Abstract
The paper focuses on the issue of the aggregation problem, which is frequently discussed within spatial econometrics. The aggregation problem is one of the 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 to consider 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 establishing 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 basing 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.
Highlights
The modifiable areal unit problem (MAUP) is a crucial issue that is given much consideration within spatial econometrics
The paper 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
The paper presents the aggregation problem, which constitutes one of the aspects of the issue that is frequently discussed in spatial economics – the modifiable areal unit problem (MAUP), one of the issues debated within spatial econometrics
Summary
The modifiable areal unit problem (MAUP) is a crucial issue that is given much consideration within spatial econometrics. The perceived problems have led to the formulation of the modifiable areal unit problem within which two aspects are considered – the scale problem and the aggregation problem (see Arbia, 1998). A positive solution of the aggregation problem will be shown based on the empirical example related to the need for designating the borderlines of SGM macroregions in Poland. This will be performed for a EU system of collecting accountancy data from farms – the Farm Accountancy Data Network (FADN). It will be proved that a positive solution consists in designating precisely one composition of territorial units at the aggregation scale accepted for the research. The issue of the modifiable areal unit problem was already considered in the works of the following: Gehlke & Biehl (1934), Yule & Kendall (1950), Robinson (1950), Blalock (1964), Openshaw & Taylor (1979), Openshaw (1984a, 1984b), Reynolds (1988), Fotheringharn & Wong (1991), Holt et al (1996), Tranmer & Steel (2001), Arbia (2006), Manley et al (2006), Suchecki (2010), Flowerdew (2011) and Pietrzak (2014a, 2014b)
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