A Novel Integrated PCA-DEA-IMF SWARA-CRADIS Model for Evaluating the Impact of FDI on the Sustainability of the Economic System

Abstract

Today’s economic systems are, on the one hand, exposed to various risks and uncertainties with their trends changing almost daily, while on the other hand, they represent an extremely complex system with a large number of sustainable influential parameters. The challenge is to model macroeconomic parameters and achieve sustainability, yet also satisfy conflict situations with an increased level of uncertainty. The aim of this paper is to create an appropriate functional model by examining the mutual influence of various macroeconomic factors. It assesses a total of four scenarios considering mutual influences of: FDI (foreign direct investments), GDP (gross domestic product), imports, exports, inflation rate, RER (real exchange rate) and employment rate as defined parameters. First, the DEA (Data envelopment analysis) model was applied to determine the initial efficiency of two countries, Bosnia and Herzegovina (BIH) and Serbia, for the period 2005–2020. Then, PCA (Principal Component Analysis) was applied in combination with DEA to obtain more precise values. In addition, IMF SWARA (Improved Fuzzy Stepwise Weight Assessment Ratio Analysis) was applied to define weight coefficients of macro-economic parameters. Finally, the CRADIS (compromise ranking of alternatives from distance to ideal solution) model was applied for the final ranking of part of decision-making units. This developed, integrated model can be classified as a mathematical method for economic analysis and gives extended opportunities for solving different problems. The results show that 2009, 2013 and 2016 were the most favorable years in terms of the conditions set when it comes to Bosnia and Herzegovina, and 2012, 2014 and 2016 when it comes to Serbia. These years have been singled out and can be a benchmark for further handling and modeling of macroeconomic elements. In addition, correlation was tested using statistical coefficients.

1. Introduction

At the same time, along with the international exchange of goods and services, foreign capital flows are also of crucial importance for economic growth and development. In the most general terms, the merging of foreign and domestic savings enables the financing of domestic investments and thus directly affects domestic capital formation. There are many examples of countries with high growth rates based on foreign capital flows that allow investment in profitable sectors with less sacrifice of domestic consumption. In addition, foreign flows enable the international integration of developing countries, which is especially important for the transfer of modern technologies. For developing countries particularly, foreign capital flows are important, especially foreign direct investments (FDIs) in production capacities, and through them also (indirectly) in terms of technology transfer, innovations, organizational and management practices, and access to international market networks; these are of crucial importance for sustainable growth. The growth of FDIs in the last few decades was quite significant across the world, but the capital flows mostly took place between developed countries. Developing countries have mainly focused their policies on measures to be taken in order to attract FDIs, but regardless of this and the growing importance of investments for these countries, foreign capital flows show variable trends. It is noticeable that in developing countries, FDIs are directed towards the sectors that are labor-intensive and with low technologies, while for developed countries, capital flows are directed mostly towards the sectors with high technologies. The identification of factors that determine capital movements is quite a complex issue, as it depends on the specifics of each country, sector and company.

In general, as determinants of FDI flows, the following can be identified: the size and growth rates of a certain economy, the wealth of natural resources, the qualifications and costs of the workforce, the state of physical, technological and financial infrastructure, the fiscal-normative framework, the degree of trade liberalization and openness to international markets, but also the general economic-system framework including security, stability and democracy of society as a whole. The ability to attract foreign capital can represent a significant potential for developing countries, as it increases domestic savings that are usually at a low level, and thus allows countries to increase the rates of capital accumulation. This improves prospects for long-term growth and increases general well-being, i.e., it accelerates the development process [1]. Access to international capital markets is a means of financing growing development needs, but benefits for developing countries are obvious.

International trade and foreign direct investments (FDIs) are important factors for economic growth in developing countries. International trade is a means to achieve economic growth, since it enables efficient production of goods and services by paying attention to production with a comparative advantage, while FDIs encourage domestic investments, support the development of human capital and institutions, and represent the most significant form of technology transfer from developed to developing countries. The discussion regarding the impact of FDIs and international trade on economic growth has not been completed, and it also examines the significant role of other economic and institutional prerequisites for stimulating FDI and international trade. There is no unique conclusion regarding the influence of FDI and international trade on economic growth; thus, there are no restrictions for development policies to encourage sustainable economic growth and development [2]. However, the results obtained by foreign capital development will be affected by selecting adequate economic policy measures for international trade diversification, new technologies and the accomplishment of the overall objective of reduction in poverty [3].

The contribution of this paper is reflected through the following:

(a)

Creating a unique integrated model that can consider the economic system in conditions of uncertainty and complexity. The model consists of individual approaches applied through different research phases: DEA, PCA, IMF SWARA and CRADIS. Thus, the literature that considers such problems has been enriched because the integrated model is presented in this way for the first time;

(b)

Additionally, one of the contributions is the implementation of such a model in the field of macroeconomics, which is a rare case in the literature.

The rest of the paper consists of the following sections: In Section 2, the problem is explained in detail through an overview of the situation in the area. Section 3 includes materials and methods, with the flow of research presented through a schematic representation. Different scenarios with different input–output parameters are defined, and the algorithms of individually applied approaches that form a unique integrated model are shown. Section 4 presents the results individually for the two countries, BIH and Serbia, with detailed explanations and analyses. The last Section 5 concludes with considerations for reference to the continuation of the research.

2. Background

According to the orthodox economic theory, foreign capital flows contribute to economic growth by raising investments, i.e., filling the space created by insufficient domestic savings and foreign exchange. Thus, certain authors, for example Chenery and Strout [4], claimed that the inflow of foreign capital contributes to economic growth, while Griffin and Enos [5] and Weisskoff [6] did not agree with that statement. The first group of authors believed that foreign capital inflows are a supplement to domestic savings, while the second group of economists believed that foreign capital replaces domestic savings, and therefore does not always enable the stimulation of growth and development since they can lead to a negative effect on domestic saving rates. In addition, foreign capital inflows can increase capital outflows abroad, which can also threaten the positive effects of foreign investments. Studies based on the neoclassical approach claim that FDI has an influence on income levels and that they have no significant impact on long-term growth, which can only result from technological progress and population growth, i.e., exogenous factors. Thus, it is considered that FDI affects growth only if it influences technology positively and permanently. Endogenous growth models suggest that FDI affects growth endogenously, i.e., they are generated into increasing yields in production through externalities and spillover effects. In these models, FDIs are considered an important factor for stimulating growth because they have a significant impact on human potential, technological diffusion, new management and organizational practices, etc. Among more significant papers based on endogenous models is the analysis of 46 developing countries, which showed that the effects of FDI on stimulating growth are more significant if the country adheres to the policy of export promotion in relation to import substitution [7]. On the other hand, a study that analyzed 69 developed countries and FDI flows in the period from 1970 to 1989 suggests that FDI is an important instrument of technology transfer, thus contributing to economic growth more than domestic investment [8].

The authors Salvatore and Hatcher [9] analyzed the export-based economic growth hypothesis and showed that exports increase the productivity of production factors due to better capacity utilization and economies of scale. In addition, Grossman and Helpman [10] claim that liberalized trade regimes go hand in hand with a favorable investment climate, transfer of technology and related knowledge. Furthermore, empirical studies by authors such as Sachs and Warner [11] and Lipsey [12] show that open economies progress faster, but there are also analyses that question the openness of the economy to foreign countries. Thus, Rodriguez and Rodrik [13] have a critical attitude towards the relationship between liberalized trade and economic growth, considering that previous studies do not consider institutional differences between economies, and that the relationship between the average tariff rate and economic growth is not even close to statistical significance. Therefore, there is no consensus in the literature regarding the relationship between FDI and trade on the one hand, and economic growth on the other hand. Most studies have analyzed the impact of trade and FDI on economic growth, like Borensztein, Gregorio and Lee, Balasubramanyam, Salisu and Sapsford, all cited in Makki [14], or the effects of economic growth on FDI (Barrel and Pain, Lipsey, cited in Makki [14]), but the positive effect of FDI and trade on growth can be simply explained by the fact that FDI is placed in countries that are expected to progress faster, or follow policies of trade openness.

It is evident that there are few theoretical assumptions, as well as empirical studies, that analyze the essential relationship between FDI, trade and economic growth. In one of the empirical studies presented under the auspices of the World Bank in an econometric model derived from a production function, GDP per capita growth is measured based on FDI, trade, domestic investment, human capital and initial GDP per capita. On the example of 66 developing countries over the three decades from 1971 to 2000, it shows that FDI and trade contribute to promoting economic growth, but unlike previous studies based on the framework of endogenous growth theory, this study also shows a strong, positive relationship between FDI and trade, with FDI as the main transmitter of technology to developing countries. Furthermore, the results show that the benefits of investments increase to a large extent if there is a better base for human resources in the country hosting the investments. It is indicated that FDIs also stimulate domestic investments, and a very important prerequisite for the materialization of growth based on FDI is favorable macroeconomic policies and institutional stability to reduce inflation rates, tax rates and government consumption [14].

Current literature and empirical analyses regarding the relationship between FDI and economic growth show the presence of a positive relationship, for example, Borensztein et al. [8] and Bende-Nebende and Ford [15]. However, Bende-Nebende [16] shows that in some countries there is a negative relationship between FDI and economic growth, depending on the variables used in the studies. There are numerous negative effects of FDI, and only one of the examples is that the goals of economic development of a certain country do not always have to coincide with the goals of transnational corporations (TNCs), which are the main operators in FDI flows, so that not all FDIs are always and automatically in the best interest of the host country. Likewise, regarding the above-mentioned Asian development model, it is important to note that after the financial crisis that hit that region in 1997/98, there was a re-examination of the factors that contributed to the development dynamism of that region, but also those factors that were a source of instability and weakness, especially the impact of the globalization process, the interdependence of international markets and other potential future challenges for this region. The main operators for FDI in the world are transnational and multinational corporations. The long-term investment relationship is based on the fact that a foreign parent company invests in its branch abroad in the long term and achieves a significant degree of control and management in order to increase income and diversify risks. Studies have shown that foreign-oriented companies achieve higher profits than those with an exclusive focus on the domestic market, and export-oriented economies achieve higher rates of economic growth than countries focused on the domestic market [17].

Casson [18] believes that the theory of FDI represents an overlap of three theories: (1) the theory of international capital markets, which defines financing and associated risks; (2) the theory of the firm, which describes the identification of advantages, management and use of resources; and (3) the theory of trade, which explains the motives for selling in the world economy. Each of the mentioned theories provides different insights into FDI flows.

The positive effects of FDI and trade depend on numerous factors in different economies, such as macroeconomic stability, trade policies, domestic investment, infrastructure, human potential, etc. A World Bank study based on an analysis of 66 developing countries over three decades states that FDI and trade significantly contribute to the improvement of economic growth in developing countries. The authors show that FDI has a positive interaction with trade and stimulates domestic investment. Necessary preconditions for FDI-based growth are good macroeconomic policies and institutional stability, which include reductions in inflation rates, tax rates and government consumption, promoting economic growth in developing countries.

Empirical studies for individual countries showed the partially correct claims of both groups of economists, i.e., a combination of the mentioned effects. Precisely for developing countries, the importance of foreign capital flows, especially foreign direct investment (FDI) in production capacities, and through them also indirectly in terms of technology transfer, innovation, organizational and management practices and access to international market networks, are of crucial importance for sustainable growth rates. In the last thirty years, there are numerous examples of developing countries, especially in Southeast Asia, which had previously unrecorded and permanent growth rates, precisely based on FDI and its accompanying effects. In the literature, therefore, it is defined as a so-called “East Asian development model” based on the advantages of using international trade and capital flows for the purpose of economic growth.

Furthermore, the well-known studies of the most important international financial institutions that were conducted in the first decade of the 21st century are followed by indicative analyses by individual authors, and even by the IMF, which contradict the predictions of standard theoretical models. A detailed analysis of non-industrialized countries that relied more on foreign capital shows that they did not record higher growth rates in the long term, which contrasts with indicators from industrialized countries where growth and the volume of foreign capital are positively correlated. The authors of the IMF study, Prasad et al. [19], believe that the causes of this difference are the limited ability of non-industrialized countries to absorb foreign capital, especially due to the difficulties in their financial systems to allocate that capital for productive purposes, with the fact that the data for FDI are somewhat more in line with the theoretical settings. In any case, this analysis suggests that there is no evidence that the provision of additional financing as a supplement to domestic flows is the way that financial integration manifests its benefits. Additionally, the papers of IMF experts summarizing arguments and findings about the correlation of FDI with economic growth and its determinants are also significant. Based on the review of the literature, it is concluded that there is significant agreement on the positive consequences of FDI, but no consensus on the conditionality of FDI and economic growth; when it comes to the determinants of FDI, market size, quality of infrastructure, political and economic stability, and free trade zones are most prominent, while the results are different regarding the importance of tax incentives, business and investment climate, labor costs and openness [20]. However, for FDI in southeast Europe, IMF experts believe that the gravity model (market size, geographical and cultural connection between FDI providers and recipients) largely explains FDI flows, but also that economic policies in the host countries are important, particularly the ones that affect unit labor costs, corporate taxes, infrastructure and trade regimes. According to Demekas et al. [21], above a certain level the importance of some economic policies regarding the attraction of FDI is significantly different. When it comes to policy instruments of the national economic and development policy related to FDI on this issue, one can distinguish between restrictive and liberal policies with different instruments, and according to world trends most countries, regardless of the development category to which they belong, strive to follow the trend of liberalization through at least several mechanisms for attracting FDI: removing barriers, improving the treatment and protecting foreign investors, promoting the inflow of FDI through various measures and incentives. According to Kozomara [22], incentives can be classified as fiscal, financial, regulatory and other.

It is evident that the FDI market throughout southeast Europe is becoming very competitive and that countries in this area are finding new ways to attract foreign investors, as FDI has been shown to bridge the gap in capital and technological knowledge between developed and developing countries and initiate economic development. In the long term, FDI can influence the overall democratic process in a certain country since a richer and more educated workforce can be able to express their needs and positions in a better way. It does not mean that there will not be certain undesirable effects in the short term. It is also clear that the experiences of the countries of southeast Europe are surprising with the extent of similarities that can be observed, but also with the complexity of the issues faced by transition economies. Likewise, Jovančević and Šević [23] claim that the achievement of development goals was quite modest, but the trends are generally positive with the fact that a more advanced form of regional cooperation and coordination would be beneficial for all countries in this region. Balancing the inflow and outflow of capital and the internationalization of domestic activities can solve many problems in the economy. Most economists agree that the good sides of greenfield investments, as well as mergers and acquisitions, especially for companies that are in an unenviable situation, cannot be disputed. In addition, foreign direct investments are important for sectors dominated and monopolized by domestic giants, but tender or auction sales of domestic companies from sectors considered strategic in the domestic economy raise numerous issues for discussion. It is indisputable that FDI can have an impact on the macro and micro level, and that macroeconomic consequences are mainly the result of microeconomic impacts in the domestic economy. The papers raising doubts that the positive effects of FDI are stronger than the negative ones, and that the positive correlation between FDI and economic growth is exaggerated, are also evident and significant by number. It is important that the authors are not exclusive, and that the vast majority agree that FDI can be quite favorable for national economies, but with the statement that sometimes they can have less positive or even negative consequences and that all this depends on a specific context of the individual economy and economic conditions, environment, etc. If there are no visions, strategies, plans and policies on which sectors and to what extent FDI is needed, or if they are of limited quality, it can be expected that they will not show the expected effects.

Experiences in the region with the inflow and outflow of capital, especially foreign direct investment, are different; so, for example, in the Republic of Slovenia during the 1990s there was a moderate inflow of foreign capital for specific reasons, such as relatively small size, strong administrative barriers, aversive and the conservative attitude towards foreign capital by leading economists (e.g., professor Mencinger), and also government and business managers, the exclusion of foreigners and foreign capital from basic privatization schemes, as well as relatively slow development of the domestic capital market. The same author states that favorable foreign loans are the most common form of financing in Slovenia. Apart from the usual positive so-called spillover effects of FDI in Slovenia, the most significant individual and general negative impact is the growing difference between FDI placed in Slovenia and Slovenian investments abroad, which created additional pressure on the stability of the currency and required constant interventions by the Central Bank that were resolved by Slovenia’s accession to the Eurozone in 2007. Oplotnik [24] makes the key conclusion that can be drawn from the Slovenian experience, which is that a certain degree of caution and gradualism is necessary to prevent negative effects that can erode stable economic and institutional reforms in transitional societies. Likewise, in the papers of Croatian economists Cvijanović and Kušić [25] the importance and necessity of FDI in transitional economies is highlighted, but also the fact that sources of financing are insufficient to finance investments that would initiate sustainable economic growth, mainly due to the risk-averse banking sector and underdeveloped capital markets. Even if there are sufficient flows of FDI, it seems that their potential is insufficiently used, and that there are spillover effects, i.e., spillover and spread of positive effects on the means of production and capital goods through the spread of modern technology and the connection of domestic and foreign firms. Empirical studies that analyze the results of FDI in the Republic of Croatia also highlight the undeniable role of economic policies that should influence FDI to be directed not only towards the most profitable sectors, but especially to export-oriented sectors that can provide a decisive impetus for economic restructuring. This undisputedly refers to the production sectors and the ability of those areas to provide the incentives and investments necessary for the transformation of the economy.

In conclusion, it is clear that very important determinants of FDI are the following: market size, favorable trade regimes, free zones and regional trade integrations, the quality of labor in the recipient country, as well as the quality of infrastructure, tax benefits and incentives, and finally, the general political–economic stability. It should also be noted that such integrated models related to FDI in literature have not been presented, and only separated models are [26,27,28]. In this way, one of the literature gaps has been fulfilled.

3. Materials and Methods

In this paper, a multiphase model has been applied to determine the efficiency of the 16-year interval for two countries of the western Balkans that border each other, and it consists of a total of 14 steps that are shown in Figure 1. The model consists of four phases that include a different number of steps and activities. After the detailed description of the applied methodology, Figure 1 shows the algorithms of methods for determining efficiency.

3.1. Defining Influential Factors and Data Collection

The first phase of the proposed model represents the defining of influential factors and data collection. First of all, the need for research was recognized considering significant changes in economic parameters at the global level. In addition, it is because of the need for the existence of an adequate model that considers a certain number of influential factors, and first of all, foreign direct investments on the most important parameters of the economic system of a country. This first step was carried out through a dialogue with experts in the field and by searching various databases and reports from the relevant field. Based on that, there was a period defined when the research and determination of the efficiency of the economic system based on the influence of foreign direct investments will be carried out. The period from 2005 to 2020 was selected, for which a set of necessary data was collected as shown in

Table 1. Collected data for Bosnia and Herzegovina in the period 2005–2020.

Year	FDI	GDP	Exports	Imports	Inflation	RER	Unemployment
2005	351.19	11,222,953,335.34	2,729,020,779.36	6,738,153,442.06	7.15	1.760	31.80
2006	554.69	12,864,610,862.59	3,378,033,928.08	6,891,778,199.50	6.13	1.836	31.11
2007	1819.24	15,778,767,410.81	4,276,291,383.02	8,907,162,053.81	1.50	2.123	28.98
2008	1001.65	19,112,739,397.89	5,131,401,466.50	11,336,685,179.28	7.43	2.186	23.41
2009	249.95	17,613,836,526.64	4,405,111,122.31	8,584,651,982.83	−0.38	2.078	24.07
2010	406.09	17,176,781,045.60	5,100,738,250.18	8,806,994,936.74	2.00	1.733	27.31
2011	496.53	18,644,723,853.58	5,973,018,513.72	10,403,825,972.83	3.67	1.575	27.58
2012	394.87	17,221,192,466.19	5,571,149,011.41	9,608,489,861.26	2.05	1.573	28.01
2013	276.36	18,172,335,776.33	6,131,899,777.52	9,847,260,684.96	−0.09	1.559	27.49
2014	550.20	18,560,861,388.64	6,308,673,474.62	10,498,609,864.98	−0.90	1.429	27.52
2015	361.14	16,219,819,017.36	5,763,281,876.70	8,727,773,964.91	−1.04	1.335	27.69
2016	349.76	16,914,287,348.98	6,146,950,591.88	8,958,903,424.78	−1.58	1.408	25.41
2017	491.89	18,079,075,770.67	7,389,376,199.37	10,320,808,221.08	0.81	1.477	20.53
2018	574.34	20,177,409,351.43	8,579,140,845.25	11,552,842,013.65	1.42	1.407	18.4
2019	400.09	20,201,323,260.07	8,176,623,885.38	11,150,214,434.49	0.56	1.522	15.69
2020	370.81	19,946,496,562.97	6,885,478,853.55	9,670,841,197.72	−1.05	1.473	15.87

for Bosnia and Herzegovina, and in

Table 2. Collected data for Serbia in the period 2005–2020.

Year	FDI	GDP	Exports	Imports	Inflation	RER	Unemployment
2005	1577.04	27,683,225,959.25	7,741,608,183.01	12,471,833,413.78	16.12	10.03	20.85
2006	4255.70	32,482,070,360.32	9,563,353,180.69	15,417,941,256.19	11.72	11.66	20.85
2007	4405.91	43,170,990,616.47	11,781,287,690.22	20,858,224,058.44	6.39	63.17	18.06
2008	3971.86	52,194,221,468.50	14,845,675,522.89	26,220,470,717.02	12.41	66.91	13.7
2009	2896.06	45,162,894,380.93	11,899,419,359.99	17,917,945,386.69	8.12	64.40	16.14
2010	1686.10	41,819,468,691.83	13,489,125,666.26	18,599,441,134.51	6.14	57.58	19.22
2011	4932.25	49,258,136,128.97	16,256,083,858.11	22,563,779,942.02	11.14	58.38	22.97
2012	1298.57	43,309,252,921.06	15,524,118,113.11	21,492,658,568.00	7.33	66.71	24
2013	2053.10	48,394,239,474.68	19,285,832,719.77	23,262,513,959.20	7.69	67.15	22.15
2014	1998.80	47,062,206,677.65	19,802,613,644.20	23,603,527,164.10	2.08	58.45	19.22
2015	2347.56	39,655,958,842.55	17,915,468,415.99	20,707,756,724.02	1.39	55.72	17.66
2016	2352.02	40,692,643,373.03	19,742,887,851.05	21,706,648,849.41	1.12	67.58	15.26
2017	2878.29	44,179,055,279.89	22,297,844,539.99	25,206,885,927.75	3.13	77.73	13.48
2018	4090.51	50,640,650,221.46	25,540,389,777.50	29,908,522,177.67	1.96	73.33	12.73
2019	4269.81	51,514,222,381.84	26,277,880,390.99	31,394,659,932.20	1.85	87.97	10.39
2020	3439.79	53,335,016,425.41	25,727,947,826.41	30,146,362,126.84	1.57	85.16	9.01

for Serbia. The data are presented in the domestic currencies of the countries participating in the research.

In the third step, inputs and outputs are defined through a total of four formed scenarios with different input–output parameters, which are presented in more detail for each individual scenario below.

3.1.1. Scenario 1—S1

Scenario 1 considered the impact of foreign direct investment (FDI) as the only input on six outputs: gross domestic product (GDP), exports, imports, inflation rate, real exchange rate (RER) and employment rate.

Table 3. Data for BIH for Scenario 1.

	FDI	GDP	Exports	Imports	Inflation	RER	Employment
2005	351.19	11,222,953,335.34	2,729,020,779.36	6,738,153,442.06	0.11	0.57	68.20
2006	554.69	12,864,610,862.59	3,378,033,928.08	6,891,778,199.50	0.13	0.54	68.89
2007	1819.24	15,778,767,410.81	4,276,291,383.02	8,907,162,053.81	0.32	0.47	71.02
2008	1001.65	19,112,739,397.89	5,131,401,466.50	11,336,685,179.28	0.11	0.46	76.59
2009	249.95	17,613,836,526.64	4,405,111,122.31	8,584,651,982.83	0.83	0.48	75.93
2010	406.09	17,176,781,045.60	5,100,738,250.18	8,806,994,936.74	0.28	0.58	72.69
2011	496.53	18,644,723,853.58	5,973,018,513.72	10,403,825,972.83	0.19	0.63	72.42
2012	394.87	17,221,192,466.19	5,571,149,011.41	9,608,489,861.26	0.27	0.64	71.99
2013	276.36	18,172,335,776.33	6,131,899,777.52	9,847,260,684.96	0.67	0.64	72.51
2014	550.2	18,560,861,388.64	6,308,673,474.62	10,498,609,864.98	1.46	0.70	72.48
2015	361.14	16,219,819,017.36	5,763,281,876.70	8,727,773,964.91	1.82	0.75	72.31
2016	349.76	16,914,287,348.98	6,146,950,591.88	8,958,903,424.78	1.98	0.71	74.59
2017	491.89	18,079,075,770.67	7,389,376,199.37	10,320,808,221.08	0.42	0.68	79.47
2018	574.34	20,177,409,351.43	8,579,140,845.25	11,552,842,013.65	0.33	0.71	81.60
2019	400.09	20,201,323,260.07	8,176,623,885.38	11,150,214,434.49	0.47	0.66	84.31
2020	370.81	19,946,496,562.97	6,885,478,853.55	9,670,841,197.72	1.88	0.68	84.13

presents the data for the first scenario as an example for Bosnia and Herzegovina. It is important to note that the data in the scenario differ from Table 1 and Table 2, because it is necessary to process the data and adapt them to the created multiphase model for determining the efficiency of the economic system.

In this scenario, it is necessary to adjust the data related to the inflation rate, real exchange rate and employment, because they represent outputs, and it is necessary to transform them into a benefit group of parameters. Equation (1) was applied to the inflation rate for BIH because there was a negative inflation rate in certain years, while for Serbia the reciprocal value was simply applied.

$${x_{ij}}^{\prime }=\left|\frac{1}{x_{ij}-min{x}_{ij}}\right|$$

(1)

where ${x_{ij}}^{\prime }$ is the new value for the inflation rate that has been transformed into a benefit group of parameters, while $x_{ij}$ represents the value of the inflation rate from Table 1.

The values of the real exchange rate were obtained as the reciprocal of the data from Table 1 for both countries, while the employment rate was obtained as the difference between the total percentage and the unemployment percentage.

3.1.2. Scenarios 2–4—S2–S4

In Scenario 2, the following parameters are defined as two inputs: foreign direct investment and inflation rate, while the remaining five indicators are modeled as outputs: GDP, imports, exports, real exchange rate and employment rate. It is important to note that the data related to the inflation rate are taken from Table 1 and Table 2 as minimization type indicators. In Scenario 3 there are also two inputs and five outputs, and instead of the inflation rate, the real exchange rate with original values appears as an input, as was the case in the previous scenario with the inflation rate. In the last one, Scenario 4, the relationship ¾ is defined, which implies three inputs and four outputs. FDI, inflation rate and RER are defined as input parameters, while other indicators represent outputs.

3.2. Determining the Initial Efficiency and Determining Significance of Inputs/Outputs

This phase partially overlaps with the previous one, as it involves data processing to determine the final efficiency and impact of foreign direct investments on economic parameters. In the sixth step it has been applied to the DEA model, which is presented in detail below. An input-oriented model was applied, and if more 1.00 values were obtained, PCA was applied to increase the discriminatory power of the model. If, even after applying the PCA-DEA model, there are more DMUs with a value of 1.00, it is applied as an integrated multi-criteria model with the IMF SWARA and CRADIS method. Below are explanations and steps of the individual methods that make up the integrated multiphase model.

3.2.1. DEA Model

In this section, the DEA CCR model [29,30,31] presented is used to obtain the DMU values in accordance with an input-oriented model (min). The DEA CCR [32] input-oriented model (min) is given below:

$$\begin{array}{c}DE{A}_{input}=min{\displaystyle {\displaystyle \sum }_{i=1}^m}{w}_i{x}_{i-input}\\ st:\\ {\displaystyle {\displaystyle \sum }_{i=1}^m}{w}_i{x}_{ij}-{\displaystyle {\displaystyle \sum }_{i=m+1}^{m+s}}{w}_i{y}_{ij}\ge 0,\hspace{1em}j=1,\dots ,n\\ {\displaystyle {\displaystyle \sum }_{i=m+1}^{m+s}}{w}_i{y}_{i-output}=1\\ w_i\ge 0,\hspace{1em}i=1,\dots ,m+s\end{array}$$

(2)

where m represents input parameters for each alternative x_ij, s represents the output parameters for each alternative y_ij, n represents the total number of DMUs, and the weights of the parameters are denoted by w_i.

3.2.2. PCA Model

Principal Component Analysis is a method used to reduce dimensionality, achieve visibility and simplify a large set of data. PCA represents a technique of creating new (“artificial”) variables that are linear combinations of initial variables. The maximum number of new variables that can be created and the number of initial variables is equal. The new variables do not correlate with each other. The main characteristics of the Principal Component Analysis are the summarization and analysis of the linear relationship of many differently distributed, quantitative, mutually correlated variables, into a smaller number of components, new variables, mutually uncorrelated, with minimal information loss. Therefore, initial variables are transformed into new variables, i.e., linear combinations called principal components. The largest part of the variance of an original data set is covered by the first principal component, and the following components contain the part of the variance that is not covered by previously identified components.

PCA is not sensitive to problems of normality, linearity and homogeneity of variances. It is also desirable as a certain degree of multicollinearity. The main steps in PCA are as follows [33,34]:

• Variable standardization;
• Computing the matrix of correlations between all initial standardized variables;
• Finding the eigenvalues of the principal components;
• Rejection of the components that carry a proportionally small share of variance (the first several components usually carry 80–90% of the total variance).

Consequently, out of many initial variables, it has been formed with only a few principal components carrying most information and creating the main form. The analysis does not provide satisfactory results in case the initial variables are uncorrelated. The greatest results can be obtained when initial variables are highly positively or negatively correlated. Then two or three principal components can be expected to cover, e.g., 20–30 variables. The results of the principal components can mainly be used for further explanation of the findings. Additionally, the principal components can be used as input variables in other methods [33].

3.2.3. IMF SWARA Method

Vrtagić et al. [35] developed the Improved fuzzy SWARA method that includes the following steps [36]:

Step 1: Defining all the criteria used for decision making, and then arranging them in descending order according to their expected importance.

Step 2: Using the previously determined ranking, it is identified as a relatively smaller importance of the criterion (C_j) in relation to the previous one (C_j−1), repeating it for each subsequent criterion. This relationship, i.e., comparative importance of the average value, is denoted by $\overline{s_j}$. An appropriate TFN scale is given in

Table 4. Linguistics and the TFN scale for evaluating the criteria in the improved IMF SWARA method.

Linguistic Variable	Abbreviation	TFN Scale
Absolutely less significant	ALS	1	1	1
Dominantly less significant	DLS	1/2	2/3	1
Much less significant	MLS	2/5	1/2	2/3
Really less significant	RLS	1/3	2/5	1/2
Less significant	LS	2/7	1/3	2/5
Moderately less significant	MDLS	1/4	2/7	1/3
Weakly less significant	WLS	2/9	1/4	2/7
Equally significant	ES	0	0	0

that facilitates accuracy and high quality, determining the importance of criteria by IMF SWARA.

Step 3: Determination of the fuzzy coefficient $\overline{k_j}$ (3):

$$\overline{k_j}=\{\begin{array}{l}\overline{1}\hspace{1em}\hspace{1em}\hspace{1em}j=1\\ \overline{s_j}\oplus \overline{1}\hspace{1em}\hspace{1em}\hspace{1em}j>1\end{array}$$

(3)

Comparative importance of the average value is denoted by $\overline{s_j}$.

Step 4: Determination of the calculated weights $\overline{q_j}$ (4):

$$\overline{q_j}=\{\begin{array}{l}\overline{1}\hspace{1em}\hspace{1em}j=1\\ \frac{\overline{q_{j-1}}}{\overline{k_j}}\hspace{1em}j>1\end{array}$$

(4)

$\overline{k_j}$ is a fuzzy coefficient from the previous step.

Step 5: Calculation of the fuzzy weight coefficients by applying Equation (5):

$$\overline{w_j}=\frac{\overline{q_j}}{{\displaystyle \sum _{j=1}^m\overline{q_j}}}$$

(5)

where w_j represents the fuzzy relative weight of the criteria j, and m represents the total number of criteria.

3.2.4. CRADIS Method

The CRADIS method is conducted by the following steps [37]:

Step 1. Formation of an initial decision matrix. The decision matrix in multi-criteria models involves defining a set of “n” criteria and “m” alternatives.

$$A=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \dots & x_{1n}\\ x_{21}& x_{22}& \dots & x_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ x_{m1}& x_{m2}& \dots & x_{mn}\end{array}\right]$$

(6)

Step 2. Normalization of decision matrix. Normalization is completed using the following expressions:

$$n_{ij}=\frac{x_{ij}}{x_{j max}}$$

(7)

$$n_{ij}=\frac{x_{j min}}{x_{ij}}$$

(8)

Step 3. Weighting the decision matrix. The weighted decision matrix is created by multiplying the values of the normalized decision matrix by the corresponding weights, based on the following expression:

$$v_{ij}=n_{ij}·w_j$$

(9)

Step 4. Determination of the ideal and anti-ideal solution. The calculation of the ideal solution is completed by identifying the largest value $v_{ij}$ in the weighted decision matrix, while the calculation of the anti-ideal solution is completed by identifying the smallest value $v_{ij}$ in the weighted decision matrix.

$$t_i=max v_{ij}$$

(10)

$$t_{ai}=min v_{ij}$$

(11)

Step 5. Calculation of deviations from ideal and anti-ideal solutions.

$$d^{+}=max t_i-v_{ij}$$

(12)

$$d^{-}=v_{ij}-min t_{ai}$$

(13)

Step 6. Calculation of deviation grades of individual alternatives from ideal and anti-ideal solutions.

$$s_i^{+}={\displaystyle \sum }_{j=1}^n{d}^{+}$$

(14)

$$s_i^{-}={\displaystyle \sum }_{j=1}^n{d}^{-}$$

(15)

Step 7. Calculation of the utility function for each alternative in relation to the deviations from the optimal alternatives.

$$K_i^{+}=\frac{s_0^{+}}{s_i^{+}}$$

(16)

$$K_i^{-}=\frac{s_i^{-}}{s_0^{-}}$$

(17)

where $s_0^{+}$ is the optimal alternative with the smallest distance from the ideal solution, while $s_0^{-}$ is the optimal alternative with the greatest distance from the anti-ideal solution.

Step 8. Ranking the alternatives. The final ranking is obtained by searching for the average deviation of the alternatives from the utility degree.

$$Q_i=\frac{K_i^{+}+K_i^{+}}{2}$$

(18)

The alternative that has the greatest value of $Q_i$ is the best alternative.

4. Results

4.1. Case Study—BIH

Based on the previously presented materials and data given in Table 1 for BIH and the detailed scenarios applying DEA and PCA-DEA [38] models, the results presented in

Table 5. Results of DEA and PCA-DEA application for all four scenarios.

	S1		S2		S3		S4
	DEA	PCA-DEA	DEA	PCA-DEA	DEA	PCA-DEA	DEA	PCA-DEA
2005	0.720	0.670	0.720	0.660	0.780	0.722	0.780	0.709
2006	0.449	0.428	0.449	0.424	0.654	0.614	0.654	0.605
2007	0.140	0.132	0.140	0.133	0.577	0.545	0.578	0.543
2008	0.318	0.296	0.318	0.296	0.632	0.580	0.632	0.583
2009	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
2010	0.649	0.643	0.649	0.642	0.772	0.757	0.772	0.755
2011	0.588	0.576	0.588	0.576	0.866	0.832	0.866	0.834
2012	0.694	0.686	0.694	0.685	0.850	0.824	0.850	0.823
2013	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
2014	0.624	0.606	0.582	0.570	1.000	0.975	1.000	1.000
2015	0.996	0.971	0.967	0.939	1.000	0.990	0.983	0.954
2016	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
2017	0.677	0.617	0.677	0.612	0.937	0.929	0.937	0.927
2018	0.673	0.566	0.673	0.566	1.000	1.000	1.000	1.000
2019	0.921	0.793	0.921	0.796	1.000	1.000	1.000	1.000
2020	1.000	0.980	0.963	0.914	1.000	1.000	1.000	1.000

were obtained.

The lowest amount of foreign direct investments in the considered period was in 2009 and the highest in 2007, while 2008 also stands out with a large amount of foreign direct investments, and in the remaining years it varies with a trend of growth and decline depending on the year. Certainly, the state of the economic system caused by the pandemic is manifested in the downward trend of foreign direct investments in 2020, in the smallest amount in the last five years. When it comes to GDP, it was the lowest in 2005, and the highest in 2018 and 2019, which was also caused by the trend of rising prices of both basic foodstuffs and certain services. In general, since 2010, according to the parameters in Table 1, it can be said that GDP is constant with minor oscillations. It is important to emphasize that the GDP in 2008 is almost at the same level as in 2020, which can be considered as a consequence of the large volume of foreign direct investments in 2008. With time passing, the trend of export growth is visible with certain minor oscillations, while the situation with exports is different, as there are larger variations from year to year. When it comes to the inflation rate, the highest rate was recorded in 2005 (7.15%), while the lowest, or negative rate, which was the most favorable, was in 2016. The most favorable real exchange rate was in 2016, and the most unfavorable was in 2008. The highest unemployment rate was in 2006, and the lowest in 2019 and 2020, which was largely caused by the outflow of labor force abroad.

The obtained results for BIH show that if we take into consideration only one input that implies foreign direct investments, then using the DEA model, a total of four years appear as efficient (2009, 2013, 2016 and 2020), while using the PCA-DEA model based on 95% information eliminates 2020 as effective and three DMUs remain. The results are similar in Scenario 2 when there are two inputs, namely FDI and the inflation rate. By applying both models, the three years mentioned above are identified as the most effective in terms of the set observation conditions. In Scenarios 3 and 4 when FDI and RER are inputs, and in Scenario 4 when the inflation rate is added as the third input, the results show more efficient years. They refer to the DMUs explained in the previous two scenarios and the last three years of observation (2018, 2019, 2020). It is important to emphasize that in each scenario, DMU5 (2009), DMU9 (2013) and DMU12 (2016) appear as efficient with a value of one.

After applying the previous models and obtaining the results, it is evident that PCA-DEA does not have full discriminatory power, so further, for DMUs equal to 1.000, it is applied a MCDM model: IMF SWARA-CRADIS, in order to measure full efficiency.

Table 6. Weighted values of input–output parameters obtained using the IMF SWARA method.

	Sj			Kj			Qj			Wj
C2				1.000	1.000	1.000	1.000	1.000	1.000	0.197	0.204	0.212
C7	2/9	1/4	2/7	1.222	1.250	1.286	0.778	0.800	0.818	0.153	0.163	0.174
C1	0.000	0.000	0.000	1.000	1.000	1.000	0.778	0.800	0.818	0.153	0.163	0.174
C3	2/9	1/4	2/7	1.222	1.250	1.286	0.605	0.640	0.669	0.119	0.131	0.142
C4	0.000	0.000	0.000	1.000	1.000	1.000	0.605	0.640	0.669	0.119	0.131	0.142
C5	2/9	1/4	2/7	1.222	1.250	1.286	0.471	0.512	0.548	0.093	0.104	0.116
C6	0.000	0.000	0.000	1.000	1.000	1.000	0.471	0.512	0.548	0.093	0.104	0.116
						SUM	4.706	4.904	5.071

shows the calculation of the IMF SWARA method for determining weighted values of input–output parameters.

The first step of the IMF SWARA method performed the ranking of the criteria (C1-FDI, C2-GDP, C3-exports, C4-imports, C5-inflation rate, C6-RER and C7-employment rate) according to their importance, which is shown in the first column of Table 6. The criteria are ranked as follows: C2 > C7 > C1 > C3 > C4 > C5 > C6. Using the linguistic scale and TFNs, it determined the s_j shown in the second column of Table 6. After that, it is necessary to calculate the matrix $\overline{k_j}$ as follows:

$$\begin{array}{l}\overline{k_2}=\left[1.000,1.000,1000\right]\\ \overline{k_7}=\left[1.222,1.250,1.286\right]=\left[1+2/9,1+1/4,1+2/7\right]\\ \overline{k_1}=\left[1.000,1.000,1.000\right]=\left[1+0,1+0,1+0\right]\\ \overline{k_3}=\left[1.222,1.250,1.286\right]=\left[1+2/9,1+1/4,1+2/7\right]\\ \overline{k_4}=\left[1.000,1.000,1.000\right]=\left[1+0,1+0,1+0\right]\\ \overline{k_5}=\left[1.222,1.250,1.286\right]=\left[1+2/9,1+1/4,1+2/7\right]\\ \overline{k_6}=\left[1.000,1.000,1.000\right]=\left[1+0,1+0,1+0\right]\end{array}$$

The elements of matrix $\overline{q_j}$ are obtained as shown below:

$$\begin{array}{l}\overline{q_7}=\frac{\overline{q_{7-1}}}{\overline{k_7}}=\frac{\overline{q_2}}{\overline{k_7}}=\frac{1.000}{1.286},\frac{1.000}{1.250},\frac{1.000}{1.222}=\left[0.778,0.800,0.818\right]\\ \overline{q_1}=\frac{\overline{q_7}}{\overline{k_1}}=\frac{0.778}{1.000},\frac{0.800}{1.000},\frac{0.818}{1.000}=\left[0.778,0.800,0.818\right]\\ \overline{q_3}=\frac{\overline{q_1}}{\overline{k_3}}=\frac{0.778}{1.286},\frac{0.800}{1.250},\frac{0.818}{1.222}=\left[0.605,0.640,0.669\right]\\ \overline{q_4}=\frac{\overline{q_3}}{\overline{k_4}}=\frac{0.605}{1.000},\frac{0.640}{1.000},\frac{0.669}{1.000}=\left[0.605,0.640,0.669\right]\\ \overline{q_5}=\frac{\overline{q_3}}{\overline{k_4}}=\frac{0.605}{1.286},\frac{0.640}{1.250},\frac{0.669}{1.286}=\left[0.471,0.512,0.548\right]\\ \overline{q_6}=\frac{\overline{q_5}}{\overline{k_6}}=\frac{0.471}{1.000},\frac{0.512}{1.000},\frac{0.548}{1.000}=\left[0.471,0.512,0.548\right]\end{array}$$

The final fuzzy criterion weights $\overline{w_j}$ are obtained using the following procedure:

$$\overline{w_1}=\frac{\overline{q_1}}{{\displaystyle \sum _{j=1}^7\overline{q_j}}}=\frac{0.778}{5.071},\frac{0.800}{4.904},\frac{0.818}{4.706}=\left[0.153,0.163,0.174\right]$$

$$\overline{w_2}=\frac{\overline{q_2}}{{\displaystyle \sum _{j=1}^7\overline{q_j}}}=\frac{1.000}{5.071},\frac{1.000}{4.904},\frac{1.000}{4.706}=\left[0.197,0.204,0.212\right]$$

The other fuzzy weights are obtained in the same way: $\overline{w_3}=\left[0.119,0.131,0.142\right]$, $\overline{w_4}=\left[0.119,0.131,0.142\right]$, $\overline{w_5}=\overline{w_6}=\left[0.093,0.104,0.116\right]$.

Then, Equations (6)–(18) of the CRADIS method are applied to determine the final inter-efficiencies of those values with a value of 1.000 in the scenarios. The results are shown in Figure 2.

The results presented in Figure 2 show the final rankings for 2009, 2013 and 2016 for scenarios S1 and S3, i.e., the additional three years, 2018, 2019 and 2020 in scenarios S3 and S4. For the first two scenarios the results are identical, and the ranking is 2016 > 2013 > 2009. When it comes to S3 and S4, the rankings are as follows: 2020 > 2019 > 2016 > 2018 > 2013 > 2009. After applying the IMF SWARA-CRADIS model, it is necessary to summarize all the results and their ranks obtained by applying the DEA, PCA-DEA and PCA-DEA-IMF SWARA-CRADIS models. The ranks are shown in Figure 3.

Based on the previously obtained values, the ranking of all DMUs for all scenarios was done using all the models explained in this paper. It is clearly noticeable that there are certain changes in the ranks depending on the scenarios and the model applied. The standard deviation (STdev) values for the ranks are: 2.657, 0.000, 0.000, 0.000, 1.875, 1.595, 1.128, 1.946, 1.505, 4.582, 2.023, 0.798, 0.492, 5.334, 2.379, 1.782, starting from Scenario 1 and the DEA model to the last scenario with the PCA-DEA-IMF SWARA-CRADIS model. Since there are changes in the ranks, it initiated the need to test the correlation between the ranks, which was determined by applying the Spearman correlation coefficient (SCC) [39] excluding the DEA model, and it is given in

Table 7. Statistical correlation test—SCC for BIH.

		S1		S2		S3		S4
		A	B	A	B	A	B	A	B	AV
S1	A	1.000	0.996	0.991	0.996	0.684	0.696	0.494	0.696	0.819
	B	0.996	1.000	0.987	1.000	0.682	0.712	0.490	0.712	0.822
S2	A	0.991	0.987	1.000	0.987	0.657	0.654	0.450	0.654	0.798
	B	0.996	1.000	0.987	1.000	0.682	0.712	0.490	0.712	0.822
S3	A	0.684	0.682	0.657	0.682	1.000	0.956	0.919	0.956	0.817
	B	0.696	0.712	0.654	0.712	0.956	1.000	0.846	1.000	0.822
S4	A	0.494	0.490	0.450	0.490	0.919	0.846	1.000	0.846	0.692
	B	0.696	0.712	0.654	0.712	0.956	1.000	0.846	1.000	0.822
A = PCA-DEA, B = PCA-DEA-IMF SWARA-CRADIS

. When observing the ranking and standard deviation for 2006, 2007 and 2008, it can be concluded that changing the input parameters and applying a different approach has no impact on the ranking since the positions are 14, 16 and 15, respectively. The greatest change when observing DMUs is in 2018 and 2014, when STdev is 5.334 and 4.582, respectively, which means great sensitivity to changing parameters and approaches.

Table 7 shows the correlation values of the applied models, A = PCA-DEA, B = PCA-DEA-IMF SWARA-CRADIS, for all scenarios. The average overall correlation is 0.802, which represents a high level of correlation considering the change in input–output parameters and the fact that by applying the PCA-DEA model, more DMUs with a value of 1.000 are still obtained, while it changes by applying PCA-DEA-IMF SWARA-CRADIS due the requirements of the study. When it comes to the first two scenarios using PCA-DEA-IMF SWA-RA-CRADIS, there are no differences in ranks, i.e., there is a full correlation. The same is the case in Scenario 3 and 4 mutually, but which differ from the first two.

4.2. Case Study—Serbia

Based on the previously presented materials and data given in Table 2 for Serbia and based on detailed scenarios applying DEA and PCA-DEA models, the results presented in

Table 8. Results of DEA and PCA-DEA application for all four scenarios for Serbia.

	S1		S2		S3		S4
	DEA	PCA-DEA	DEA	PCA-DEA	DEA	PCA-DEA	DEA	PCA-DEA
2005	1.000	0.936	1.000	0.857	1.000	1.000	1.000	1.000
2006	0.379	0.354	1.000	0.395	1.000	1.000	1.000	0.456
2007	0.320	0.317	0.443	0.441	0.505	0.481	0.735	0.435
2008	0.399	0.376	0.473	0.448	0.665	0.625	0.776	0.544
2009	0.495	0.491	0.612	0.607	0.675	0.624	0.755	0.611
2010	0.835	0.816	0.952	0.941	0.919	0.881	1.000	0.923
2011	0.300	0.285	0.382	0.346	0.540	0.521	0.757	0.438
2012	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
2013	0.786	0.727	0.845	0.809	0.932	0.906	0.932	0.850
2014	0.978	0.930	1.000	1.000	1.000	1.000	1.000	0.954
2015	0.902	0.826	1.000	0.949	1.000	1.000	1.000	0.806
2016	1.000	0.937	1.000	1.000	1.000	1.000	1.000	0.840
2017	0.690	0.642	0.780	0.752	0.823	0.723	0.839	0.683
2018	0.591	0.557	0.791	0.756	0.847	0.777	1.000	0.585
2019	0.586	0.556	0.878	0.825	0.768	0.718	0.963	0.562
2020	0.742	0.701	0.989	0.952	0.852	0.820	1.000	0.696

were obtained.

When it comes to determining the efficiency of DMUs for Serbia, it can be noticed that the PCA-DEA model has a much better applicability, since compared to the initial DEA, it has a much higher discriminatory power that can be seen from three scenarios: S1, S2 and S4, when there are fewer DMUs with a value of 1.00 by applying the PCA-DEA model, which is certainly desirable. For this reason, and the fact that only in Scenario 1 the year 2012 was identified with the maximum value, i.e., as efficient, there was no need for applying the second model and further calculations, unlike in the other scenarios.

The rest of the model has been applied in the same way as for BIH, so there will be no detailed explanation here. The weight values of the parameters calculated with the IMF SWARA method are the same, so below are the results of DEA, PCA-DEA for all models and the IMF SWARA-CRADIS model for scenarios S1-S3. Figure 4 shows the results as rankings.

From Figure 4 it is noticeable that there are significant changes in the ranks depending on the scenarios and the model applied. The standard deviation (STdev) values for the ranks are 2.453, 6.604, 0.809, 0.405, 1.572, 2.212, 0.674, 1.036, 1.912, 1.300, 2.412, 1.940, 1.214, 2.841, 1.629, and 2.639, starting from Scenario 1 and the PCADEA-DEA model to the last scenario with the PCA-DEA-IMF SWARA-CRADIS model. Since there are changes in the ranks, it initiated the need to test the correlation between the ranks, which was determined by applying the Spearman correlation coefficient (SCC) and the WS coefficient [40] excluding the DEA model, and it is given in

Table 9. Statistical correlation tests—SCC and WS for Serbia.

		S1	S2		S3		S4
	SCC	A	A	B	A	B	A	B	AV
S1	A	1.000	0.910	0.906	0.684	0.844	0.940	0.944	0.890
S2	A	0.910	1.000	0.993	0.550	0.769	0.800	0.816	0.834
	B	0.906	0.993	1.000	0.543	0.782	0.807	0.824	0.836
S3	A	0.684	0.550	0.543	1.000	0.919	0.594	0.593	0.697
	B	0.844	0.769	0.782	0.919	1.000	0.754	0.765	0.833
S4	A	0.940	0.800	0.807	0.594	0.754	1.000	0.999	0.842
	B	0.944	0.816	0.824	0.593	0.765	0.999	1.000	0.849
		S1	S2		S3		S4
	WS	A	A	B	A	B	A	B	AV
S1	A	1.000	0.924	0.875	0.932	0.855	0.893	0.903	0.912
S2	A	0.840	1.000	0.900	0.952	0.828	0.729	0.729	0.854
	B	0.854	0.963	1.000	0.915	0.951	0.805	0.806	0.899
S3	A	0.232	0.196	0.096	1.000	0.500	0.129	0.096	0.321
	B	0.846	0.924	0.952	0.928	1.000	0.780	0.783	0.887
S4	A	0.899	0.747	0.682	0.940	0.710	1.000	0.967	0.849
	B	0.948	0.857	0.792	0.922	0.789	0.982	1.000	0.899
A = PCA-DEA, B = PCA-DEA-IMF SWARA-CRADIS

. When observing the ranking and standard deviation, it can be concluded that the smallest changes in the ranks are when it comes to the best DMUs and the last-ranked DMU.

The average overall correlation is 0.826 for SCC, which represents a high level of correlation considering the change in input–output parameters and the fact that the application of the PCA-DEA model still results in more DMUs with a value of 1.000, while it changes by applying the PCA-DEA-IMF SWARA-CRADIS due to the requirements of the study. In addition, the WS coefficient was applied to determine the correlation between the ranks because this coefficient indicates less correlation if there are changes in the best-ranked positions. This coefficient shows a correlation of 0.803, which still represents a high correlation.

5. Conclusions

Taking into account everything previously stated in the paper, it can be pointed out that both theoreticians and practitioners agree that FDI has an impact on economic growth and development in many ways, such as improving the quality of workforce, technology transfer and related know-how effects, and finally capital formation. In the paper, a mutual comparison of macroeconomic parameters for BIH and Serbia was made for the period 2005–2020, in order to establish certain rules that can serve to reduce the uncertainty and complexity of the economic system. Based on the created unique and integrated PCA-DEA-IMF SWARA-CRADIS model, a multiphase determination of the efficiency of each year has been carried out individually within the observed period, and certain years have been singled out that can be benchmarks in further handling and modeling of macroeconomic elements. The results show that 2009, 2013 and 2016 are the most favorable years in terms of the conditions set when it comes to Bosnia and Herzegovina, and 2012, 2014 and 2016 when it comes to Serbia. The creation of such a model is extremely significant in terms of observing the uncertainty of the economic market, global crises caused by various influential factors and finally the rate of inflation, which mostly affects developing countries.

Future research should definitely be focused on updating macroeconomic parameters from the aspect of determining their trend in view of the current crises that are prevailing in the world. Additionally, it is necessary to identify in more detail the interrelationships of macroeconomic parameters under new conditions and risks that are an integral part of the everyday economic system. It is expedient to consider the components of sustainable development (economic, social, and environmental) and assess the impact of FDI on each of them separately. We can determine the harmony of economic development of the economic systems in the context of sustainable development as in this study [41].