This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This study presents a systematic method for aggregating firm level sustainable value indicators to sector, region or industry levels. The proposed method applies the generalized sustainable value that is based on frontier production functions. The method is illustrated by an empirical application to the Finnish crop and dairy sectors, where the benchmark technology is estimated by data envelopment analysis. Our efficiency assessment shows that the representative crop farm achieves only about a half of its potential output. Efficiency of the representative dairy farm is somewhat higher.

Sustainability is a multidimensional concept covering environmental, social and economic dimensions. Operationalizing the qualitative concept of sustainability to practical quantitative measures has proved challenging due to the variety of meanings attached to sustainability [

The recent study by Kuosmanen and Kuosmanen [

Previous empirical applications of the conventional SV and GSV methods assess data of individual firms or aggregate entities such as industries, sectors, or countries (see [

The objective of this paper is to develop a systematic framework for a consistent aggregation of the firm level GSV indices to a sectoral, a regional, or an industry levels. By consistent aggregation, we mean that the generalized sustainable value measures of individual firms can be added up to obtain the generalized sustainable value measure of the aggregate entity, and that the same result is obtained if we assess the generalized sustainable value of the aggregate entity directly. The main contribution of this study is to show that the GSV method proposed in [

We first develop a consolidated theoretical framework for estimating an aggregate sustainability measure of firm’s performance for any group of firms in a specific sector, specialization, region, or any other group, such that resulting measures are consistent with the firm level estimates. We then apply data of the Farm Accountancy Data Network (FADN) for Finland and illustrate the proposed method by an empirical application to crop and dairy sectors. We estimate the benchmark technologies by data envelopment analysis (DEA) [

The remainder of the paper is organized as follows.

Following the definition of the

The rationale behind Equation (1) is analogous to the conceptual definition of the conventional SV method proposed in [

Since opportunity cost of resources is not directly observable, it must be estimated in one way or another. In economics, the opportunity cost of using a resource for a specific activity refers to the income foregone by not using the resource in the best alternative activity. However, the best alternative use is not always self-evident: it generally depends on the technology and the other resources available for the alternative activity. In mathematical terms, the technology available to a firm is described by a neoclassical production function

Applying the previous insights, the GSV measure (1) can be rewritten as:

Note that Equation (2) is not restricted to any particular functional form of the production function

We next consider an aggregation of firm level GSV measures to a sector, region and an industry level. This exercise is not as straightforward as it might seem. Firstly, consider the following example.

In theory, the optimal allocation in this example would involve creating an infinite number of infinitesimally small firms that use a positive but infinitesimally small quantity of resource, i.e.,

Hence, the average of the firm level GSV is different from the GSV of the average vector. Whether we use the firm level or the aggregate level data, it is important to ensure that the firm level GSV measures match with their counterparts at the aggregate level.

The purpose of the previous numerical example is to illustrate the importance of coordination and efficient allocation of resources across firms at the aggregate level efficiency assessment. In the previous example, the production function exhibits decreasing returns to scale, which favors small scale production. However, the example could be easily adapted to constant or increasing returns to scale. The main point of the example is to demonstrate that the SV or GSV statistics of the firm do not always add up to their counterparts at the industry level.

To develop a simple but systematic aggregation scheme, we propose the following aggregate GSV measure. Consider a group of firm

To pave the way for the aggregate GSV formulation, we introduce a

The average output of group

These average values

Given the production function

Alternatively, the aggregate GSV can be presented as:

Note that the proposed aggregate GSV measure has a compelling profit interpretation. Define the profit function as:

Without loss of generality, the output price can be normalized as one, so that

The aggregate GSV can be interpreted as the profit efficiency of the group

The proof to the theorem is provided in the appendix.

Formulation of the aggregate GSV can be extended to any group of firms, for example, firms located in a specific region. For estimating production frontier and aggregate GSV measures, the evaluated groups of firms should be sufficiently comparable, in the sense that all firms have access to the same production technology

We next outline two extensions to the aggregation method developed above.

Firstly, suppose we observe a sample of

Secondly, suppose the firms located in a specific region do not engage in a similar set of operations and have different production technology, e.g., dairy and crop farms. In this case, one can estimate the aggregate GSV of each group first. Since the GSV measure is expressed in monetary units (e.g., euros, dollars, or pounds), one can subsequently add together the resulting GSV measures. For example, the aggregate GSV of dairy and crop farms as two separate groups located in the same region can be calculated as the sum of the aggregate GSV measures of each group:

This section presents two illustrative applications of estimating the aggregate GSV measure at sector level based on the data of 332 Finnish dairy farms and 142 crop farms. The data were extracted from the Farm Accountancy Data Network (FADN) database. According to [

The economic output of crop farms is the total revenue from crops and crop products and the economic output of dairy farms is the total revenue from milk and other products in euro. Economic resources include labor in hours, total utilized agricultural area (UAA) measured in hectares and farm capital, which is comprised of livestock, permanent crops, land improvements, buildings, machinery and equipment, circulating capital, and measured in euro. Environmental resources include the total energy cost and cost of fertilizers. An overview of the key characteristics of the data is presented in

Descriptive statistics for the sample of dairy farms; year 2004, sample size n=332.

Variable | Mean | St. Dev. | Min | Max |
---|---|---|---|---|

Total output, € | 91,676 | 52,336 | 16,671 | 393,392 |

Labor, hr | 5,123 | 1,719 | 399 | 13,458 |

Farm capital, € | 261,150 | 191,099 | 18,779 | 1,481,375 |

Energy, € | 5,843 | 3,561 | 713 | 25,541 |

UAA, ha | 49.1 | 25.4 | 13.1 | 146.8 |

Fertiliser, € | 4,746 | 3,558 | 0 | 22,922 |

Descriptive statistics for the sample of crop farms; year 2004, sample size n = 141.

Variable | Mean | St. Dev. | Min | Max |
---|---|---|---|---|

Total output, € | 54,838 | 54,349 | 2,493 | 342,863 |

Labor, hr | 2,139 | 1,286 | 160 | 6,807 |

Farm capital, € | 228,020 | 162,428 | 32,599 | 997,866 |

Energy, € | 7,074 | 4,770 | 692 | 34,973 |

UAA, ha | 80.5 | 44.5 | 22.1 | 324.3 |

Fertiliser, € | 7,018 | 5,209 | 0 | 28,535 |

Firstly, the average values for the

The resulted efficiency score of the representative crop farm was 0.513, which means that the representative crop farm achieved only about half of its potential output. The efficiency score of the representative dairy farm was 0.649, that is, somewhat higher than for the representative crop farm. Next, the GSV values for both representative farms were calculated and resulted in about −52,102 euro for the representative crop farm and −49,615 euro for the representative dairy farm. The results are negative by construction, since in the DEA model, the frontier envelopes the observed data from above and only farms with GSV = 0 are diagnosed as efficient. This means that the loss due to inefficiency was about 50 thousand euro for both the representative crop and the representative dairy farm.

To obtain the aggregate GSV measures for dairy and crop sectors, the estimated GSV values of the representative farms were multiplied by the number of farms in the sectors (17,480 dairy farms and 28,979 crop farms). Thus, the aggregate GSV of the Finnish crop sector resulted in about −1,510 million euros in year 2004 and the aggregate GSV of the Finnish dairy sector resulted in about −876 million euros for the same year.

Finally, it is worth to recognize the limitations of the previous analysis, which is intended as an illustration of the methodological development. Firstly, the FADN sample is not a random sample, and hence not necessarily representative of the Finnish agriculture as a whole. We would expect the FADN farms to be on average more efficient than the non-FADN farms. Secondly, the environmental indicators considered in this application are very rough proxies. Thirdly, the DEA method used for estimating the frontier assumes away noise, which is a very restrictive assumption in the present application. Addressing these problems would provide a fruitful avenue for future research.

This paper extends the scope of previous studies of the firm level generalized sustainable value measures, by proposing a systematic approach to measuring sustainability performance of firms at the aggregate level. An aggregate sustainability measure can be estimated from empirical data by applying frontier approaches and is consistent with the firm level estimates. The proposed aggregation method was illustrated by an empirical application to the Finnish crop and dairy sectors. The estimated efficiencies of the representative farms allow, firstly, to assess the performance of an average farm in each sector in terms of resources used and, secondly, to compare the performance of average farms between the sectors. Finally, the estimated GSVs for each sector provide a simple, but practical, measure of sustainability performance. This measure can be usefully applied not only in the comparative analysis of different agricultural sectors, but also for any other group of firms in a specific specialization, region, or other category.

Supplementary materials can be accessed at:

The authors declare no conflict of interest.