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26ЭКОНОМИЧЕСКИЕ НАУКИ
ANALYSIS OF SELECTED COUNTRIES' TRADE EFFICIENCY BASED
ON THE DEA MODELS Bakoyev M.T.1, Rakhimova M.S.2, Alimova S.R.3
1Bakoyev Matyokub Teshayevich - Doctor of Physical and Mathematical Sciences, Professor; 2Rakhimova Margarita Sergeevna - Teacher; 3Alimova Sofiya Rozumbayevna - Teacher, DEPARTMENT OF SYSTEM ANALYSIS AND MANAGEMENT, UNIVERSITY OF WORLD ECONOMY AND DIPLOMACY, TASHKENT, REPUBLIC OF UZBEKISTAN
Abstract: recently, the efficiency of international trade has been investigated from various aspects. One of them is the measurement of efficiency of trade companies per individual countries by means of Data Envelopment Analysis (DEA). This aspect of research into the efficiency of international trade is used in this paper. In other words, this paper explores the efficiency of international trade in the selected countries, with a particular reference to Uzbekistan. The efficiency of international trade in the selected countries and Uzbekistan differs depending on the applied input - or output-oriented DEA model. As a whole, the efficiency of international trade in Uzbekistan is satisfactory when compared to the observed countries.
Keywords: DEA models, GDP, lab our cost, FDI, international trade, efficiency, selective countries, Uzbekistan.
Introduction. The analysis of international trade efficiency has constantly been an ongoing topic. By applying various accounting and mathematical and statistical models, it has been investigated from various points of view. The main research issue in this paper is the analysis of factors affecting the efficiency of international trade, primarily in Uzbekistan, applying the appropriate methodology, which is to serve as the basis for improving the future trade by taking appropriate actions. This improvement can be made by the change of input or output values or both, input and output values. The possibilities on the input side are certainly wider. In terms of methodology, this research is based on the parallel comparative application of the DEA models with the input and output orientation. The Free Disposable Hull (FDH) model has also been used. To a certain extent, comparative analysis, ratio analysis, and statistical analysis have been used. For the purpose of researching the abovementioned issue, applying respective methodology empirical data were collected from www.ilostat.ilo.org - labour cost, www.worldbank.org - GDP, https://tradingeconomics.com\https://trendeconomy.com - turnover, www.invest.gov.uz, www.stat.uzwww.nordeatratde.com - FDI in 2019.
1. DEA models. DEA was first developed by Farrel in 1957, which later been modified by Charnes-Cooper-and Rhodes in 1978. It is a non-parametric method that utilizes linear programming to measure the level of efficiency of comparable decision-making units (DMU) by employing multiple inputs and outputs [1, p. 65]. This technique of measuring efficiency was first introduced by Farrel in 1957 based on the basic theory of production on single input and single output such as "output per work hour" in a form of ratio [2, p. 36].
This measurement does not entirely represent efficiency as commonly multiple inputs are used to produce single or more outputs, which lead to the modification of original equation to include measurement of multiple inputs and multiple outputs. This concept was further extended into basic CCR DEA model developed by CCR in 1978 by altering the original equation to [3, p. 16]:
Weighted sum of output Efficiency Weighted sum of input
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In DEA, methods to measure efficiency of DMUs are referred to a group of firms under study such as banks, hospital etc. DEA is a most accurate technique to measure efficiency given limited number of DMUs [4, c. 364]. In the theoretical analysis of the DEA models, we shall briefly present CCR and BCC models with input and output orientation as these models were applied in the examination of trade efficiency for the selected countries and Uzbekistan.
1.1. CCR model. The CCR model, named by its developers Charnes, Cooper and Rhodes, is based on fixed or constant returns-to scale. This actually means that the proportional increase of all the inputs results in the same proportional increase of all the outputs. Accordingly, the mathematical equation to find the maximum efficiency of DMUs using weighted input-output efficiency measure can be expressed as [5, p. 7]:
Since the above equation is in the fractional function, it is difficult to compute, thus, CCR transform the equation into linear programming equation by setting the denominator of the ratio to one or unity to form a linear programming equation Model 2 or equally known as output-
maximization CCR model [6, p. 523]:
When DEA is employed to measure banks efficiency for a set of DMUs, the linear programming algorithm will calculate the efficiency of each DMU given the identical inputs and outputs variables to find the maximum ratio of weighted sum of output to the weighted sum of input (most efficient DMU) and to be used as benchmark against other DMUs, causing the best-practice DMUs to lie on the efficient frontier line. It means the best-practice units are relatively efficient and identified by DEA efficiency score as 100% (efficiency = 1) [7, p. 5]. Charnes imposed non-negativity restrictions to ensure inputs and outputs have positive weight values, so as the efficiency score assigned will be between 1 and 0, and no efficiency index greater than one. The less productive units or inefficiency are identified with efficiency score of <100% (efficiency <1). The relative units to this frontier represent the degree of inefficiency [8, p. 339].
1.2. BCC model. The concept of the CCR model was modified by the introduction of the BCC model. The model is named after its developers Banker, Charnes and Cooper who replaced constant returns-to-scale by variable returns-to scale. The DMU operates under VRS if the input increase does not result in proportional changes of the output. The BCC model is formulated as [9, P- 6]:
Basically, in BCC model, the formula calculates the efficiency of DMUs and most efficient DMUs that lie on the convex line creating efficient frontier after passing through the area of DMUs (production possibility set).
2. FDH model. The theoretical characteristics of the FDH model shall be briefly presented as this model was also applied in the analysis of trade efficiency in the selected countries and Uzbekistan. The non-parametric FDH model formulated by Deprins, Simar and Tulkens does not include the conditions of local convexity. This means that only the real existing observations (nonlinear combination of observations) are used while comparing efficiency. The model includes only the assumption of free access to resources and consequently less limitation than other models [10, c. 198]. The idea of FDH is to ensure that efficiency measurements are the results of actual observed performances. The basic FDH model is an easy method to use, in fact, it can be extended from the CCR or BCC model with an additional constraint.
3. Defining input/output data. While defining trade efficiency of the selected countries (China, Russia, Kazakhstan, South Korea, Turkey, Germany, Kyrgyzstan, USA, Afghanistan, Turkmenistan - top 10 countries with the largest foreign trade turnover with the Republic of Uzbekistan), we used the CCR model. The input variables used were: GDP, lab our cost (average salary per day), FDI, overall turnover and the number of foreign companies while the output variable used was turnover with Uzbekistan (Table 1).
Table 1. Input/output data, 2019 (in million dollars)
Top 10 countries with the largest FTT GDP (I) Labour (I) FDI (I) Turnover (I) Fo-reign (I) Turno ver Uzb (O)
China 14342903 5,51 1514000 4632980,00 1306 7791
Russia 1699877 15,93 479700 672000,00 1864 5969
Kazakhstan 180162 8,94 156200 96079,00 766 3365
South Korea 1642383 7,23 193000 1045430,00 824 2692
Turkey 754412 14,13 143700 391182,00 1690 2376
Germany 3845630 42 1455000 2733338 160 900
Kyrgyzistan 8455 0,94 5860 6869,00 115 893
USA 21427700 20,38 4084000 4750130,00 241 619
Afghanistan 19101 5,86 1595 7640,00 144 532
Turkmenistan 40761 6,23 3061 12608,00 11 514
4. Measuring trade efficiency of the selected countries using the CCR model. The analysis of trade efficiency of the selected countries was conducted using the CCR model with the CCR-input (CCR-I) and CCR-output (CCR-O) orientation. The results for the CCR models are given in Table 2 [11].
Table 2. Trade efficiency of the selected countries measured by CCR models
CCR-I CCR-O
China 1 Efficient 1 Efficient
Russia 0.411 Inefficient 0.411 Inefficient
Kazakhstan 0.548 Inefficient 0.548 Inefficient
South Korea 0.418 Inefficient 0.418 Inefficient
Turkey 0.181 Inefficient 0.181 Inefficient
Germany 0.22 Inefficient 0.22 Inefficient
Kyrgyzistan 1 Efficient 1 Efficient
USA 0.196 Inefficient 0.196 Inefficient
Afghanistan 1 Efficient 1 Efficient
Turkmenistan 1 Efficient 1 Efficient
The data in Table 2 suggest that by the CCR-I model, trade of China, Kyrgyzstan, Afganistan and Turkmenistan is efficient while trade of Russia, Kazakhstan, Turkey, South Korea, Germany and USA is inefficient. In the case of countries whose international trade is inefficient there is given the table above which shows the amount of inputs that give the efficiency level to these countries. The data in CCR-O show that in terms of trade efficiency of the observed countries, the
results are similar to those obtained using the CCR-I model. Six countries have inefficient trade (Russia, Kazakhstan, South Korea Turkey, Germany, and USA), while China, Kyrgyzstan, Afghanistan and Turkmenistan have efficient trade.
5. Measuring trade efficiency of the selected countries using the BCC model. Comparative analysis of trade efficiency of the selected countries was also made using the BCC model with input and output orientation, which is characterized by a variable return -to-scale. Table 3 [11] presents the results of this analysis using the BCC-I and BCC-O models.
Table 3. Trade efficiency of the selected countries (Model = BCC-I\BCC-O)
Countries BCC-I BCC-O
China 1 Efficient 1 Efficient
Russia 1 Efficient 1 Efficient
Kazakhstan 1 Efficient 1 Efficient
South Korea 0.83 3 Inefficient 0.868 Inefficient
Turkey 0.66 Inefficient 0.752 Inefficient
8
Germany 0.49 8 Inefficient 0.666 Inefficient
Kyrgyzistan 1 Efficient 1 Efficient
USA 0.20 8 Inefficient 0.343 Inefficient
Afghanistan 1 Efficient 1 Efficient
Turkmenistan 1 Efficient 1 Efficient
In table 3 BCC-I model suggests that in this case only the trade with South Korea, Turkey, Germany and USA is inefficient. The value of returns-to-scale (RTS) is reduced in Russia and Kazakhstan. For other observed countries, its value is constant. BCC-O model suggests that in terms of trade efficiency of the observed countries, the results are similar to those obtained using the BCC-I model. Only the trade of South Korea, Turkey, Germany and USA is inefficient.
6. Measuring trade efficiency of the selected countries using the FDH model. This part of the paper brings the comparative analysis of trade efficiency of the selected countries using the FDH model. Table 4 [11] presents the research results.
Table 4. Trade efficiency of the selected countries measured by the FDH model (Output oriented) Efficiency
The data in this table suggest that the trade of all the observed countries except USA, measured by the FDH model, is efficient.
Conclusion. The research presented in the paper focused on the comparison of trade efficiency in selected countries with Uzbekistan (China, Russia, Kazakhstan, South Korea, Turkey, Germany, Kyrgyzstan, USA, Afghanistan and Turkmenistan). The trade with Uzbekistan, measured by all the presented DEA models and the FDH model, has been identified as efficient with China, Kyrgyzstan, Afghanistan and Turkmenistan. When compared to the trade with other countries, measured by CCR-I, CCR-O models, the trade with Uzbekistan has been identified as inefficient. The efficiency of trade with Uzbekistan has been primarily affected by improved economic conditions in the recent period as well as by the increased presence of foreign retail chains with "new business models". This is particularly evident in terms of the application of private brands, sales of organic products, information and communication technology. The improved efficiency of trade in Uzbekistan requires stronger implementation of modern business concepts, cost management as well as information and communication technology.
References
1. Klimberg R.K., Lawrence K.D., Lawrence S.M."Improved Performance Evaluation of Comparable Units with Data Envelopment Analysis (DEA)". Advances in Business and Management Forecasting. Volume 5. Elsevier Ltd. Pp. 65-75, 2008.
2. Cooper W.W., Seiford L.M., Tone K. (2006), Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software. 2nd ed. NewYork: Springer.
3. Sherman,H.D., Zhu ,/.(2006), Service Productivity Management: Improving Service Performance Using Data Envelopment Analysis (DEA). NewYork: Springer.
4. Ahmad W., Luo R.H. (2010), Comparison of banking efficiency in Europe: Islamic versus conventional banks. International banking in the New Era: Post-Crisis challenges and opportunities. International Finance Review. 11. 361-389.
5. Charnes A., Cooper W.W., Rhodes E. (1978). Measuring the efficiency of decision making units, "European Journal of Operational Research". Vol. 2. № 6.
6. Chen T.Y., Chen C.B., Peng S.Y. (2008), Firm operation performance analysis using data envelopment analysis and balanced scorecard: A case study of a credit cooperative bank. International Journal of Productivity and Performance Management. 57(7). 523-539.
7. Charnes A., Cooper, W.W., Lewin, A.Y., Seiford, L.M. (1994). Data Envelopment Analysis: Theory, Methodology and Application. Boston: Kluwer Academic Publishers.
8. Charnes A., Cooper W. W., Rhodes E. (1979). Short Communication: Measuring Efficiency of Decision Making Units. European Journal of Operations Research. 3, 339.
9. Banker R.D., Charnes A., Cooper W.W. (1984), Some models for estimating technical and scale inefficiencies in data envelopment analysis, "Management Science". Vol. 30. № 9.
10. Panayides, P.M., Maxoulis, C.N., Wang, T. (2009). A critical analysis of DEA applications to seaport economic efficiency measurement. Transport Reviews. 29(2). Pp. 183-206.
11. [Electronic Resource]. URL: http://www.soft.onlineoutput.com/dea/ (date of access: 10.05.2021).
