Change in Productivity as the Primary Determinant of the Income of Agriculture After Poland’s Integration into the European Union

Abstract

The article aimed to verify the development of the productivity level of Polish agriculture after EU integration as a key determinant of agricultural income. The research in this area was concerted because the productivity of agriculture (its technical efficiency) is a specific measure of its social efficiency, as it determines the level of wealth and social welfare and, at the same time, it is a determinant of its competitiveness in the long term. At the same time, it should be noted that after integration, agricultural production in Poland was carried out under conditions of extensive restrictions resulting from the adopted principles of the common agricultural policy aimed at increasing environmental sustainability. Productivity was measured on individual farm data using the Data Envelopment Analysis (DEA) Slacks-Based Model. The results were then extrapolated to the broader collective of commodity farms in Poland and indirectly applied to the entire population. The obtained results allowed for the conclusion that, during the first years of membership, there was a systematic decrease in productivity, which was observed from 2004 to 2011. The average value of the productivity factor for the research sample decreased from 0.230 to 0.208, while for the population it decreased from 0.224 to 0.202. After then, there was a reversal in the direction of the development trend, and in the following years, an upward trend emerged. Thus, the phenomenon of convergence in agricultural productivity with other EU countries, as the main factor influencing the direction of its changes in Poland after accession to the European Union, was not confirmed. Also, in the post-integration period, there was no change in the expected directions of interaction between the main determinants of agricultural income. Indeed, the theoretically formulated and empirically verified relations between subsidies and price relations and productivity were confirmed. Using the world price index as an explanatory variable in the multiple regression model, it was possible to explain, to a large extent, the variability of the productivity of Polish agriculture. Hence the implication for policymakers is that, despite high levels of subsidisation, the market is the main determinant of productivity changes. The weak impact of the price ratio index in Poland (‘price scissors’) on productivity volatility indicates that the increase in production costs, including those related to environmental protection (sustainability), has been effectively offset.

1. Introduction

1.1. Implications for Agriculture Resulting from Poland’s Accession to the European Union

Poland’s accession to the European Union (EU) was a fundamental event that had a significant impact on the direction of agricultural development in Poland [1,2,3]. It was preceded by the negotiation process for Poland’s membership, which began on 8 April 1994 with the submission of the accession application and ended on 1 May 2004, the date of entry into force of the Accession Treaty. Along with Poland, seven post-communist countries of Central and Eastern Europe (CEE) as well as Malta and Cyprus joined the EU. Considering that Romania and Bulgaria also became EU members in 2007, this was the largest eastward expansion of the EU [4].

For farms, accession meant access to the single market, including food products, financial support under the Common Agricultural Policy (CAP), but also the obligation to adopt EU regulations and legal standards. The scope of regulations affecting agriculture was very broad and generated not only benefits but also significant costs, e.g., in terms of the environment, the Nitrates Directive, the Water Framework Directive [5,6]. This had serious implications for agriculture in Poland. This is because there was a change in the subsidy system for this sector, resulting from an increase in the level of subsidies, changes in the type of budget support instruments used, or modifications to the legal conditions for conducting production activities and placing food on the market [7,8]. Integration also influenced the immediate environment of agriculture, specifically the functioning of the market for means of production and food recipients and led to a significant expansion of the market for agricultural raw materials, as well as the opening of the sector to competition from other EU countries [9,10,11]. It has also had an impact on the macro-environment of agriculture, including the labour market and capital market, and thus on the socio-economic development of the country [12,13,14,15,16,17,18].

The increase in subsidies was accompanied not only by the rise in the income of agricultural producers but also by an increase in agricultural production in Poland, both at the level of the entire sector and of individual groups separated by the scale of activity and output orientation [19,20,21,22,23,24,25,26].

Thus, the inclusion of Polish agriculture in the Common Agricultural Policy led to a shift in the primary factors influencing the income of agricultural producers, both at the macroeconomic and microeconomic levels. Under the assumption of a constant scale of production until integration with the EU, the income of farm producers in Poland was determined mainly by technical efficiency/productivity and market conditions defined as the relation of prices of sold products to unit prices of purchased means of production (Figure 1a).

This relationship follows directly from the deterministic formula for income and its straightforward transformation:

$$I=\left(P_y\cdot y\right)-\left(P_x\cdot x\right)$$

(1)

i.e., revenue $\left(P_y\cdot y\right)$ minus costs $\left(P_x\cdot x\right)$.

By rearranging Equation (1), we obtain:

$$I=\left(\right({\displaystyle \frac{P_y}{P_x}}\cdot {\displaystyle \frac{y}{x}})-1)\cdot (P_x \cdot x)$$

(2)

After accounting for subsidies (S) and taxes (T), the final form becomes:

$$I=\left(\right({\displaystyle \frac{P_y}{P_x}}\cdot {\displaystyle \frac{y}{x}})-1)\cdot (P_x \cdot x)+(S-T)$$

(3)

and for profitability (P):

$$P= {\displaystyle \frac{I}{\left(P_x\cdot x\right)}}=\left(\right({\displaystyle \frac{P_y}{P_x}}\cdot {\displaystyle \frac{y}{x}})-1)+{\displaystyle \frac{(S-T)}{(P_x \cdot x)}}$$

(4)

where

I—income; P—profitability; $P_y$—price of output (sold products); $P_x$—input costs; $\left({\displaystyle \frac{P_y}{P_x}}\right)$—price ratio (market conditions); $y$—output (quantitative terms); x—input (production scale); $\left({\displaystyle \frac{y}{x}}\right)$—productivity (technical efficiency); S—subsidies; T—taxes; (S − T)—net budgetary transfers.

Both elements were the central stimulants of the income/profitability of agricultural holdings and the agricultural sector as a whole on which the influence of the other factors was focused (made visible). The level of direct budget transfers to agriculture before 2004 (the moment of integration) was relatively small and thus had minimal impact on farm incomes. Instead, the intervention process focused on maintaining and stabilising prices in the agricultural market [27,28]. After the integration with the EU, to a large extent, transfers to agrarian holdings in Poland, mainly in the form of Single Area Payment Scheme (SAPS) [29] and title: Less Favoured Area (LFA) and production payments, increased by subsidies: ecological, agri-environmental, investment [30], etc., became the third primary determinant of agricultural income/profitability, exceeding many times the level of tax and para-tax burden of this sector [31] and individual entities (Figure 1b and Figure 2).

1.2. Relationships Between the Main Determinants of Income in Agriculture

There is a direct and indirect interaction between the main determinants of agricultural producers’ incomes, and it is usually identified as negative.

The impact of budget subsidies on market prices of agricultural raw materials and food products has been recognised on theoretical grounds and described. Both production-linked [32] and decoupled direct subsidies [33,34], which were introduced as part of decoupling, result in a decrease in expected agricultural commodity prices and, consequently, food prices [35]. Although in the latter case, the introduction of direct subsidies in the EU since 2003 brought about an adjustment of prices of agricultural raw materials on the EU market to world prices, which resulted in a decrease in the former, it was, however, an effect of the subsidy system reform and referred to the pre-Pacific period of Poland [36]. Indeed, the literature indicates that world prices without decoupled direct subsidies would have been at a higher level [37,38]. It is also assumed that budget subsidies influence the prices of the means of production used in agriculture, causing their increase. This phenomenon is particularly well documented in terms of its impact on agricultural land prices and the number of rents (the main factor of production) [39,40,41,42,43,44], with no consensus on the degree to which subsidies are capitalised in them [45,46,47,48,49]. This problem does not affect those combining the ownership of agricultural land with its use and at the same time not increasing the stock of land. However, the impact of subsidies on the increase in the price of other inputs, especially those with primary or exclusive use in agriculture (fertilisers, plant protection products, etc.) affects a broad group of actors [50,51,52,53]. Thus, after EU integration, a negative impact of budget transfers on agricultural market conditions was theoretically to be expected. However, during the period under study, despite significant changes in individual years, the trend gradually improved, as indicated by the development of the index of the ratio of the prices of agricultural products sold by farms to the prices of purchased goods and services [54].

Studies also indicate a negative impact of improving price relations on technical efficiency (agricultural productivity) [55,56,57], although this may be an exception in underdeveloped countries [58,59], which Poland is not.

The same direction of impact would be expected for the dependence of technical efficiency/productivity of agriculture on subsidies. The impact of budget subsidies on farm productivity can take place through various mechanisms and channels, among others: (1) price effect—a change in the relationship between the prices of applied inputs and the prices of marketed products even in a decoupling situation, which may affect the use of inputs and the volume of production. A good example of this in Poland is the cultivation of marginal land, facilitated by the link between Single Area Payment and agricultural areas. (2) income/wealth effect affecting investment, access to credit and the amount of farm labour involved and the level of labour activity of the farm owner and family members, (3) insurance/risk mitigation effect by guaranteeing part of the income, (4) at the macroeconomic level, impact on the flow of inputs as a result of less economic impetus to liquidate inefficient farms and creating barriers to entry into the agricultural sector [60,61,62,63].

Through not all of these mechanisms and channels, subsidies negatively affect farm productivity and not in every case. Both income and asset effects, as well as insurance effects, can be positive, especially when contributing to overcoming farmers’ financial constraints in the case of capital market distortions and mitigating risks in the case of insurance market distortions [39,64]. It is also believed that subsidies, whether directly or indirectly, provide an investment impulse, including the use of innovative solutions to increase agricultural productivity [60,65]. The use of such mechanisms is encouraged by all countries in their Organisation for Economic Co-operation and Development (OECD) report [66]. However, examining this problem would require a situational approach, as at the microeconomic level, not every farm is able or interested in innovation [67]. At the same time, there may also be overinvestment in certain groups of actors or the sector as a whole [68]. However, most empirical studies indicate a negative impact of subsidies as an overall support stream, although they emphasise their heterogeneous nature due to the type of interventions applied, the country, the size of farms, and the production orientation [60,69,70,71,72,73,74,75,76,77,78,79,80].

The opposite of the expected phenomenon was also observed for this primary income determinant after EU integration. The activation of a broad stream of subsidies in Poland at the sector level did not halt the trend of Total Factor Productivity (TFP) improvement, and a systematic improvement in productivity, measured in aggregate for the whole sector, was observed from 2004 to 2019 (Figure 3). This is indicated both by calculations made, inter alia, for Polish agriculture on behalf of the U.S. Department of Agriculture using the Törnqvist index [81,82,83], as well as by calculations made using the Fischer index to monitor the impact of the Common Agricultural Policy [84,85]. In addition to the Baltic states, Poland was included in the group with the fastest TFP [86,87] and sub-indices of productivity [24] since its integration.

Thus, the question arises whether, taking into consideration the divergence between the expected dependencies of the main determinants of agricultural income and the actual direction of their changes after Poland’s integration with the EU, another factor was predominant, e.g., the phenomenon of convergence, consisting in equalisation of income of agricultural producers in Poland about the countries of the so-called old fifteen (mainly as a result of the so-called β convergence) [24], including the convergence at the level of TFP [86,88,89]? Should the outlined theoretical pattern of expected dependence after Poland’s integration into the EU be overruled due to the exceptional situation in which Polish agriculture found itself (

Table 1. The expected direction of the interaction between agricultural income and its main determinants.

Direction of Impact (Correlation Sign)	Income	Market Conditions	Technical Efficiency/ Productivity	Subsidies
Market conditions	positive	-	negative	-
Technical efficiency/ productivity	positive	negative	-	negative
Subsidies	positive	negative	negative	-

)?

1.3. Convergence as a Determinant of Income and Productivity Changes

Convergence based on the neoclassical theory of trade and the notion of comparative advantage can be partly explained by the improvement of market conditions of Polish agriculture. It assumes the equalisation of prices of products and inputs in conditions of abolishing trade barriers, i.e., the effect of introducing a single agricultural market for raw materials and agricultural products and means of production [90]. However, the improvement in market conditions may also be a result of the transmission of world market prices and a systematic increase in the price index of agricultural products in both nominal and real terms. Such a trend was observed almost uninterrupted from 2002 to 2011, followed by a decrease from 2012 to 2015 and stabilisation from 2016 to 2020 [91,92] (Figure 4).

Convergence, on the other hand, cannot fully explain the change in the level of productivity in Poland, given the results in other countries that joined the EU in a similar period [93,94,95,96]. Taking into account Robert Solow’s model of economic growth and theories of factor movements [97] in countries such as Hungary, Malta, and Croatia, as well as partly in the Czech Republic and Slovenia, there should also be an improvement in total factor productivity at a rate reflecting the process of convergence in their agriculture. Although this situation can be explained by the different degrees of preparation of the farms themselves and the institutions servicing it for EU integration, the various levels of technical infrastructure, the development of the agri-food industry, the organisation of supply chains and logistics costs [98], and even the different level of agricultural productivity before EU integration—the base effect [99], these explanations seem insufficient.

Other reasons are suggested by the study’s results on the total productivity of different agricultural sectors, as reported by Čechura et al. [100]. Using unit data from 24 EU countries, they did not confirm the phenomenon of regional or country convergence but rather indicated that other factors influence the change in productivity in particular groups of entities. Following this line of reasoning, Baráth and Fertő [86] highlighted a serious problem resulting from data aggregation, which could lead to a significant bias in the results obtained. This is because productivity measurement carried out jointly for the entire sector requires homogeneity of inputs and outputs, which is achieved through the adopted price relations. As a result of the aggregation of data, errors may, therefore, arise that weigh down the results obtained. The aggregation of data for the entire sector in a given country may also result in an overestimation or underestimation of effects and/or inputs, especially among subsistence farms, i.e., entities with no formal production accounting records. It should be added that for taxation reasons—the functioning of the so-called grey economy (especially in the tax system applicable to agricultural holdings in Poland), not all outlays can be reported by agricultural input supply companies and thus taken into account in the global agricultural account.

This work aimed to verify how the level of productivity of Polish agriculture, following accession to the EU, has served as a key determinant of farm income. Using data from individual farms representative of the group of commercial farms (i.e., those producing for the market) and indirectly accounting for potential distortions at the aggregation level, this study examined the direction of productivity changes across the entire population of agricultural holdings in the country. An attempt was also made to find out which of the main determinants of farm income had the most significant impact on productivity change in each period and what the direction of this impact was.

It was decided to verify the following research hypotheses:

• It is not possible to simultaneously increase income in the agriculture sector and all its main determinants.
• The increase in the productivity of Polish agriculture was caused by the phenomenon of convergence, which disrupted the negative impact of subsidies and price relations on productivity.

2. Materials and Methods

The research utilised unit data from farms participating in the Polish FADN (Farm Accountancy Data Network), for which information was collected for events from 2004 to 2019. The choice of the initial time interval was dictated by the range of available data representative of the general population of commodity farms [101] and the date of Poland’s integration into the EU. The lack of a representative sample of the agricultural population prior to accession (before 2004) ruled out the possibility of creating a control and research group and, consequently, of using methods based on causal inference according to Rubin [102]. Therefore, it was not possible to apply, among others, the Propensity Score Matching [103] and Difference in Differences [104,105]. The choice of the final time interval, on the other hand, was dictated by the occurrence of significant market shocks after 2019, which directly affected the operation of global and Polish agriculture, as well as its environment, and may lead to changes in productivity. This applies in particular to the COVID-19 pandemic [106,107,108] and the war in Ukraine [109,110,111,112,113], and in the latter case, especially to the significant influx of Ukrainian products on the European market, including Poland [114]. A total of 191,291 observations were used in the study for the period 2004–2019, averaging almost 12,000 farms per year. A panel of subjects was used, the level of imbalance of which was due to the participation of approximately 10% of new farms each successive year, i.e., those not participating in the survey in the previous year. However, none of the farms or the observations based on them were excluded to maintain representativeness and to allow for extrapolating the results to the general population surveyed.

The study used technical efficiency calculated using the non-parametric Data Envelopment Analysis (DEA) method. This is a widely used method for measuring technical efficiency and productivity, having been applied in numerous studies based on data from diverse disciplines [115,116]. The originator of the DEA concept is Farrell [117], who was the first to define the reference curve used in this method as efficiency frontiers determined from empirical data. In contrast, the first model for linear programming with multiple inputs and fixed production scale effects was developed by Charnes et al. [118]. In contrast, the present study employed a classical model developed later, using the equation proposed by Banker et al., known as the BBC model, which assumes variable dependence on the scale of production [119].

According to its assumptions, the optimal technology for the units is determined by the equation [120]:

$$P(x,y) =\{xj\ge X\lambda j, yj\le Y\lambda j, yj \ge 0,{\sum }_{j=1}^n\lambda j=1, \lambda j\ge 0\}$$

(5)

where

• P(x,y)—the set of production possibilities in the sample,
• x_j—the vector m of inputs in the j-th unit,
• X—matrix for m inputs of dimension (n × m) for all n objects,
• y_j—the vector s of effects in the j-th unit,
• Y—matrix for s effects of dimension (n × s) for all n objects,
• λ_j—the weights being the linear combination coefficients (saturation parameters).

This model was further developed by Tone, who additionally introduced slacks (s), thereby transforming the inequalities contained in Equation (1) into equations [121]:

$$xj=X\lambda j,+ s^{-}$$

(6)

$$yj=Y\lambda j,-s^{+}$$

(7)

and assuming that the conditions are met: $s^{-}\ge 0 \mathrm{i} s^{+}\ge 0$.

Determining the set of production possibilities further allows the measurement of the distance between the leaders representing the optimal technology and the other sites. In an input-oriented model, it comes down to a mathematical notation of this exercise as follows [122].

$$E(xj,y\mathrm{j})=min \{\theta :\theta xj, xj\in P(x,y) \}$$

(8)

where

• E(x,y)—a function of the distance between the point characterising the technology of a given farm and the object with the optimal technology (envelope),
• x_j—a vector of m inputs in j this unit,
• y_j—the vector s of effects in j this unit,
• θ—facility efficiency factor.

Finally, the efficiency coefficients in the Slacks-based model were calculated according to the formula [123]:

$$\theta = \begin{array}{c}min\\ \lambda j, s^{-},s^{+}\end{array} 1-{\displaystyle \frac{1}{m}}{\sum }_{j=1}^m{\displaystyle \frac{s_j^{-}}{xj }}$$

(9)

The model presented above for cross-sectional data is used to measure technical efficiency and is therefore used in a static approach. The transition to a dynamic approach productivity (In this study, I use technical efficiency, measured relative to the pooled frontier, as an indicator of productivity. It should be noted that this differs from the classical definition of productivity, which is usually calculated using Total Factor Productivity (TFP) [124]) calculations for an unbalanced panel and pooled frontier (Appendix A) was made by using the total number of observations (Decision-Making Units—DMUs) from all years, i.e., 2004–2019, in a single computational model. A single reference curve (the best effect-input combination) was therefore created for the DMUs from the entire study period. This approach, however, unlike the most commonly used calculations for balanced panels such as the Fisher, Törnqvist, Hicks-Moorsteen, Malquist, and Färe-Primont indexes, does not allow for disaggregation of the results, e.g., into an element characterising technological and technical progress. Thus, there are limitations to interpreting the productivity obtained. However, given the stated aim of the research, this was not a limitation in the analyses carried out.

Due to the use of a relatively huge number of objects to measure efficiency, and in particular, to obtain a relatively small number of DMUs with the maximum value of efficiency scores, i.e., equal to 1, the bootstrap procedure proposed by Simar and Wilson [125] was abandoned. This is because the distribution of the results obtained was close to a normal distribution, which entitled, among other things, the use of regression models calculated by the classical least squares (Ordinary Least Squares—OLS) method or the use of the generalised least squares (GLS) estimator. Regression models were used to determine the variability of productivity over time and the factors that determine it. Due to the use of an unbalanced panel, individual effects were omitted, and mainly group averages were used as explanatory variables [126] to determine the direction of productivity changes over time P = $\overline{E}$(x_j,y_j), while the time factor (t) and other main determinants of income were used as explanatory variables. The population average was calculated as a weighted mean, where the weight was the conversion factor assigned to each agricultural holding during the selection of objects for the FADN sample. This factor, determined by the farm’s economic size and production orientation, allows the results to be generalised to the entire population.

The choice of a non-parametric method for calculating productivity/efficiency in the conducted research was supported by the fact that it concerned agricultural holdings representing the entire agricultural sector in Poland, i.e., a quite significantly heterogeneous group. Unlike parametric methods, e.g., the method of stochastic frontier analysis (SFA), in DEA, there is no problem of inappropriate choice of the analytical form of the production function, which in this case could be subject to error [127,128], as well as there is no problem of endogeneity of inputs when productivity shocks occur [129], e.g., during drought the reduction in fertilisation by farmers relative to the target level. Although there are proposals to deal with both the problem of heterogeneity and endogeneity in models using a stochastic frontier [79,130], a more straightforward solution was chosen. There was also no danger of significant measurement error, which is impossible to identify in a non-parametric method, giving an advantage to parametric methods [131,132]. An undoubted disadvantage of the DEA method is also the possibility of overestimating the results due to the consideration of the optimal input-effect relationship (in an input-oriented model) as the reference curve rather than the theoretical production possibilities. However, this phenomenon occurs when the sample size is insufficient and when there is significant technological variation [133]. However, as already mentioned in the study conducted, the proportion of DMUs for which productivity was set at 1 in the total set of observations was very small.

In the determination of productivity, the sum of the value of crop production (variable code SE135—variable codes and their definitions according to FADN) and animal production (variable code SE206) was taken as the effect. During the measurement as an effect, all kinds of forms of budget subsidies and subventions were not taken into account according to the assumption that they are not elements of the technical efficiency of the farm but compensatory instruments of an allocative nature. To eliminate the impact of changes in agricultural commodity prices over time on the value of production, they were deflated before summing the two parameters. The purchase price index of plant products (and the purchase price index of animal products calculated by the Central Statistical Office (GUS) [134,135,136,137]. The 2004 index levels were taken as 100, which allowed the value of production throughout the analysed period to be expressed in 2004 prices.

The use of such a deflator did not significantly affect the calculated level of productivity, as there were no significant changes in consumer preferences regarding the type of food purchased during the period under review, nor in the share of agriculture in the Polish Gross Domestic Product (GDP) [138].

The following independent variables were taken as inputs:

• agricultural area (ha)—the total area of land in agricultural use, both owned and rented, including set-aside and fallow land (code SE025);
• total labour input (code SE010) expressed in AWU (full-time equivalent units);
• balance sheet fixed assets less the value of own land (code SE411 less item code SE446);
• intermediate consumption (code SE275) comprising direct costs and overheads associated with operating activities. They were deflated by the index of changes in the prices of goods and services purchased by farms for current agricultural production set by the CSO [134,135,136,137].

The value of fixed assets has not been deflated due to their long useful life on farms (a multi-year period) and the accounting practices followed. This involves including the value of fixed assets in the balance sheet at their acquisition cost minus the depreciation incurred during their useful life. Thus, the initial value of fixed assets (with the aforementioned exclusion of land) in the absence of investments has hardly fluctuated over time.

The subdivision and allocation of inputs to the various input groups were dictated by their specific characteristics. In the separation process, the different possibilities of their reduction (substitution) and the extent of complementarity were taken into account. The selection of inputs and effects was thus very similar to the classic one used in the work by Farrell [117].

MaxDEA software version 8.0 was used for the productivity and technical efficiency measurement calculations, while Gretl 2023c was used for the other statistical and econometric calculations.

When measuring correlations, a non-parametric method was used due to the small number of observations and the lack of equal variation among the variables, which, in the case of Pearson correlations, could affect the level of significance of the results. In this way, correlations between variables were also identified that were non-linear in nature [139,140].

3. Results

The results of the technical efficiency measurement obtained in the conducted study show moderate variability of productivity in the FADN sample and a relatively high level (indicating high potential) for potential productivity improvement relative to the optimum level (

Table 2. Productivity in the FADN sample 2004–2019.

Years	Number of Observations (DMUs)	Measures of Central Tendency			Coefficient of Variation	Number of DMUs for $\theta$ = 1
		Average	Median	Standard Deviation
2004	11,155	0.2302	0.2173	0.0735	31.93	8
2005	11,869	0.2307	0.2156	0.0771	33.42	9
2006	11,939	0.2280	0.2144	0.0747	32.76	8
2007	12,178	0.2221	0.2081	0.0768	34.58	9
2008	12,477	0.2170	0.2028	0.0749	34.52	7
2009	12,431	0.2183	0.2024	0.0810	37.10	13
2010	11,191	0.2194	0.2060	0.0722	32.91	4
2011	11,082	0.2082	0.1966	0.0680	32.66	1
2012	11,114	0.2129	0.2009	0.0698	32.79	2
2013	12,232	0.2099	0.1980	0.0708	33.73	3
2014	12,330	0.2163	0.2032	0.0738	34.12	2
2015	12,312	0.2185	0.2021	0.0850	38.90	8
2016	12,302	0.2197	0.2053	0.0783	35.64	1
2017	12,292	0.2226	0.2079	0.0815	36.61	6
2018	12,220	0.2318	0.2081	0.1076	46.42	28
2019	12,167	0.2093	0.1932	0.0801	38.27	10
Together 2004–2019	191,291	0.2197	0.2053	0.0788	35.87	119

).

Indeed, the coefficient of variation calculated based on the standard deviation and the mean for the whole period was 35.87% and ranged from 31.9% in 2004 to 46.4% in 2018, while the mean productivity ranged from 0.2082 in 2011 to 0.2318 in 2018. What is noteworthy is the relatively small number of effective objects marking the reference curve ($\theta$ = 1). During the period under review, their share represented only 0.62% of all DMUs and was, therefore, marginal. This testifies to the absence of the phenomenon of significant overestimation of the results obtained as a result of using the DEA method in this case and the influence of the heterogeneity of the objects studied. Thus, there was no phenomenon associated with an excess number of objects for which a more optimal combination of inputs about the effect was not found, and therefore, with a different (atypical about the sample) production technology.

Analysing the direction of change in productivity over time in the FADN sample based on changes in mean and median, it should be stated that they did not follow a unidirectional course after EU integration. Based on the results obtained, two subperiods can be identified (Figure 5 and Figure 6). Between 2004 and 2011, the productivity for the FADN sample declined systematically over time, with the mean reaching a minimum value in 2011. For the median, it reached the second lowest level during the period under study, i.e., 0.1980 (the minimum for median productivity was found in 2019). Then, from 2012 onwards, a change in the direction of the development trend and a systematic increase in productivity was observed. Due to the level of the measures of central tendency in the last year of observation, it was not possible to conclude whether this trend would continue in subsequent years under the conditions prevailing at that time.

Very similar results were obtained for the productivity calculated for the entire general population, i.e., after multiplying the individual results by weights corresponding to the number of represented farms in the general population established for production orientation, economic size and location in the region [144]. Between 2004 and 2014, the averages in the general collective were slightly lower than in the sample, but the difference in productivity was small, ranging from 0.3% in 2008 to 4.7% in 2012. In contrast, between 2013 and 2019, average productivity in the general population was at a level slightly higher than that observed in the FADN sample. The only exception was in 2018, when the largest difference between the averages was found, with the sample being 9.5% higher than the level in the general collective. However, as in the FADN sample, two sub-periods could also be distinguished in the direction of productivity changes for the general collective. From EU integration to 2011, there was a systematic decline in productivity, followed by a reversal in the direction of development, with factor productivity increasing in subsequent years. However, they declined slightly from 2017 (Figure 7).

It should be noted, however, that the time factor is not an explanatory variable that precisely identifies the cause of changes in the direction of efficiency in Polish agriculture, especially in the case of the general population. This is because the correlation analysis conducted during the studied period reveals a significant impact of the other main determinants of farm profitability on productivity during the same period (

Table 3. Spearman’s rank correlation level and p-value significance level from 2004 to 2019.

	Measures of Central Tendency Productivity (P)
Variable	FADN Sample		General Public
	Average ${\mathit{Y}}_1$	Medians ${\mathit{Y}}_2$	Average ${\mathit{Y}}_3$
$X_1$ Annual FAO Food Price Index	−0.691176 p = 0.003025	−0.650000 p = 0.006416	−0.629412 p = 0.008988
$X_2$ Real FAO Food Price Index	−0.698235 p = 0.001093	−0.623529 p = 0.009856	−0.520588 p = 0.038691
$X_3$ Price ratio index 1	−0.270588 p = 0.310761	−0.235294 p = 0.380356	−0.173529 p = 0.520408
$X_4$ Subsidies	−0.423529 p = 0.316254	−0.661765 p = 0.005234	−0.267647 p = 0.316254
$X_5$ Subsidies less production taxes	−0.370588 p = 0.157650	−0.614706 p = 0.011279	−0.232353 p = 0.386511

¹ Price ratio index in Poland (“price scissors”) of agricultural products sold to goods and services purchased by farms—1995 = 100.

). Indeed, for all measures of central tendency for the FADN sample and the general collective, an adverse and strong effect of the productivity correlation index with the FAO Food Price Index was found in both nominal and real terms. The correlation in all cases was statistically significant at the level of p < 0.05. Taking into account the predicted causal relationship and its consistency with the established direction of dependence and the high strength of the correlation relationship, it can be concluded that after the integration into the EU, a significant effect of changes in world market prices on changes in productivity of Polish agriculture was confirmed. An increase in prices was correlated with a decrease in efficiency until 2011, and a decline in prices after that period led to a rise in productivity in the agricultural sector in Poland.

In contrast to world prices, however, no statistically significant relationship was found between changes in productivity and the domestic price relationship index.

The change in the direction of productivity also ran in the opposite direction to changes in the stream of subsidies directed to agriculture, as indicated by the expected negative sign of the correlation. In the case of averages, however, the level of correlation was found to be statistically insignificant (p > 0.05), while a strong relationship was found to be statistically significant in the case of the median for the FADN sample. However, it should be emphasised that the period studied was after the introduction of a substantial level of subsidy amounts, including direct payments, and the correlation was due to changes in the level of support that took place between 2004 and 2019. It, therefore, does not reflect the impact of the introduction of subsidies itself, which would have required the use of the pre-accession period and could not be verified due to the lack of sufficient representativeness for the general population studied.

The level of correlation reflects only the influence of one factor on the other (interdependence) and does not allow one to conclude what the combined effect of the determinants of agricultural income on productivity was. A multiple regression model was therefore drawn up using the least squares (OLS) method, which, for the general population, allowed 45.69% of the variation in productivity variance to be explained by a constant and the nominal FAO Food Price Index according to the equation:

$$Y_3=0.245223-0.000275204X_1$$

There was no problem of heteroskedasticity in the model drawn up. White’s test allowed the null hypothesis to be accepted. The test statistic:$LM=3.69043$ with a p-value of 0.157992. A p-value for the F-test of p = 0.002423 was obtained, so the model was statistically significant, as were all variables (p < 0.05). The model furthermore had a level of centred R² = 0.456893. The null hypothesis of normality of the distribution of the random component was confirmed using the Doornik-Hansen test. The test statistic: Chi-square ${(X}^2)$ = 2.47887 with p-value = 0.289548.

In the case of the median for the FADN sample, the multivariate regression analysis equation was performed using the GLS method, and the equation took the following analytical form:

$$Y_2=0.235093-0.000204764X_1 -0.0000005942X_4$$

There was a heteroskedasticity problem in the model, as the White test did not allow the null hypothesis to be rejected. Test statistic: LM = 12.404856 with p-value = 0.029642. The GLS method was therefore used. For this regression, a p-value for the F-test of p = 0.000098 was obtained, so the model was statistically significant and also had a very high centred R² = 0.994223. All variables were statistically significant (p < 0.05). However, using the Doornik-Hansen test, the null hypothesis, assuming the normality of the distribution of the random component, was not confirmed. Test statistic: Chi-square ${(X}^2)$ == 6.8401 with p-value = 0.0327108. However, the distribution of the residuals was symmetrical and close to a normal distribution.

Thus, in addition to the FAO Food Price Index, another explanatory variable in the model used for medians was the level of production subsidisation.

4. Discussion

Given the fact that technical efficiency or agricultural productivity is a specific measure of social efficiency [145] and is a component of productivity in the economy regardless of its nature (open/closed economy) determines the level of wealth and social welfare [146], and is often treated as a measure of competitiveness in the long term [147], it is not surprising that its level in Poland after integration with the EU has been the subject of numerous studies and publications. All the more so, as it is the only primary determinant of profitability of an endogenous nature in relation to the farm owner’s decision [148]. Most studies on the productivity of Polish agriculture have employed the non-parametric method (DEA), and the change in productivity has been calculated most frequently using the Malquist index and the Färe-Primont index (

Table 4. Studies on changes in productivity in Polish agriculture.

Authors	Period Examined	Sector/Industry/Group	Level of Aggregation Research Unit	The Dominant Direction of Productivity Change
Malquist index
Kagan [149]	2004–2009	large-scale farms	farm	mixed/increase advantage
Floriańczyk, et al. [150]	2002–2010	all agriculture	country	increase
Bieńkowski, et al. [151]	2005–2010	all agriculture	country	decrease
Jankowiak, et al. [152]	2004–2010	all agriculture	country	increase
Domańska, et al. [153]	2007–2011	all agriculture	country	decrease
Bayyurt, et al. [154]	2003–2006	all agriculture	country	decrease
Baran [155]	2005–2011	all agriculture	province	decrease
Kijek, et al. [156]	2009–2013	all agriculture	country	decrease
Záhorský, et al. [92]	2007–2012	all agriculture	country	increase
Nowak [157]	2005–2014	all agriculture	province	increase
Madau et al. [158]	2004–2012	milk	country	decrease
Syp, et al. [159]	2014–2016	pigs, milk, field crops	farm	decrease: pigs and field crops; increase: dairies
Adamski [160]	2006–2015	milk	groups of farms	decrease
Smędzik-Ambroży, et al. [161]	2006–2017	all agriculture	country	no change
Sass [162]	2004–2018	all agriculture	groups of farms	mixed/decrease advantage
Färe-Primont index
Baráth, et al. [86]	2004–2016	all agriculture	country	increase
Kijek, et al. [89]	2004–2013	all agriculture	country	increase
Rusielik [163]	2009–2019	all agriculture	country	increase
Świtłyk, et al. [164]	2008–2012	milk	farm	increase
Świtłyk, et al. [165]	1999–2018	all agriculture	province	increase
Świtłyk, et al. [166]	2008–2017	all agriculture	groups of farms	mixed, increase for the sector
Zawalińska, et al. [167]	2006–2015	all agriculture	farm	increase
Hicks-Moorsteen TFP index
Czyżewski, et al. [57]	2008–2013	all agriculture	groups of farms	heterogeneous after 2010 decreases
Rusielik, et al. [168]	2009–2019	all agriculture	country	increase advantage
Others
Čechura, et al. [100]	2004–2011	pigs, milk, field crops	farm	decrease field crops, increase dairy and pigs
Marzec, et al. [169]	2004–2011	field crops	farm	increase

), which allows for the disaggregation of indicators and broadens the field of interpretation.

The results obtained by individual researchers, due to their inconsistency, do not allow for the determination of an unambiguous expected direction of changes in the TFP of Polish agriculture after integration with the EU. An undoubted problem in their interpretation was also the use of aggregated data for groups of farms, as well as for voivodeships and the entire sector in the country, as input variables. Thus, the aforementioned problem, resulting from the aggregation of data and others, may have occurred, e.g., the type of results and inputs taken into account, as well as the selection of the reference sample (e.g., countries for which efficiency calculations were made and compared with Poland). A relatively small number of studies utilised unit data from agricultural holdings, typically focusing on a specific production type (production orientation). Therefore, it is also difficult to compare the obtained results with the productivity of a selected narrow group in the absence of research on the impact of this feature on productivity. The only exception is the work of Zawalińska et al. [167], which used unit data from a large number of Polish FADN farms. However, even in this case, due to methodological reasons, the obtained results are not representative of the whole set of commercial agricultural holdings in Poland, let alone the whole population. The calculations were limited only to the panel of entities balanced in time, omitting a very numerous group of farms and observations made for them, which did not meet this requirement. Since they were not included in the study, the obtained results cannot be attributed to the entire sample, let alone extrapolated to the broader Polish FADN observation field [170]. This could also have influenced the systematic increase in TFP of Polish agriculture after integration with the EU, as shown by these authors, and thus, the discrepancy with the results obtained in the presented paper. To the author’s knowledge, so far, no one has attempted to make productivity calculations for the entire FADN sample in Poland while facing the problem of the lack of balancing of entities over time, and thus, in a way, allowing to indicate in what direction the TFP change for the entire sector after the EU integration took place. No one has also attempted to extrapolate the results to the entire population represented by the FADN sample, i.e., to the collection of commodity farms and, indirectly, the whole population.

5. Conclusions

Based on the conducted analyses, it was found that in the period immediately after Poland’s integration with the EU (2004–2011), there was a systematic decline in productivity in the general population of commercial agricultural holdings in the country, and taking into account potential distortions resulting from aggregation and the shadow economy in Poland, it should also be assumed that in the whole population of agricultural holdings. The downward trend was reversed in the following years when productivity increases were observed for the majority of the period. Despite the occurrence of significant changes in Polish agriculture related to the change in production technology as a result of the substitution of labour with capital [171], the phenomenon of convergence with other EU states was not confirmed, let alone the dominant influence of this phenomenon on shaping the direction of productivity changes in Poland. In the post-integration period, there was also no change in the expected directions of interaction between the main determinants of income. The theoretically formulated and empirically verified relations between subsidies and price relations (in this case, prices of agricultural raw materials on the world market) and productivity were confirmed. In the latter case, the level of determination was high enough to explain to a large extent the variability of productivity of Polish agriculture in the analysed period. This may therefore confirm the existence of an economic mechanism causing a technological “treadmill effect” in agriculture. This concept was first formulated by Cochrane in 1958 [172]. The decline in world market prices forces farms to improve productivity, optimise production costs, and seek innovation. In conditions of low-price elasticity of supply, this benefits the group of farms that are the first to introduce technological changes. They experience an increase in productivity and a decrease in unit costs. However, the adaptation and adoption of new technology by most farms (the spread of change) causes a further decline in agricultural product prices and a spiral of technological change [173].

On the other hand, the inclusion of Polish agriculture in the Common Agricultural Policy and the introduction of environmental and food safety requirements as production conditions may have contributed to the initial decline in productivity observed during the first years of EU membership. The necessity of non-productive investments and additional compliance costs likely worsened the output–input ratio. However, this does not fully explain why the downward trend reversed only eight years after integration; as such, an adaptation period appears excessively long given the increase in the scale of Polish agricultural production.

In the conducted study, only the dependencies and potential impact of the main determinants of profitability were taken into account, so the group of variables potentially explaining the change in productivity in Poland was significantly narrowed down. Indeed, the study omitted not only such macroeconomic variables as the exchange rate and interest rates, the level and change of GDP [174,175], but also the impact of changes in agrarian structure in agriculture [145,176], R&D expenditures and the extent to which new developments are put into practice and transmitted to farms [177], weather and climate change [178,179], the digitalisation of agriculture [180], the quality of farm labour [181,182], or the level of wealth as measured by the amount of agricultural household savings [183]. However, this requires separate research, the scope of which is beyond that assumed in this study.

The observed differences in measures of central tendency of productivity for the FADN sample and the results obtained after extrapolation to the whole general population may indicate the occurrence of the heterogeneity phenomenon. Therefore, it is recommended to deepen the research based on separate homogeneous groups of agricultural holdings, for which productivity changes may follow a different course over time than those presented in the study and which may be a result within the framework of the general population. Undoubtedly, the analysis of changes in productivity in groups separated based on the scale of production—among other things, such a feature based on differences in efficiency in Polish agriculture could be used in further research [145,162]—could also make it possible to state more precisely to what extent other main factors determining income had an impact on productivity and whether this impact was also homogenous. Building regression models for variables at the microeconomic level would also allow a wider list of potential explanatory variables to be included.