Redefining the Modifiable Areal Unit Problem within spatial econometrics, the case of the aggregation problem.

The paper focuses on the issue of the aggregation problem which is frequently discussed within spatial econometrics. Aggregation problem is one of two aspects of the modifiable areal unit problem (MAUP). The aggregation problem is connected with the volatility of the obtained results occurred when various compositions of territorial units for the same aggregation scale were applied. The objective of the present paper is considering the redefinition of aggregation problem and showing positive solution of the aggregation problem based on the empirical example of determining agricultural macroregions. In the article the aggregation problem was defined as a problem of establishment a particular composition of territorial units at a selected aggregation scale in a such a way that is remains in the quasi composition of regions within the undertaken research problem. The paper also presented the procedure for determining agricultural macroregions where the analysis of the spatial volatility of the agrarian structure and the current knowledge on the agriculture in Poland were applied. In addition, the paper considered the final areal interpretation problem connected with the incorrect determination of the area in relation to which final conclusions are drawn. The problem was presented based on the example of the establishment of the average concentration of the area of agricultural land in Poland with the use of the Gini index calculated for districts. The paper emphasised that ignoring the final areal interpretation problem in spatial analyses may lead to an apparent identification of the modifiable areal unit problem.