QUANTITATIVE ASSESSMENT OF THE DYNAMICS OF SOCIOECONOMIC PROCESSES

The efficiency of correlation-regression analysis would significantly expand if both of its essential variables – a dependent and an independent – conveyed the information on the dynamic rather than static state of a phenomenon under consideration. For this objective, the dynamic development of the socioeconomic processes should be based on the quantitative assessment. Existing methodologies call for improvement as they do not fully reflect the state of particular phenomena. In this article, authors provide the quantitative assessment methodology to analyse the dynamics of socioeconomic processes. It was applied for assessing real situations, which confirmed adequacy and applicability of this methodology.


Introduction
All economic agents that conduct production, service provision, maintenance, consumption and similar processes belong to particular socioeconomic systems, i.e. the social systems incorporating material, technical, informational and other resources. In order to survive, they need to be in constant evolvement process. It is a condition of their existence. Development refers to the changes in system parameters. Evolution of these changes, ongoing consistently in the course of time, forms the development process. Thus, development is a process. Because it is a process of a socioeconomic system development, it can be understood as a socioeconomic process (SEP) (Ginevicius, et al., 2018). It defines the situation in a socioeconomic system.
Correlation-regression is the most universal and most common method of the SEP analysis and fluctuation forecast. It is based on determination of the strength and nature of the effects that independent variables, or determinants, have on the phenomenon under consideration. The core of regression analysis is the correlation field which helps to determine the nature of the effect. A point in this field represents the intersection between a dependent and an independent variable. If an independent variable, for instance, represents the condition of the SEP development over particular time period, and a dependent variable represents the value of a particular determinant affecting the condition of the phenomenon researched, the question arises as to how informative the abovementioned point is, i.e. how much and what sort of information the point has accumulated. From what the point reflects, it becomes clear that it represents the information about the statistical condition of the SEP, but it does not provide the information on the nature of the development of either a dependent or an independent variable. On the other hand, if a point in the correlation field represents the intersection between the development of an independent variable over particular period and the development of a dependent variable over the same period, it will contain an incomparably larger amount of information as it will reflect a dynamic rather than a static condition of the variables, i.e. it will indicate long-term fluctuations and tendencies. Hence, if a correlation-regression analysis incorporates the variables that reflect a dynamic rather than a static condition, it provides more opportunities to raise research efficiency and expand applicability and adequacy of the results because it indicates how long-term fluctuations and trends affect the long-term changes in the phenomena under research.

The potential of quantitative assessment of the dynamics for the SEP development
Being multiple and complex by their nature, socioeconomic processes are affected by a number of destabilising factors. Together, they form the environment that requires a constant adaptation. The result of such situation is that the development of the socioeconomic processes is not ideal, i.e. it is not smooth, and its intensity may vary in different time slots. The development is considered to be ideally smooth, if an increase in the SEP development is equal over all time slots during the entire period under consideration, i.e. if qi = qi + 1; here qi represents an increase in the SEP development over the i th time slot of the entire period T, e.g. a year ( n i , 1 = ). In this case, an ideal trajectory of the SEP development would look as depicted in Figure   The method of Measuring of Dynamics of Development (MDD) is proposed as the one that allows to quantitatively assess the factual trajectory of the SEP development depicted in Figure no. 2. Based on this method, the dynamics of economic development was estimated for a group of the EU member states (Ginevičius, et al., 2018). The SEP development itself

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compromises two sidesqualitative and quantitative, which represents the intensity of the development and also the smoothness of the process. The combination of both indicators produces and integrated indicator, which could be applied for the analysis of the dynamics of SEP development.
The smoothness indicator calculated as the ratio of the length of the analysed time period and the length of the SEP development factual trajectory over this time period. The length of the factual trajectory is based on the development fluctuations over the particular time slots of the entire period researched (a year). The fluctuations are expressed as the difference between the development values based on two adjacent time slots. The length of the SEP development factual trajectory over the entire period under consideration is a diagonal of a right triangle. One perpendicular of this triangle is the difference between the development values estimated for nearby time slots, while the other perpendicular is the length of the entire analysed period. For this situation, the length li of the diagonal line of the right triangle i is estimated as follows (Ginevičius et al.,2018): The length Li of the SEP development factual trajectory over the entire analysed time period T is equal to the sum of the values li: The indicator DT represents the SEP development smoothness over the analysed period T is estimated by formula: Intensity, another partial indicator of the SEP development dynamics, is evaluated as the ratio of of the SEP development the value at the start of period T and the SEP development value at the end of this period: here DI represents intensity of the SEP development over the entire period T; Qf marks the value the SEP development at the beginning of period T; Qb stands for the value of the SEP development at the end of period T.
The main SEP development dynamics indicator is described as the result of the development smoothness and intensity factors:

SEP development dynamics quantitative assessment methodology
Practical application of the MDD methodology for quantitative assessment of the SEP development dynamics revealed that this methodology calls for improvement. As it can be Amfiteatru Economic seen in Figure no. 2, the length of one perpendicular in the right triangle in time slot i over the period T is equal to the difference in the values at the beginning and the end of this time slot. The length of the other perpendicular is evaluated based on the duration of period T (in years), is divided by the number years. For example, if T = 10 years, it covers 10 time slots. In this case, length li of the perpendicular is equal to li = 10 : 10 = 1.
In order to improve the existing methodology and not to abandon its principles, it is necessary to clarify the estimation of both the ideal and factual trajectories of the SEP development and calculate the development intensity indicator.
Evaluation of the SEP development ideal trajectory length. Based on MDD methodology, this length is equal to the duration of period T. In essence, a separate case of the SEP development is faced when no increase in the development is recorded during all time slots of period T, i.e. q = qi+1. The indicators of the SEP development show that such cases are practically non-existent because any process functions only when it evolves. Thus, real processes develop with varying intensity.
The structure of the ideal trajectory length estimation for the SEP development over time period T is represented in Figure no. 1 which shows that the length of this trajectory is equal to the length of the diagonal line Qb Qf in the triangle Qb Qf Qb. It is represented in following formula (Ginevičius, et al., 2018): LTthe length of SEP development ideal trajectory.
LT is equal to the sum of the SEP development ideal trajectories lengths in different time slots over period T (Figure no. 1): li is the SEP development ideal trajectory length in i th time slot over period T.
The SEP development value for i th time slot corresponding to the ideal trajectory of the SEP development over the period under consideration is estimated as follows: is calculated by formula: The factual trajectory length of the SEP development over period T is equal to: Estimation of the SEP development dynamics index. With reference to formulas (6) and (10), the index representing the SEP development smoothness over period T can be estimated as follows: here: DT marks the index representing the SEP development smoothness over period T.
Formula (11) shows that the SEP development smoothness value in an ideal situation is equal to 1 regardless of the existing development intensity. Based on the MDD methodology for the quantitative analysis of the dynamics of SEP development, the smoothness indicator should be applied in combination with the development intensity indicator. The MDD methodology proposes to estimate this index based on formula (5). A deeper analysis of its implication, however, shows that the methodology calls for qi Amfiteatru Economic index should be equal to 0. Considering this, the SEP development intensity index should be estimated as follows: Formula (13) indicates that when Qf = Qb, then DI = 0. With growing Q, i.e. the difference Qf  Qb, the value of the SEP development intensity index is also rising.
Formula (5), for the quantitative analysis of the dynamics of SEP development, remains unchanged, only both of its variablesthe development smoothness DT and the development intensity DIare determined in a different way: The economic development analysis in different countries revealed that there exists a rather elastic relationship between the development smoothness and intensity: when intensity is growing, smoothness is decreasing (Ginevičius, et al., 2018). This proposes that formula (5), representing the SEP development dynamics, should incorporate both quantitative and qualitative factors affecting this dynamics. Methods that take into account both the values and significance of the indicators, i.e. multi-criteria assessment methods (Hwang and Yoon, 1981;Hwang and Lin, 1987), are best suited for this purpose. These days multi-criteria assessment methods are applied for quantitative assessment of a wide variety of complex engineeringtechnological (Álvarez, et al., 2017;Juodagalvienė, 2018;Bielinskas, 2018;Binkytė, 2018), socio-economic (Ejdys, et al., 2016;Gedvilaitė, 2018;Oželienė, 2019;Volkov, 2018) and other phenomena and processes. Some of them are less (Hwang and Yoon, 1981;Hwang and Lin, 1987;Zavadskas, et al., 1994), while others are more sophisticated (Balcomb and Curtner, 2000;Saaty, 1980;Vallee and Zielniewicz, 1994;Hwang and Yoon, 1981).
In any case, the philosophy of multi-criteria assessment is embodied in the most common classical SAW (Simple Additive Weighting) method, expressed as follows (MacCrimmon 1968;Hwang and Yoon 1981): here kj marks the value of the multi-criteria assessment by the SAW method estimated for j th variation of a phenomenon under consideration; i is the significance of the i th indicator; i qa normalised value of the i th indicator. Based on formula (14), the SEP development dynamics is quantitatively assessed as follows: here Dthe SEP development dynamics index incorporating the significance of both the development intensity and smoothness; 1the SEP development intensity significance; 2the SEP development smoothness significance.

Analysis of the economic development dynamics of in Cyprus and Romania (2009-2018)
Quantitative analysis methodology for the dynamics of SEP development, which is referred to as MDD-M, will be illustrated by the assessment of the GDP per capita shifts in Cyprus and Romania over the 20092018 period (Jia, et al., 2017;Čiegis, et al., 2010;Chursan, 2013;Babu and Datta, 2015;Bolcarova and Košta, 2015;Lisiński, et al., 2020;Molendowski and Petraškevičius, 2020;Nikonenko, et al., 2020;Radlińska, et al., 2020). The abovementioned countries were selected due to the significant differences in the nature of their economic development observed over the period under consideration (Table no.    Source: compiled by the author with reference to Eurostat, 2020   The  (Table no. 3). For the comparison of GDP development dynamics in both countries, it is necessary to assess the level they have achieved. For this purpose, coefficient Kj will be employed:

Amfiteatru Economic
Kjis the coefficient for the economic development intensity adjustment of in the jth country in relation to the other country; Qfjis the economic development value of the jth country at the end of the analysed period; max f Q is the economic development value of the country which is higher at the end of the analysed period.
For further analysis formulas (12) and (16), are used for the evaluation of the intensity of the economic development in the jth country in relation to the other country: After application of the formula (17) and reassessment of the economic development intensity indicator in the analysed countries, the development dynamics values also changed ( Implemented analysis shows that the dynamics indicator value is more affected by the development intensity rather than the development smoothness.

Conclusions
1. In order to increase the efficiency of correlation-regression analysis, which these days is the most common method of the SEP analysis and fluctuation forecast, both independent, i.e. input, and dependent, i.e. output, variables need to be expressed in their dynamic rather than static condition. For this purpose, their fluctuations over a particular period, i.e. the dynamics of their fluctuations, need to be quantitatively assessed.
2. The main point if the SEP development dynamics quantitative analysis is the difference ratio between the ideal and the factual trajectory lengths of the development. Ideal trajectory length reflects the maximum possible smoothness. The current MDD (Measuring of Dynamics of Development) methodology calls for improvement for several reasons: firstly, it does not fully reflect the real SEP development; also, the factual trajectory length of the SEP development in all cases is compared with the duration of analysed time period T.
3. Based on the proposed methodology, which is named as MDD-M, SEP development factual trajectory length is evaluated based on the length of the diagonal line in the triangle. Perpendicular in this triangle represents the SEP development scale over the analysed period of time, while the other one is represents to the duration of this time period.
4. For the evaluation of the SEP development factual trajectory length the sum of the diagonals in the triangles based on separate time slots inside the analysed whole time period. In order to evaluate the length of a perpendicular inside triangles it is needed to divide the total duration of the analysed time period by the number of separate time slots. In this analysis the length of another perpendicular is evaluated as the difference between the the development factual value at the end of the i th time slot and the ideal trajectory value in this time slot.
5. The more accurate result of quantitative assessment is obtained by considering the significance of both quantitative and qualitative sides of the SEP development, represented by the development intensity and smoothness respectively.
The proposed quantitative assessment methodology, for the analysis of the SEP development dynamics, can be applied not only to raise the adequacy of correlationregression. It can also be applied for analysing the development of various socio-economic processes: assessment of GDP, investment, sectoral economic, social, shadow economy related fluctuations and tendencies, etc.