How Can Overinvestment in Farms Affect Their Technical Efficiency? A Case Study from Poland

Abstract

Farm overinvestment is highly dangerous in how it affects productivity and profitability. Therefore, it imperatively needs to be measured in the context of investment support offered under the Common Agricultural Policy. In turn, technical efficiency is one of the best methods for measuring farm investment. This paper analyzes the technical efficiency of 3273 Polish farms based on unpublished FADN (Farm Accountancy Data Network) data from 2010–2019. The purpose of this study was to indicate the level of, and changes in, technical efficiency of Polish farms in function of their investment levels, with particular emphasis on overinvested holdings. Technical efficiency was examined using stochastic frontier analysis (SFA). The study proved a decline in technical efficiency in underinvested farms and in those affected by absolute overinvestment (i.e., ones where the assets-to-labor ratio grows while labor productivity drops).

1. Introduction

1.1. Investment in Farms

Farming continues to be a major part of the Polish economy [1,2,3], and serves the overarching goal of delivering food [4,5]. Hence, it is justified to place focus on operators who constitute that sector, i.e., agricultural holdings. Their major commitment is to make agricultural production more efficient on a continuous basis [6,7]. One of the ways to achieve that is by making a better use of inputs [8] which, under certain conditions, may involve (if not imperatively require) investment measures. In this context, note that agricultural investments are driven by the basic characteristic of farm production, i.e., it being dependent on natural conditions [9,10,11]. Adjusting the use of productive inputs enables a better use of farm resources, while also ensuring that environmental quality is preserved [12]. Due to its numerous particularities, agriculture requires a broader use of political instruments than other sectors [13,14,15]. The purpose of subsidizing it is to enhance farmers’ incomes as well as to improve food security [16,17]. This is one of the reasons why Polish agriculture has received strong financial support over recent years under the Common Agricultural Policy (CAP) [18], one of the oldest European Union policies [19]. While public support usually carries positive effects, it also has negative impacts, including the way it interferes with economic systems [20,21]. This is also true for agricultural investment subsidies [22]. Although farm investments are supposed to be development-oriented, their implementation differs in function of available resources or the economic conditions the farm operates in [23,24]. The Polish farmers’ interest in investing is all the more important since Polish agriculture still requires restructuring efforts, despite a considerable increase in investment expenditure after Poland’s accession to the EU [25]. What makes it even more relevant is that today’s farmers must find the right balance between investing, developing their production and being more environmentally friendly [26].

Polish agriculture needs investment in order for farms to become more competitive and technically efficient [27]. Investment in new productive inputs, as a part of agricultural modernization efforts, contributes to improvements in farming efficiency [28]. Investing is essential in making economic sectors more efficient, and is a common practice in many industrialized countries [29].

1.2. Overinvestment in Farms

Numerous studies point to the need for agricultural investments because they provide the basis for an increase in food production volumes and for improvements in technical and economic efficiency [30]. The extent to which humans intervene in the food production process to ensure food security [31,32,33] is usually measured by the amount of investment expenditure [34,35]. Therefore, farms need efficient, innovative investments [36,37,38,39].

However, some studies claim that smaller farms make excessive investments, while others point to the growing gap between small and large farms because of the latter investing more. Although investment is supposed to be positively correlated with efficiency, the studies carried out so far [40,41] identify overinvestment as a major problem which does not result in greater efficiency. This is especially true for investments co-financed with public funds. Thus, subsidizing the agricultural sector may lead to conflicts between the co-financing institution (whose goal is to make agricultural production more efficient) and the recipient of funds, i.e., the farmer (who seeks financing not only in order to enhance their production efficiency but also for the sole purpose of adding a gain to their resources) [42]; this is also referred to as moral hazard [43]. That hazard would be smaller if the farmers were held personally accountable for all investment subsidies [44]. All of these conflicts may lead to a suboptimal use of cash flows [45,46], because a relationship exists between external financing and investment decisions [47,48]. It is manifested in a number of ways, including overinvestment at farm level [49].

Irrespective of the sector to which they belong, economic operators get overinvested because of an irrational use of assets which is intended to increase company value or have a positive effect on financial performance, but is based on an overly optimistic evaluation of market conditions [50,51,52,53]. Ultimately, the expected return on investment projects is below the interest rate offered in capital markets [54,55,56]. In agriculture, overinvestment is manifested by an increase in the assets-to-land ratio [57] accompanied by an inefficient use of resources [58]. The reason for this situation may be excessive access to public funding sources. This leads to a decline in production efficiency, a disruption in profits [59], an increase in production costs and a drop in competitiveness [60]. Note that an efficient use of productive inputs determines the level of competitiveness at local, regional and international levels [61]. Also, overinvestment can entail fluctuations in agricultural production volumes and prices [62,63], or may result in a high risk of greater environmental pollution [58]. Therefore, it is not only the optimization of the size of the investment that is important, but also the directions. The most effective may be high-technology investments, which not only improve economic results at the farm level, but also contribute to achieving social goals, such as caring for the environment.

1.3. The Importance of Technical Efficiency of Farms

Technical efficiency (TE) is an important aspect from the perspective of investigating the problem of overinvestment. Viewed as improvements in using the potential of farming resources, it also is a development driver for farms [64]. This development is implied by various factors, but the search for the relationship between investment and technical efficiency is legitimized by seeking the optimal level of investment. Efficiency of agricultural production has an impact in making farms more competitive [65] and is one of the key drivers of competitiveness at the sector level [66]. This, in turn, increases the monetary benefits to farms from their production. Investing some of the capital in efficient investments can help the farm grow even better. Inefficiency carries a number of different consequences, including low production levels at a given level of inputs, under-use of resources and an increase in production costs [67]. Looking for ways to improve technical efficiency by involving various factors can be an important approach in investment research. Technical efficiency is a widely employed category in research on agricultural holdings. For instance, it has been demonstrated that improvements in technical efficiency may reduce agricultural greenhouse gas emissions [68], and that the higher farmers’ education level, the greater their technical efficiency [69]. In a study based on stochastic frontier analysis, Vogel et al. [70] proved that the farmers may improve their production performance by an average rate of 9.4% while reducing methane emissions by 8.7%. Using coffee manufacturing as an example, Tamirat and Tadele [71] pointed to the fact that technical inefficiency of agricultural production is impacted by education, age, gender, area of land resources, animal numbers, reliance on loans, non-agricultural activities and the kind of seeds used [72]. Ngango and Hong [73] reported similar findings in their study on Rwandan maize production volumes. They also proved the existence of a relationship between farm size, livestock numbers and technical efficiency. The cited studies prove that various factors can influence improvement in technical efficiency of farms. It is therefore important to compare different variants and constantly search for the most important factors. The technical efficiency of farms can be examined using stochastic frontier analysis, a tool employed by researchers in investigating the technical efficiency of economic operators [74,75]. High levels of technical efficiency indicate that the farm optimizes its production expenditure, whereas low levels suggest there is room for improvement in how efficiently the inputs are used [76].

Instead of focusing on investment projects on a case-by-case basis, this study examines the level and efficiency of investments in farm groups (based on results derived from microdata). Therefore, the need arose for adopting a broader approach that also takes account of other factors, such as agricultural labor productivity.

The aim of this study is to indicate the level of and changes in technical efficiency of Polish farms depending on the level of their investment, with particular emphasis on overinvested farms. The research objective was achieved by answering the following research questions:

-

How can overinvestment be measured using labor productivity and assets-to-labor ratio?

-

What factors determine the technical efficiency of farms?

-

Can overinvestment in farms affect their technical efficiency?

The proposed study provides an important contribution to the research on farm efficiency in the context of investment optimization. An additional aspect addressed in this study is the analysis of the investment level, with particular emphasis on overinvestment in farms and its impact on technical efficiency.

2. Data and Methods

This research used Polish farm microdata from the European Union’s Farm Accountancy Data Network (FADN), a European system for accounting data collection from all member countries of the EU. Data are collected from commercial farms in accordance with a unified methodology [77]. This study needed to determine how the phenomena evolved over time, and therefore data were retrieved from farms which kept continuous records from 2010–2019. The choice of the research period (2010–2019) was based on several considerations. Poland became a member of the European Union in 2004. The period of increased investment in agriculture began around 2006. The first year of this analysis, 2010, is one of the first years in which the effects of investments made with the support of the Common Agricultural Policy can be observed. The last year of analysis adopted is 2019, and the authors dealt with a 10-year analysis. In addition, the available data after 2019 are subject to changes that have taken place in global markets and may have affected farms, such as changes in fertilizer prices. In total, there were 3273 farms in the database, which accounts for ca. 27% of farms covered by the system each year (12,167 in 2019).

The study defines agricultural overinvestment as a condition where investment is excessively high compared to production potential [49]. This is the case when an increase in the assets-to-labor ratio does not enhance—or grows faster than—labor productivity. Hence, two essential parameters need to be developed in order to determine the levels of overinvestment: the assets-to-labor ratio and labor productivity.

The calculations were based on microdata and used the FADN’s system variables. The study period is 2010–2019. Panel data were created by calculating two-year arithmetic means for the results in each group (which resulted in obtaining 5 periods) in order to determine the changes in labor productivity (Equations (1) and (2)) and in the assets-to-labor ratio (Equations (3) and (4)). The two parameters were calculated by comparing the last period against the first. Investment levels were calculated separately for each farm.

$${LP}_t={\displaystyle \frac{\sum _t^{t+1}(\frac{SE410-SE360-SE406-SE605}{SE010})}{2}}$$

(1)

$$\Delta LP=\left({\displaystyle \frac{{LP}_{t5}-{LP}_{t0}}{{LP}_{t0}}}\right)\ast 100\mathrm{\%}$$

(2)

where:

LP: labor productivity

SE410: gross value added

SE360: depreciation

SE406: investment subsidy installments

SE605: operating subsidies

SE010: total labor inputs in AWU (Annual Work Unit)

Gross value added is a key metric used in calculating farm efficiency. Also, after depreciation is excluded, it shows the net value added—the basic category of agricultural income [78].

After determining labor productivity, the study proceeded to calculating the changes in the assets-to-labor ratio (Equations (3) and (4)). The value of fixed assets less the value of land per full-time employee was used as the metric. The rationale behind the above approach is that overinvestment is a problem which ultimately boils down to a mismatch between the output and the extent of investment in machinery and buildings. Just as in the case of labor productivity, average values were calculated for the selected periods, and the growth/decline rate was defined.

$${ALR}_t={\displaystyle \frac{\sum _t^{t+1}(\frac{SE441-SE446}{SE010})}{2}}$$

(3)

$$\Delta ALR=\left({\displaystyle \frac{{ALR}_{t5}-{ALR}_{t0}}{{ALR}_{t0}}}\right)\ast 100\mathrm{\%}$$

(4)

where:

ALR: assets-to-labor ratio

SE441: fixed assets

SE446: land, permanent crops and production quotas

SE010: total labor inputs (AWU)

The farms were divided into five groups according to levels of overinvestment, where the basis was the relationship between labor productivity growth and fixed assets growth. The separation of the 5 groups was dictated by the possibility of analysis in the database. Using 5 groups allowed us to show different configurations in the relationship between labor productivity and assets-to-labor ratio. More groups could cause difficulties in analysis and lack of universality of results.

I.

Absolute overinvestment: this is the case for farms where labor productivity drops while the assets-to-labor ratio grows:

ΔLP < 0     ∧     ΔALR > 0

II.

Relative overinvestment: this is the case for farms where both labor productivity and the assets-to-labor ratio increase but the increase in the assets-to-labor ratio is greater than the increase in labor productivity:

ΔLP > 0     ∧     ΔALR > 0     ∧     ΔLP < ΔALR

III.

Underinvestment: this is the case for farms where both labor productivity and the assets-to-labor ratio are on the decline:

ΔLP < 0     ∧     ΔALR < 0

IV.

Optimum investment: this is the case for farms where both labor productivity and the assets-to-labor ratio are on the increase, and labor productivity grows faster than the assets-to-labor ratio:

ΔLP > 0     ∧     ΔALR > 0     ∧     ΔLP > ΔALR

V.

Optimum investment with no increase in the assets-to-labor ratio: this is the case for farms where labor productivity grows while the assets-to-labor ratio does not:

ΔLP > 0     ∧     ΔALR < 0     ∧     ΔLP > ΔALR

In the case of some underinvested farms, farms were detected that invested very little (below PLN 10,000) in the period under study. This meant that they could not be classified as farms investing optimally or overinvested. Therefore, an additional group was distinguished: other (there were 318 such farms in the database). It is important to study this group in the model, because it is necessary to analyze in which direction investment decisions will lean in the future. Will they be underinvested in the future, or, conversely, by gradually increasing their investments, will they be able to optimize their investment approach?

Having determined the different investment levels for the sample considered, the study moved to estimating the technical efficiency of farms at different investment levels, with particular emphasis on overinvested holdings.

Technical efficiency can be examined using a parametric technique, namely stochastic frontier analysis (SFA), or a non-parametric model, i.e., data envelopment analysis (DEA). As DEA fails to take statistical noise into account, this study relies on SFA, and uses a method developed by Aigner et al. [79] and by Meeusen and van den Broeck [80]. Stochastic frontier analysis is a way to describe the relationships prevailing in the sector or industry considered by comparing the operators’ inputs and outputs, taking two components into account: the random effect and inefficiency [81]. At the beginning, it requires a function (e.g., a production function) to be defined because output and input levels must be known. Any deviations from the estimated frontier are considered to be caused by inefficiency. This study uses a model enhanced with time variables [82]. A generalization of the model was proposed by Battese and Coelli [83]. A stochastic frontier model can also be estimated with time-invariant inefficiency by adjusting the conventional techniques for the estimation of fixed effects. This would allow us to correlate inefficiency with frontier regressors and to avoid the assumptions regarding the distribution of the coefficient ui (the inefficiency error term) [84]. However, the time-invariant inefficiency was called into question, especially in the case of empirical analyses based on datasets spanning over multiple years. In an effort to mitigate that restriction, Cornwell et al. [85] approached the problem by proposing the following stochastic frontier model with specific individual slopes (Equations (5) and (6)):

$$\begin{array}{ccc}{y}_{it}=\alpha +{x^{\prime }}_{it}\beta +v_{it}\pm u_{it},& i=1,...,N,& t=1,...,T_i\end{array}$$

(5)

$$u_{it}={\varpi }_i+{\omega }_{i1}t+{\omega }_{i2}{t}^2$$

(6)

where:

y: output of unit i in period t;

x: inputs of unit i in period t;

v: two-sided exogenous production shocks which may either increase or reduce output volumes;

u: non-negative single-sided inefficiency term.

The parameters of the model are estimated by extending conventional estimators of panel data with fixed or variable effects; this allows us to determine a specific inefficiency pattern for each unit. The purpose of SFA is to estimate the basic production technology and to measure technical inefficiency [86]. Hence, SFA was used in examining farm overinvestment with a view to indicating the most and the least efficient farms at each investment level.

The assumption behind the production function is that all enterprises are technically efficient, and the function can be employed in gauging the level of inputs used to attain a given production volume (output). In turn, the assumption behind the stochastic frontier model boils down to extracting the units which are inefficient compared to the most efficient unit in the group considered (which determines the frontier of efficiency). Hence, the deviations from the frontier correspond to inefficient units, and their inefficiency is caused by random or erroneously defined terms. As a result of stochastic estimation procedures, two random effects are taken into account, which increase the distance from the “frontier”. The first one reflects random noise while the role of the second is to model the potential inefficiency [87]. If units distant from the frontier are inefficient, this allows us to estimate the relative efficiency of groups identified in the study, based on the relationship between observed production data and an ideal (potential) production scenario [88].

This study relies on an equation of the production function for panel farm data, expressed as [89] (Equation (7)):

$$y_{it}=\exp f\left(x_{j,it},t,\beta \right)\ast \exp \left(v_{it}\right)\ast \exp \left(-u_{it}\right),$$

(7)

where:

i: successive farm indexes, i = 1, …, I, with I as the sample size,

j: successive input indexes, j = 1, …, l,

yit: output of farm i at time t (production volume),

xj,it: input j of farm i at time t (productive inputs used),

β: vector of parameters to be estimated,

vit: measurement errors or random effects caused, e.g., by atmospheric impacts,

uit: positive random variable related to inefficiency (TE),

f(.): appropriate function form.

Next, the study measured the efficiency index which, in the case of the stochastic frontier function, is the ratio between the observed output (production) and the maximum output attained in the environment in the context of available technologies [90]. Thus, it takes the following form [89] (Equation (8)):

$${TE}_i={\displaystyle \frac{y_i}{y_i^{\mathrm{*}}}}={\displaystyle \frac{\exp (\beta x_i+v_i-u_i)}{\exp (\beta x_i+v_i)}}=\exp (-u_i)$$

(8)

TE ranges from 0 to 1 [91], whereas inefficiency is measured as the ratio between the output of object i and the output attained by an efficient object through the use of the same vector of inputs. The parametric SFA method allows us to determine the relative efficiency whose maximum physical value of y_i, i.e., $\mathrm{e}\mathrm{x}\mathrm{p}({\beta }_0+\sum _{j=1}^k{\beta }_j\ln x_{ij}+v_i)$, is reached when u_i = 0, and thus TE_i = 1 (for an efficient object) [89].

Stochastic frontier analysis is an important method for investigating agricultural efficiency as it takes account of measurement errors, missing variables, and weather factors [92]. The estimation of the model made it possible to determine what portion of the total variation was caused by inefficiencies and what portion was due to random effects. Once the index was “cleaned” of random errors, the next stage estimated the technical efficiency for each farm in each year. That index falls within the interval 0 to 1; if a farm’s efficiency is zero, the index is 0. In turn, in the case of a reference farm which maximizes the use efficiency of its inputs, the index is 1.

3. Results and Discussion

At the initial stage of distinguishing groups of farms according to the level of investment, it was established that the largest percentage in the studied sample were underinvested farms (26%); followed by absolutely overinvested farms (25%); optimum investment, no increase in ALR (22%); optimum investment, increase in ALR and LP (19%); and relatively overinvested farms (8%). The justification for examining technical efficiency results from the large percentage of underinvested and absolutely overinvested farms. In addition, these were farms that significantly worsened their economic results in the last year of analysis, compared to the first. The situation was different for the remaining investment levels. All of them improved their economic results.

As stochastic frontier analysis is a benchmarking method, the study developed one common model for all farms, and separate models for each investment level. The purpose of this approach was to compare the farms at different investment levels against the benchmark. The model was built based on variables whose descriptive statistics are presented in

Table 1. Descriptive statistics of the variables included in the model.

Variable (Unit)	Overinvestment Group	Mean		Std. Dev.		Min.		Max.
		2010	2019	2010	2019	2010	2019	2010	2019
Q: SE131 (PLN thousand)	underinvested	185.37	199.82	312.12	368.60	−12.25	−12.41	5114.00	5766.09
	other	111.91	117.92	161.62	197.40	2.67	5.84	1589.01	1877.48
	optimum investment, no increase in ALR	217.60	351.31	352.27	578.71	12.12	6.52	3720.03	5478.26
	optimum investment, increase in ALR and LP	325.33	620.29	998.22	1580.48	11.75	11.53	18,800.00	30,200.00
	absolute	315.78	360.05	759.91	594.86	21.74	5.92	14,700.00	7688.76
	relative	435.56	616.22	1374.99	1224.53	9.45	11.51	14,500.00	10,500.00
L: SE010 (ha)	underinvested	1.80	1.89	0.97	1.11	0.25	0.20	12.89	17.96
	other	1.80	1.379	1.57	0.72	0.46	0.20	27.27	6.50
	optimum investment, no increase in ALR	2.07	2.29	1.81	2.43	0.33	0.44	30.05	46.89
	optimum investment, increase in ALR and LP	2.64	2.48	5.27	4.69	0.62	0.28	111.35	95.00
	absolute	2.34	1.97	3.23	1.86	0.66	0.17	61.99	26.74
	relative	2.86	2.42	5.29	3.45	0.73	0.22	66.13	40.41
Z: SE025 (ha)	underinvested	34.05	34.42	57.94	55.23	0.00	0.07	906.00	963.00
	other	20.23	17.76	20.68	17.71	0.08	0.00	163.89	158.98
	optimum investment, no increase in ALR	31.90	38.04	45.11	54.79	0.00	0.00	743.00	715.00
	optimum investment, increase in ALR and LP	49.43	57.84	162.36	147.18	0.00	0.00	2654.00	2424.61
	absolute	56.88	58.35	128.97	84.06	0.00	0.00	2126.00	1288.69
	relative	73.96	77.40	283.43	242.34	0.00	0.00	3487.70	3141.24
K: SE441-SE446 (EUR thousand)	underinvested	147.09	179.28	272.31	356.27	10.41	6.61	4860.00	6099.40
	other	92.44	89.67	131.39	157.03	11.45	10.48	1287.90	1849.45
	optimum investment, no increase in ALR	175.02	249.65	285.86	442.45	13.67	15.34	3078.73	5213.12
	optimum investment, increase in ALR and LP	276.63	471.58	1088.77	1634.06	13.23	12.79	20,900.00	32,600.00

SE131—total production. SE010—total labor input. SE025—agricultural area. Source: own compilation based on the FADN microdatabase, n = 32,356, STATA/MP 17 (2 cores).

. The model estimation results are presented in

Table 2. Parameters of the estimated stochastic frontier analysis model for the whole sample of farms.

Specification	Coeff.	Std. err.	P > |z|
Frontier
lnK	0.7245	0.0057	0.000
lnL	0.1047	0.0063	0.000
lnZ	0.1494	0.0076	0.000
Usigma
_cons	−3.8432	0.0265	0.000
Vsigma
_cons	−3.9453	0.0181	0.000
sigma_u	0.1464	0.0019	0.000
sigma_v	0.1391	0.0013	0.000
lambda	1.0524	0.0029	0.000

lnK—natural logarithm of capital; lnL—natural logarithm of work; lnZ—natural logarithm of land. Source: own compilation based on the FADN microdatabase, n = 32,356, STATA/MP 17 (2 cores).

.

The coefficients presented in Table 2 and

Table 3. Parameters of estimated stochastic frontier analysis models for each overinvestment level.

		Frontier				Usigma				Vsigma
		Coeff.	Std. err.	P > |z|		Coeff.	Std. err.	P > |z|		Coeff.	Std. err.	P > |z|
underinvested	lnK	0.7240	0.0117	0.000	_cons	−3.5697	0.0415	0.000	_cons	−4.0027	0.0336	0.000
	lnL	0.0719	0.0135	0.000	-	-	-	-	sigma_u	0.1678	0.0035	0.000
	lnZ	0.1824	0.0174	0.000	-	-	-	-	sigma_v	0.1351	0.0023	0.000
	-	-	-	-	-	-	-	-	lambda	1.2417	0.0052	0.000
other	lnK	0.7290	0.0197	0.000	_cons	−3.6225	0.0772	0.000	_cons	−3.9167	0.0587	0.000
	lnL	0.0865	0.0170	0.000	-	-	-	-	sigma_u	0.1634	0.0063	0.000
	lnZ	0.0407	0.0211	0.053	-	-	-	-	sigma_v	0.1411	0.0041	0.000
	-	-	-	-	-	-	-	-	lambda	1.1585	0.0095	0.000
optimum investment, no increase in ALR	lnK	0.7326	0.0144	0.000	_cons	−4.1244	0.0719	0.000	_cons	−3.9911	0.0432	0.000
	lnL	0.1547	0.0164	0.000	-	-	-	-	sigma_u	0.1272	0.0046	0.000
	lnZ	0.1542	0.0167	0.000	-	-	-	-	sigma_v	0.1359	0.0029	0.000
	-	-	-	-	-	-	-	-	lambda	0.9355	0.0070	0.000
optimum investment, increase in ALR and LP	lnK	0.8937	0.0125	0.000	_cons	−4.4346	0.0941	0.000	_cons	−3.7436	0.0396	0.000
	lnL	0.0168	0.0157	0.000	-	-	-	-	sigma_u	0.1089	0.0051	0.000
	lnZ	0.1267	0.0159	0.000	-	-	-	-	sigma_v	0.1538	0.0030	0.000
	-	-	-	-	-	-	-	-	lambda	0.7078	0.0076	0.000
absolute	lnK	0.5571	0.0124	0.000	_cons	−3.7205	0.0559	0.000	_cons	−4.0650	0.0441	0.000
	lnL	0.2076	0.0131	0.000	-	-	-	-	sigma_u	0.1556	0.0043	0.000
	lnZ	0.1835	0.0171	0.000	-	-	-	-	sigma_v	0.1310	0.0029	0.000
	-	-	-	-	-	-	-	-	lambda	1.1880	0.0066	0.000
relative	lnK	0.6814	0.0166	0.000	_cons	−4.5922	0.1394	0.000	_cons	−4.0922	0.0663	0.000
	lnL	0.0585	0.0200	0.003	-	-	-	-	sigma_u	0.1006	0.0070	0.000
	lnZ	0.1988	0.0245	0.000	-	-	-	-	sigma_v	0.1292	0.0043	0.000
	-	-	-	-	-	-	-	-	lambda	0.7788	0.0105	0.000

lnK—natural logarithm of capital; lnL—natural logarithm of work; lnZ—natural logarithm of land. Source: own compilation based on the FADN microdatabase, n = 32,656, STATA/MP 17 (2 cores).

describe the relationships between the independent variables (labor, land and capital resources) and the dependent variable (production value). From the point of view of the analysis, the relationship between inefficiency and the random component is important.

Next, stochastic frontier models were built in a similar way for each overinvestment level. The authors intentionally developed separate models for each overinvestment model, and a single model for all farms covered by the database. The purpose of this approach was to create a single benchmark for all farms. The absence of a model estimated for all farms would make it difficult to determine the differences in technical efficiency between overinvestment levels.

The p-value allowed us to determine the statistical significance of each variable in the model, and proved all of them to be significant. These results made it possible to determine what portion of variation is caused by inefficiencies and what portion is due to random effects (

Table 4. Components of variation in technical efficiency of farms grouped by overinvestment level.

Specification	Underinvested	Other	Optimum Investment, No Increase in ALR	Optimum Investment, Increase in ALR and LP	Absolute	Relative
sigma_u	0.1678	0.1634	0.1272	0.1089	0.1556	0.1006
sigma_v	0.1351	0.1411	0.1359	0.1538	0.1310	0.1292
%u	60.66%	57.30%	46.67%	33.38%	58.53%	37.76%
%v	39.34%	42.70%	53.33%	66.62%	41.47%	62.24%

%u: contribution of inefficiency to variation in technical efficiency; %v: contribution of random effects to variation in technical efficiency. Source: own compilation based on the FADN microdatabase, n = 32,656, STATA/MP 17 (2 cores).

).

It turns out that inefficiency contributed 60.66% to variation in underinvested farms, 58.53% in those affected by absolute overinvestment and barely 33.38% in holdings at optimum investment levels in which random effects were accountable for the remaining portion of variation (66.62%). It means that investments make farms more technically efficient if they lead to improvements in labor productivity at the same. Investment in capital significantly improves agricultural productivity [93]. Gaviglio et al. [94] showed that there is scope to improve farm technical efficiency (for example, by improving production technology for crops). Optimization of labor resources in agriculture is achieved precisely through investment. The release of surplus labor is also beneficial to other sectors of the economy. At the same time, it is important that subsequent investments made in farms do not lead to overinvestment. This study shows the relevance of the study of overinvestment, in which one of the parameters determining it is labor productivity along with technical efficiency.

Next, the study estimated the efficiency ratio for each farm, and then analyzed it at each overinvestment level. The efficiency ratio was estimated for each year covered by the analysis, i.e., within a 10-year period, for a single common benchmarking model. This approach allowed us to identify the trends at each overinvestment level, and then to compare the efficiency ratios between the initial and final year (2010 and 2019, respectively).

At each overinvestment level and in each year, the efficiency ratio fell in the interval of 0 to 1, and was closer to 1 in the most technically efficient units. Conversely, it moved closer to 0 for farms at lower levels of efficiency. Underinvested farms and holdings affected by absolute overinvestment proved to have had the best initial efficiency levels (in 2010). However, over the study period, their efficiency ratio clearly followed a downward trend. As a consequence, in 2019, farms facing underinvestment or absolute overinvestment reported the lowest technical efficiency. In turn, farms at optimum investment levels, whether accompanied by growth in the assets-to-labor ratio or not, were initially the least technically efficient. However, they embarked on a growth path which resulted in them reaching the highest levels of technical efficiency at the end of the study period. Their technical efficiency ratios improved by 8 and 6 percentage points, respectively, reflecting a positive trend. In the last year covered by the study, farms affected by relative overinvestment witnessed a slight improvement in their technical efficiency, compared to 2010 figures. Also, their technical efficiency ratio fluctuated over the study period.

The study proves that both underinvestment and overinvestment can negatively affect the technical efficiency of farms. It is significant that at both levels of overinvestment (underinvestment and absolute overinvestment), labor productivity decreases. Other factors, such as farm size, also have a significant impact on the change in labor productivity. For larger farms, by economic size class, the change in labor productivity is significantly affected by the level of investment, capital productivity and direct payments [95]. Studies show a stronger relationship between improvements in labor productivity and the productivity of land and capital [96].

These findings make it reasonable to estimate the level of overinvestment because of the clear growth trend recorded in farms who made sound investments. Again, there are grounds for concluding that reasoned investments which result in improving technical efficiency must be accompanied by growth in labor productivity in the farm concerned. Indeed, improvements in labor productivity are a condition for enhancing the economic performance of businesses, which indicates the existence of a relationship between the amount of investment and labor productivity. Hence, optimum investments lead to an increase in technical efficiency (Figure 1).

4. Conclusions

Engaging in investment projects is among the decisions of key importance for a farm’s development. Hence, the choice of financing method is determined not only by expected modernization outcomes, but also by potential future liabilities (e.g., the need to repay a loan). This makes subsidies offered under the CAP a popular financing option.

A boost in investment should drive improvements in technical efficiency, as is the case in farms dealing with relative overinvestment. Another finding is that the greatest improvement in technical efficiency was witnessed in farms at optimum investment levels (whether accompanied by growth in the assets-to-labor ratio or not). The analysis of technical efficiency proved the rationale behind investigating the levels of overinvestment, because investments which lead to enhancements in technical efficiency are justified if they also result in increased labor productivity.

Of course, the research conducted and the results obtained have their limitations. Some overinvested farms may rationalize their investment policy in the future, becoming optimal entities. The opposite situation may also take place. Nevertheless, the existence of the phenomenon of overinvestment, especially if it occurs among beneficiaries of public support, makes it necessary to point out some recommendations for policymakers. First of all, individual projects should be evaluated more strictly, not only in terms of meeting formal requirements, but above all in terms of their economic rationality. In addition, farmers should be made aware of the negative consequences of overinvestment.