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European Science Review 2024, No 1-2.
ISSN 2310-5577
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ppublishing.org
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Section 1. Economic
DOI:10.29013/ESR-24-1.2-3-9
THE ECONOMETRIC ANALYSIS OF FINANCIAL INDICATORS OF COMMERCIAL BANKS ACTIVITIES
Mohira Mutalova1
1 University of World Economy and Diplomacy
Cite: Mutalova M. (2024). The Econometric Analysis of Financial Indicators of Commercial Banks Activities. European Science Review 2024, No 1-2. https://doi.org/10.29013/ESR-24-1.2-3-9
Abstract
As the result of the econometric analysis of the financial instruments of a concrete joint-stock commercial bank, it was carried out the efficiency of transformation of bank activities in Uzbekistan.
Keywords: bank, transformation, efficiency, financial indicators, net commission income, bank transaction costs, net profit
Introduction
Nowadays in Uzbekistan the process of Transformation of the economy on the basis of digitalization is considered as one of the most urgent issues that need to be implemented in Uzbekistan. In this field, commercial banks have achieved great technical and especially financial successes.
Therefore, in order to determine the level of efficiency of the activities of a concrete joint-stock commercial bank (the name of the bank has not been given in order to protect the trade secret) that successfully works in the field of digitization and transformation
in our country we will conduct an econometric study of its financial indicators.
Econometric analysis
In the econometric analysis of this bank, net interest income is Y as a result factor (billion soums), and the influencing factors are - net commission income - X 1 (billion soums), operational expenses of the bank - X 2 (billion soums) and net profit X 3 (billion soums) has been received.
We will conduct descriptive statistics based on the performance indicators of the bank for the quarters of 2018-2022 (Table 1).
Table 1. Descriptive statistics
X,
X
X
Mean
111.5050
54.55500
74.98000
33.31000
Y Xi X2 X3
Median 99.70000 46.35000 76.70000 30.75000
Maximum 189.5000 104.8000 99.10000 61.60000
Minimum 57.80000 22.40000 40.60000 22.30000
Std. Dev. 34.42180 27.58429 17.43377 9.887946
Skewness 0.606590 0.633415 -0.379521 1.799375
Kurtosis 2.583561 1.997886 1.954918 5.649504
Jarque-Bera 1.371024 2.174241 1.390284 16.64240
Probability 0.503832 0.337186 0.499004 0.000243
Sum 2230.100 1091.100 1499.600 666.2000
Sum Sq. Dev. 22512.35 14456.97 5774.792 1857.658
Observations 20 20 20 20
The normal distribution function is de termined by the following formula:
-(x-a )2
, 2a"
As can be seen from Figure 1, all factors obey the law of normal distribution.
p(x) -
1
V2
KG
, -œ < x < œ , (1) Figure 1. Checking factors for normal distribution
X1
.012
.016
.012
.008
0 20 40 60 80 100 120 140 160 180 200 220 240
X2
100 120 140
X3
20 30 40 50 60 70 80 90 100 110 120 130
0
Normal
10
20
30
40
50
60
70
As can be seen from Figure 1, all factors obey to the law of normal distribution.
One factor has a negative skewness coefficient (lnX2), so the "tail" of this variable is skewed to the left, and also three factors have positive skewness coefficients (lnY, lnX1 and lnX3), the "tails" of these factors are skewed to the right.
In all factors, the value of the kurtosis coefficients is less than 3, except for the factor lnX3, and therefore the top of the graph of the functions of these factors is lower than the theoretical graph, i.e. flat.
Y
Kernel
Table 2. The Correlation matrix
Probability Y X1 X2 X3
Y 1.000000
X1 0.954628 13.60017 0.0000 1.000000
X2 -0.626636 -0.625296 1.000000
-3.411458 -3.399473 ---
0.0031 0.0032 ---
X3 0.847719 0.278655 -0.152048 1.000000
10.20268 0.870362 -0.652675 ---
0.0000 0.4211 0.5222 ---
As can be seen from Figure - 2 that, visually there is a close direct relationship between the dependent variable and the factors influencing it.
We will calculate this relationship through the coefficients of private and paired correlation (Table 2).
Two types of correlation coefficients are calculated here: partial and pairwise correlation coefficients.
Private correlation coefficients show the relationship of the dependent variable with each influencing factors. For example, the relationship between net interest income of the bank (lnY) and net fee income - (lnX1) the private correlation coefficient is 0.9546. This shows that there is a close relationship between these indicators. The correlation coefficient between the bank's net interest income (lnY) and the bank's operating expenses (lnX2) took a negative value and is equal to -0.6266. This shows that an increase in
the bank's operating expenses leads to a decrease in the bank's net interest income. The correlation coefficient between bank's net interest income (lnY) and bank's net profit (lnX3) is 0.8477. There is a direct strong correlation between these indicators. (Table 2)
We check the multicollinearity in the connections between the influencing factors (Xi, Xj). Multicollinearity refers to the case where the pairwise correlation coefficient value is greater than 0.7 between two influencing factors. It can be seen from the indicators of Table 2 on the bank data that the connection densities between the influencing factors are not greater than 0.7. This indicates that there is no multicollinearity between the influencing factors and it is the basis for including all factors in the multifactor econometric model.
In order to verify the above, let's look at their dot graphs to determine the relationship of each factor with the resulting indicator (Figure 2).
Figure 2. Relationship between the dependent variable and influencing factors
To investigate autocorrelation in the series of residuals of the dependent variable,
we calculate VIF (Variance Inflation Factors) coefficients (Table 3).
Table 3. Results of calculation of VIF (Variance Inflation Factors) coefficients
Variable Coefficient Variance Uncentered VIF Centered VIF
X1 0.013361 9.613669 1.878628
X2 0.033147 38.11069 1.861707
X3 0.064822 15.16167 1.171169
C 146.0899 28.41732 NA
According to the rule, the value of VIF coefficient of each factor should be less than 10. From the coefficients of the table we can see that the VIF coefficients of the factors are less than 10. This indicates the absence of au-
tocorrelation in a number of residuals of the dependent variable.
Table 4 below presents the estimation of autocorrelation between factors and specific autocorrelation.
Table 4. Determination of autocorrelation and private autocorrelation between factors
The autocorrelation and private autocorrelation test between the factors also corresponded to the high obtained results.
It results that there is no autocorrelation in the studied time series, and it can be seen
that all the residuals have probability values less than 0.05.
At the next stage, we will create a multi-factor econometric model of the bank's net interest income (Table 5).
Table 5. Estimated parameters of the multifactor econometric model
Variable Coefficient Std. Error t-Statistic Prob.
X1 1.225424 0.115589 10.601562 0.0000***
X2 -0.013803 0.182063 -2.2765957 0.0015***
X3 0.448323 0.254601 1.7608846 0.0974**
C 30.75328 12.08676 2.5443774 0.0216***
R-squared 0.926925 Mean dependent var 111.5050
Adjusted R-squared 0.913224 S.D. dependent var 34.42180
Variable Coefficient Std. Error t-Statistic Prob.
S.E. of regression 10.13990 Akaike info criterion 7.647689
Sum squared resid 1645.080 Schwarz criterion 7.846835
Log likelihood -72.47689 Hannan-Quinn criter. 7.686564
F-statistic 67.65149 Durbin-Watson stat 1.777335
Prob (F-statistic) 0.000000
Note: *** - 0.05 accuracy, ** - 0.1 accuracy
Using the data of Table 5 above, the mul-tifactor econometric model of banking activity shows:
lny = 30,7533 + 1,2254Xj - ( ) -0,0138x2 + 0,4483x3 .
The calculated multifactor econometric model (4) shows that the bank 's net commission income averages 1 bln. If it increases to com (X 1), the net interest income of the bank (Y) average 1.2254 billion. as it may increase to soums. Bank 's operating costs (X2) average 1.0 bln. increase in soum, net interest income of the bank (Y) an average of 0.0138 billion. and the net profit (X3) is on average 1.0 bln. An increase in soums will increase the interest income of the bank (Y) average 0.4483 billion. it is observed that it will increase to soum.
To check the quality of the multifactor econometric model (4), we examine the coefficient of determination. The coefficient of determination shows how many percent of the resulting factor is made up of the factors included in the model. The calculated coefficient of determination (R2 - R-squared) is equal to 0.9269. This shows that 92.69 percent (4) of the bank's net interest income (Y) is made up of the factors included in the multi-factor econometric model. The remaining 7.31 percent (1.0-0.9269) is the influence of unaccounted factors.
In order to be able to compare models with different number of factors and this number of factors does not affect the R2 statistic, a smoothed coefficient of determination is usually used, i.e.:
R2dj. - 1 " -T
(5)
Adjusted coefficient of determination (Adjusted R-squared) is equal to 0.9132 and its closeness to R2 means that the model can accept values around the change in the number of influencing factors.
We check the statistical significance of the multifactor econometric model (4) using Fisher's F-criterion. Fisher's calculated F-cri-terion value is compared with its value in the table. If F >F „,, then the multivariate
count table,
econometric model (4) is said to be statistically significant.
Given the level of significance a — 0,05 and the degrees of freedom k1 = 3 and, k2 = 20 - 3 -1 = 16 the table value of the F-criterion F „ = 3.24 is equal to. The calcu-
count
lated value of the F-criterion is F =
count
67.6515 and the table value is equal to F table = =3.24 and the multifactor econometric model (4) is called statistically significant because the condition of F >F table is fulfilled.
count
We check the reliability of calculated parameters of the multifactor econometric model (4) using Student's t-creation. The table value of t-criterion is equal to confidence probability and degree of freedom.
From the regression calculations, it can be seen that the calculated values of the t-cri-terion for all factors are greater than the table value in accuracy (Table 5). This allows these factors to participate in the multifac-tor econometric model. The resulting factor according to the multivariate econometric model (4). We use the Darbin-Watson (DW) criterion to check autocorrelation in the residuals.
The calculated Darbin-Watson value is compared with the DWL and DWU in the table. If DWcount < DWL, the residuals are said to have autocorrelation.
If DWcount > greater than DWU, the residuals are said to have no autocorrelation. The lower limit value of the Darbin-Watson criterion is DWL = 1.00 and the upper limit value is DWU = 1.68. DW = 1.7773. Therefore, since DWAccount>DWU, there is no autocorrelation in the net interest income (Y) balances of the resulting factor bank.
The absence of autocorrelation in the residuals of the resulting factor also shows that the
multi-factor econometric model given above (4) can be used in forecasting (Figure. 3).
Figure 3. Graph of the actual (Actual), calculated (Fitted) values of the bank's net interest income and the differences between them (Residual)
30 20 10 0
200
160
120
80
40
II III IV I 2018
II III IV I 2019
II III IV I 2020
II III IV I II III IV 2021 2022
Residual
Actual
Fitted
It can be seen from Figure 3 that (4) the graph of the calculated values of the bank's net interest income according to the multi-factor econometric model is very close to the graph of its actual values, and the differences between them are not so great. This is another proof that the multifactor econometric model (4) can be used in forecasting the bank's net interest income for near future.
From the multifactor econometric model calculated (4), we calculate the value of the MARE coefficient in forecasting the output indicator for future periods.
If the calculated MARE coefficient value is less than 15.0 percent, the model can be used to predict the resulting factor, otherwise it cannot be used. The value of the MARE coefficient on the bank's net interest income is 8.3294 percent (Figure 4).
Figure 4. Indicators of using the estimated multifactor econometric model in forecasting
200 180 160 140 120 100 80 60 40
Forecast: YF Actual: Y
Forecast sample: 2018Q1 2022Q4 Included observations: 20
Root Mean Squared Error 9.069398
Mean Absolute Error 7.046402
Mean Abs. Percent Error 6.299383 Theil Inequality Coefficient 0.039003
Bias Proportion 0.000000
Variance Proportion 0.018968
Covariance Proportion 0.981032
I II III IV I II III IV I II III IV I 2018 2019 2020
II III IV I II III IV 2021 2022
YF -----± 2 S.E.
References
Mutalova, M. A., Ishnazarov, A. "Transformation of banks using the St. Gallen Management Model". Monography - Tashkent.: 2022.- 73 p.
Mutalova, M. A., Mutalov, A. "On improvement of taxation of small business in the Republic of Uzbekistan" - Theses of the report at the Republican scientific-practical conference "On improvement of taxation of small business" - Tashkent, 2022.
Mutalova, M. A., Fayziyev, R. "Empirical economic and mathematical models of inventory management in Ms excel" - Theses of the Report on the Republican scientific-practical conference on the theme of: "New business models of economic management in Uzbekistan as a basis for ensuring economic growth and reducing poverty" - Tashkent, 2022.
Mutalova M. A. "Тижорат банкларини трансформациялаш - давр талаби" - Report at the Republican Scientific and Practical Conference on the topic: "Iqtisodiyotning raqamlashu-vi sharoitida bank-moliya tizimini rivojlantirish istiqbollari" - Tashkent, 2022.
Mutalova M. A. «Экономическое моделирование трансформации банков (на примере Санкт-Галленской модели управления)» - Journal Economics and Entrepreneurship - Moscow, № 6. 2022.
submitted 27.01.2024;
accepted for publication 12.02.2024;
published 23.03.2024
© Karimkulov K., Uzahkov I., Karimkulov M. Contact: karimkulov@mail.ru
