The agricultural cooperative is an important institution as it offers benefits not only to producers, but also to workers and rural communities in terms of employment in many countries, including Greece. Agricultural cooperatives, therefore, can perform various functions in market economies based on cooperative values ​​and principles that are rarely addressed in the financial literature. In essence, this analysis reflects the need for the size of the business activity carried out by agricultural cooperatives to be measured [3, 6].

This is a useful starting point to identify the unique contributions of cooperatives in relation to other forms of business organization. To determine how these “deeper effects” can be quantified, a number of international publications have provided important insights into how the contribution of agricultural cooperatives to the local and national economy can be reliably measured [13].

Among other things, the different functions of cooperatives are supported by other external market players and serve as vehicles for social innovation, support social entrepreneurship, to promote ethical business practices and to assist in growth [14]. While the economic literature has focused mainly on the structure of ownership, operation and control as sources of difference in agricultural cooperatives, it is argued that this focus presents an incomplete picture. Principles of cooperation can provide additional knowledge to address issues in areas with low labor mobility, prevailing market failures, oligopoly markets and labor-intensive industries, where cooperatives could be an effective business model. They can also provide information on the strategies and survival in the global markets of successful cooperatives and can ultimately contribute to a country's economic development [15]. Therefore, the focus and purpose of this study is to try to assess the overall financial contribution of agricultural cooperatives to the rural development of the country and, consequently, their contribution to the national economy. In addition, analysis of the financial contribution of agricultural cooperatives enables understanding of the direct activity of the cooperative sector, as well as the value of financial ties with other businesses, households, and the overall economy of the country.

The applied methodologies were evaluated on a case-by-case basis over time and classified in groups based on the method for each case. The most appropriate and common methodologies for measuring the contribution of a business sector, such as cooperatives, in the local or national economy, include:

(a) The “enumeration” approach. The “head-count” approach starts by recording and estimating the relative size of a sector by simply inventorying the assets held, the amount of capital investment, revenue and profits generated, and wages and dividends paid, among other indicators [15]. The advantage of this approach is the limited amount of information required in its computational simplicity. Conversely, it does not fully provide a measure of economic impact, i.e. the results are impossible to generalize as the method does not capture the “multiplier effect” nor does it produce indirect and induced results. In addition, it is a static measurement, recording the impact of a sector at a single point in time.

(b) The input-output analysis. In brief, an input-output (I-O) model includes a matrix that describes, in value, the sales and purchases of goods and services between all sectors of the economy over a given period. The columns in the table represent the market sectors in economy or demand, while the rows represent the sales or supply sectors. For each financial sector, total sales must be equal to total markets [16]. It should be noted that the input-output model presents a snapshot of the economy which details the sales and purchases of goods and services between all sectors of the economy for a certain period within a conceptual framework derived from economic theory. The algebraic manipulation of the empirical I-O model, that is, the inversion of the matrix, enables the effects of the change in demand on the products of a sector throughout the economy to be determined. Impacts are calculated on the basis of revenue from the sale of produce, the number of jobs created, wages and benefits paid to employees, the total money spent on other variable inputs, and payments to cooperative farmers. This economic activity generates additional income and there is an increase in demand for agricultural products, i.e. food. To meet this new, higher level of demand, producers must increase the production of agricultural products, which means that they must purchase additional supplies and means of production, actions that require additional professional services such as agricultural services and additional work. Therefore, these sectors' involvement increases their production and corresponding inputs to meet the new level of demand. That is to say, increased production of agricultural products results in increased demand, and resonates in the economy as a whole, thus, the multiplier effect. Besides the multiplier estimates, the input-output analysis calculates for the direct, indirect and induced effects of the change in economic activity and the total economic impact is the sum of all effects. These direct, indirect and induced outcomes are defined as follows: The direct results are due to the actions of a company, and in this case to agricultural cooperatives, as a result of the change in final demand. The indirect effects are created, in the regional economy studied by the markets, by the company to face the change in the final demand.

The advantages of the input-output model are the limited data requirements and the relatively simple application and presentation of the results. It also facilitates the comparability of results between sectors and countries. Its main disadvantage is the assumption that the input supply is completely elastic and infinite [11, 14, 17].

(a) The social accounting matrix approach. The Social Accounting Matrix (SAM) models work in the same basic way as the input-output models, i.e. with the same set of assumptions and solution method. The important difference is that they do not focus on productive activities but describe the structure of an economy in terms of the relationships between production, income distribution, consumption of goods and services, savings and investment, and trade [18].

Thus, a SAM model is a more complete database than the trading matrix of an I-O model. Transactions recorded in SAM are not limited to buying or selling goods and services (as in model I-O) but can incorporate any type of transaction. This includes transactions during the production process, such as the purchase of intermediate goods and the recruitment of agents. It also includes current transactions with institutions (households, businesses, and government), such as inter-institutional transfers and the payment of various taxes, and additional capital account transactions of institutions, such as savings and investments. Finally, it can include any international transaction, such as foreign direct investment and foreign trade [19].

The main feature of the SAM model is its focus on the distributive aspects, for example, the estimated effects in a SAM model are broken down into fractions with excellent analytics. Thus, SAM models are better adapted when special attention is paid to economic growth instead of simple economic growth. The approach has mainly been used by academics to analyze the economic impact of tourism. Since it works with the same basic case set as the I-O models, the SAM method can be criticized for many of the same reasons as the I-O. That is, the SAM approach also uses fixed productivity ratios, is static, and does not consider the behaviors and responses of producers and consumers to price changes [20, 11].

(a) The computational model of general equilibrium. The Computable General Equilibrium (CGE) computational model includes not only cross-sectoral links but also models for purchases of goods and services and factors that influence markets, recognizes resource constraints, shapes consumer spending, and allows for government spending and taxation. More specifically, in a general equilibrium computational model (CGE), each transaction flow in the social accounting matrix (SAM) is divided into two components, namely price and quantity, which may be adjusted according to the growth of the economic activity of the examined sector.

From a technical point of view, a general equilibrium model (CGE) consists of a system of (a) simultaneous equations, that is, supply and demand equations describing the behavior of economic agents; and (b) macroeconomic constraints, that is, macroeconomic variables and balances, such as investments and savings, and payments. CGE models can be static (timeless) or dynamic (explicitly looking at time and time-related adjustments) and solved by equilibrium calculation, that is, equilibrium is achieved when a price operator is found that “clears” all markets, while satisfying all macroeconomic constraints. Despite their long-term use in economic policy analysis in general and their growing popularity in regional policy analysis, computational general equilibrium (CGE) models have not yet become the dominant approach to regional economic development policy analysis. The methodological improvements that are likely to lead to the wider use of CGE models in the practice of economic development are empirical evidence and the capability to record the relevant policy elements and the structure of the study area [21]. A typical CGE model will measure the overall change in economic output through its impact on GDP, while also providing output for individual sectors. Impact on key variables such as employment or public revenue will also be part of the model output. The most obvious advantage of the general equilibrium computational model (CGE) is the more realistic assumptions on which it is based in that it represents the whole economy and considers resource constraints and the reactions of producers and consumers to price changes. CGE models provide information on the economic impact of specific activities occurring in a country, and which of those positively or negatively affect the economy as a whole. The benefits of additional production do not have to be the same as the value of production.

Of both the CGE and I-O models, the I-O model ignores the interactions between industries, thus maximizing the impact on gross government product and labor. Meanwhile, CGE modeling also allows different results to be distinguished in other areas. However, given the specific aspects of the activities, CGE models need to be adapted to take account of this [6, 17, 22-25].

The description of the above methods and the presentation of their respective data requirements, as well as the combination of the data with the calculation method and how well the model reflects the reality, emphasizes that the input-output model (Input-Output) is the most common tool for financial impact analysis in general, but also for measuring the financial impact of cooperatives. It also seems that all methods that measure the financial contribution of cooperatives, when treated like other business structures, cannot assess the unique value of cooperatives for their members and communities, such as the compensatory power in the market and goods and missing services. Neither do they take into account the contribution of cooperatives to the long-term development and resilience of the communities in which they operate, which is perhaps the most important measure of their financial impact. Therefore, a further analysis should be carried out if an accurate estimate of the total contribution of cooperatives in their communities is to be achieved. Most importantly, there is the possibility of extending existing methodologies to ascertain the contribution of cooperatives in improving market power, the participation of some goods and services that have been omitted and the contribution to local economic stability to understand the widest possible and real economic impact of cooperatives [11, 21, 22, 26, 27, 29].

The input-output analysis method measures the economic impact that businesses have on their local economies. It is a model of the economy and is applied in a defined area such as a prefecture or a country and shows how it is possible to determine the interactions and economic behavior in said economic area within a particular sector. It measures the flows of financial transactions of the sector in view of the overall economy. The model predicts the effect of a certain change in production on final demand in the economy. In this case, it concerns the change of production by the various companies belonging to the cooperatives. The effects of this change can be described as direct, indirect and induced. These direct, indirect and induced effects are defined as follows [29, 30]:

(a) The immediate results are due to the actions of the cooperative enterprise as a result of the change in the supply and consequently in the final demand.

(b) The indirect effects are created in the regional economy under study, by the markets and by the cooperative enterprise to face the change in the final demand. An example would be the inputs purchased by the company in response to the change in production to meet the new final demand.

(b) The induced effects are changes in local household expenditure due to changes in income (mainly wages) as a result of the direct and indirect effects of changes in demand.

These effects are expressed in the form of multipliers. The multiplier summarizes the total impact or contribution that can be expected from the change in a given economic activity. For example, the entry of a new production unit or an increase in exports by a local company creates economic changes that can have additional effects on the overall economy. That is, multipliers measure the economic impact of new production or new exports, including related activities.

Multipliers are measures by which a total final change of size to the initial state can be evaluated. Four multipliers commonly used to estimate the effects of economic change, such as the increase in output resulting from the increase in sales and demand, typically referred to as final demand in multiplier analysis, are:

(1) Production. The production multiplier estimates the total change in local sales or in a country. The multiplication of the sales increase in the case of the export sector with the production multiplier gives an estimate of the total sales increase for the study area, including the export sales. The output multiplier is used to evaluate the interdependence of sectors in the local or national economy.

(2) Employment. Communities often want to know the number of jobs that will be created as a result of a new economic activity. The employment multiplier measures the total change in employment resulting from the initial change in employment of a manufacturing and exporting sector. The additional employment in the new production output for export multiplied by the employment multiplier for the production unit gives an estimate of the total number of new jobs created in the study area (i.e. prefecture, region or state).

(3) Income. The income multiplier measures the total increase in income resulting in the local economy from an increase of 1 euro to the income received by the workers in the export unit. Multiplying the change in initial income by the income multiplier for the production unit provides an estimate of the income increase for all individuals in the study area resulting from the initial development of a production unit.

(4) Value-Added. The value-added multiplier estimates the added value of a product or service as a result of the economic activity. Value-added includes employee compensation, tax on production and imports, and property and other property income. The sum of the value added of all businesses in a situation is equivalent to Gross Domestic Product [16, 25, 26, 28, 29, 30].

This analysis makes various assumptions about the economy and its reaction to the changes applied. The assumptions that apply to the model include:

• The supply of labor and other resources is sufficient and does not change prices.
• The percentage of imports in relation to the economy as a whole will not change with demand.
• The consumption of households will change depending on their income.
  • -Production technology is known and stable, resulting in continuous production factors.
• There are no economies of scale.
• There is no substitution of inputs due to price changes.

The analysis of the model for application in this study is the Input-Output system (I-O) and the Social Accounting Matrix (SAM). A system of linear equations is used to identify the interdependence of enterprises, which in this case are the agricultural cooperatives in the country's economy. SAM (Social Accounting Models) analysis is an extension of I-O that includes institutions, households, governments, investments and trade. This accounting system oversees all financial transactions in a public economy and is considered essentially a complement to the input-output model [11].

Based on Wassily Leontief’s general theory of production, which stems from the idea of ​​industrial interdependence in an economy, input-output tables were created, which formed the basis for Input-Output analysis [9]. The most important element of the model is the production sectors. That is, cooperatives produce with the means at their disposal, creating financial transactions by selling and buying goods and services among themselves during the production process. Thus, an intermediate demand may arise at one stage if the exchange of output from one sector is used as input from another. Total production demand includes consumption in local and state communities and consumption of products produced within the region by cooperative industries, households and governments outside the region. The collection of goods and transactions of services at all levels and between all these factors are recorded in an entry-exit table. The resulting table represents the total exchanges in a given economy [6, 13].

Most studies [15, 17, 30-32], mainly use the method “Input-output analysis” to estimate the added value of cooperatives in the economy.

The model also estimates the impact of a given change in output on a final demand within the economy. It can be valued at the cooperative sector level or for a specific cooperative [33]. The various links and effects of a change can be direct, indirect, or induced. Input-output analysis, first developed by W. Leontief [34], evaluates the various transactions that occur in the economy and uses them as data to assess the economic impact of any changes in the economy. The various studies carried out with the input-output model would show the direct and indirect effects, which industries benefit most such as the number of jobs created, wages, estimates of indirect taxes and subsidies created. Thus, the input-output model is based on the relationships between different economic sectors using revenues, salaries, taxes and other expenses.

On the one hand, the previous analysis showed the importance of the different effects, and on the other hand, the need to evaluate the multipliers. These effects are expressed in the form of multipliers. In economics a multiplier is expressed by a simple formula [28]:

Multiplier = (Total change) / (Initial change))

In economic phraseology, multipliers are classified into two broad categories depending on their final expression [17]. Formula I reflect the direct and indirect effects and Formula II includes the induced effects along with the direct and indirect effects. The indirect effects are those associated with changes in companies that have been delayed due to increased demand from the industry directly affected. Therefore, the Type I multipliers are calculated as follows:

Multiplier Type I = (Direct and Indirect Effects) / (Direct Effects)

By analogy, the Type II multiplier is expressed by the ratio that is included in the numerator above:

Multiplier Type II = (Direct, Indirect and Induced Effects) / (Direct Effects)

Economic multipliers provide estimates of the total impact resulting from the initial economic output to final demand. The higher the multiplier, the greater the impact on the local economy or the country's economy.