МЕДИЦИНА, ПЕДАГОГИКА И ТЕХНОЛОГИЯ:
ТЕОРИЯ И ПРАКТИКА
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ECONOMETRIC ASSESSMENT OF THE EFFECT OF INVESTMENTS
ON THE VOLUME OF CONSTRUCTION PRODUCTION
R.A. Khurramov
Teacher of Termiz State University
Abstract.
In this article, a regression analysis of the impact of investments on the
volume of construction production was carried out. Conclusions about short-term
and long-term changes were made by creating an autoregression model.
Key words:
model, autoregression, regression equation, Student t test, Fisher,
instrumental variable.
In order to assess the impact of investments on the volume of construction
production of Surkhondarya region, data for 2010-2023 were obtained from
www.surkhonstat.uz (Table 1).
Table 1
Construction production and investment volume indicators of
Surkhandarya region
1
Year
𝒚
𝒙
Year
𝒚
𝒙
2010
335,9
655,3
2017
1 827,0
3 551,0
2011
470,6
802,9
2018
2 879,7
7 240,6
2012
605,3
980,3
2019
3 979,7
11 835,1
2013
849,5
1 371,0
2020
4 774,7
10 068,2
2014
1 051,5
1 509,1
2021
5 868,4
12 037,8
2015
1 351,3
1 843,6
2022
6 521,9
11 569,4
2016
1 554,8
2 142,4
2023
7 353,3
17 956,0
Autoregression models are useful in assessing the short-term and long-term
impact of investments on the volume of construction production. The general
appearance of the
𝐴𝑅(1) + 𝑥
model is as follows:
𝑦
𝑡
= 𝑎 + 𝑏
0
∙ 𝑥
𝑡
+ 𝑐
1
∙ 𝑦
𝑡−1
+ 𝑒
𝑡
(1)
To calculate model (1), it is necessary to first create a model that evaluates the
instrumental variable:
1
Information from the Surkhandarya Region Statistics Department website www.surkhonstat.uz
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𝑦̂
𝑡−1
= 𝑑
0
+ 𝑑
1
⋅ 𝑥
𝑡−1
(2)
To estimate the model (2), we need to determine the lags of the
𝑦
𝑡
and factor
indicators for the period t-1 (Table 2).
Table 2
Values of the indicators of the volume of construction production and
investments in fixed capital of Surkhandarya region in the period
𝒕 − 𝟏
2
Year
𝒚
𝒕
𝒙
𝒕
𝒚
𝒕−𝟏
𝒙
𝒕−𝟏
2010
335,9
655,3
-
-
2011
470,6
802,9
335,9
655,3
2012
605,3
980,3
470,6
802,9
2013
849,5
1 371,0
605,3
980,3
2014
1 051,5
1 509,1
849,5
1 371,0
2015
1 351,3
1 843,6
1 051,5
1 509,1
2016
1 554,8
2 142,4
1 351,3
1 843,6
2017
1 827,0
3 551,0
1 554,8
2 142,4
2018
2 879,7
7 240,6
1 827,0
3 551,0
2019
3 979,7
11 835,1
2 879,7
7 240,6
2020
4 774,7
10 068,2
3 979,7
11 835,1
2021
5 868,4
12 037,8
4 774,7
10 068,2
2022
6 521,9
11 569,4
5 868,4
12 037,8
2023
7 353,3
17 956,0
6 521,9
11 569,4
Using the OLS method in the Gretl program, we estimate the form of association
of the lag indicators in Table 2 (Table 3).
Table 3
Results of regression analysis
3
Model 2: OLS, using observations 2011-2023 (T = 13)
Dependent variable: yt1
Coefficient
Std. Error
t-ratio
p-value
2
Information from the Surkhandarya Region Statistics Department website www.surkhonstat.uz
3
Development of the author
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xt-1
0.464409
0.0256488
18.11
<0.0001
***
Mean
dependent
var
2466.947
S.D.
dependent
var
2138.834
Sum squared resid
4731975
S.E. of regression
627.9580
Uncentered
R-
squared
0.964690
Centered
R-
squared
0.913800
F(1, 12)
327.8440
P-value(F)
4.44e-
10
Log-likelihood
−101.6781
Akaike criterion
205.3562
Schwarz criterion
205.9211
Hannan-Quinn
205.2400
rho
0.444907
Durbin-Watson
1.079236
From Table 3, the general view of the regression equation of the instrumental
variable
𝑦̂
𝑡−1
is as follows:
𝑦̂
𝑡−1
= 0,464409 ⋅ 𝑥
𝑡−1
(3)
The calculated value of Fisher's F criterion is equal to
𝐹
𝑒𝑠𝑡
= 327,844
4. This
value is greater than Fisher's table value
𝐹
1;12;0,05
= 4.75
at
𝛼 = 0,05
significance
level. Also, the value of the Student's t criterion are equal to
𝑡
𝑑
1
= 18,1
, which is
greater than the table value of the Student's t criterion
𝑡
13;0,05
= 2,16
at the degree
of freedom
𝑑𝑓 = 𝑛 − 𝑚 = 13
. Therefore, the model is statistically significant.
We determine the theoretical values of the instrumental variable
𝑦̂
𝑡−1
. (Table 4).
Table 4
Theoretical values of the instrumental variable
4
Year
𝒚
𝒕
𝒙
𝒕
𝒚
𝒕−𝟏
𝒙
𝒕−𝟏
𝒚
̂
𝒕−𝟏
2010
335,9
655,3
-
-
-
2011
470,6
802,9
335,9
655,3
304,3
4
Information from the Surkhandarya Region Statistics Department website www.surkhonstat.uz
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ТЕОРИЯ И ПРАКТИКА
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2012
605,3
980,3
470,6
802,9
372,9
2013
849,5
1 371,0
605,3
980,3
455,3
2014
1 051,5
1 509,1
849,5
1 371,0
636,7
2015
1 351,3
1 843,6
1 051,5
1 509,1
700,9
2016
1 554,8
2 142,4
1 351,3
1 843,6
856,2
2017
1 827,0
3 551,0
1 554,8
2 142,4
995,0
2018
2 879,7
7 240,6
1 827,0
3 551,0
1 649,1
2019
3 979,7
11 835,1
2 879,7
7 240,6
3 362,6
2020
4 774,7
10 068,2
3 979,7
11 835,1
5 496,3
2021
5 868,4
12 037,8
4 774,7
10 068,2
4 675,8
2022
6 521,9
11 569,4
5 868,4
12 037,8
5 590,4
2023
7 353,3
17 956,0
6 521,9
11 569,4
5 372,9
It is possible to evaluate the model (1) with the participation of variables
𝑦
𝑡
,
𝑥
𝑡
and
𝑦̂
𝑡−1
in Table 4. For this, we again used Gretl's capabilities. (Table 5).
Table 5
Results of regression analysis
5
Model 2: OLS, using observations 2011-2023 (T = 13)
Dependent variable: y
Coefficient
Std. Error
t-ratio
p-value
const
346.814
187.231
1.852
0.0937
*
x
0.216391 0.0574790
3.765
0.0037
***
yt-1_fitted
0.546096
0.149724
3.647
0.0045
***
Mean dependent var
3006.744 S.D. dependent var
2422.853
Sum squared resid
1933064 S.E. of regression
439.6662
R-squared
0.972558 Adjusted R-squared
0.967070
F(2, 10)
177.2045 P-value(F)
1.56e-08
Log-likelihood
−95.85904 Akaike criterion
197.7181
Schwarz criterion
199.4129 Hannan-Quinn
197.3697
5
Development of the author
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rho
0.399093 Durbin-Watson
1.173993
Test for normality of residual -
Null hypothesis: error is normally distributed
Test statistic: Chi-square(2) = 1.99324
with p-value = 0.369125
Based on Table 3, autoregression equation has the following general form:
𝑦
𝑡
= 346,814 + 0,216391𝑥
𝑡
+ 0,546096𝑦
𝑡−1
(4)
It can be seen from the model (4) that the short-term multiplier is equal to
𝑏
0
=
0,216391
, and the long-term multiplier is equal to
𝑏 =
𝑏
𝑜
1−𝑐
=
0,216391
1−0,546096
=
0,476733
In conclusion, an increase in the volume of investments in fixed capital by 1
billion soums increases the volume of construction production by an average of
0.216391 billion soums. An increase of
𝑥
𝑡
by 1 billion soums increases
𝑦
𝑡
by
0.546096 billion soums in the long term.
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