**3. Methodology**

The process of design of the FA assessment model for rural municipalities started with problem definition, substantiation of the research period, definition of the data, limitations, and sampling.

**Problem and research period.** The problem under the investigation was defined in the form of the following question: *How could the FA level of rural municipalities be assessed?* FA assessment of rural municipalities is important as it leads to solutions of development of economy and social welfare of rural municipalities, sustainable allocation, redistribution and growth of financial resources. It also pinpoints the need for new scientific insights into this economic phenomenon in the areas of the economic, fiscal policy, decentralisation, and regional growth theories.

The studies dedicated to FA assessment of rural municipalities tend to apply the longest assessment period possible. The reason behind this is that the econometric research methods used for assessment of data for a longer period tend to generate more accurate research results.

**Data and limitations.** Any research starts with data collection, gathering and systematisation. FA assessment of rural municipalities required using statistical data for calculation of the revenue and expenditure autonomy indicators. The limitations affecting appropriateness, validity, and correctness of the indicator calculation and determining database selection and data normalisation decisions were identified in the study.

**Sample selection.** The analysis of scientific and regulatory sources suggested clear absence of a definition of "rural municipalities". Scientists and researchers (Kriauˇciunas ¯ 2018; Horlings and Marsden 2014; Normann and Vasström 2012; Žukovskis et al. 2013; Ward and Brown 2009; Atkoˇciunien ¯ e 2008 ˙ ; Vidickiene and Melnikien ˙ e 2008 ˙ ) mostly analyse the definitions of "rural areas", "rural regions", "countryside", and "rural communities". Lithuania does not have any officially recognized classification of regions into rural and urban. The criteria for identification of rural regions remains under the theoretical scrutiny not only in Lithuania, but also worldwide (Copus and Macleod 2006; Mueller et al. 2004;

Kostov and Lingard 2004). The scientific literature analysis has shown that the issue of delineation of urban and rural areas is generally a fairly complex scientific issue.

Hence, the design process for the model of FA assessment of rural municipalities followed the methodology proposed by the Organisation For Economic Co-operation and Development. The methodology employs three-fold classification of municipalities as rural, semi-rural, or urban. Quantitative boundaries were proposed for definition of rural municipalities under the methodology, where:


Based on the above criteria of the quantitative boundaries, the group of rural municipalities could be formed in order to reflect the set of alternatives *A* = (*A*1, *A*2, *A*3, ... *Ai*.... *Am*).

**Model design stages.** The assessment model based on the multi-criteria TOPSIS method was designed for FA assessment of rural municipalities. The following model design stages could be identified:

Stage 1. Selection and calculation of the partial indicators describing FA of rural municipalities.

Stage 2. Assessment of FA level of rural municipalities and formation of the synthetic indicator/index.

#### **Process of stage 1.**

Step 1. The model design process primarily involved identification of the revenue autonomy indicators defining the FA of rural municipalities, the revenue autonomy being one of the distinctive properties of FA of a rural municipality. Hence, the set of revenue autonomy indicators was formed: *R* = (*<sup>r</sup>*1, *r*2, *r*3, ... , *rn*). The revenue indicators assessing FA of rural municipalities were selected according to the following criteria:


Step 2. Direction, i.e., minimization or maximization, was determined for each indicator.

Step 3. The sets of *n* indicator values of rural municipalities, each containing m elements, were created in Excel database (all the calculations were performed using this tool) in accordance with the registration year of the revenue indicator values for the FA of the rural municipalities (2009–2019). Decision matrices were formed using the data sets (Simanaviˇciene 2011 ˙ ):

$$P = \begin{bmatrix} r\_{11} & r\_{12} \ \cdots & r\_{1n} \\ r\_{21} & r\_{12} \ \cdots & r\_{2n} \\ r\_{m1} & r\_{m2} \ \cdots & r\_{mn} \end{bmatrix} \tag{1}$$

Step 4. The objective significance of the indicators was then determined using the entropy method. The entropy method is applicable in the cases where maximization is required for all the indicators of the decision matrix. In case the decision matrix contained the indicators that required minimization, they were rearranged using the following formula (Simanaviˇciene 2011 ˙ ):

$$
\overline{r\_{ij}} = \frac{1}{r\_{ij}} \tag{2}
$$

Values of the indicators that required maximization remained unchanged:

$$
\overline{r\_{ij}} = r\_{ij\prime}\text{ where }i = \overline{1, m}; \; j = \overline{1, n}.\tag{3}
$$

The rearranged decision matrix was formed in the following way:

$$\overline{\mathbb{R}} = \begin{bmatrix} \overline{r\_{\overline{i}\overline{j}}} \end{bmatrix}, \text{ ( $i = \overline{1, m}$ ;  $j = \overline{1, n}$ )}. \tag{4}$$

Step 5. It should be noted that assessment of multi-criteria phenomena using the TOPSIS method employ the indicators that have different units. Hence, prior to any calculations (alternative ranking procedure), the data must be transformed to align the dimensions of the variables. Linear, non-linear, and vector transformations may be used for normalization of the indicators. The possibilities for normalization are very diverse, and the rules of six formulas can be applied (Simanaviˇciene 2016 ˙ ).

The set of revenue indicators defining the FA of rural municipalities included highly asymmetric or outlying properties caused by differences in the units used. Consequently, the decision matrix was normalized (to make sure that all of its elements were dimensionless values) by applying two methods. For the revenue indicators determined under the objective significance principles, normalization was performed using the linear normalization formula (Simanaviˇciene 2011 ˙ ; Gineviˇcius and Podvezko 2008):

$$p\_{ij} = \frac{\overline{r\_{ij}}}{\sum\_{i=1}^{m} \overline{r}\_{ij}} \; , \; (i = \overline{1, m}; \; j = \overline{1, n}) . \tag{5}$$

The researchers (Simanaviˇciene 2011 ˙ , 2016; Gineviˇcius and Podvezko 2008; Podvezko 2008) often propose applying vector normalization using the following formula:

$$
\overrightarrow{p\_{ij}} = \frac{r\_{ij}}{\sqrt{\sum\_{i=1}^{m} r\_{ij}^2}},
\tag{6}
$$

The normalization method generally depends on the circumstances of the research and possibilities for minimization or maximization of the indicators. Hence, linear normalization was performed primarily in order to empirically verify the applicability of the FA assessment model to rural municipalities. The task was then solved by vector normalization after the research results had been obtained and assessed. Afterwards, comparison of the empirical study results was performed.

Following the normalization, the matrix of normalized values of the revenue indicators was develope *P* = *pij* (Simanaviˇciene 2011 ˙ ):

$$\overline{P} = \begin{bmatrix} p\_{11} & p\_{12} \cdots & p\_{1u} \\ p\_{21} & p\_{12} \cdots & p\_{2u} \\ p\_{m1} & p\_{m2} \cdots & p\_{mn} \end{bmatrix} \tag{7}$$

Step 6. Entropy level *Ej* of each revenue indicator was determined using the following formula (Simanaviˇciene 2011 ˙ ):

$$E\_j = -k \cdot \sum\_{i=1}^{m} p\_{ij} \ln p\_{ij} \quad (i = \overline{1, m}; \ j = \overline{1, n} \text{ )}, \text{ where } k = \frac{1}{\ln m} \tag{8}$$

The value of entropy varied within the interval [0, 1]; hence, 0 ≤ *Ej* ≤ 1, the variation level of *j*-the indicator was determined by calculating the revenue indicators:

$$d\_{\dot{l}} = 1 - E\_{\dot{l}'} \ (\dot{j} = \overline{1, n}). \tag{9}$$

The study did not employ any subjective (expert's) assessment of the indicators, and the decision was made to consider all the FA indicators of rural municipalities as equally important. Hence, objective significance of the revenue indicators was determined using the following formula (Simanaviˇciene 2011 ˙ ):

$$q\_{\circ} = \frac{d\_{\circ}}{\sum\_{j=1}^{n} d\_{j}} \; , \; (j = \overline{1, n}), \tag{10}$$

where: *qj*—the values of objective significance of indicators.

The calculated values of objective significance of the revenue enabled the authors to determine the significance and importance of the indicator in the empirical study. Researchers usually sugges<sup>t</sup> eliminating the indicators that are insignificant for the research upon consideration of significance of the respective indicator.

It should be noted that, where individual FA indicators are analyzed, only singledimension profile research for the type analyzed may be performed and may cause difficulties in formulation of general conclusions (Głowicka-Wołoszyn and Satoła 2018). Hence, during the second stage of the model design, a synthetic indicator/index for FA assessment of rural municipalities was developed using the partial indicators by applying the TOPSIS method (Hwang and Yoon 1981).

#### **Process of stage 2.**

Step 1. Distance of each rural municipality to the positive and negative ideal decision was calculated. Under the TOPSIS method, the coordinates of the positive, i.e., ideally best (A+), and negative (A−) ideal points helped determine closeness of each rural municipality to the development model (A+) and opposite negative model (A−).

Positive, ideally best, and negative ideal points were calculated (see Formulas (12) and (13)).

Positive, ideally best point was calculated using the formula (Hwang and Yoon 1981; Simanaviˇciene 2011 ˙ ):

$$A^{+} = \left\{ \left( \max\_{i} v\_{ij} \, \middle| \, j \in J \right), \left( \min\_{i} v\_{ij} \, \middle| \, j \in J' \right) \, \middle| \, i = \overline{1, m} \right\} = \left\{ a\_1^{+}, a\_2^{+}, \dots, a\_n^{+} \right\},\tag{11}$$

where: *j*—set of indices of the indicators with higher values as a more preferable option; *j*'—set of indices of the indicators with lower values as a more preferable option. Negative ideal variant was determined using the following formula (Simanaviˇciene 2011 ˙ ):

$$A^{-} = \left\{ \left( \min\_{i} v\_{ij} \, \middle| \, j \in J \right), \left( \max\_{i} v\_{ij} \, \middle| \, j \in J' \right) \, \middle| \, i = \overline{1, m} \right\} = \left\{ a\_1^{-}, a\_2^{-}, \dots, a\_n^{-} \right\},\tag{12}$$

Step 2. Following the calculation of the positive, ideally best, and negative ideal variant, it became possible to determine the closeness of each rural municipality to the positive ideal solution of development ( *A*<sup>+</sup>) and negative ideal solution ( *A*−) in the *n*-dimensional Euclidean space under the formula (Hwang and Yoon 1981; Simanaviˇciene 2011 ˙ ):

$$L\_i^+ = \sqrt{\sum\_{j=1}^n \left(v\_{ij} - a\_j^+\right)^2}, \ (i = \overline{1, m}), \tag{13}$$

$$L\_i^- = \sqrt{\sum\_{j=1}^n \left(v\_{ij} - a\_j^-\right)^2}, (i = \overline{1, m}). \tag{14}$$

Step 3. The final step of the TOPSIS method (Hwang and Yoon 1981) involved determination of the value of synthetic indicator/index of FA of each rural municipality. The index was mathematically expressed by the formula (Hwang and Yoon 1981; Gineviˇcius and Podvezko 2008; Simanaviˇciene 2011 ˙ ):

$$K\_i = \frac{L\_i^-}{L\_i^+ + L\_i^-}, \text{ (\$i = \overline{1, m\_\prime}\$), where \$K\_i \in [0, 1]. \tag{15}$$

where: *Ki*—value of the *i*-ths alternative generated by assessment under the TOPSIS method, with the highest *Ki* value corresponding to the best alternative.

*L*<sup>+</sup> *j* —total closeness of the *i*-ths alternative to the ideally best variant;

*L*− *j*—total closeness of the *i*-ths alternative to the ideally worst variant.

Step 4. The determined synthetic indicator/index values were rearranged in a linear manner and became the basis for grouping of the municipalities into typological classes by

the FA level (Satoła et al. 2019; Łuczak et al. 2018b). The typological classes/clusters of rural municipalities were determined in view of the mean indicator value ( *M*) and standard deviation (S) (see Table 3).

**Table 3.** Classification of rural municipalities into classes/clusters by financial autonomy level.


Source: made by the authors according to (Satoła et al. 2019).

In general, the following components could be identified in the methodology for design of the FA assessment model for rural municipalities:


Depending on the specifics of the research problem and possibilities for application of the multi-criteria TOPSIS method, the model for FA assessment of rural municipalities could be summarized schematically (see Figure 2).

**Figure 2.** Model for FA assessment of rural municipalities. Source: made by the authors.

The decomposition of the model into main components does not necessarily imply that the problem indicators will not be revised or the problem solution part will not be revisited after definition of the problem and the related variables (indicators) or before the decision making part. Analysis of the problem could actually be repeated multiple times using an expanded the set of alternatives, including new variables, revising the research stages and limitations, verifying the reliability of application of the methods of descriptive statistics, until the most appropriate solution is reached.

Application of the designed model was demonstrated further in the present research by performing the FA assessment of rural municipalities in the regions of Lithuania.

#### **4. Results and Discussion**

Upon Lithuania's accession to the EU, particular focus was placed on rural areas and rural municipalities, representatation of their interests, and their financial autonomy. The issues of rural areas have been emphasized in the EU's and national documents, the ideas expressed and assessments made by policy makers and economists. This particularly relates to the issue of low financial autonomy thereof. This topic is noticeably becoming increasingly relevant on the national level, as rural municipalities account for the two thirds of Lithuania's territory and 60% of all the municipalities.

During the empirical study, a group of 36 rural municipalities was formed from Lithuania's 60 municipalities. However, in the present pilot study, the rural municipalities of Panevežys and Kaunas were chosen to assess their FA levels. The set of possible ˙ alternatives consisted of 5 rural municipalities of Panevežys region (Biržai— ˙ *A*1, Kupiškis— *A*2, Panevežys— ˙ *A*3, Pasvalys—*A*4, Rokiškis—*A*5 district municipalities) and 4 Kaunas region municipalities (Kaišiadorys—*A*6, Kaunas—*A*7, Prienai—*A*8, Raseiniai—*A*9 district municipalities). The resulting set of alternatives: *A* = ( *A*1, *A*2, *A*3, *A*4, *A*5, *A*6, *A*7, *A*8, *A*9).

The choice of rural municipalities of the specific regions was prompted by certain economic and social changes that were challenging for the majority of Lithuania's regions. Nonetheless, distinctive changes were observed in the chosen regions in relation to their demographic and socioeconomic potential, and even greater differences between individual municipalities were noticed.

Over the preceding eleven years, the population of Panevežys region had decreased ˙ by almost 25%, while the birth rate had decreased by 22% (Department of Statistics of the Republic of Lithuania 2020). This was one of the greatest drops among Lithuania's counties. The demographic changes affected the supply of labour force in the region, posed risks to the economic development of the region, impaired region's attractiveness to foreign investments and, at the same time, financial development of the rural municipalities. In Panevežys region, rural municipalities comprised the major part of the territory (5 of 6). ˙

The modern character of Kaunas region was provided by the advanced economic development that assured high quality of life and rapid modernisation of the countryside with particular focus on the harmony between the human and the environment. This guaranteed sustainable development of the region (The Regional Development Department under the Ministry of the Interior of the Republic of Lithuania 2020). For example, over the preceding 11 years, population increase by 11.7% and an increase in business concentration, which was considerably lower in other rural municipalities, were observed in the rural municipality of Kaunas district [the Department of Statistics of the Republic of Lithuania].

The present research involved the data analysis and assessment covering the 11-year period, i.e., 2009 to 2019. The period specified is associated with the recently growing interest in not only local economic growth and regional development, but also improvement of the FA of municipalities. Extension of the period would be considered following the assessment of the results of the pilot study.

The FA of the alternatives chosen in the empirical study was defined from the perspective of revenue autonomy; hence, nine revenue indicators were primarily selected on the basis of specific criteria (see Table 4). In relation to maximization and minimization of the revenue indicators, it was assumed that, in the case considered, indicator *R*8—state

financial intervention indicator, indicator *R*9—transfers per capita, EUR had a minimizing character (a dampening effect on the FA), and all other indicators had a maximizing character (a driving effect on the FA). The lowest value of the minimizing indicator was its best value. The set of indicators was formed: *R* = (*<sup>r</sup>*1, *r*2, *r*3, *r*4, *r*5, *r*6, *r*7, *r*8, *r*9).


**Table 4.** Revenue indicators for financial autonomy measurement of rural municipalities and description of the indicators.

> Source: made by the authors.

The study involved identification of the limitations affecting appropriateness, validity, and correctness of the indicator calculation, and determining the decisions on database selection.

1. Pre-2014 data are presented in the former national currency litas, while post-2014 data—in euros. The data reflect the municipal tax and non-tax revenues and grants. The data are published in the statistical databases of the Ministry of Finance of the Republic of Lithuania (2020) and State Tax Inspectorate under the Ministry of Finance of the Republic of Lithuania (2020) (hereinafter—the STI). Due to the difference in the currency, the data were recalculated to be presented using a single currency. This enabled further comparative analysis of the indicators. Nevertheless, certain calculation inaccuracies could have appeared as a result of the recalculation.

2. The databases (reports) by the Ministry of Finance of the Republic of Lithuania (2020) contained predicted rather than actual municipal tax and revenue data, which also could have led to certain calculation inaccuracies. This could have also influenced objective assessment of the FA of the municipalities;

3. The predicted and actual municipal revenue data are provided in the reports available in the archive databases of the STI. Nevertheless, the greatest challenge is presented by the presentation of the data on the personal income tax (hereinafter—the PIT). The latter is determined by the procedure of PIT allocation to municipalities governed by the Law on the Approval of Financial Indicators of the State Budget and Municipal Budgets. Pursuant to the procedure:

3.1. before 2017, the municipal budget revenues from PIT consisted of the transfers of tax instalments from the STI and grants from the state budget;

3.2. from 2017, the municipal budget revenues from PIT consisted of the transfers of tax instalments from the STI in accordance with the tax allocation share (%) established by the law, including the grants from the state budget and excluding the amounts transferred into the state budget.

Considering the above limitation determining the level of accessibility, validity and objectivity of the empirical research data, it was decided to use the statistical data available in the databases of the Department of Statistics of the Republic of Lithuania (2020). Actual data of the municipal revenues (taxes) were presented in the databases of the Department of Statistics of the Republic of Lithuania and corresponded to the data presented in the reports on implementation of the municipal budget. Moreover, the data for all the years of the research period were accurately recalculated/expressed in euros, and the PIT included all the final transfers from the STI.

Descriptive characteristics of statistics revealed the tendencies of financial autonomy in rural municipalities of two regions of Lithuania during the analyzed 11-year period from 2009 to 2019 (see Tables 5 and 6).

**Table 5.** Descriptive statistics of indicators describing the level of financial autonomy in rural municipalities of Panevežys ˙ region, 2009–2019.


Source: own calculations based on Department of Statistics of the Republic of Lithuania (2020).

**Table 6.** Descriptive statistics of indicators describing the level of financial autonomy in rural municipalities of the Kaunas region, 2009–2019.


Source: own calculations based on Department of Statistics of the Republic of Lithuania (2020).

The change of PIT per capita differed by 2.67 times (Panevežys region) and 2.57 ˙ (Kaunas region) between the municipalities. This suggests that allocation of the PIT could have been different for each rural municipality and did not encourage the less affluent municipalities to undertake the measures to increase it. This may have been due to the fact that competition for the tax is a slow acting instrument.

The share of own revenue per capita showed that the difference between the less affluent and affluent municipalities was 2.9-fold (Panevežys region) and 2.8-fold (Kaunas ˙ region). On the other hand, high value of the indicator (EUR 754.66) was registered in only one rural municipality of Panevežys region, while the median of own revenue per ˙ capita was EUR 360 (in rural municipalities of Panevežys region) and EUR 365 (in rural ˙ municipalities of Kaunas region).

The share of own revenue in the total revenue (1st degree financial autonomy indicator, %) had an upward trend, increasing by 46 percentage points on average in the rural municipalities of Panevezys region and by 52 percentage points in the rural municipalities of Kaunas region.

The results support the importance of the transfers into the revenue structure of rural municipalities and, at the same time, high dependence of the local governments on the state budget, signalling unfavorable conditions for the development initiatives, multifunctional growth, or progress in local self-regulation.

Hence, the research results have revealed that the redistribution function of the fiscal policy in Lithuania was defective and did not promote financial autonomy and economic well-being of municipalities in the analysis period. This was due to the fact that support was granted to the weaker municipalities, and they received larger amounts of the redistributed PIT. If not for the redistributed PIT, the municipalities making active efforts to attract investors and help create jobs would have retained more funds.

To group the rural municipalities of the selected regions into classes by FA level, the multi-criteria decision-making task was solved using the TOPSIS method.

The sets of values of each indicator, each containing 11 elements, were formed in the Excel database according to the years of the respective values of the revenue indicators (2009–2019). Eleven solution matrices were formed on the basis of the data for each selected alternative, i.e., the respective rural municipality. The revenue indicators were expressed in different units, i.e., either euros or %, and were primarily subjected to normalization. As a result, the indicator values became dimensionless. Given that the revenue indicators had been determined under the objective significance principles, normalization of the indicators was performed on the basis of the linear method. Values of the normalized indicators were further used in the subsequent FA assessment of the rural municipalities.

Objective significance of the revenue indicators was determined using the entropy approach involving assessment of the level of variation and weight of each indicator (see Table 7).

Assessment of the revenue indicators for the FA of rural municipalities of Panevežys ˙ and Kaunas regions revealed the fluctuation in their variation level. Fluctuating and changing variation level of the FA indicators of individual rural municipalities was observed in Panevežys and Kaunas regions in the assessment period. ˙

Upon calculation of the objective significance values of the revenue indicators of rural municipalities in the regions analyzed, the indicators with the greatest weights were identified: non-tax revenues per capita, EUR. (*r*7), PIT per capita, EUR (*r*1), own revenues per capita, EUR (*r*4), indicator of the level of own revenues, % (*r*5), and fiscal wealth index or tax revenues per capita, EUR (*r*2). The result showed that the indicators of the rural municipalities became more significant in terms of their variation in the assessment period. However, insignificant variation was also observed for certain indicators. The indicators of the first-degree FA or the share of own revenues in the total revenues, % (*r*6) became particularly distinctive for all the rural municipalities analyzed. Hence, it could be concluded that the share of own revenues in the overall revenue structure of the municipalities varied insignificantly, which also supported the minor changes in the

FA levels of the municipalities. It could therefore be claimed that the FA of the rural municipalities analyzed remained medium low.

**Table 7.** Level of variation and weight of the revenue indicators of the financial autonomy of rural municipalities, 2009–2019.


The weights of significance of the FA indicators of the rural municipalities in Panevežys ˙ and Kaunas regions (see Table 8) were used further for the calculations of stage II of the empirical study using the TOPSIS method. The values of synthetic indicator/index of the FA of rural municipalities in the assessment period are presented in Table 8.


**Table 8.** Synthetic indicators of the FA level of rural municipalities, 2009–2019.

Source: own calculations.

The results of assessment of the FA level of rural municipalities using the TOPSIS method suggested relative closeness of the "best" rural municipalities in Panevežys and ˙ Kaunas regions to the "ideally worst" variant, which remained constant over the years. For example, the first alternative—Biržai district rural municipality of Panevežys region— ˙ maintained the first position in terms of the closeness to the "negatively ideal" variant in the assessment period 2009–2019. The same result was observed for Kaunas district

rural municipality of Kaunas region, which also maintained the first position in the period 2009–2019. However, the relative closeness of all other rural municipalities to the "ideally worst" variant fluctuated over the years (see Figure 3).

**Figure 3.** Variation of the priority of rural municipalities by the indicator of the level of financial autonomy, 2009–2019. Source: made by the authors.

The figure shows the change of the priority of the rural municipalities over the years. However, Table 8 and Figure 3 do not sugges<sup>t</sup> which of the alternatives, i.e., rural municipalities, was the top alternative in terms of the FA level. To obtain a measurable result, the mean, median, minimum and maximum rationality values of the FA level of rural municipalities were calculated (see Figure 4).

**Figure 4.** Assessment of the FA level of rural municipalities. Source: made by the authors.

The priority order of the alternatives, i.e., rural municipalities, by mean values of the FA level was formed: *A*7 > *A*1 > *A*4 > *A*6 > *A*5 > *A*2 > *A*9 > *A*3 > *A*8.

The last step in the empirical study involved grouping of the rural municipalities of the selected regions into typological classes by the mean values of the synthetic indicators/indices of their FA levels. The results calculated using the TOPSIS method and the descriptive statistics methods of the mean and standard deviation were used as the basis for identification of the 4 types of the FA levels of rural municipalities in the selected regions. 4 typological classes of rural municipalities were identified in accordance with the FA levels (high, medium high, medium low, and low) based on Table 3. The rural municipalities of the selected Panevežys and Kaunas regions fell into the typological class ˙ of medium low level by their FA level (see Table 9).


**Table 9.** Classification of the rural municipalities by the financial autonomy level \*.

\* Values of the FA level of rural municipalities are presented as the respective mean values of the last 3 years (2017–2019). Source: made by the authors.

> Following the multi-criteria assessment of the FA of rural municipalities using the TOPSIS method, the mean values of financial indicators were then calculated and compared within the identified classes by regions. The article presents the indicators of the rural municipalities of the analyze regions which varied the most significantly in the assessment period (see Figure 5). Comparison of the indicators describing the financial autonomy of rural municipalities of the two selected regions and their mean values showed that the situation of the financial condition of rural municipalities in Panevežys region was better ˙ than that of the rural municipalities in Kaunas region.

**Figure 5.** Indicators of FA of the rural municipalities which varied the most significantly, 2009–2019. Mean values of the FA indicators of the rural municipalities which varied the most significantly.

The research results have demonstrated the homogeneity of the rural municipalities in relation to the FA level. On one hand, the empirical research results have pinpointed the issue of "convenient dependence" of the rural municipalities in the analyzed regions on the centralised allocation. On the other hand, the lack of the incentives for them to make use of the capacities and create sustainable, stable economic and social prospects has become evident. In individual rural municipalities, the State intervention ratio (%) of public intervention varied greatly. In the rural municipalities of Panevežys region, transfers ˙ from the state budget (grants) accounted from 36% to 62%, and in Kaunas region—from 36% to 60% in the total income of the respective municipalities. The PIT as the main revenue of municipalities was also redistributed. The PIT accounted for 40.6% of the total income in the rural municipalities of Panevežys region, and for 41.8% in the rural ˙ municipalities of Kaunas region (see Tables 7 and 8). The data show high dependence of the municipalities on centralized financial management, which is regulated by legal acts enabling municipalities to refrain from being financially active and autonomy.

The changing legal base causes an increase only in the number of the state and allocated functions that continue to be under the influence of the state-level authorities, and the autonomous competence of the municipalities is not expanded. It should be noted that Lithuanian legal acts do not establish a definition of the concept of "own revenues". Therefore, the questions arise as to which tax and non-tax revenues are the ownership of the municipality, and how the indicators of own revenues should be assessed. Even one of the key sources of municipal revenues, the PIT, collected within the municipalities, is subject to centralized redistribution. The municipalities have limited capacity to collect local taxes: the revenues from the local taxes make just up to 10% of the total municipal revenues. On one hand, this obviously shows the reluctance of the Lithuanian state authorities to abandon their influence in certain activity areas and increase the financial autonomy of the municipalities. On the other hand, the municipalities supported by the central governmen<sup>t</sup> eventually become passive and make little use of own resources and potential in terms of improvement of own financial autonomy. This, therefore, raises the issue of municipalities' "convenient dependence" on centralized allocation. The conducted empirical study of financial autonomy assessment of the rural municipalities also showed the medium low level of financial autonomy. Hence, there is currently the need in the country to analyze the financial autonomy of the municipalities, assess the situation, and explore the possibilities for improvement.

It could be claimed that the model used in the present empirical study is reliable in various aspects. FA assessment of rural municipality using the multi-criteria TOPSIS method enabled the authors to design a single summarizing indicator of financial autonomy of rural municipalities, assess the FA level of rural municipalities of the selected regions, and form the typological classes. It should be noted that limitations of the empirical research data, methods of verification and assessment of the FA indicators, sensitivity of the TOPSIS method towards the normalization rules applied may considerably affect the objectivity of the assessment.
