Application in international market selection for the export of goods: A case study in Viet Nam

element is : s+r( y+−r )2/ B(y+r − yr0) (6) where B is a large positive value, and the value of B is about 100. It is a fact that if the denominator is relatively low, y+−r, it increases with the decrease of the distance (y + r − yr0), and vice-versa. Therefore, the non-positive values are significantly affected in this model. The obtained score is a one-dimensional unit for using units of the measurement and constant [66]. The higher the value, the more efficient the unit [64]. 3.3.2. Malmquist Productivity Index (MPI) The Malmquist Productivity Index concept was originally developed for assessing the consumption of inputs by Malmquist [68]. Later, it was used as a productivity index—directly from input and output data by using DEA, defined as DEA–MPI—and also to be applied in various fields as a tool to measure the productivity change of DMU’s over time [69]. Suppose there are “N” DMU’s, where each country is consuming “m” different inputs for the production of “s” different outputs. xrj and yrj represent the ith input and rth output, respectively, of the jth DMU at time “t” [46]. Dto ( xto, y t o ) = Minimize θ (7) Subject to n ∑ j=1 λjxtij ≤ θxtio, i = 1, 2, . . . , m, n ∑ j=1 λjytrj ≤ θytro, r = 1, 2, . . . , s, λj ≥ 0, j = 1, 2, . . . , n, The reduction in the DMU0’s outputs is denoted by θ (0 < θ≤ 1). The DEA efficiency score is equal to the distance function of the DMU0 in year t (i.e., Dto (xto, yto)). If the value of θ = 1, then the DMU will be efficient, and its input–output combination lies on the efficiency frontier. If the value of θ < 1, then the DMU will be inefficient, and its input–output combination lies inside the efficiency frontier. Using t + 1 instead of t for the above model can be interpreted in a similar way, and the efficiency score of DMU0 in the time period t + 1, can be obtained as Dt+1o (x t+1 0 , y t+1 0 ). For the mixed-period measures, the first is defined as Dto (x t+1 0 , y t+1 0 ) for DMU0. which is computed as the optimal value resulting from the following linear programming problem, as follows: Dt+1o ( xt+10 , y t+1 0 ) = minimize θ (8) Subject to n ∑ j=1 λjxt+1ij ≤ θxt+1io , i = 1, 2, . . . , m, ∑nj=1 λjy t+1 rj ≤ θyt+1ro , r= 1, 2, . . . , s, λj ≥ 0, j = 1, 2, . . . , n, This model compares xt+10 , y t+1 0 to the frontier at time t. Similarly, the mixed-period measure Dt+1o ( xto, yto ) = can be obtained, and it compares (xto, , yto, ) to the frontier at time t + 1. Therefore, DEA–MI estimates the productivity change of a specific DMU0 at time t + 1 and t, can be shown by the following equation: Sustainability 2018, 10, 4621 12 of 24 MI0 = Dto ( xt+10 , y t+1 0 ) Dto (xto, yto) Dt+1o ( xt+10 , y t+1 0 ) Dto (xto, yto) 1/2 (9) where MI0 shows the progress in the total factor productivity of the DMU0 from the period t to t + 1, while MI0 = 1 and MI < 1 indicates the status quo and decay in the productivity, respectively [48]. If MPI = 1, there is no productivity change, and if MPI < 1, it reflects that there is a productivity reduction MPI = D t+1 o (x t+1 0 , y t+1 0 Dto (xto , yto) [ Dto (xt+10 , y t+1 0 ) Dt+1o (xt+1o , yt+1o ) Dto (xt0, y t 0 Dt+1o (xto , yto) ]1/2 = efficiency change × technological change (10) 4. Results 4.1. Pearson Correlation Now, there is a need to perform a correlation test between the input and output variables in order to check that each variable provides different information from the other variables in the model, increasing the differentiation among the evaluated countries. A significant correlation between the input and output variable shows the relatedness between different factors. Therefore, this input–output combination will be suitable for the test. The correlation values imply that the “exports of goods and services” are inversely influenced by the exports values, tariffs of exports of the countries, exchange rates, and ease of doing business. This indicates that if the exports of goods increase, then there must be a decrease in the tariffs on exports and a reduction in the exchange rates. So, the greater the opposing relationship between the values, the better a country’s export feasibility is, and improves the international market selection. 4.2. Super SBM Model of Efficiency It was assessed that the forecasting values for every 15 countries were worked out, because the means absolute percentage error (MAPE) is results small in Table 3, with 7.07%. Table 3. Average means absolute percentage error (MAPE) of 15 DMUs. DMU Country Average MAPE % DMU1 Australia 22.77% DMU2 China 1.53% DMU3 France 4.15% DMU4 Germany 3.92% DMU5 Indonesia 5.33% DMU6 Italy 1.41% DMU7 Japan 1.88% DMU8 Korea, Rep. 2.35% DMU9 Malaysia 10.07% DMU10 Netherlands 1.02% DMU11 Singapore 20.68% DMU12 Thailand 2.73% DMU13 United Arab Emirates 2.11% DMU14 United Kingdom 3.51% DMU15 United States 22.62% Average of 15 DMUs 7.07% Source: calculated by researchers. MAPE is used to verify the accuracy of the forecast, in order to ensure suitable predictive methods, and to act as a source of highly reliable assessments and to identify the prediction with a good performance. The MAPE is divided into our ranks, and the results are shown in Table 3. The forecast Sustainability 2018, 10, 4621 13 of 24 is calculated by the actual data, and if the error is in the allowable range, then it will be a reliable and usable model for the study. The average MAPE of the 15 DMU’s is less than 10% of the limit. Therefore, based on these rules, the forecasted results of this study have a high level of accuracy, as the average MAPE of 15 DMU’s comes out to be 7.07%. If the MAPE is smaller, the volatility in the forecasts will be less, so the slacks-based measure of efficiency can be predicted. The study applies forecasted results as input factors so as to assess the performance of the DMUs being exported from the period of 2018–2021, as shown in Table 4. The forecasting shows the results for the exports of goods and services and the exports of the 15 countries from 2018–2021. Moreover, for future countries wanting trade with Vietnam, it helps by providing information on the output factors, which is very important for partner selection. The forecasting results indicate that there are slight changes of output factors in five of the DMUs during 2018–2021, for DMU1 (Australia), DMU2 (China), DMU9 (Malaysia), DMU11 (Singapore), and DMU15 (USA). The decreasing tendency in the output factors means that these countries must have a suitable strategy in place in order to create and sustain a competitive advantage, or to start up a new investment in order to meet the increased demand. The results indicate that the ranking of the exporting countries to Vietnam vary in the future. The DMUs are divided into the following three major groups: • Group 1: DMUs get effective market; they are always at the top position and include DMU1, DMU2, DMU9, DMU11, and DMU15; • Group 2: DMUs can prosper in the future: DMU8 and DMU12 (ranking for both of these DMU’s has increased from 2018–2021; • Group 3: DMUs have an inefficient market in the future: DMU3, DMU4, DMU5, DMU6, DMU7, DMU10, DMU13, and DMU14. Table 4. Forecasted scores and rankings of importing countries for the period of 2018–2021. DMU 2018 2019 2020 2021 Score Rank Score Rank Score Rank Score Rank Australia 1 1 1 1 1 1 1 1 China 1 1 1 1 1 1 1 1 France 0.159965 15 0.160916 15 0.271704 15 0.161972 15 Germany 0.316569 12 0.338189 12 0.738029 8 0.308298 12 Indonesia 0.358944 10 0.397058 10 0.280123 13 0.325125 11 Italy 0.225878 14 0.259066 14 0.277475 14 0.200859 14 Japan 0.587428 8 0.608799 8 0.339322 12 0.418777 9 Korea, Rep 1 1 1 1 0.482415 11 0.571975 7 Malaysia 1 1 1 1 1 1 1 1 Netherlands 0.444143 9 0.473891 9 1 1 0.425346 8 Singapore 1 1 1 1 1 1 1 1 Thailand 0.67847 7 1 1 0.50937 10 0.588595 6 United Arab Emirates 0.352797 11 0.340657 11 0.527494 9 0.38715 10 United Kingdom 0.267177 13 0.280908 13 1 1 0.25785 13 United States 1 1 1 1 1 1 1 1 Source: calculated by researchers. This also reflects the intense competition of exports in the international market of Vietnam, and provides good information to the future countries looking to choose an international market for trade. From the DEA Super SBM model and the results shown in Table 5, it is analyzed that the United States and Singapore remained the most efficient amongst the 15 DMU’s from 2014–2017. Malaysia showed a declining trend in efficiency, by achieving a score of 1.29237 in 2015, down from 1.59239 in 2014. Although the Republic of Korea showed a slow improvement, Italy remained in 10th position for all of the years. France showed an increasing trend in efficiency from 0.42375 in 2014 to 0.47215 in 2015. Moreover, the Netherlands followed a very poor trend of efficiency change, and hence remained at the bottom rank amongst all of the other countries. Similarly, the UAE and United Kingdom too showed poor efficiency change, and hence drooped as per their ranks from 2014 through to 2017. Sustainability 2018, 10, 4621 14 of 24 Table 5. Efficiency of export market of Vietnam with 15 countries. DMU 2014 2015 2016 2017 Score Rank Score Rank Score Rank Score Rank Australia 1.32187 8 1.16277 8 1.0352 9 1.38287 8 China 1.18618 9 1.14112 9 1.20929 8 1.15254 9 France 0.42375 14 0.47215 14 0.61744 11 0.72927 11 Germany 0.64516 11 0.60961 12 0.4737 13 0.53281 13 Indonesia 1.45393 7 2.50836 3 2.69678 2 2.67817 4 Italy 1.01639 10 1.05405 10 0.68713 10 1 10 Japan 0.59594 12 0.69987 11 0.4634 14 0.48403 14 Korea, Rep. 1.88485 4 2.43165 4 1.32409 7 1.63548 7 Malaysia 1.59239 6 1.29237 6 2.34065 3 3.7905 2 Netherlands 0.40196 15 0.42268 15 0.29303 15 0.35496 15 Singapore 3.58182 2 5.01653 1 2.30061 4 6.06523 1 Thailand 2.76579 3 1.86414 5 2.15397 6 2.49881 5 United Arab Emirates 1.61585 5 1.22191 7 2.17378 5 1.69867 6 United Kingdom 0.56068 13 0.59951 13 0.53716 12 0.62256 12 United States 8.62062 1 3.87277 2 2.94118 1 3.09057 3 Mean 1.844479 1.624633 1.416494 1.847765 Source: calculated by researchers. The development of the efficiency showed that the average efficiency increased during the period of 2014–2017. This can be the result of the technological advancement and integration of economies. Therefore, the countries may either decrease or increase their inputs in order to increase or decrease the output of the country, and to improve its efficiency values. 4.3. Malmquist Index In this study, the Malmquist Productivity Index is used to assess the performance of 15 DMU’s. DEA-solver-pro was used for the further analysis. This index also helps in identifying the productivity change in the international export market, as well as to assess the productivity change within groups, therefore giving an opportunity to the poor performers in the export markets to catch up. To facilitate the analysis, the values of efficiency change, technological change, and MPI are depicted in details in Tables 6–8 below. 4.3.1. Catch Up Effect The catch-up effect in Table 6 identifies the value needed by a DMU to enhance its productivity and efficiency; Germany and Singapore are the only two countries that need constant catch-up with the efficiency values. Figure 2 shows the “efficiency change” (catch-up effect) of the 15 DMUs from 2014–2017. It hs been found that DMU3 (France), DMU4 (Germany), DMU11 (Singapore), and DMU14 (United Kingdom) represented a decreasing trend of closeness between the frontier and a decision-making unit. France needs to catch-up to its efficiency values by 5% on average, while Germany need 6%, Japan 4%, Singapore and Malaysia 1%, and the United Kingdom 5%. On the other hand, Australia, China, Indonesia, Korea, Thailand, the USA, and UAE are efficient enough and do not need to catch-up. However, the trend of the catch-up values implies that most of the DMU’s had started improving their efficiency. Sustainability 2018, 10, 4621 15 of 24 Table 6. Catch up effect or efficiency change from 2014 to 2017. Catch-Up 2014–2015 2015–2016 2016–2017 Average Australia 1 1 1 1 China 1 1 1 1 France 0.685442313 1.044792384 1.135194 0.955142955 Germany 1.242960551 0.786861232 0.796453 0.942091514 Indonesia 1 1 1 1 Italy 1 1 1.023671 1.007890326 Japan 1.0409872 0.926214615 0.893418 0.953540009 Korea, Rep. 1 1 1 1 Malaysia 1 0.999998937 1 0.999999646 Netherlands 1.04005555 0.818725695 1.359795 1.072858738 Singapore 1.000006492 1.000001411 0.999991 0.999999745 Thailand 1 1 1 1 United Arab Emirates 1 1 1 1 United Kingdom 0.781232285 1.105032829 0.975372 0.953879072 United States 1 1 1 1 Average 0.986045626 0.97877514 1.01226 0.992360134 Max 1.242960551 1.105032829 1.359795 1.072858738 Min 0.685442313 0.786861232 0.796453 0.942091514 SD 0.121361093 0.080184441 0.119353 0.031787641 Source: calculated by researchers. Sustainability 2018, 10, x FOR PEER REVIEW 15 of 25 Netherlands 1.04005555 0.818725695 1.359795 1.072858738 Singapore 1.000006492 1.000001411 0.999991 0.999999745 Thailand 1 1 1 1 United Arab Emirates 1 1 1 1 United Kingdom 0.781232285 1.105032829 0.975372 0.953879072 United States 1 1 1 1 Average 0.986045626 0.97877514 1.01226 0.992360134 Max 1.242960551 1.105032829 1.359795 1.072858738 Min 0.685442313 0.786861232 0.796453 0.942091514 SD 0.121361093 0.080184441 0.119353 0.031787641 Source: calculated by researchers. Figure 2 shows the “efficiency change” (catch-up effect) of the 15 DMUs from 2014–2017. It hs been found that DMU3 (France), DMU4 (Germany), DMU11 (Singapore), and DMU14 (United Kingdom) represented a decreasing trend of closeness between the frontier and a decision-making unit. France needs to catch-up to its efficiency values by 5% on average, while Germany need 6%, Japan 4%, Singapore nd Malaysia 1%, and the United Kingdom 5%. On the other hand, Australia, China, Indonesia, Korea, Thailand, the USA, and UAE are efficient enough and do not need to catch- up. However, the trend of the catch-up values implies that most of the DMU’s had started improving their efficiency. Figure 2. Graphical presentation of catch-up effect changes from 2014–2017. Source: calculated by the researchers. 4.3.2. Frontier Shift Table 7 and Figure 3 show the “technological changes” or frontier shift of 15 DMU’s from 2014– 2017. It was assessed that almost all of the DMU’s were enhancing their technology and going for technological efficiency, except for Australia, Italy, and the United Kingdom. This results in an increased overall efficiency. This also implies most of these DMUs continued to improve their 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 2014=>2015 2015=>2016 2016=>2017 Australia China France Germany Indonesia Italy Japan Korea, Rep. Malaysia Netherlands Singapore Thailand United Arab Emirates United Kingdom United States Figure 2. Graphical presentation of catch-up effect changes from 2014–2017. Source: calculated by the researchers. 4.3.2. Frontier Shift Table 7 and Figure 3 show the “technological changes” or frontier shift of 15 DMU’s from 2014–2017. It was assessed that almost all of the DMU’s were enhancing their technology and going for technological efficiency, except for Australia, Italy, and the United Kingdom. This results in an increased overall efficiency. This also implies most of these DMUs continued to improve their technological capabilities. In terms of “technological change”, DMU8 (the Republic of Korea), DMU2 (China), and DMU12 (Thailand) are the top three best countries, while the three worst countries are DMU6 (Italy), DMU3 (France), and DMU9 (Malaysia). Thus, it may be implied that the overall frontier shift of the countries increased. The highest frontier shift was found for Korea, followed by Sustainability 2018, 10, 4621 16 of 24 Thailand and China. The Netherlands on the other hand, along with Indonesia and UAE indicated the low frontier shift. This might be because these countries are constantly efficient and did not need to benchmark any other country for improving their efficiency. Table 7. Frontier effect or technological change of the importing countries (2014–2017). Frontier 2014–2015 2015–2016 2016–2017 Average Australia 1.01974988 1.024927916 1.433444 1.15937405 China 1.04295869 1.237231846 1.037435 1.105875197 France 1.024510195 0.988152039 0.934774 0.982478772 Germany 1.000878903 1.056034964 1.065723 1.040878864 Indonesia 0.568492946 1.056457431 0.832706 0.819218769 Italy 1.087808504 0.954934429 1.157299 1.066680716 Japan 1.008400785 1.070540644 1.107637 1.062192772 Korea, Rep. 1.14318066 1.536062677 1.264216 1.314486437 Malaysia 1 1.000000531 1.003646 1.00121547 Netherlands 1.050714389 1.020277879 1.079089 1.050027181 Singapore 0.999996754 0.999999294 1.066184 1.022059958 Thailand 0.882299602 1.308632075 0.942753 1.044561622 United Arab Emirates 1 1.029940603 1 1.009980201 United Kingdom 1.082792048 1.064054352 1.278963 1.141936369 United States 1.095557362 1.080935085 0.857004 1.011165398 Average 1.000489381 1.095212118 1.070725 1.055475452 Max 1.14318066 1.536062677 1.433444 1.314486437 Min 0.568492946 0.954934429 0.832706 0.819218769 SD 0.133556956 0.153290758 0.162379 0.106123057 Source: calculated by researchers. Sustainability 2018, 10, x FOR PEER REVIEW 17 of 25 Figure 3. Graphical presentation of frontier shift of the importing countries (2014–2017). Source: calculated by the researchers. 4.3.3. Malmquist Productivity Index Table 8 shows the MPI. The total productivity of the 15 DMUs from 2014–2017 noted that DMU5 (Indonesia), DMU4 (France), DMU15 (UAE), DMU2 (China), and DMU14 (Thailand) had a long-term upward trend during 2014–2017. However, DMU4 (Germany) and DMU10 (Netherlands) experienced a drop during 2015–2016. According to Figure 4, the countries with an upward trend indicate that the efficiency change over time either remained constantly efficient or exceeded their predicted efficiency values. In terms of MPI, DMU2, DMU8, and DMU14 are the top three best exporting countries, while the three worst exporting countries are DMU4 (Germany), DMU6 (Italy), and DMU7 (Japan), while DMU10 (Netherlands) appears unstable as it has the largest fluctuation. Therefore, it requires increasing trade relations with these countries. As the majority of countries were found to be effective, it may be implied that trade with these countries is important so that there is an improvement in the economics and growth of the trading countries. Table 8. Malmquist Productivity Index of the importing countries (2014–2017). Malmquist 2014–2015 2015–2016 2017–2018 Average Australia 1.024927916 1.01974988 1.433444 1.15937405 China 1.237231846 1.04295869 1.037435 1.105875197 France 1.032413725 0.702242638 1.06115 0.931935482 Germany 0.830952973 1.244052993 0.848798 0.974601257 Indonesia 1.056457431 0.568492946 0.832706 0.819218769 Italy 0.954934429 1.087808504 1.184694 1.075812184 Japan 0.991550391 1.04973231 0.989583 1.010288556 Korea, Rep. 1.536062677 1.14318066 1.264216 1.314486437 Malaysia 0.999999469 1 1.003646 1.001215116 Netherlands 0.835327716 1.092801331 1.46734 1.131823072 Singapore 1.000000706 1.000003246 1.066175 1.022059512 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2014=>2015 2015=>2016 2016=>2017 Australia China France Germany Indonesia Italy Japan Korea, Rep. Malaysia Netherlands Singapore Thailand United Arab Emirates United Kingdom United States Figure 3. Graphical presentation of frontier shift of the importing countries (2014–2017). Source: calculated by the researchers. 4.3.3. Malmquist Productivity Index Table 8 shows the MPI. The total productivity of the 15 DMUs from 2014–2017 noted that DMU5 (Indonesia), DMU4 (France), DMU15 (UAE), DMU2 (China), and DMU14 (Thailand) had a long-term upward trend during 2014–2017. However, DMU4 (Germany) and DMU10 (Netherlands) experienced a drop during 2015–2016. Ac ording to Figur 4, the cou tries with an upward trend in icate that the Sustainability 2018, 10, 4621 17 of 24 efficiency change over time either remained constantly efficient or exceeded their predicted efficiency values. In terms of MPI, DMU2, DMU8, and DMU14 are the top three best exporting countries, while the three worst exporting countries are DMU4 (Germany), DMU6 (Italy), and DMU7 (Japan), while DMU10 (Netherlands) appears unstable as it has the largest fluctuation. Therefore, it requires increasing trade relations with these countries. As the majority of countries were found to be effective, it may be implied that trade with these countries is important so that there is an improvement in the economics and growth of the trading countries. Table 8. Malmquist Productivity Index of the importing countries (2014–2017). Malmquist 2014–2015 2015–2016 2017–2018 Average Australia 1.024927916 1.01974988 1.433444 1.15937405 China 1.237231846 1.04295869 1.037435 1.105875197 France 1.032413725 0.702242638 1.06115 0.931935482 Germany 0.830952973 1.244052993 0.848798 0.974601257 Indonesia 1.056457431 0.568492946 0.832706 0.819218769 Italy 0.954934429 1.087808504 1.184694 1.075812184 Japan 0.991550391 1.04973231 0.989583 1.010288556 Korea, Rep. 1.536062677 1.14318066 1.264216 1.314486437 Malaysia 0.999999469 1 1.003646 1.001215116 Netherlands 0.835327716 1.092801331 1.46734 1.131823072 Singapore 1.000000706 1.000003246 1.066175 1.022059512 Thailand 1.308632075 0.882299602 0.942753 1.044561622 United Arab Emirates 1.029940603 1 1 1.009980201 United Kingdom 1.175814991 0.845912106 1.247465 1.089730546 United States 1.080935085 1.095557362 0.857004 1.011165398 Average 1.073012135 0.984986151 1.082427 1.046808493 Max 1.536062677 1.244052993 1.46734 1.314486437 Min 0.830952973 0.568492946 0.832706 0.819218769 SD 0.181255111 0.173060274 0.19888 0.111671044 Source: calculated by researchers. Sustainability 2018, 10, x FOR PEER REVIEW 18 of 25 Thailand 1.308632075 0.882299602 0.942753 1.044561622 United Arab Emirates 1.029940603 1 1 1.009980201 United Kingdom 1. 7581 991 0.845912106 1.247465 8 730546 United States 1.080935085 1.095557362 0.857004 1.011165398 Average 1.073012135 0.984986151 1.082427 1.046808493 Max 1.536062677 1.244052993 1.46734 1.314486437 Min 0.830952973 0. 946 706 218769 SD 0.181255111 0.173060274 0.19888 0.111671044 Source: calculated by res archers. Figure 4. Graphical presentation of the Malmquist Index of the importing countries (2014–2017). Source: calculated by the researchers. 5. Discussion The aim of the paper was to evaluate Malmquist DEA analysis approach and Super SBM for the efficiency of DMU’s. Another objective was to adopt a forecasting model to make a prediction about the future export market during the period of 2014–2017. The MPI models were used to evaluate the productivity change in Vietnam’s export industry. This research is conducted on 15 of Vietnam’s leading exporting countries during the period of 2014–2017. On the basis of the completed data, the study showed the forecast future export performance. The accurate forecasting value was significant, showing a reliable accuracy of 7.07%. The empirical analysis of this research gives a broad support to the study, and confirms that the DEA analysis is able to explain the efficiency in Vietnam’s export market. Amongst these 15-leading export markets for Vietnam, the results shown by the Super-SBM model implies that the performance of the top three from 2014–2017 is DMU9, DMU11, and DMU15. With the lowest score, the three DMUs with an inefficient market in the past include DMU1, DMU3, and DMU6. However, in the period of 2018–2021, there were five of the most efficient markets for Vietnam (i.e., DMU1, DMU2, DMU8, DMU9, and DMU15). On the other hand, with the lowest score, three DMUs with an 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2014=>2015 2015=>2016 2017=>2018 Australia China France Germany Indonesia Italy Japan Korea, Rep. Malaysia Netherlands Singapore Thailand United Arab Emirates United Kingdom United States Figure 4. Graphical presentation of the Malmquist Index of the importing countries (2014–2017). Source: calculated by the researchers. Sustainability 2018, 10, 4621 18 of 24 5. Discussion The aim of the paper was to evaluate Malmquist DEA analysis approach and Super SBM for the efficiency of DMU’s. Another objective was to adopt a forecasting model to make a prediction about the future export market during the period of 2014–2017. The MPI models were used to evaluate the productivity change in Vietnam’s export industry. This research is conducted on 15 of Vietnam’s leading exporting countries during the period of 2014–2017. On the basis of the completed data, the study showed the forecast future export performance. The accurate forecasting value was significant, showing a reliable accuracy of 7.07%. The empirical analysis of this research gives a broad support to the study, and confirms that the DEA analysis is able to explain the efficiency in Vietnam’s export market. Amongst these 15-leading export markets for Vietnam, the results shown by the Super-SBM model implies that the performance of the top three from 2014–2017 is DMU9, DMU11, and DMU15. With the lowest score, the three DMUs with an inefficient market in the past include DMU1, DMU3, and DMU6. However, in the period of 2018–2021, there were five of the most efficient markets for Vietnam (i.e., DMU1, DMU2, DMU8, DMU9, and DMU15). On the other hand, with the lowest score, three DMUs with an inefficient market in the future included DMU3, DMU6, and DMU14. They needed action with a strong improvement to get an effective performance in the future. It can be interpreted that three DMU’s were the most efficient for the selection of the export market (i.e., Malaysia, Singapore, and the United States) in the year 2017. The reason behind increasing the trade of Vietnam with these countries can be their involvement with world trade organization, ASEAN (Association of South East Asian Nations) and TPP (Trans-Pacific-Partnership), and their regional comprehensive economic partnership negotiations with other economies, among others. After ASEAN’s free trade agreement, there was a significant reduction in the tariff and non-tariff barriers with 10 countries, which included Singapore, Indonesia, Malaysia, and Thailand. On the other hand, the United States–Vietnam bilateral trade agreement in 2001 and after the effect of the United States–Vietnam Comprehensive Partnership 2013 improved their relations, and both became increasingly cooperative and comprehensive. However, if the TPP with the United States brings the tariff rates down for export–import between these economies to near zero, then Vietnam’s exports to the United States are going to surge. With Australia, although Vietnam started its diplomatic relations in 1973, there are existing differences in the system and in political values. After the initiative of the bilateral relationship into a strategic partnership in 2018, a significant amount of changes can be seen between Australia and Vietnam. Also, Malaysia used to be an efficient country for the export market of Vietnam in 2014, but its decline in efficiency can be seen in the later years, from both of the Super SBM and DEA-MPI techniques. Despite the fact that Vietnam has good relations with Japan because of the Vietnam–Japan Economic Partnership Agreement (VJEPA), Vietnam needs to change its export structure concerning reducing its share of primary goods, and needs to increase the ratio of processed products and also industrial products, in order to improve its efficiency and to remain consistent with sustainable economic development and market orientation. In addition, there is a need to strengthen its cooperation with Japan, and it should work on information provision and trade promotion as well. 6. Conclusions The results of this study can be considered as a basis for selecting a market that will help the government and businessmen make for profitable deals in exports with a long-term vision. The effective market will have positive conditions in order to achieve better results, which is helpful for the economy of Vietnam. Vietnam is a developing nation and over the years has mainly focused on exports and FDI to improve its economic conditions. Trade agreements and exports with strategic and developed nations were a key to their success, and hence the case of Vietnam is relevant for other developing nations to consider for the selection of an international market. Moreover, developing nations may also improve their tariff rates and exchange rates to increase the ease of doing business. Sustainability 2018, 10, 4621 19 of 24 However, it is also important that the developing nations need to improve their trade and export policies for foreign investments. Larger foreign investments mean better business capabilities and larger volumes of export. This study should not only be a reference point to the selection of the international market, but should also act as a benchmark to improve the economy. The paper also demonstrates that DEA is an effective model for identifying and selecting the most effective international markets for the export of goods. In the context of previous studies, the DEA integration method used in this study widely provides a novelty in the application of a model in the IMS, and is not limited to any field. This method is not only suitable for evaluating and selecting international markets for a country’s export activities, but can also be applied in enterprises and companies to find the best market, limit risk, and promote strategy to expand to overseas markets. This study provides an overview of Vietnam’s commodity export markets from 2014–2017, through the assessment of the export performance of Vietnamese goods to the 15 selected countries. The analysis is similar to previous studies that give an insight into the choices of international export markets. This research seems to be the first to apply the DEA model to highlight Vietnam’s export performance and to provide some basic forecasts for future market choices. The MPI model is applied to approach the performance of 15 DMU’s, such as the changes in technical efficiency, changes in technological change, changes in pure technical efficiency, and changes in scale of efficiency as well as in the total factor productivity in the period of 2014–2017. The next model to be used is the Super-SBM model, which identifies and ranks the countries in which Vietnam has the highest export performance and also gives positive results for the export activities of Vietnam for the period 2018–2021. By using the integrated DEA model to measure Vietnam’s export performance through 15 countries, this study can summarize the following conclusions: (i) an overview of export performance Vietnamese goods for 15 countries, through the integrated model DEA for the period 2014–2017; (ii) based on the performance targets, we found three countries—Malaysia, Korea, and the United Stated—with the most efficient exports of goods, while Australia, France, and Italy were the most inefficient; (iii) Vietnam may seek new markets besides traditional markets such as Europe, the United States, and Northeast Asia; (iv) seriously implement the economic and trade commitments when the ASEAN community was put into operation on 31 December 2016. Strictly implementing the agreement reached in Vietnam in the future for export will be advantageous and achieve good results. Although this study tried to show that DEA is an optimum method of selecting good export markets, there is no denying that there are still many limitations in these statistical methods for further studies. Other DEA models like the BCC (Banker, Charnes, and Cooper) models and the algorithm can also be tested to explore more changes. Different DEA models and optimization algorithms can also be tested to reveal more changes, and other industries can be studied in the future using this model. This study is based on only the quantitative model, and the external environmental factors are not considered. In addition, recently, Vietnam will be signing some bilateral agreements with other countries, therefore it would be more useful to study the export market changes to get the reliability and for stable indicators. In addition, only a few countries were chosen for study as DMUs. A lack or gap of secondary data with respect to export and economic information also acts as a limitation of the study. This paper provides an evaluation of the export market efficiency in these countries. Furthermore, this research gives further measures to analyze the market efficiency of the countries in the export market selection. Lastly, a larger dataset of DMUs and output/input variables must be chosen for future studies. Another important future scope is the exploration of the export market of other developing nations. This will help provide a comparative study of the most productive international market for developing nations globally. Author Contributions: C.N.W. guided the research direction, guided the analysis method, and edited the content; A.P.L. designed the research framework, analyzed the empirical result, and wrote the paper. Both of the authors contributed to issuing the final results. Sustainability 2018, 10, 4621 20 of 24 Funding: This research was partly supported by MOST107-2622-E-992-012-CC3 from the Ministry of Sciences and Technology in Taiwan. Acknowledgments: The authors appreciate the support from the National Kaohsiung University of Science and Technology, and the Ministry of Sciences and Technology in Taiwan. Conflicts of Interest: The authors declare no conflicts of interest. Abbreviations and Acronyms The following abbreviations and acronyms are used in this manuscript: DEA Data envelopment analysis DMU Decision-making units FDI Foreign direct investment MPI Malmquist Productivity Index IMS International market selection SBM Slack-based measure Appendix A Table A1. Data of 15 decision-making units (DMUs) in 2014. DMU (I) IT (I) ER (I) EDB (O)EGS (O) Export Australia 2.29 1.33 10 20.013 2,905,591.7 China 2.07 6.23 90 21.348 16,567,686 France 5.36 0.9 31 30.593 2,977,755.9 Germany 5.03 0.9 14 46.875 5,707,416.1 Indonesia 0.63 13,389.413 114 21.16 2,847,607.2 Italy 5.75 0.9 56 29.926 2,847,802.6 Japan 2.62 121.04 29 17.589 14,100,341 Korea, Rep. 3.06 1131.16 5 45.337 8,915,383.9 Malaysia 1.09 3.91 18 70.602 3,577,076.6 Netherlands 6.25 0.9 27 83.426 4,759,560 Singapore 4.14 1.37 1 177.39 3,256,607.3 Thailand 1.59 34.25 26 68.714 3,177,666 United Arab Emirates 2.2 3.67 22 100.87 5,690,916.1 United Kingdom 6.8 0.66 8 27.381 4,645,219.8 United States 3.62 1 7 12.499 33,475,029 Table A2. Data of 15 DMUs in 2015. DMU (I) IT (I) ER (I) EDB (O) EGS (O) Export Australia 1.83 1.11 11 21.076 3,988,213.8 China 2.84 6.14 96 23.495 14,928,318 France 5.74 0.75 38 29.667 2,477,754.8 Germany 3.41 0.75 21 45.704 5,174,944.2 Indonesia 1.69 11 865.211 120 23.666 2,890,397.3 Italy 6.87 0.75 65 29.307 2,740,093.5 Japan 2.69 105.95 27 17.54 14,674,923 Korea, Rep. 3.86 1,052.96 7 50.276 7,167,478.7 Malaysia 1.93 3.27 6 73.793 3,926,398.3 Netherlands 6.11 0.75 28 82.565 3,762,224.9 Singapore 4.58 1.27 1 191.27 2,942,039.9 Thailand 2.1 32.48 18 69.289 3,473,523.4 United Arab Emirates 1.41 3.67 23 99.115 4,626,998.9 United Kingdom 5.67 0.61 10 28.248 3,647,172.4 United States 3.24 1 4 13.62 28,649,809 Sustainability 2018, 10, 4621 21 of 24 Table A3. Data of 15 DMUs in 2016. DMU (I) IT (I)ER (I) EDB (O) EGS (O) Export Australia 1.7 1.04 10 19.988 3,488,123.4 China 3.04 6.2 91 24.505 13,177,694 France 3.26 0.75 34 29.365 2,202,728.6 Germany 3.79 0.75 20 45.398 4,736,995.9 Indonesia 1.43 10,461.24 128 23.924 2,502,204.3 Italy 8.74 0.75 73 28.863 2,290,696.8 Japan 3.54 97.6 24 15.915 13,544,245 Korea, Rep. 3.96 1,094.85 8 53.875 6,682,944.9 Malaysia 1.72 3.15 12 75.629 4,984,467.9 Netherlands 5.8 0.75 31 82.01 2,936,240.6 Singapore 4.72 1.25 1 194.08 2,691,473.6 Thailand 2.27 30.73 18 68.118 3,069,559 United Arab Emirates 1.35 3.67 26 100.63 4,138,413.2 United Kingdom 5.02 0.64 7 29.666 3,696,265.2 United States 2.65 1 4 13.639 23,869,949 Table A4. Data of 15 DMUs in 2017. DMU (I) IT (I) ER (I) EDB (O) EGS (O) Export Australia 3.16 0.97 15 21.519 3,208,732.9 China 3.77 6.31 91 25.408 12,835,976 France 3.25 0.78 29 29.203 2,163,399.4 Germany 3.87 0.78 19 45.983 4,094,940.3 Indonesia 1.44 9,386.63 129 24.594 2,357,706.3 Italy 8.77 0.78 87 28.586 1,876,555.6 Japan 5.2 79.79 20 14.545 13,064,524 Korea, Rep. 3.85 1,126.47 8 56.34 5,580,893 Malaysia 1.54 3.09 18 79.3 4,500,284.1 Netherlands 5.86 0.78 31 81.936 2,476,218.4 Singapore 1.57 1.25 1 197.06 2,367,682.5 Thailand 2.16 31.08 17 69.776 2,832,178.3 United Arab Emirates 1.28 3.67 33 100.32 2,078,323.1 United Kingdom 5.13 0.63 7 29.732 3,033,600.6 United States 2.72 1 4 13.607 19,680,929 References 1. Herr, E.; Schweisshelm, T.-M.V. The integration of Vietnam in the global economy and its effects for Vietnamese economic development. In Global Labour University Working Papers; Global Labour University: Berlin, Germany, 2016. 2. Tran, V.K. 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