Theoretical background

The accumulation of assets in the classical approach is based on the production function:

The transformation of savings that arise from agricultural income into investments undertaken by the agricultural producer refers to Eq 1. In the traditional approach, analogies can be found in the Solow model [14], whereby the greater the amount of capital, the greater the investment (Fig 1). A shortcoming of Solow’s theory is the assumption that other inputs are not relatively important. Consequently, environmental issues are omitted, which are increasingly important at the level of shaping development conditions for farms within the EU (the CAP instruments). There are examples in the literature of the application of Solow’s theory in agriculture [15].

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Fig 1. Capital accumulation and growth–The Solow model.

Source: based on [14]. S–savings rate, c–consumption, I–investment, k–capital per worker, f_agr−accumulation function for agriculture.

https://doi.org/10.1371/journal.pone.0265128.g001

As evidence in Fig 1 the slope of production function is positive but increasingly flattened, this results from the decreasing productivity of capital. Hence, the existence of marginal effects in the context of the relation between profit and capital is relatively universal in economic processes influencing farm operation. However, the uniqueness of the decreasing productivity of capital for farms comes down to the fact that agriculture has a weak market position due to, for example, its distance from the final consumer, as well as generally unfavourable price relationships between the products sold and purchased by farmers [16]. Moreover, there is an increase in the importance of non-productive assets, for example, larger building areas for livestock stands. The increasing role of non-productive assets is a consequence of the need for agricultural producers to meet the requirements for receiving subsidies. As a result, the decreasing productivity of capital acts more restrictively, weakening the relationship between income and assets. In Fig 1, this is reflected by the sf_agr(k) curve. Its position, above a certain scale of production, is higher than average in the economy due to the intrinsic growth in land prices that increases the value of the assets specially when farmers own their land.

The curve for agriculture (Fig 1) can be considered to be more flattened due to the increased importance of non-productive assets (the need to meet environmental standards), as well as the aforementioned generally unfavourable price relations stated in [16]. In turn, for agriculture, the initial course of the curve results from the fact that for low-scale agricultural outputs, meeting the consumption needs of the farming family takes precedence. Subsequently, regarding investment outlays, the scope of institutionalization of market relations is small and fixed costs are relatively high. Consequently, production effects grow slowly, and the course of the function will change only when a certain threshold of production is exceeded.

In the case of agriculture, we often have to deal with a situation whereby agricultural income alone is sufficient solely to satisfy (not always fully) the consumption needs of the farmer and his family due to the small scale of activity minimal farm income and the domination of non-agricultural sources of income. Thus, there are limited possibilities for financing investments and growth in asset value in agricultural holdings. In consequence, we have the decapitalisation of farm assets, which is additionally aggravated by low creditworthiness or a lack of successors. Analysed issues have been studied in the literature in the context of the so-called `wealth of farm households`[8, 17]. So agricultural activity alone, despite the considerable accumulation of farm assets, is not able to generate income parity. Therefore, the importance of off-farm sources of income increases. Indeed, according to data derived from the Farm Accounting Data Network (FADN) system (EU21), in 2004, the share of non-farm income from farms (agritourism, income from rent, forest, rent of equipment) as agricultural income was 17.1%, while in 2018 it was 24.5%.

Larger farms, which are strongly linked to the market, function on a kind of treadmill. The increase in the value of depreciable assets derived from the desire to improve their competitive position generates ever-greater costs due to the necessity of renewing the assets–higher depreciation costs. In this way the increase in the value of depreciable assets creates pressure for further investments. Part of this type of investment is non-productive or is related to the obligatory fulfilment of requirements under the EU’s CAP, such as the cross-compliance rules in terms of animal welfare. The cross-compliance rules refer i.a. to stock density, For example, [18], based on studies of EU agriculture in the period 1995–2015, found the occurrence of a growth-rate i.e. an increase in real productivity caused a decrease in the growth rate of agricultural income. Hence, while the processes of increase in real productivity stimulate investments, and enhance the value of assets, t they only to a small extent, contribute to the growth of income.

Interesting considerations concerning capital accumulation were presented in [19], where it was pointed out that capital accumulation in agriculture was a function of the past (primary accumulation). Consequently, it is very difficult for smaller farms with a lower level of assets to `catch up`with economically stronger units.

Swinnen and Gow [20] exposed the importance of external sources of financing in capital creation. Thus the value of assets is shaped not only by income, but also by liabilities. In turn, [21] showed that, in the case of farms in the USA, the value of assets in the farm sector between 2009 and 2016 increased by about 34%, while agricultural income only enlarged by about 11%. Similar trends were also reported in earlier studies [22]. In contrast, for farms covered by the FADN system, the median of average annual growth in agricultural income in the EU23 countries was 1.42% over the period 2004–2018, while total assets were 2.49%. Higher growth in the value of assets than in income indicates the functioning of agriculture under conditions of decreasing marginal effects, but also the loosening of the links between assets and income.

Sustainable development

There are very many proposals for quantification of sustainable development at farm level [23–25], and in the literature we can find theoretical and empirical studies that suggest the existence of synergies between different dimensions of sustainability. For instance, Martínez-Sastrea et al. [26] mention the simultaneous positive effects of animal diversity on pest-control and pollination in apple orchards in Spain.

At present, the operation of agricultural holdings in EU countries is being implemented in conditions that increasingly take into account the context of sustainable development. Therefore, the analysed issues correspond in practical terms currently with a set of initiatives of European Commission to achieve climate neutrality in Europe, the so-called European Green Deal [27]. From the perspective of the relationship, the approach to resource management can be discerned [28, 29]. Among other issues, the idea is to reduce the pressure from farms on the environment while not worsening the productivity of the used resources [30]. At the farm level, not worsening the productivity of resources while reducing the pressure on environment, means that the relationship between income and assets should not be weakened, while environmental sustainability is simultaneously maintained. In practice, however, the objectives of farmers that are linked to economic and environmental dimensions can be contradictory. This can lead to situations in which growing farm income and assets are accompanied by greater pressure on the environment or increasing stratification of incomes and assets among farmers. For example, [31], on investigating sheep farms (in different farming systems) in north-eastern Spain, a clear trade-off between the economic and environmental goals was evident, whereby the higher the economic sustainability, the lower the environmental sustainability. Moreover, [32] underlined how the risk of the negative impact of farms on the environment increased with the growing accumulation and intensification of production. The authors of [33, 34] also affirmed the interchangeability between environmental and economic dimensions in the functioning of farms. In turn [35–37] indicate that a balance between these dimensions is possible and the relationship between economic and environmental objectives is positive.

Different studies stress that larger units, and therefore those with more assets and income, have a better chance of having a positive relationship between the economic and environmental spheres [38]. Moreover, Špička et al. [39], based on the experience of farms in the Czech Republic, underline, that a trade-off between environmental sustainability and economic performance occurs primarily among farming specialisation categories.

Capitalisation of subsidies

The process of asset accumulation mainly occurs, as mentioned earlier, through income. However, there is another channel through which accumulation occurs – subsidy capitalisation [7, 40]. Direct payments are captured in lease rates and in land. Consequently, the links between income and assets are weaker. The CAP reinforces the pressure on land prices due to decoupled payments. As a result, the rapid growth in land prices has become a significant barrier for farmers who want to increase the scale of their farming activities [41]. For example, as reported by Ciaian et al. [7], in new EU member countries, the capitalisation rate was 79% after the budgetary reform period in 2013. In the old member countries, the capitalisation rate was 43%. The biggest beneficiaries of subsidy capitalisation are landowners, as they have gained from increase value of agricultural land, whereas the actual users i.e. farmers have obstacles because of the increase in lease and land prices.

The importance of the subsidy capitalisation process can be proven by the fact that, after integration with the EU, agricultural land prices in the new member states (e.g. in Poland rose significantly. The data about agricultural land prices published by EUROSTAT indicate that between 2011 and 2019, only in Greece, Lithuania, Slovakia and Italy did average land prices decrease. In contrast, in the remaining countries, there was an increase, and this was significant (more than 1.5-fold) in the Czech Republic, Estonia, Latvia, Luxemburg, Hungary, Poland and Sweden. The additional amenities of land are important here. Moreover, the capitalization of subsidies can create a wealth effect. Farmers may be willing to expand production through activities that they would consider risky in the absence of guaranteed income from direct payments [42]. On the macroeconomic level, therefore, this may stimulate investment in agriculture

Data

In the study, FADN data were employed. The origin of the sources is a website https://agridata.ec.europa.eu/extensions/FarmEconomyFocus/FADNDatabase.html. The mentioned website contains economic and production information about farms covered by the FADN system in the EU Member States. The term `assets`refers, especially in the empirical part, to the value of assets of the economic units (farms) for both current and fixed components. Such definition of `total assets`is in line with the FADN system (fixed assets + current assets) [43]. Only assets in ownership are taken into account, based on the value at closing valuation for the year. As a result, we have the same counting of assets across EU countries, which makes it possible to compare them.

Data of the FADN system are publicly available because of the assured confidentiality of the participating farms and the data are published in the different cross-sections only if there are at least 15 agricultural holdings in the group. Such data are microeconomic and refer to the arithmetic mean of the average farm for a given group of farms (by type of production, economic size, region, country). Thus, the data illustrate the situation of the representative farm for a given country, which is the result of the behaviour of many agricultural producers. The time scope of analysis refers to the period 2004–2018, which was dictated by the availability of data for the studied countries at the time of writing of the article.

The value of total assets was used as a dependent variable (SE436). Total assets, both fixed and current, create and determine the level of income, regardless of whether they are owned by the farmer or not. Moreover, the value of capital in the classical sense (as a factor of production) was used as a dependent variable. In this case, the value of land was subtracted from the value of assets (SE436-SE446). This approach resulted from the intention to possibly identify the impact (in the comparative, indirect sense) of the value of land on the relationship under study. Because there is an intrinsic growth in the value of the land, this complicates the analysis of the relationships between income and assets. This problem is confirmed by many research results [44, 45].

The selection of explanatory variables for the panel models was dictated by substantive considerations. The idea was to include, in addition to the agricultural income variable (SE420) and variables related to the context of economic and environmental sustainability, control variables that have a reasonably consistent theoretical economic impact on the relationships under study [46]. Therefore, the variable of acreage of arable land (SE025), liabilities (long and short term, SE485) and the share of fixed assets to total assets (SE441/SE436) were employed [47, 48].

In the analyses, the context of economic and environmental sustainability was taken into account. The economic sustainability was estimated based on income per 1 hour of work by the farmer’s own family. The level of this income was then compared with the median income of the analysed group of EU countries for a given year. If it was higher than the median, then such an observation was considered to be economically sustainable. Thus, economic sustainability is contractual here. A similar approach can be noted in the case of estimating the so-called sustainable value and setting the benchmark [49].

Environmental sustainability was established based on two sub-measures: the share of cereals in the sowing structure and the intensity of animal stocking per 1 ha of utilised agricultural area (UAA). The choice of these measures was because their use allowed a determination of threshold values that enabled the critical values to be set for the given areas of sustainability. Regarding the share of cereals in the sowing structure, the measure should not exceed 66%. For the stocking density, values in the range of 0.5–1.5 so-called large livestock units [43] per 1 ha UAA are desirable, which is conducive to maintaining appropriate fertiliser management on farms [50, 51]. Hence, these two proposed metrics for environmental sustainability represent both the issues surrounding the diversity of agricultural production and excessive pressure on the environment. This does not mean that they comprehensively address environmental sustainability. However, in the context of the adopted research objectives, this should not be a problem. Furthermore, the applied approach was driven by the availability of data at such an aggregate level.

In the analyses, the original data of the FADN system have been deflated, because indices of changes in income and means of production derived from EUROSTAT data have been applied. In addition, the purchasing power of currency exchange rates was taken into account to eliminate the impact of nominal changes to the exchange rate. At the same time, due to significant variability in economic data of farms, three-period moving averages were used. In the calculation, the mean of the value of the analysed variable for the current year and the previous and next year were employed. For the outlier years i.e. 2004 and 2018, the means respectively, of 2004–2005 and 2017–2018 were applied in order not to lose time series information. In this way the seasonality of data has been reduced.

The explanatory variables in the models were verified by the variance inflation factor (VIF) test for collinearity. Values exceeding 10 indicate the appearance of a collinearity problem. In all models included in the study, the VIF test values did not exceed 5, which means that this problem did not occur in the analysed models [52].

The spatial range of the research concerns agricultural holdings from the EU21 countries. From the group of 25 countries, which have been EU members since at least 2004, Cyprus and Malta were excluded due to the marginal importance of their agriculture in the EU. Following preliminary analyses (Fig 2), farms from Denmark and Slovakia were then omitted because those farms recorded high asset values alongside negative agricultural income in the analysed period (2004–2018). Additionally, their farm income showed very high variability. Such effect also distorted the analyses due to the significant levels of achieved values in terms of both income and assets.

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Fig 2. Graphical illustration of the relationship between income (EUR) and assets (EUR; e.g. 1,4E6 means 1,4x10⁶) in farms (FADN system) in the EU countries (23) (2004–2018).

Source: own calculation based on data of the FADN system (S1 Table).

https://doi.org/10.1371/journal.pone.0265128.g002

Econometric strategy

The scatter diagram (Fig 2) helped in selecting appropriate forms of functions for models relating to the relationship between income and assets for the examined panel of farms. The analysed observations were concentrated in the lower income and assets value range. Herein, increasing income was accompanied by growing changes in the value of assets. There were, however, quite a few units that were outliers, e.g. farms in Slovakia and Denmark, wherein, especially in some years in the first decade of the 21st century, there were situations where negative income was accompanied by high asset values. From Fig 2 it follows that the most appropriate function for panel regression was an exponential type of function.

The linear functions provided a weak fit to the empirical data, and there was a problem with insignificance with some variables. For the power functions, the fit of the models to the empirical data was similar to the exponential function, but there was statistical insignificance of the variables in some cases. In the case of an exponential function: (1) after being bilaterally logarithmised, it becomes: (2) where x_1, x_2… are explanatory variables, ß₀ –is the intercept; ß₁ –structural parameter; ε_it−random error.

When we have exponential function, then assets change relatively with the income scale. So increasing income has a different effect on the value of farm assets, depending on the scale of income [18, 53]. The exponential function reduces the problems associated with the variance of the random component and the normality of the distribution. Moreover, it allows for more accurate models.

The econometric models were estimated via the panel data, assuming that the development of a dependent variable influences, in addition to the explanatory variables, non-measurable, time-fixed and object-specific factors called `group effects`[54]. In this case, because there are often individual effects, fixed (which we can assign to specific objects) or random panel models with fixed effects (FE) and random effects (RE) are used. The advantage of panel data is that we can control the heterogeneity in the model by considering heterogeneity as constant or random, which solves the endogeneity problem.

To choose an appropriate estimation method, the heteroskedasticity of the random component was assessed. In all analysed models, based on Hausman tests (p < 0.05), the null hypothesis of a model with RE was rejected in favour of a model with FE. The rejected model with RE is due to significant across farm differences between the EU countries due to the existence of individual effects. The Wald test was also applied to assess the heteroskedasticity of the random component and the Breusch-Pagan (Br.-Pag.) test [55] was employed to check the constancy of variance of the random component, as well as to verify between classical least squares method estimation and random effects.

In econometric studies the panel model with fixed effects is most often used (also in this paper): (3) where: ß0 –is the intercept; ß₁ –structural parameter; x–explanatory variable; u_i−individual effect, ε_it−random error.

In a panel model with fixed effects, fixed individual effects are eliminated by averaging the model over time (index t) [56]. The Beck–Katz panel-corrected standard error procedure was applied, as this allows us to reduce problems linked to the autocorrelation of the random component.

The use of panel models resulted from the possibility to assess the studied relationships, also taking into account economic, environmental sustainability and control variables. In addition, the use of panel models provides an opportunity to select the form of the function, which was in the article, an exponential function (cf. further consideration).