Calculation of weighting coefficients In the Total Calculation, the results for the whole country are obtained by summing up the figures of the profitability bookkeeping farms. Since there are about 650 bookkeeping farms and approximately 42,000 enterprises in the whole country, the figures of each bookkeeping farm are included in the total sum multiple times according to the weighting coefficient determined for that specific farm. The weighting coefficients of the bookkeeping farms differ in size. This is because, in terms of type of farming and size class, certain types of farms are proportionately more represented among the bookkeeping farms compared to all farms in Finland than other types of farms. Therefore, as a rule, bookkeeping farms representing better-represented farm types receive a smaller weighting coefficient than other bookkeeping farms. In the Total Calculation, one bookkeeping farm always represents at least one, but typically a rather large number of all Finnish farms. The weighting coefficients are determined in such a way that the overall picture of agriculture calculated using them corresponds to reality as closely as possible. The calculation method for the weighting coefficients is a two-step process. In the first step, preliminary weighting coefficients are calculated for each farm using a system in accordance with the EU's FSDN system and the basic reviews of profitability bookkeeping. In this process, the weighting coefficient of each bookkeeping farm in any given year depends on how large a number of farms the farm represents within its own type of farming and farm size class in its respective subsidy area. Throughout the review period, the type of farming and farm size classification is based on the Standard Outputs (SO) introduced by the EU in 2010. The preliminary weighting factors obtained in this way are refined in the second stage of the calculation using constrained nonlinear optimization, such that the number of farms and the cultivated areas--multiplied by the weighting factors and summed--correspond to the actual total number of farms and total cultivated area at the national level. The weighting factors are adjusted so that the numbers of farms by size class and production type, as well as the cultivated areas by support region, calculated using these factors correspond to the actual numbers of farms and cultivated areas. In all the aforementioned constraints, a maximum difference of one percent compared to the actual values is allowed for the farm numbers and cultivated areas calculated with the weighting coefficients. Through these constraints, the results of the weighting are made to correspond even better to Finland's actual distributions of farm sizes, types of farming, and cultivated areas. Taking the constraints into account, the aim is to keep the changes in the weighting coefficients compared to the preliminary weights as small as possible, so that the impact of individual bookkeeping farms on the result does not become too large. In practice, the function to be minimized in the non-linear optimization is the sum of squared differences between the final and original weighting coefficients. Iterative quadratic optimization is used as the optimization method. Naturally, there is some degree of inaccuracy associated with the results calculated through weighting, as the set of bookkeeping farms subject to weighting cannot perfectly depict Finnish agriculture across all variables. In the weighting system, however, the most important indicators describing the scale of agricultural activity have been made to correspond to reality as closely as possible through the constraints described above. The Total Calculation for agriculture, based on the weighting system, thus provide a very coherent overall picture of the entire sector. Classification of enterprises Enterprises are classified in the profitability bookkeeping in accordance with the EU farm typology.
