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Fedotov D.A. Improvement of the mechanism of rationing the initial contract price in the field of public procurement on the example of econometric modelling of the price of laptop // Research Result. Economic Research. - T.4, Vol.4,2018
УДК : 330.4
DOI: 10.18413/2409-1634-2018-4-4-0-7
Федотов Д.А.
СОВЕРШЕНСТВОВАНИЕ МЕХАНИЗМА НОРМИРОВАНИЯ НАЧАЛЬНОЙ ЦЕНЫ КОНТРАКТА В СФЕРЕ ГОСЗАКУПОК НА ПРИМЕРЕ ЭКОНОМЕТРИЧЕСКОГО МОДЕЛИРОВАНИЯ ЦЕНЫ НОУТБУКА_
Челябинский государственный университет, ул. Братьев Kashirinyh 129, Челябинск,
454001, Россия, e-mail: [email protected]
Научный руководитель: Любожева Лионелла Николаевна-доцент факультета лингвистики и перевода Челябинского государственного университета, кандидат филологических наук
Аннотация
В статье рассмотрены проблемы формирования начальной (максимальной) цены контракта в сфере госзакупок на примере поставки ноутбуков. Для обоснования начальной цены использовались методы эконометрического моделирования. Выявлены основные факторы, которые влияют на цену ноутбуков, то есть при увеличении: объема оперативной памяти, количества пикселей, производительности видеокарты, количество usb-портов цена ноутбука будет резко расти. Результаты исследования могут быть использованы в сфере контроля за расходованием бюджетных средств.
Ключевые слова: эконометрическое моделирование, государственные закупки, начальная цена контракта, бюджетный контроль
Academic adviser: Lubozheva Lionella Nikolaevna - Associate Professor, Faculty of Linguistics and Translation of Chelyabinsk State University, Candidate of Philology
The article deals with the problems of formation of the initial (maximum) price of the contract in the field of public procurement on the example of laptop supply. Methods of econometric modeling were used to justify the initial price. The main factors that affect the price of laptops are revealed, that is, with an increase in: the amount of RAM, the number of pixels, the performance of the video card, the num-
Fedotov D.A.
IMPROVEMENT OF THE MECHANISM OF RATIONING
THE INITIAL CONTRACT PRICE IN THE FIELD OF PUBLIC PROCUREMENT ON THE EXAMPLE OF ECONOMETRIC MODELLING OF THE PRICE OF LAPTOP
Chelyabinsk State University, 129 Bratev Kashirinyh St., Chelyabinsk,
454001, Russia
e-mail: [email protected]
Abstract
Fedotov D.A. Improvement of the mechanism of rationing the initial contract price in the field of public procurement on the example of econometric modelling of the price of laptop // Research Result. Economic Research. - T.4, Vol.4,2018
ber of usb ports, the price of the laptop will grow sharply. The results of the study can be used in the field of control over budget spending.
Keywords: econometric modelling, state procurements, initial contract price, budget control.
Введение
In recent years, the number of public contracts for the purchases of laptops has increased. Due to the increasing number of disruptions in the public procurements system, a large number of scientific researches are being conducted into the background causes and for avoiding negative effects of an inefficient use of budgetary funds. Single and clear mechanism of monitoring activities during the state tenders has not yet been developed in Russia. So Rybnikova G.I. states that it is important «to study those stages of public procurement at which the supervisory authorities have difficulties» [Rybnikova G.I., Tevosyan K.M., 2016].
One of the key stages of any public procurement is planning in which the major diffi-
cult lies in analysis the price calculation and justification of proposed procurements. Therefore, the purpose of this article is to analyze the factors affecting the initial (maximum) price of laptops at the planning stage of state and municipal procurements with subsequent econometric model specification.
Основная часть
The core of any econometric analysis is based on the correct determining of model parameters which are more likely accounted for estimated value.
Modern laptops are delicate pieces of technology that consist of many elements. The significant factors affecting the laptop's price are listed in Table 1.
Data, their designations and units of measurement
Table 1 Таблица 1
Factor Designation in Gretl Units of measurement
1. Quantative variables
CPU frequency CPU Number of GHz
Core Core Core count
Random access memory (RAM) memory Number of GB
Hard disk drive HDD Number of GB
Solid state driver SSD Number of GB
Monitor inch screen size Number of inches
Pixels pixel Number of pixels
Performance of video card videocard_performance As the percentage of the best Nvidia Titan V video card at 24.10.2018 [6]
USB port 2.0 usb2 Number of pieces
Usb port 3.x usb3 Number of pieces
Battery baterry Number of hours
2. Dummy variables
Operation System (OS) OS 1 - Windows 0 - other О s
DVD-drive DVDRW 1 - yes 0 - no
Keyboard lightning keyboard 1 - yes 0 - no
Fedotov D.A. Improvement of the mechanism of rationing the initial contract price in the field of public procurement on the example of econometric modelling of the price of laptop // Research Result. Economic Research. - T.4, Vol.4,2018
Factor Designation in Gretl Units of measurement
Laptop's material material 1 - metal 0 - plastic
AMD video card AMD 1 - yes 0 - no
Nvidia video card Nvidia 1 - yes 0 - no
Intel video card Intel 1 - yes 0 - no
For this study, 102 laptops were randomly selected from the official websites of the largest Russian online retailers of digital and home appliances: M.Video, DNS, TechnoPoint, Eldorado, Citilink. Laptops were selected into
all price categories for accurate and reliable conclusions. The model was specified by Ordinary Least Squares (OLS-model) based on the data obtained using the GRETL program.
Модель 1: MHK, использованы наблюдения 1-102 Зависимая переменная: price
Пропущены из-зг совершенной коллинеарности: Intel
const
CPU
core
memory
HDD
SSD
screer._3lze pixel
videоcard_perfor-OS
DVDRW
keyfcord
material
battery
AMD
Nvidia
jsb2
jsfc3
Коэффициент
-26377, 1316, -1000, 312 3, -6, -5, 300, 0, 7-73, —5890, 1354, 6598, 10206, 352 , -3035, -6406, 4744, 3223,
Ст. сшибка
6 66 27
32
66356 3134 6 3 33
00714360
756
35
2 3
27
2
433
33 31 72 12
143-34, 2361, 113 3, 377,
Э, 331, О, 164, 252 6, 2417, 2872 , 2556, 467, 3616, 2 8 Э 6 , 14 63, 1345,
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t-статистика
-значение
2
37
55
763
37373
33607
236
0010 30 35 676 20 2 3 22 17 304 33 84 43 73
-i. 300 0, 0754 *
0, 3115 o. 4134
340 3 402 3
8, 2 33 1, 65e-012 * * ft
"2, 237 0, 0273 » A-
-a. 5316 o. 5624
3 600 3322
6, 553 4, 30е-0 3 ***
72 3 Э, 00e-06 * ft- д-
-2, 332 0, 0221 ft*
0, 7671 4452
2, 2 37 0, 0241 ft ft-
3, 333 a. 0001 ft ft A-
0, 7543 o. 452 3
355 3 0, 3345
211 0, 02 37 ft ft-
3, 231 Q, 0013 ft ft A-
4, 22 6 6, 01e-05 ft ft *
Среднее зав. перемен 50 3 33,50
Сумма кв. остатков б,31е+0Э
R-квадрат 0,357033
F(17, 84} 110,1317
Ст. откл. зав. перемен 33647,2 3
Ст. сшибка модели 3006,376
Испр. R-квадрат 0,343337
Р-значение [F) 5,37е-50
Fig. 1. Multiple Linear Regression (MLR) model with all variables Рис. 1. Модель множественной линейной регрессии (МЛР) со всеми объясняющими переменными
It is necessary to assess the quality of the resulting model for further analysis.
1. The significance of the coefficients of the explanatory variables. It is considered in the Gretl program that coefficient is significant at a significance level of 10%», if the achieved level of significance (p-value) of the coefficient is
less than 0.1 [Econometrics. Regression analysis using the package Gretl: Laboratory Workshop, 2014]. This requirement is satisfied by the variables const, memory, HDD, pixel, vide-ocard_performance, OS, keyboard, material, Nvidia, usb2 and usb3 satisfy. For the other variables, the p-value of the coefficients has
Fedotov D.A. Improvement of the mechanism of rationing the initial contract price in the field of public procurement on the example of econometric modelling of the price of laptop // Research Result. Economic Research. - T.4, Vol.4, 2018
turned out to be greater than 0.1, they were insignificant and therefore were excluded from further analysis.
2. t-statistics. Since the sample was 102 observations, so t-critical by t-Student is equal to 1.659 at a significance level of 10%. Comparing the obtained values, it appeared that the coefficients of const, memory, HDD, pixel, videocardperformance, OS, keyboard, material, Nvidia, usb2 and usb3 have t-statistics modulo more than t-critical, which indicates their statistical significance. And the remaining coefficients of CPU, core, SSD, screen_size, DVDRW, battery and AMD have t-statistics less than t-critical, it means they are not significant.
3. The significance of the regression equation in general according to Fisher's F-test (P-value (F)). «If the P-value (F) is less than 0.01, the equitation is significant at a significance level of 1% (at an assurance level of 99%)» [Econometrics. Regression analysis using the package Gretl: Laboratory Workshop, 2014]. Because of the P-value(F)=2.33e-26<0.01, the regression equitation is significant and it can be used in further analysis.
4. Standard error of the estimate is 9006.38 RUB with an average laptop's price at 50998.5 RUB (or 17.66%), which indicates the satisfactory accuracy of the model.
5. Goodness of fit to selected data by the adjustable coefficient of determination (adj. R-squared). Using the coefficient of determination, one can be defined «the matching rate of the found equation to the actual data. Adj. R-squares in this model was 0.9484, so the factor of laptop's price change is explained sum of squares by 94.84%. Thus, the quality of the fit equation is very accurate.
6. Goodness of fit to selected data by the mean absolute percentage error (MAPE). In this regression equation was 16.4%. «If the model is fitted with high accuracy, so MAPE<10%, good - 10% <MAPE<20%, satisfactory - 20%<MAPE<50%, unsatisfactory -MAPE>50%». That was, the goodness of fit is good [Absolute approximation error, 2018].
The MLR model after eliminating insignificant explanatory variables is presented in Figure 2.
Модель 2 : MHK, использованы н а блюдежил 1-102 Зависимая переменная: price
Коэффищелт Ст. спибка t- статистика F- значение
const -142 95,1 4004,31 -3,570 0006
memory 3015,16 322,166 9, 359 5, б0е-015
HDD -4,74393 2,17351 -2,183 0316
pixel 0,00667310 0,000882544 7,561 3, 07е-011
Videocard perfor~ 685,802 130,763 5,245 1, 01е-06
OS -62 07,3 9 2447,57 -2,536 012 9
keytord 5971,24 2503,69 2 , 335 0192
material 9596,99 2434,56 3, 942 0002
Nvidia -5902,24 2474,71 -2,335 0192
usb2 5216,64 1415,97 3, 634 0004
usb3 10099,6 1663,05 6,073 Збе-ОЗ
Средлее зав. перемел 50998,50 Ст. откл. зав. перемел 39647 ,29
Сумма кб. остатков 7,25е+09 Ст. спибка модели 3 923, 054
R-квадрат 0,954363 Испр . R-квадрат 0,949343
F(10, 91} 190,2 932 Р-значение (F) 1, 34е -56
Лог. правдоподобие -1066,744 Крит . Акаике 2155, 488
Крит. Шварда 2134,3 63 Крит . Хеннана-Куинна 2167, 131
* * * * * * * * * * * * * * * * * * * * *
Fig. 2. MLR model after eliminating insignificant explanatory variables Рис. 2. Модель МЛР после исключения незначимых объясняющих переменных
Fedotov D.A. Improvement of the mechanism of rationing the initial contract price in the field of public procurement on the example of econometric modelling of the price of laptop // Research Result. Economic Research. - T.4, Vol.4, 2018
Adj. R-squared improved from 0.9484 to 0.9493. Thus, the eliminating insignificant explanatory variables has turned out to be true. All coefficients were significant (p-value less than 0.1).
At the next stage, «the existence of the strong correlation between explanatory variables» was determined [Econometrics. Regression analysis using the package Gretl: Labora-
tory Workshop, 2014], so multicollinearity test was performed (Fig. 3).
All values of variance inflation factors (VIF) of explanatory variables were less than 10; it has shown the absence of multicollineari-ty between these variables.
Further, the data were checked for the unequal spread (heteroscedasticity), to the White test for heteroscedasticity was carried out (Fig. 4).
Значения > 10.0 могут указывать на наличие мупьтиколлинеарности
memory 2,853
HDD 1,696
pixel 1,991
videocard performance 3,561
OS 1,066
keybord 1,995
material 1,711
Nvidia 1,33 6
■js£2 2,106
лзЬЗ 4,405
Fig. 3. Multicollinearity test Рис. 3. Тест на мультиколлинеарность
Тестовая статистика: = 32,693Э52,
р-значете = Р(Хи-квадрат(61) > 82,693952} = 0,033706
Fig. 4. White test for heteroscedasticity Рис. 4. Тест Вайта на гетероскедастичность
Since the p-value was equal to 0.0337 and it was less than 0.05; this indicated the presence of heteroscedasticity. Therefore, calculations of robust errors were conducted, which has corrected the values of standard errors of the coefficient estimates. The MLR model adjusted on heteroscedasticity is shown in Figure 5.
Thus, from an economic point of view the interpretation of all coefficients of the explanatory variables was correct. All coefficients were significant. The standard error of the model was 8923.05 with a mean of 50998.5 (or
17.5%). Adjusted R-square has increased to 0.9484 (more than 0.9 is considered to be highly accurate) [Afanasev V.N., Semenychev E.V., 2014].
At the final stage, it was important to understand whether the specification of the model was correct or whether it was switching from a linear to a non-linear model. To this end, Regression Equation Specification Error Test (RESET-test Ramsey) was carried out on the correctness of the linear specification. RESET-test is shown in Figure 6.
Fedotov D.A. Improvement of the mechanism of rationing the initial contract price in the field of public procurement on the example of econometric modelling of the price of laptop // Research Result. Economic Research. - T.4, Vol.4,2018
Модель 3: МНК, ис^ользовг:-щ наблюде ния 1-102
ЗаЕисимая переменная: price
Робастные оценки стандартных опибок (С поправкой на гетероскедастичность), вариант HCl
Ко э ффицие нт Ст. ошибка t- статистика. Р- значение
const -142 35,1 3798,60 -3,763 о, 0003 ^ й- *
memory 3015,16 330,561 7,720 1, 45е-011 fr * fr-
HDD — 4,743 33 1,89609 -2,502 0, 0141 fr fr-
pixel 0,00667310 0,00107630 6,137 1, 65е-03 fr fr fr-
videocard perfor- 6-35, -302 112,826 6,078 2, ■ЗОе-О-З fr
OS -62 07,3 3 2 344,68 -2,182 0, 0317 fr fr-
keybord 5371,24 2143,88 2,785 0065 fr *■ fr-
material 3536,33 2335,47 4,103 8, 67е-05 fr fr fr
Nvidia -5302,24 2148,21 -2,748 0, 0072 fr fr fr
■jsb2 5216,64 1332,18 3, 316 0, 0002 fr fr fr
usb3 10033,6 1635,75 5, 356 4, 30е-03 fr fr fr
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Среднее зав. перемен 50998,50 Ст. откл. заЕ. перемен 33647 ,29
Сумма КБ. остатков 7,25е-ЮЗ Ст. спибка модели 8 323, 054
R-квадрат 0,354363 Испр . R-квадрат 0,343343
F(10, 91} 133,0351 Р-значение (F) 3,77е -57
Пор. правдоподобие -1066,744 Крит . Акаике 2155, 488
Крит. Шварца 2134,3 63 Крит . Хеннала-Куинна 2167, 181
Fig. 5. The model adjusted on heteroscedasticity Рис. 5. Модель МЛР с поправкой на гетероскедастичность
Вспомогательная регрессия для тесте Рамсея МНК, использованы наблюдения 1-102 Зависимая переменная: price
Коэффициент
Ст. опибка
t-статистика Р-значение
const memory HDD pixel
vldeocard_perfor-05
keyfcord
material
Nvidia
usb2
usb3
yhat"2
-2513,36 2316,56 -2,67431 0,00531517 495,931 -5935,64 7567,27 8611,90 -2340, 67 2216,16 733 6,30
Э,52 3 63e-07
Тестовая статистика: F = 5,356467, p-значение = P(F(1,90) > 5,85647} =
62 33,91 426,459 2,23332 О,00102 673 14 9,623 2 337,42 2527,02 2406,76
2722.34 1354,90
1370.35
3, 9353 бе-07
-0,4029 0,6330
5,432 4,70e-07 * * *
-1,171 0,2446
5,177 1,37e-06 fr fr fr
3, 314 0,0013 fr fr *
-2,43 6 0,0143 fr fr
2, 995 0,0035 fr fr *
3, 573 0,0006 fr fr fr
-1,043 0,2 ЭЭ6
1,195 0,2353
3,749 0,0003 fr fr *
2,420 0,0175 fr fr
0,0175
Fig. 6. RESET-test Рис. 6. RESET тест
Since p-value was equal to 0.0175 and less than 0.05; the MLR model in Figure 5 was presented in the wrong functional form (with a 95% assurance level). Therefore, non-linear terms were added to this regression equation, so a polynomial was considered (Fig. 7).
Polynomial model. Adding squared variables haven not helped to improve the goodness of the model: all variables were insignificant. As for the multiplication of explanatory variables, there were several significant coefficients
Fedotov D.A. Improvement of the mechanism of rationing the initial contract price in the field of public procurement on the example of econometric modelling of the price of laptop // Research Result. Economic Research. - T.4, Vol.4, 2018
(in this case, quantitative variables were multiplied by dummy):
1. Multiplication of battery (quantitative) and Intel (dummy): battery_OS;
2. Multiplication of SSD (quantitative) and Intel (dummy): SSD_Intel;
3. Multiplication of CPU (quantitative) and OS (fictitious): CPU_OS;
4. Multiplication of screen_size (quantitative) and Intel (dummy): screen_size_Intel.
When non-linear terms were introduced, it was also necessary to introduce the desired variables into the model, so as not to disturb the economic interpretation. The model with new non-linear variables (polynomial model) is presented in Figure 7.
Folinom: MHK, использованы .наблюдения 1-102 Зависимая переменная: price Робасггные оценки стандартных спибок (с поправкой на гетероскедастичность), вариант НСJ
Коэффициент
Ст. спибка
t -статистика. Р-значение
const -112 4 31 21744,3 -5,173 1,54e-06 * * *
memory 2462,34 407,316 6, 033 4,07e-03 * * fr
pixel 0,00716330 0,00113523 6, 315 1,23e-03 ***
videocard perfor~ 423,525 161,603 2 , 653 0,0034 * * *
OS 34334,6 13530,2 2 , 536 0,0114 fr fr
keybord 5636,04 2735,55 2 , 060 0,0425 * *
material 6510,67 2462,76 2, 644 0,0033 * * *
usb2 5233,82 1345,18 3, 3 31 0,0002 * * fr
usb3 32 61,76 1623,32 5, 633 1,37e-07 * * *
battery OS -3253,75 1013,63 -3,133 0,0013 * * *
battery 3330,43 1053,12 3,163 0,0022 * * fr
Intel 53330,6 21300,3 2 , 711 0,0031 * * *
SSD 46,3337 15,6622 3, 000 0,0035 * * fr
SSD Intel -45,8205 17,7633 -2,573 0,0116 * *
CPU 11206,7 3333,33 2 , 303 0,0062 * * *
C FU_C S -35 31,30 413 6,30 -2,047 0,0433 * *
screen 3ize 3034,64 1226,40 2 , 523 0,0135 * *
screen 3ize Intel -3337,57 137 3,31 -2,462 0,0153 * *
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Среднее зав. перемен 50ЭЭЗ,50
Сумма кв. остаткоЕ 5,55е403
R-квадрат 0,365013
F (17, 84) 145, 6543
Ст. откл. зав. перемен Ст. опибка модели Испр. R-квадрат Р-значение (F)
33647,23 8131,815 0,357332 8,02е-55
Fig. 7. Polynomial model Рис. 7. Полиномиальная модель
From an economic point of view the interpretations of all coefficients of the explanatory variables have turned out to be correct. Compared to the model in Figure 5, all coefficients were significant; the standard error of the estimate decreased from 8923.05 RUB to 8131.81 RUB (or 15.94%); adj. R-squared increased to 0.9579, which means the inclusion of new variables has turned out to be true. MAPE was evaluated to be 14.44% that was a little better than 16.4% in Figure 5. That was, the goodness of fit to selected data was good [Absolute approximation error, 2018].
Because of the result of RESET-test, the hypothesis of a well-chosen model specification has declined, models in nonlinear forms were considered: exponential, logarithmic, power-law, semi-logarithmic.
1. Exponential model: the dependent variable was represented by the logarithm, and the independent variables were in the original form. Verification of all problems: multicollin-earity, heteroscedasticity, equality of coefficients. After their recovering the following model was obtained (Fig. 8).
Fedotov D.A. Improvement of the mechanism of rationing the initial contract price in the field of public procurement on the example of econometric modelling of the price of laptop // Research Result. Economic Research. - T.4, Vol.4, 2018
Exponent: MHK, использованы аабгащежя 1-102 !Э а Еисимг я пер еме нна я: 1_р rice
Коэффициент Ст. списка
t-статистика Р-эначенне
const 3,6 3552 0,237334 36, 64 2,87e-056
CPU 0,153713 0,0463443 3,446 0,0003
memory 0,0134330 0,00750123 2,531 0,0111
SSD 0,000450035 0,000200036 2,250 0,02 63
scree:. 3ize 0,0564403 0,0168817 3, 343 0,0012
pixel 4,23035e-03 2,330 6 3e-03 1,341 0,0 63 3
OS -0,102005 0,0573663 -1, 77.3 0, 07-37
keybord 0,314172 0,0607564 5,171 1,37e-06
material 0,2 3052 3 0,0563303 4, 331 3,66e-06
Nvidia 0,125030 0,0543137 2,303 0,0236
usfc3 0,125623 0,0323534 3, 32 3 0,0002
**+
it it
fr fr
fr fr fr
fr
fr
fr fr fr-fr fr fr-fr fr fr fr fr-
Среднее зав. перемен 10,62 606
Сумма кв. остаткоЕ 4,037543
R-квадрат О, 302434
F(10, 91} 84,21824
Ст. откл. зав. перемен О,640266
Ст. списка модели 0,210633
Испр. R-квадрат О,891768
Р-эначенне (F) 1,43е-41
Fig. 8. Exponential model Рис. 8. Экспоненциальная модель
All coefficient were significant. The standard error of estimate was low: 0.2106 with a mean of 10.6261 (or 2%). Adj. R-squared was equal to 0.8918 (about 0.9 is considered to be highly accurate) [Afanasev V.N., Semenychev E.V., 2014]. MAPE was 1.55%, that was significantly lower than 10%, therefore it indicat-
ed a high accuracy fit of the model to the sample data.
2. The logarithmic model: the dependent variable was presented in its original form, and the independent variables were represented by the logarithm (Fig. 9).
Logarifm : MHK, использованы наблюдения 1-102 Зависимая переменная: price
Робастные оценки стандартных спибок (с поправкой на гетероскедастичность}, в
Коэффициент Ст. спибка. t-статистика Р-эначенне
const -452 61Э
lmemory 3-3116,3
l_pixel 27774,8
l_videocard_perf~ 333 9,72
l_battery 10322,3
Среднее зав. перемен 50 3 33,50
Сумма кв. остатков 3,52е+10
R-квадрат 0,773434
F (4, 97} 20,76432
33333,1 7126,43 6319,38 2100,04 4388,69
-4,347 5,343 4,335 3, 971 2,352
Ст. откл. зав. перемен Ст. спибка модели Испр. R-квадрат Р-эначенне (F)
4,77е-0 б 5,Э0е-07 2,ЗЗе-05 0,0001 0,0207
33647,23 13043,20 0,7632 37 2,1Эе-12
fr fr » fr fr fr fr fr fr-fr fr fr fr fr
Fig. 9. Logarithmic model Рис. 9. Логарифмическая модель
Fedotov D.A. Improvement of the mechanism of rationing the initial contract price in the field of public procurement on the example of econometric modelling of the price of laptop // Research Result. Economic Research. - T.4, Vol.4,2018
All coefficient were significant. The standard error of estimate was high: 19043.20 RUB with a mean of 50998.50 RUB (or 37.34%). Adj. R-squared was equal to 0.7693 (about 0.75 is considered to be the lower acceptable value) [Afanasev V.N., Semenychev
E.V., 2014]. MAPE was 34.33%, so the model fit was satisfactory.
3. The power-law model: dependent and independent variables were presented in logarithm (Fig. 10).
stepen: MHK, использованы наблюдения 1-102 Зависимая переменная: l_price Коэффициент Ст. ошибка t- статистика Р-значение
const 4,31504 0,858471 5,096 1,73е-06 * * *
1_соге -0,190388 0,0772941 -2,463 0,0156 * #
1 memory 0,657717 О,0707091 9, 302 4,71е-015 * * *
l_pixel 0,306154 0,0652644 4, 696 8,S4e-G6 * * *
l_videocard_perf- 0,245423 0,03585S6 6,844 7,23е-010 * * *
X battery 0,210947 0,0657475 3, 208 0,0018 * * *
Среднее зав. перемен 10,62606 Ст. откл. зав. перемен 0, 640266
Сумма кв. остатков 5,859630 Ст. ошибка модели 0, 247058
R-квадрат 0,858477 Испр. R-квадрат о, 851106
F(5, 96) 116,4669 Р-значение <F> з. 61е-39
Fig 10. The power-law model Рис. 10. Степенная модель
All coefficient were significant. The standard error of estimate was low: 0.2471 with a mean of 10.6261 (or 2.32%). Adj. R-squared was equal to 0.8511 (less than 0.9 indicates a lack of high accuracy). MAPE was 1.87%, that
was significantly lower than 10%, therefore it indicated a high accuracy fit of the model to the sample data.
4. The semi-logarithmic model is shown in Figure 11.
polulog: MHK, использованы наблюдения 1-102 Зависимая переменная: 1 price
Коэффициент Ст. спибка t-статистика Р-значение
const 6,43 6 63 0,716631 8, 931 4,lle-014 * * *
1 nenory 0,412 343 0,0578832 7,132 2,52 e-010 * * *
1 pixel 0,163344 0,0432 913 3,393 0,0010 * * *
1 videocard perf~ 0,0979744 0,0314642 3,114 0,0025 * * *
keyfcord 0,239623 0,0537734 4,456 2,42 e-05 * * *
material 0,13 9 603 0,0433 63 6 3,330 0,0002 * * *
AMD -0,118747 0,0587931 -2,020 0,0464 * *
ust3 0,100179 0,0271164 3, 694 0,0004 * * *
CPU 0,0989105 0,0430334 2,296 0,0240 * *
Xll XI2 0,000291091 0,000113619 2,562 0,0121 * *
HDD -0,000374044 0,000114036 -3,230 0,0015 * * *
OS -0,206033 0,0708899 -2,907 0,0046 * * *
screen 3ize 0,0379929 0,0160310 2,363 0,0203 * *
Среднее зав. перемен 10,62 60 6
Сумма кв. остатков 2,623745
R-квадрат 0,936631
F (12, 89} 10 9, 62 2 2
Ст. отел. зав. перемен 0,6402 66
Ст. спибка модели 0,1716 93
Испр. R-квадрат 0,928087
Р-значение (F) 7,05е-43
Fig. 11. The semi-logarithmic model Рис. 11. Полулогарифмическая модель
Fedotov D.A. Improvement of the mechanism of rationing the initial contract price in the field of public procurement on the example of econometric modelling of the price of laptop // Research Result. Economic Research. - T.4, Vol.4,2018
All coefficient were significant. The standard error of estimate was low: 0.1717 with a mean of 10.6261 (or 1.62%). Adj. R-squared was equal to 0.9281(more than 0.9 is considered to be highly accurate). MAPE was 1.21%, that was significantly lower than 10%, therefore it indicated a high accuracy fit of the
model to the sample data.
The next stage, the comparison of the resulting models was carried out. Comparison is possible only if the models are presented in the same type of dependent variables, so in the same units of measurement. The comparative Table 2 is below.
Table 2
Comparative table on models
Таблица 2
Model/Criterion Adj. R-squared Standard error of the estimate Mean absolute percentage error (MAPE)
1. The dependent variable is in rubles
Multiple Linear Regression 0.9493 8923.05 16.95%
Polynomial 0.9579 8131.81 14.44%
Logarithmic 0.7693 19043.20 34.33%
2. The de pendent variable is presented in logarithm-rubles
Exponential 0.8918 0.2106 1.55%
Power-law 0.8511 0.2471 1.87%
Semi-logarithmic 0.9281 0.1717 1.21%
Thus, according to all indicators the polynomial model was better in the first case and the semi-logarithmic - in the second case. The choice of the best model was carried out to the non-nested models test (PE-test). Figure 12 shows the models with predictions of a competing model.
For the PE-test, the coefficient of the variable lin (the difference between the logarithm of the forecast of the polynomial model and the forecast of the semi-logarithmic model) and log (the difference between the forecast of the polynomial model and the exposed forecast of the semi-logarithmic) were calculated [Econometrics. Regression analysis using the package Gretl: Laboratory Workshop, 2014]. For the
polynomial model, the coefficient for the variable lin has turned out to be significant (the p-value was 0.0041), so the model can be improved.
For the semi-log model, the coefficient of the variable log has also turned out to be significant (the p-value was 0.0009), so the model can be improved too. Since the coefficients in the both models are significant, it was not possible to make a definite conclusion. Therefore the models were compared by the value of significance. Since the p-value (0.0041) was larger in the polynomial model than in the semi-logarithmic model (0.0005), then the coefficient in the polynomial was less significant.
Fedotov D.A. Improvement of the mechanism of rationing the initial contract price in the field of public procurement on the example of econometric modelling of the price of laptop // Research Result. Economic Research. - T.4, Vol.4,2018
Коэффициент
Ст. сшибка
t-статистика Р-значение
const -114949 21875,3 -5,255 1,13e-06 к А к
ir.eir.ory ¿¿62,53 373,981 6,050 4,01e-08 кк к
pixel 0,00775341 0,00100198 7,738 2,16e-Qll к* к
videccard perfor~ 467,163 129,704 3, 602 0,0005 к к к
OS 42566,7 10164,7 4,188 6,98e-05 к к к
keybcrd 4685,35 2366,93 1,979 0,0511 к
material 6706,07 2326,43 2,383 0,0050 к* к
usb2 5246,92 1181,76 4, 440 2,75e-05 к* к
usb3 9373,13 1426,37 6,571 4,12e-09 к к к
battery OS -3734,24 745,255 -5,078 2,31e-06 к* к
battery 4076,93 761,322 5,352 7,5Эе-07 кк к
Intel 39901,7 20917,1 1, 908 0,0599 к
SSD 48,1242 13,5567 3,550 0,0006 кк к
55D_Intel -45,1367 15,7974 -2,357 0,0054 к к к
CPU 130 85 f 3499,36 3,739 0,0003 к* к
X2 X7 -10411,4 3562,02 -2,923 0,0045 кк к
screen 3ize 2639,72 1136,47 2, 323 0,0226 к к
screen 3ize Intel -2097,31 1314,45 -1,596 0,1144
lin -19889,9 6729,83 -2,955 0,0041 А А *
Коэффициент Ст. сшибка t-статистика Р-значение
const 7,10665 o, 704300 10,09 2, 35e-016 A A A
1 ir.eir.ory 0,443669 Or 0553911 9,010 4, 43e-012 к К *
1 pixel 0,101632 0, 0490655 2,071 o, 0413 A A
1 videocard perf- 0,102 ЭЭ1 0, 0297480 3,462 o, 0008 A A A
Jceybord 0,251649 0, 0509041 4, 944 3, 64e-06 к к к
material 0,199354 0, 0462298 4,312 4, 21e-Q5 AAA
AMD -0,123047 0, 0555851 -2,304 o. 0236 А к
usb3 0,106707 0, 0256768 4,156 7, 50e-05 AAA
CPU 0,102227 0, 0406957 2,512 o, 0133 A A
X11_X12 0,000325709 0, 000107764 3,022 o, 0033 AAA
HDD -0,000444604 0, 000109626 -4,056 o, 0001 AAA
OS -0,195801 0, 0670092 -2,922 0, 0044 AAA
screen size 0,0430734 0, 0154666 3,109 0, 0025 AAA
log 9,19642e-Q6 2, 67650e-06 3, 436 0, 0003 AAA
Fig. 12. PE-test results Рис. 12. Результаты PE-теста
Заключение
Thus, the polynomial model was chosen or further econometric analysis (Fig. 7). Let us give an economic interpretation of the coefficients of the explanatory variables in the total influence of all factors:
1. If the amount of RAM is increased by 1GB, the laptop's price will increase on average by 2,462.94 RUB, other things being equal.
2. If the number of pixels is increased by 1000000, the laptop's price will increase on
average by 7168.90 RUB, other things being equal
3. If the performance of the video card is increased by 1% the laptop's price will increase on average by 429.53 RUB, other things being equal.
4. If the number of usb-ports 2.0 is increased by 1 unit, the laptop's price will increase on average by 5233.82 RUB, other things being equal.
Fedotov D.A. Improvement of the mechanism of rationing the initial contract price in the field of public procurement on the example of econometric modelling of the price of laptop // Research Result. Economic Research. - T.4, Vol.4, 2018
5. If the number of usb-ports 3.x is increased by 1 unit, the laptop's price will increase on average by 9,261.76 RUB, other things being equal.
6. If the battery life is increased by 1 hour, the laptop's price will increase on average by 3330.49 RUB.
7. If the CPU's frequency is increased by 1 GHz, the laptop's price will increase on average by 11206.7 RUB.
8. The laptops with keyboard lightning will cost more on average by 5636.04 RUB than laptops with non-lightning.
9. The laptops with a metal case will cost more on average by 6,510.67 RUB than laptops with a plastic case.
10. The price of the laptops with the Windows OS is on average by 34994.60 RUB higher than other operating systems, provided that:
- if the battery life is increased by 1 hour, the price of the laptops with Windows OS will grow less on average by 3,258.75 RUB than laptops with another OS;
- if the CPU's frequency is increased by 1 GHz, the price of the laptops with Windows OS will grow less on average by 8591.80 RUB than laptops with another OS;
11. If the volume of solid-state drive (SSD) is increased be 1 GB, the laptop's price will increase on average by 46.99 RUB;
12. If the diagonal of the screen is increased by 1 inch, the laptop's price will increase on average by 3094.64 RUB;
13. The price of the laptops with Intel graphics card will cost more on average by 59380.60 RUB higher than laptops with AMD and Nvidia under two conditions:
- if the value of SSD is increased by 1 GB, the price of the laptops with Intel graphics cards will grow less on average by 45.82 RUB less than laptops with AMD and Nvidia videocards;
- if the diagonal of the screen is increased by 1 inch, the price of the laptops with Intel graphics cards will grow less on average by 3397.57 less than laptops with AMD and Nvidia videocards.
So during the research the model was built based on econometric analysis which allowed to draw the conclusion on the optimal laptop's price under the influence of various factors. These factors were explained the laptop's price by 95,79%.
The model has an error of 15,95%. The error can be reduced by increasing the number of observations and the number of factors. If an econometric model is built for using in practice, we can add factors such as laptop weight, processor generation, battery capacity, RAM frequency, display matrix type, memory card support, the presence of Kensington lock slot, etc.
Use the resulting econometric model on a specific example. Take from official website of the State Procurement the Purchase №31807033837 to deliver the computers and one laptop, posted on 10.23.2018 [5]. Under the contract, one laptop is purchased with a stated initial contract price of 134750.49 RUB. These terms of purchase are suitable for the resulting econometric model as the delivery is carried out at retail. According to the information that is specified in the technical project, it is expected to purchase a laptop model Dell XPS15 15.6". In this laptop model uses the following parameters, listed in Table 3.
Table 3
Dell XPS15 15.6" laptop settings shown in the information card
Таблица 3
Factor Measurement
CPU frequency 2,5 GHz
Core 4 cores
Random access memory (RAM) 8 GB
Hard disk drive 1000 GB
Solid state driver 128 GB
Monitor inch 15,6
Pixels 2073600
Fedotov D.A. Improvement of the mechanism of rationing the initial contract price in the field of public procurement on the example of econometric modelling of the price of laptop // Research Result. Economic Research. - T.4, Vol.4, 2018
Factor Measurement
Performance of video card 2б,9%
USB ports 2.0 G
USB ports 3.x 4
Battery 1G hours
Operation System (OS) Windows OS (1)
DVD-drive No (G)
Keyboard lightning Yes (1)
Laptop's material Metal (1)
Nvidia video card Yes (1)
Substituting these data into the econometric model, the average price of a laptop was 80906.75 RUB. Taking into account the standard error of regression, the maximum contract price should not exceed 93807.33 RUB. The stated contact price of 134750.49 RUB significantly exceeds the optimal price of the laptop by 40943.16 RUB.
Thus, using the econometric model allows to create a rationing mechanism for initial (maximum) contract price of purchases and to increase the efficiency of budget spending.
Список литературы
1. Афанасьев В.Н., Семенычев Е.В., 2014. Критерии качества моделей экономической динамики // Вестник Самарского муниципального института управления. 2014. №2 (29). С. 7-17.
2. Рыбникова Г.И, Тевосян К.М., 2016. Контроль государственных закупок в системе повышения эффективности бюджетного процесса // Территория наук. Экономика и экономические науки. 2016. №5. С. 168-173.
3. Эконометрика. Регрессионный анализ с использованием пакета Gretl: Лабораторный практикум, 2014. / Т.Б. Багильдеева, Е.А. Постников // Центр научного сотрудничества. 2014. - 80 с.
4. Абсолютная ошибка аппроксимации, 2018. [Электронный ресурс] // URL: https://math.semestr.ru/trend/prim3.php (дата обращения 24.10.2018).
5. Единая информационная система в сфере закупок. Закупка №31807033837 // URL:http://zakupki.gov.ru/223/purchase/public/pur chase/info/common-
info.html?regNumber=31807033837 (дата обращения 24.10.2018).
6. Рейтинг производительности видеокарт, 2018. // URL: https://technical.city/ru/video/rating (дата обращения 24.10.2018).
References
1. Afanasev V.N., Semenychev E.V., 2014. Performance Criteria of Models of Economic Dynamic // Bulletin of Samara Municipal Institute of Management. 2014. No. 2 (29). P. 7-17. (in Russian)
2. Rybnikova G.I., Tevosyan K.M., 2016. Control of the state purchases in the system of increasing the efficiency of the budget process // Territory of Sciences. Economics and Economic Sciences. 2016. No 5. P. 168-173. (in Russian)
3. Econometrics. Regression analysis using the package Gretl: Laboratory Workshop, 2014 / T.B. Bagildeeva, E.A. Postnikov // Center for Scientific Cooperation. 2014. 80 p. (in Russian)
4. Absolute approximation error, 2018 [Electronic resource] // URL: https://math.semestr.ru/trend/prim3.php (date of access: October, 24 2018).
5. The official website of the Unified Procurement Information System. Purchase No 31807033837 // URL: http://zakupki.gov.ru/223/purchase/public/purchase/ info/common-info.html?regNumber=31807033837 (date of access: October, 24 2018). (in Russian)
6. Video card performance rating, 2018. // URL: https://technical.city/ru/video/rating (date of access: October, 24 2018). (in Russian)
Информация о конфликте интересов:
авторы не имеют конфликта интересов для декларации.
Conflicts of Interest: the authors have no conflict of interest to declare.
Федотов Д.А. - студент Челябинского государственного университета, директор ООО Финансовый центр «Кредитная линия»
Fedotov Danil Aleksandrovich - student Chelyabinsk State University, director of «Credit Line» Financial Center LLC
