Under the street level If CT1 = 1; CT2 = 0: Above the street level If CT1 = 0; CT2 = 1: In the street level	-
	Inclination of the land	IT1, IT2	If IT1 = 0; IT2 = 0: Bumpy If IT1 = 1; IT2 = 0: Uphill/Slope > 10% If IT1 = 0; IT2 = 1: Flat/semiflat	-
	Area of the land	AT	Total area of the land of the valuated land	(m²)
	Front of the land	FT	Measurement of the front land	(m)
	Situation of the land	ST	Placement of the land in relation to the square: mid block = 0 corner = 1	-
Constructive characteristics of construction	Number of floor	NP	Number of floor of the construction 1 floor = 0 2 or 3 floors = 1	-
	Age	ID	Age of the construction	(years)
	Age²	ID2	Age of the construction squared	(year)²
	Standard of finishing	PA1, PA2, PA3	If PA1, PA2, PA3 = 0: Minimum or between low and minimum If PA1 = 1; PA2, PA3 = 0: Low or Between normal and low If PA2 = 1; PA1, PA3 = 0: Normal or Between normal and high If PA3 = 1; PA1, PA2 = 0: High	-
	State of conservation of the property	EC1, EC2	If EC1 = 0; EC2 = 0: Bad If EC1 = 1; EC2 = 0: Regular If EC1 = 0; EC2 = 1: Good	-
	Garage	GA	There is no garage = 0 There is a garage = 1	-
	Constructed area	AC	Total constructed area of the assessed property	(m²)
	Number of Rooms/Suites	NQ	Total number of rooms and/or suítes of the assessed property	-
	Number of Bathrooms	NB	Total number of bathrooms in the assessed property	-
Characteristics of assessment	Assessment Date	DA	Year of assessment of the property 2012 = 0 2013 = 1	-

Variable	Coefficient	Error-Standard	Statistics t	Value-p	FIV
Constant	6.4907	0.28	22.91	0.00
Ln(AC)	0.9095	0.04	22.66	0.00	1.61
PA3	0.4983	0.10	5.05	0.00	1.19
DA	0.1287	0.03	4.40	0.00	1.06
PA2	0.0985	0.03	3.26	0.00	1.14
Ln(AT)	0.1648	0.06	2.81	0.01	1.39
IT2	0.0602	0.03	2.06	0.04	1.03
R² adjusted: 0.87			Normality test
F: 185.42 P-value: 0.00			Jarque-Bera: 72.18 P-value: 0.00
Heterocedasticity test			Akaike: -93.41
Breusch-Pagan: 87.64 P-value: 0.00			Schwarz: -71.62
Koenker-Bassett: 35.19 P-value:0.00

Test	M₂		M₃		M₄		M₅
Test	Statistics	Value-p	Statistics	Value-p	Statistics	Value-p	Statistics	Value-p
LM robust (lag)	11.8050	0.0006	6.1260	0.0133	11.3380	0.0008	9.4160	0.0022
LM robust (error)	0.1650	0.6847	3.9310	0.0474	0.1570	0.6919	6.3920	0.0115

Variable	Coefficient	Error-Standard	Statistics t		Value-p	FIV
Constant	6.0180	0.03	199.01		0.00
AC	-2.16E-04	0.00	-2.71		0.01	3.49
EC1	0.2003	0.02	8.18		0.00	9.46
EC2	0.1932	0.03	7.57		0.00	11.33
GA	-0.0494	0.01	-6.76		0.00	1.21
ID	-0.0148	0.00	-11.04		0.00	8.87
ID2	5.56E-04	0.00	11.93		0.00	6.23
NB	0.0301	0.00	8.38		0.00	1.94
NP	-0.0750	0.01	-7.78		0.00	1.31
NQ	-0.0444	0.00	-9.20		0.00	1.48
PA1	0.0391	0.02	2.19		0.03	13.55
PA2	0.1195	0.02	6.37		0.00	14.47
PA3	0.5063	0.03	19.39		0.00	2.75
VHU	9.41E-04	0.00	74.71		0.00	1.02
R² adjusted: 0.98				Normality test
F: 530.89 P-value: 0.00				Jarque-Bera: 2381.98 P-value: 0.00
Eterocedasticity tests				Akaike: -667.83
Breusch-Pagan: 169.68 P-value: 0.00				Schwarz: -624.26
Koenker-Bassett: 17.48 P-value: 0.18

Variable	Coefficient	Error-Standard		Statistics t	Value-p	FIV
Constant	5.9697	0.05		122.58	0.00
AC	-1.01E-03	0.00		-4.95	0.00	2.86
AT	6.60E-04	0.00		5.76	0.00	1.61
ID	-0.0205	0.00		-5.96	0.00	7.20
ID2	7.57E-04	0.00		5.69	0.00	6.32
IT2	0.0514	0.01		3.56	0.00	1.03
NB	0.0310	0.01		3.07	0.00	1.90
PA2	0.0785	0.02		5.19	0.00	1.17
PA3	0.4563	0.05		8.93	0.00	1.31
VH_U1	9.46E-04	0.00		23.35	0.00	1.01
R² adjusted: 0.81			Normality test
F: 79.89 P-value: 0.00			Jarque-Bera: 0.51 P-value: 0.77
Heterocedasticity tests			Akaike: -325.06
Breusch-Pagan: 7.41 P-value: 0.59			Schwarz: -293.94
Koenker-Bassett: 8.56 P-value: 0.48

Models	COD		R² adjusted	Attendance for assumptions
	All samples (166)	Validation samples (18)		Normality	Heterocedasticity		Multicolinearity
	All samples (166)	Validation samples (18)		Jarque-Bera	Breusch-Pagan	Koenker-Bassett	Multicolinearity
M₁	12.65	13.14	0.87	no	no	no	yes
M₆	1.98	11.23	0.98	no	no	yes	no
M₇	7.07	9.99	0.81	yes	yes	yes	yes

Error Range	Number of favorite values		% of favorite values		% accumulated of favorite values
Error Range	All Samples	Validation Samples	All Samples	Validation Samples	All Samples	Validation Samples
0-5%	63	5	34.2	27.8	34.2	27.8
5-10%	81	3	44.0	16.7	78.3	44.4
10-15%	30	6	16.3	33.3	94.6	77.8
15-20%	6	2	3.3	11.1	97.8	88.9
20-30%	4	2	2.2	11.1	100.0	100.0
Total	184	18	100.0	100.0

Universidade Federal de São Carlos Departamento de Engenharia de Produção , Caixa Postal 676 , 13.565-905 São Carlos SP Brazil, Tel.: +55 16 3351 8471 - São Carlos - SP - Brazil
E-mail: gp@dep.ufscar.br

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[1] The variables Ln(AT) and Ln(AC) are the logarithmic change of the variables land area, front of the land and constructed area, respectively.