Navigation – Plan du site

AccueilTransversalitésDossiers2006-200413ème Colloque Européen de Géogra...Spatially aggregated data and var...

13ème Colloque Européen de Géographie Théorique et Quantitative, Lucca, Italie, 8-11 septembre 2003

Spatially aggregated data and variables in empirical analysis and model building for economics

Agrégation spatiale des variables dans l’analyse des données et la construction de modèles économiques
Tamás Dusek


Les problèmes posés par l’agrégation spatiale sont évoqués, d’un point de vue général et plus particulièrement en sociologie et en économie. On propose ensuite une typologie des données et des analyses spatiales en fonction de l’agrégation spatiale. La question des maillages modifiables est traitée sous deux aspects : celui de l’échelle et celui des limites, à partir de données hongroises. L’agrégation spatiale des données implique une analyse précise des relations entre théorie et données, ainsi qu’entre échelles micro et macro.

Haut de page

Texte intégral


1In the field of economics or sociology all statistical data observed in a population within a defined geographical area, at a definite point or over a period of time is a piece of historical information in numerical terms. Because the spatial and the temporal characters are inseparably connected to the data, the two main methods of their aggregation will be spatial grouping and temporal. The spatial data is available within the frame of the partially invariably arbitrary zoning system made for regular measuring. The paper focuses on issues arising from the spatial aggregation of data.

2If the results of the different quantitative analyses were independent of the zoning system, the spatial aggregation problem would not exist. However, according to both theoretical conceptions and all empirical examinations, the results of all quantitative analytical procedures are influenced by the aggregation method.

3It is useful to distinguish here at least five aspects of this question:

  • the effect on the results of descriptive statistics;

  • the effect on the interpretation of the results;

  • practical-political effect;

  • effect on the applicability of the inferential statistics;

  • effect on building theories and models.

4The effect of aggregation, mostly called the “modifiable areal unit problem” (MAUP), consists of two related but distinctive components: the scale effect and the zoning effect. The scale effect is the variation in results, that may be obtained, when the same areal data are combined into sets of increasingly larger areal units of analysis. The zoning effect is any variation in the results, due to alternative units of analysis, where the number of units is constant.

5The scale and zoning effects on the results of descriptive statistics are illustrated through several database and numerous methods e.g. correlation (Gehlke–Biehl 1934; Robinson 1950; Openshaw, 1977; Openshaw, 1984a), spatial autocorrelation (Jelinski–Wu, 1996; Qi–Wu, 1996), spatial interaction models (Batty–Sikdar, 1982), location-allocation models (Bach, 1981; Fotheringham et al., 1995). Their dependence on the given zoning system should be taken into account when interpreting the results.

6The practical side of the question must be addressed, namely that it depends on the application of the analysis. Though the results of the studies describing the historical situation or satisfying our curiosity can be deceiving and have a more restricted validity, than those of the authors. However, they can only have their practical effect, if they are used for administrative, regional development reasons or in political decision-making. This problem is most noticeable in the establishing new regional units, when it has a delimiting factor on the region´s participation in the different regional development subsidies. Drawing the boundaries of the constituencies can influence the result of the elections. The method of aggregation can critically effect the results on designating the optimal locations of new institutions as well (Bach, 1981; Fotheringham et al., 1995).

7Surprisingly the study of theoretical and technical effects on statistical inferences, despite its enormous significance, is pushed into the background. The effects on putting forward a theory and on model building is a rarely investigated issue. The economical and within that, the macro-economical aspects of the latter are dealt with near the end of this study.

Discussion of spatial aggregation in technical literature

General survey

8Spatial aggregation is mostly mentioned under the expression the “modifiable areal unit problem” (MAUP). The spatial character of the MAUP is emphasised in terminology such as the problem of spatial system design, the problem of zone system design and zone definition, area delimitation and spatial definition, spatial aggregation and others, as well as gerrymandering and statistical gerrymandering. These terms refer to the grouping of data according to spatial continuity criteria. Of course not the terminology is significant, but the contents. In the following, I shall use the expression, the MAUP.

9Robinson’s fundamental 1950 article in sociology covered the studies about the interpretation of ecological inferences, the effects of group composition, structural versus individual effects and the relation between individual and collective properties. This not only to revealed the traps involved in data interpretation but to analyse the connection between individual action and the social environment (Robinson, 1950; Davis et al., 1961; Lazarsfeld–Menzel, 1970). However, within the framework of a given research, data can be interpreted in several ways, even observing the accordance between the different quantitative and qualitative information.

10A minor side issue of the MAUP is the problem of the ecological inference. Within this problem we seek to make use of data aggregated at the level of ecological (spatial) units, to make inferences about the behaviour of individuals. The ecological fallacy occurs when relationships between variables obtained at the aggregate level are not found at the individual level. The atomistic or individualistic fallacy is similar to the ecological fallacy. In this case the model being tested corresponds to the group level, but the data is collected for an individual level.

11There are three main streams of the discussion regarding the question: mathematical statistical methods, interpreting data and the presentation of the empirical significance. The latter one has already been introduced. Mathematical statistical methods were first developed in connection with the minor partial problem of the MAUP, ecological inference. After the proposal of a simple method, the method of ecological regression (Goodman, 1953) and the methods of bounds (Duncan–Davis, 1953) developments in computing technology enables an increasing number of “sophisticated guessing games” like King’s method (Anselin, 1999; King, 1997). Although the individual behaviour cannot be reconstructed from the aggregated data due to lack of information. “Increasingly complex approaches, however, do not lead to better and better estimates but only to more complicated versions of the ecological fallacy” (Flanigan–Zindale, 1986, p. 88.).

12The MAUP goes beyond the issue of ecological inference. The statistical data involved in the MAUP does not always have natural units as in the EIP but is in itself an average, a rate or a proportion, that does not have natural units. On the other hand, there can be no structure and regularity observed in the effect of zoning, other than the one resulting from the scale effect (Openshaw, 1984b). Developments in computing has resulted in new opportunities to explore the issues of MAUP. Sophisticated mathematical simulations were developed, as well as in the field of synthetic spatial data generators (Amrhein, 1995; Reynolds, 1998). However, in the lack of certain given basic spatial units it is doubtful what the possible regular zoning effects can be compared with.

Spatial aggregation in the field of economics

13In the field of economics we mostly come across the issue of spatial aggregation implicitly within the framework of general aggregation. As Theil writes: ”A serious gap exists between the greater part of rigorous economic theory and the pragmatic way in which the economic systems are empirically analysed. Axiomatically founded theories refer mostly to individuals, for instance the consumer or the entrepreneur. Empirical descriptions of the economic actions in large communities, on the other hand, are nearly always extremely global: they are confined to the behaviour of groups of individuals. The necessity of such a procedure can scarcely be questioned: How could one handle the tremendous mass of relations governing the actions of millions of individuals?” (Theil, 1954, p. 3.)

14Regarding the micro foundation of macroeconomics, Theil distinguishes between aggregation over individuals – such as firms and consumers – aggregation over commodities and aggregation over time periods (Theil, 1954, pp. 3-4). In Theil’s terminology aggregation over individuals means, the aggregation of individual economic actors (consumers, enterprises), but the true part of this process is spatial, the temporal and the qualitative aggregation, because of the spatial and temporal character of the individuals, as well as the qualitative differences between their properties and behaviour. It can be observed that Theil - and his successors – handle microeconomics and macroeconomics traditionally, disregarding spatial dimensions. Spatial aggregation raises significantly more difficulties than temporal aggregation, because of the basic differences between time and space. Conceptual change has not occured in the treatment of space in connecting with the general aggregation problem.

Types of spatial data and analysis

Types of spatial data

15The classification of statistical data and analyses from the spatial viewpoint represents the starting block of the apprehension regarding the matter of aggregation. From the spatial point of view the statistical data can be divided into three types: individual data, areal data and spatial parameter data (see Table 1). Individual data consists of discrete, segregating elements of populations, that individually describe the elements. The descriptive summaries of the populations e.g. the average, the variance, characterise the whole of the population collectively. Entirely different individual data can produce the same average and variance.

Table 1 : Classification of the statistical data and analysis from the spatial point of view

16We can speak of the pure non-spatial data within the individual data, that is without a spatial point of view. These are for example the statistics of gamble, dice, card games which are brought up as examples for the discussion of mathematical statistics. A large part of the database that resulted from the physical and biological statistical observations, can be put into this category. Data, that has spatial properties differ from non-spatial data in spatial dependence/independence, the issue that Stephan raised as early as 1934: “Data of geographic units are tied together, like bunches of grapes, not separate, like balls in an urn. Of course mere contiguity in time and space does not of itself indicate lack of independence between units in a relevant variable or attribute, but in dealing with social data, we know that by virtue of their very social character, persons, groups and their characteristics are interrelated and not independent. Sampling error formulas may yet be developed which are applicable to these data, but until then the older formulas must used with great caution.” (Stephan, 1934, p.165)

17The areal data characterizes the areal units themselves in an indirect way, namely by describing some properties of populations brought into collective relation with the given areal unit in form of an absolute number, an average, an aggregate, a propensity, rates or density indices. So the areal data is the data derived from the original individual data. The observation unit is not originally the areal unit, but a social-economic object, entity or process that can be localised through its spatial properties. This can be seen in Figure 1. which is the visual record of a part of Table 1. The groups of individual data belonging to the observation units that have spatial properties, are described as potential areal data.

Figure 1: The connection between individual data and areal data

18The mathematical background of analytical procedures developed for the individual data, regardless of weighting, do not differ in relevance of the areal data analyses. However, the interpretation of the results can differ, because the data is spatially grouped and not individually. This explains the spatial classification of the statistical data. Table 2 shows the most important differences between individual and areal data.

Individual data

Areal data

Observational unit

Discrete, indivisible, naturally given individuals

Principally continous, divisible, partly arbitrary areal units


Total set of individual items

Total set of areal units

The number of observational units can change

Increasing by new observational units

Decreasing by leaving the observational units

Increasing by enlargement of the study area or by change in scaling space partition

Decreasing by restriction of the study area or by change in scaling space partition

Dimension of observed properties

Absolute number




Average of rates

Average of average

Examples of observational units

People, cars

All people and cars belonging to areal units

Table 2: The main difference between individual data and areal data

19The arbitrariness of the observation units of areal data does not mean that all zoning systems can be legitimated to the same extent, but that there are several zoning systems at the same time that can be legitimated in a similar way. There is data that can only be interpreted from an areal viewpoint (such as spatial density and proportions) these are not shown in the table. The data relating to human communities will always be areal data, so the demographic indices will characterise the groups of people living in a given geographical area. General descriptive statistical methods and statistical inference theory on the basis of the probability theory, were developed on individual populations with no spatial properties. The simple adaptation of these tools on the data relating to the areal units, is not obvious at all: the weighting has no unambiguous solution, the elements are heterogeneous and modifiable, most part of the data are derivative, the areal data is not optionally repeatable mass phenomena. The existence of a superpopulation, from which the data could be taken as a sample, is also questionable.

20Spatial parameter data can characterize the components of the space separately and the entire spatial pattern can also be characterized with one or more indices. The observational unit is the space itself and the various components of space, such as points, lines, regions, flows. The study of the relation between different spatial parameters and between other characters, constitute one of the most important parts of spatial research. Spatial parameters are an inseparable part of the areal units, meaning that merging or separation of the areal units changes a great part of the parameters. For the point patterns and networks, a new point and a new element of the network will modify the properties of the whole point pattern or network.

Types of analyses

21We can observe the types of analysis belonging to each data type, from the spatial viewpoint in Table 1. The following six types can be distinguished:

  • aspatial analyses;

  • spatial analyses using individual data only;

  • spatial analyses using aggregates in a single-region system;

  • spatial analyses using individual data and aggregates in a single-region system;

  • spatial analyses using aggregates in a multi-region system;

  • spatial analyses using individual data and aggregates in a multi-region system.

22The analyses belonging to the third and fourth groups can be called researches that are to be interpreted in a broad sense or are quasi-spatial ones. In this case an areal unit is examined alone, regardless of its internal spatial configuration and relations, by means of the aggregated data. Such researches are called spatial, regional or local, when they are performed in spatial frames which are different from the country level. This term is misleading because apart from the method of zoning system and the constitutional differences, there is no methodological difference between the examination of a given country or any other area, that has come to exist through areal delimitation.

23The fifth and sixth groups contain the actual and originally spatial researches by which the study region is partitioned to subregions. Distinguishing from the former ones, these researches can be called spatial researches in a narrow meaning. These investigations do not aim at the analysis of the study region alone but at the exploration of the internal spatial configuration and relations, the areal distribution of each property and the relations between them.

24In the field of economics and sociology, there are many theories and models which are built with the methods developed to the analysis of individual data and phenomenon but which use spatially aggregated data. Part of this problem will be examined in the end of this study.

Two levels of MAUP

25Selecting the zoning system means selecting the aggregation level and method of the data as well. It is useful there to distinguish between two levels of the MAUP. On the first level the study area should be separated from the areas left out of the examinations. We can only disregard this by the examination of the whole world, apart from this special case this move is needed during the research of single- and multi-region systems. The second level appears during the spatial analysis in a multi-region system. In such cases internal boundaries should be marked as well the internal structure.

26The first level of the MAUP appears only as far as the examination of a given areal unit is reasonable. One can always say that some areal units are of overriding importance from some viewpoint. Then one could only criticise the arguments, not the boundaries itself. When the study area is determined by the regional competence of some organisation, one feels rarely, that the question of boundaries would cause any difficulty. It is so, because we have a priori accepted the fact, that, for example in the case of countries, they constitute relevant examination units.

27Therefore it would not even occur to us to question the rightfulness of foreign trade, financial or demographic indices for the whole of Italy. Just as well, if we were to analyse the same facts without the those of Tuscany or of those of the countryside of the Garda Lake without a plausible explanation, would surprise most of our readers. On the other hand the examination of the change in price level calculated separately, at a country level, within the Euro-zone of the countries using Euro is believed natural, while the examination of the change in price level calculated at county or region level is not.

28Due to the issues above mentioned, the MAUP does not always appear in an explicit way. This is especially valid in the case of the first level of the MAUP. On the second level of the MAUP the problems are multiplied. Most difficulties appear when comparing the internal spatial configuration and relations of several areas. An example if this is when countries or towns are compared to each other in a multi-region system. In this case, both levels of the MAUP should be dealt with. The information content of such comparisons is therefore slight, moreover, results can be misleading. At the same time temporal data produced with the same zoning system, are suitable for analysing changes in time. In Figure 2 we can see the classification of areal analyses according to three dimensions – single-region or multi-region, alone or compared to other areas and the type of zoning system. The methodological difficulties of analysis are multiplied as we proceeded rightwards and downwards.

Figure 2: Types of spatial analysis


Scale effect on spatial autocorrelation

29The effect of scaling can be forecasted and easily understood for the simpler univariate analysing methods. In the case of more sophisticated methods questions will get extremely complex, therefore empirical studies are very important in order to understand them. This is why the questions concerning spatial autocorrelation will be illustrated using Hungarian data.

30In the areal distribution of the income per capita in Hungary the following facts play significant roles:

  • size of the settlement;

  • east-west location;

  • distance from Budapest;

  • distance from the county capital;

  • transport-geographical location.

31All of the listed factors played an important role in the differentiation of incomes in the period between 1990 and 2000, although naturally not the same extent and in such manner, that changes during the time period. In Figure 3 the moving average of the incomes calculated with a circle of 65 kilometres radius in 1990 and 2000 is shown, on which we can see the regional split of Hungary and its changes. The radius was chosen because in Hungary it is equal to the NUTS2 order. The source of basic data is the Hungarian Statistical Office and the Ministry of Finance.

Figure 3: Spatial distribution of income per capita (with spatial moving average on settlement level, r=65 km.; Budapest not included)

32The role of neighbourhood had been examined in several ways:

  • on spatial levels (settlement, small region, county, region);

  • partial areas, such regions and counties;

  • indices: Moran’s I, Geary’s c;

  • unweighted matrix and weighted matrix.

33Weighting in the case of counties and small regions in such a way, that the elements of the unweighted matrix were divided by the numbers of the neighbours per areal unit. The settlements were interpreted as point patterns and the most accessible six settlements of each settlement were taken as neighbours. The weights were the invert of the quotient of the distance from the given neighbour and the total distance of the six neighbours. The values of the indices were calculated separately as well, in increasing order of the neighbours. The results of Moran’s I are shown in Figure 4. Since Geary’s c has the same pattern, thus these results are not reported here. The technical details of the calculations can be found in the Appendix.

Figure 4 : Effect of data aggregation on spatial autocorrelation (Income per capita in Hungary)

34The significant results contribute to the importance of the role of neighbourhood in the development of the spatial difference of incomes at all levels. Higher results that have come to exist through weighting, prove the significance of the spatial factor because the closer neighbours got larger weights. Data can only be compared in a limited way, although tendencies are the same at all levels. In the first part of the time period one can observe a decrease of the neighbourhood effect and in the second part an increase. If this is compared with the development of the extent of spatial differences, then such conclusions can be drawn which are in itself do not originate from one of the calculations, but from both of them (Figure 5).

Figure 5 : Effect of data aggregation on standard deviation (Income per capita in Hungary)

35In the decreasing period of the neighbourhood effect, that took place up until 1993, the large and fast development of the areal differences occurred. In this time period the areal changes were sectorally determined by the partial disappearance of socialist industry and not by the neighbourhood effect. The areal differences increased moderately after 1993, although the neighbourhood effect had gradually increased and comparing to previous periods the small regions or settlements that differed from their environment in a positive or negative way, became more similar to their neighbours. County level data confirm this as well, but such an amount of data in itself would be too little to describe the process, because of the few areal units. The changes in coefficients are not significant on county level, since the significant change would be not less than 0.25 (the significant difference at 5 per cent significance level on small region and settlement level are 0.07 and 0.0145, respectively).

36To sum up, it can be stated that in the spatial differences of income in the whole country, the neighbourhood effect is significant and it has played a more increasing role in the recent years, after decreases between 1988 and 1992. All this is supported by the autocorrelations calculated with the Geary’s c, but not shown here.

37As a consequence of the scale effect, the smaller areal units merged into larger ones, the value of spatial autocorrelation has decreased. This has not only happened at country level but was also typical in the case of regionally calculated results. These results are similar to those of other studies that empirically characterising the scale effect on autocorrelation (Jelinski–Wu, 1996; Qi–Wu, 1996). This can be explained intuitively, by the division of the areal units, hidden internal autocorrelations within the areal units can also come to the surface. However, it would result the decrease of the indicator, if within the specific areal units, a rather negative autocorrelation were characteristic. The likelihood of this cannot be excluded either; but in any case, like the total negative auto-correlation, this is a rare image. We know that the possible maximum value of Moran’s I increases if the number of areal units increase. The direction of the scaling effect, considering its tendency, corresponds to the different databases but it is not linear and its extent is different (Jelinski–Wu, 1996; Qi–Wu, 1996).

Spatial moving correlation

38Whole-map statistics of the study region conceal the differences within the region and describe the whole region as a homogeneous entity (Brunsdon et al., 2002). This exaggerated data reduction has many negative consequences such as the following:

  • The loss of significant descriptive information about spatial distribution.

  • It suggests a false image of the homogeneous space with its map visualisation in single-region analyses and gives a false image of suddenly changing space mosaics in multi-region analyses, contrary to the continuous character of space.

  • The local estimation based on whole-map data will be biased.

  • It raises the question of the epistemological relation between data and theories.

39The last question will be discussed in the end of the study, here the problem shall be illustrated within the framework of correlation, and the potential possibilities inherent in the calculations of local statistics. In connection with the correlation calculated from areal data, Nephrash pointed out in an early study, that “there is also the question of the significance of correlation where the area concerned is not homogeneous. Within one homogeneous area the correlation may be high in one part and absent in another part” (Nephrash, 1934, p. 168).

40The correlation between the income per capita and the number of cars per 1000 inhabitants at settlement level in Hungary was +0.58 in 1996. In 1996 there were 3126 settlements (the number of settlements increased moderately year by year). Calculations made in the case of each of the 150 small regions, the sum of the same indicator is between –0.31 and 0.95. The spatial distribution of the results are shown in Figure 6. The results do not differ significantly form zero in many cases, partly because of the small number of observations. In spite of this fact negative values have an exceptional meaning because in these small regions the connection between the two variables may be exactly the opposite of those summarised by whole-map statistics. Small regions with an agricultural character and a peripherical status without bigger towns belong here, especially those of the southern parts of the Hungarian Great Plain (area east of the Danube). If we would like to make some areal estimation from the results calculated on the country level, then because of such anomalies our estimations will not be reliable.

41For the local statistics the correlation was calculated between the first 50 neighbours of each settlement. This method, comparing to the method mentioned earlier is a more advanced one, not only because of the moving boundaries, but also because it was calculated with the same number of settlements and therefore can be better compared (Figure 7). If we increase the number of settlements then the range and variance of correlation decreases (Figure 8). This also occurs due to the increase in the number of elements (which leads to the increasing in variance) and from the increasing distance between settlements (which leads to greater spatial variability). For example, when n=20, then the minimum is –0.54, and the maximum is 0.94; and when n=100, then the minimum is –0.08, and the maximum is 0.88.

Figure 6 : Correlation between the income per capita and cars per 1000 inhabitants at settlement level (in each small region)

Figure 6 : Correlation between the income per capita and cars per 1000 inhabitants at settlement level (in each small region)

Figure 7: Spatial moving correlation between the income per capita and cars per 1000 inhabitant at settlement level (the first 50 neighbours at each settlement)

Figure 7: Spatial moving correlation between the income per capita and cars per 1000 inhabitant at settlement level (the first 50 neighbours at each settlement)

Figure 8 : The distribution of the results of spatial moving correlation between the income per capita and cars per 1000 inhabitant at settlement level (with various numbers of settlements)

42The lowest values of the index can be found on the southern part of the Great Hungarian Plain. A negative connection can be found here instead of the positive one typical for the country as a whole. It can be connected with the significant income from agriculture and the larger proportion of the concealed incomes. In addition, the negative values can be found in the micro-areas on those internal peripheries having significant agricultural production and household activities in the small villages.

43This procedure was used to illustrate the calculation of correlation between several further characteristics, some greater than those mentioned above. For example the correlation on county level between incomes and the number of telephones per capita was 0.32, on the local level (calculated for the first 20 settlements) this number is between -0.84 and +0.95. The performance of such calculations is often impossible because of overaggregated data, however their theoretical possibility helps us to get rid of the false image of a homogeneous space.

Spatial aggregation and macroeconomics

44It is fair to ask how the partial dependence of the statistical results of data analysis from the areal delimitation influences the testing of theories which explain the connection between spatially aggregated variables. Even if the modification of the zoning system, the same and in an objective sense unmodified basic data corroborated one theory and then another it would be impossible to test different theories with the help of data; or could be formulated through a non-mathematical probability (not based on exact, known distribution and on random samples).

45The question is not going to be investigated here on a general level, but on within an important research activity in macroeconomics. We can see such macro variables within the models of macroeconomics, that can only be interpreted under the form of spatial aggregation, even if they retain their individual basic data. Such variables are for example price level and its change, investment, value added, unemployment, the quantity of money, rate of interest, interregional trade, average propensity to consume, aggregate demand etc. By the single-region macro model, one has to deal with the issue of external boundaries in fact what areal unit can be seen as relevant to the observed data and how one can deal with external effects.

46The problem appears in the multi-region macro-models and therefore in international economics and in regional economics too, and not only through the drawing of internal boundaries. Countries are taken as basic units in stating the subject of macroeconomics. Actually, countries are relevant observatory units from an economical-political point of view and for historical description. This, however, cannot be accepted as a theoretical explanation for the fact, that in the case of economical theory, countries are a starting point of the analysis; as they merge spatially, temporally, in their degree of quality, in quantity and in behaviour heterogeneous economical actors.

47The spatial importance of this heterogenity is being recognised in regional economics and therefore questions the main importance of the country level theoretical analysis. But even regional economics cannot put forward a theoretically stated areal unit to replace a country, nor one, that would be free of the dilemma of MAUP (Figure 9). The number of individual actors and their connections are much larger than those of the connections of aggregated macroeconomics, but these are not possible to depict. Each of the A, B and C region is separately representing the one point economy, that has external relations, by which the first level of the MAUP appears.

48The partial zoning system dependence of the results dependent on the epistemological status and logical legitimacy of the economic theories, could become an actual problem or present no difficulty at all. For those approaching economic theory in a positivistic way, the spatially aggregated nature of data can create difficulties that are impossible to overcome, because of both the first and second level of the MAUP. Within a theoretical explanation, we could not speak of a problem only in the case of homogenous populations, but in this case we would not need statistics either.

49By assuming a casual relationship between the spatially aggregated data you have to manage the problem of the qualitative difference between the basic elements. It is useful to distinguish three types of differences as well as the spatial and temporal ones, namely the differences in value, behaviour and composition. Differences are defined here in value as the different values of a variable in different basic elements, for example the different income of two people or two enterprises. Differences in behaviour means the different behaviour of basic units, which can be ignored in some cases or at group level. When this behaviour for the working of the whole system is significant, ignoring it would produce errors. For example, the distribution of demand among the different goods is of great importance (Hayek, 1984). Finally the compositional difference means that the variables (e. g. GDP, indices of price level), which were created by weighting methods and using various auxiliary assumptions, often do not have natural basic unit.

Figure 9: The MAUP in macroeconomics and regional economics

50The micro level explanations of macro-phenomena are problematic that natural sciences also have to deal with. The same macro-arrangement can go hand in hand with many different micro-arrangements. These micro-arrangements are unobservable, but it is not necessary for describing and explaining the system as a whole. This is possible, because the material components of the systems vary from each other only in pure quantitative or in quantitative expressible qualitative but not in behavioural or in compositional characteristics. For explanation of economic-social phenomena, which are much more complex, the knowledge of such relative frequency is not sufficient. The knowledge of the manner in which the individual elements are connected is also needed, which can not be replaced by statistical information (Hayek, 1967). “Aggregate phenomena are influenced by the way that individuals at the micro level behave and by the way that individuals interact with one another” (Fotheringham–Rogerson, 1993, p. 15). In this case full information about each element is required in order to derive practical and specific conclusions and predictions about the individual elements. “Without such specific information about the individual elements we shall be confined to (…) mere pattern predictions – predictions of some of the general attributes of the structure that will form themselves” (Hayek, 1984, p. 270).

51The problem of general aggregation is discussed in the technical literature about the method of macroeconomics. For example Stoker deals with technical issues (Stoker, 1993) and Spadaro with principal (Spadaro, 1956). Carl Menger saw the difficulties of aggregation clearly in 1870: ”In what follows I have endeavored to reduce the complex phenomena of human economic activity to the simplest elements that can still be subjected to accurate observation, to apply to these elements the measure corresponding to their nature, and constantly adhering to this measure, to investigate the manner in which the more complex economic phenomena evolve from their elements according to definite principles” (Menger, 1994, pp. 46-47). Hayek writes similarly in 1931: ”Neither aggregates nor averages do act upon one another, and it will never be possible to establish necessary connections of cause and effect between them as we can between individual phenomena, individual prices etc. I would even go so far as to assert that, from the very nature of economic theory, averages can never form a link in its reasoning” (Hayek, 1935, pp. 4-5).

52In spite of this and other similar reflections, the connection between macro variables is treated in the process of model building often as simply as a connection between micro variables. This is done when for example the price elasticity of export, the average propensity to consume, the capital intensity of production, the qualification of the workforce, which are categories that can be interpreted individually, are used in models. But the discussion of spatial aggregation can only be rarely found. Steiness proved in his study, in which he criticised an aggregated model about the causal relation of minority job losses and residential segregation, that because of the statistical gerrymandering, the model can explain both job loss and gain of minority as a result of segregation. This problem can be seen as a specific characteristic of each econometric model using spatially aggregated data (Steiness, 1980).

53The MAUP in the empirical analysis could be solved by using scale independent individual data. We can find an example of this in the use of individual locational data in the analysis of spatial concentration (Arbia, 2001; Duranton–Overman, 2002). On one hand though, this is an exceptional alternative, which is impossible to attain in the majority of the analysis, because most variables in the explanation can not be interpreted at an individual level. On the other hand the first level of MAUP appears even in the point pattern analysis.

54These difficulties can be solved theoretically by the reduction of macro phenomena to micro phenomena. When such a postulate is carried out in a consistent way every connection between macro phenomena can also be reduced to connections between micro phenomena. Actually the MAUP can be solved in macroeconomics by a clear distinction between theoretical and historical research. Theoretical models can not adequately based on aggregates, which are provided by the economic statistic helping historical description, without a careful account of its parts.

Haut de page


Amrhein, C. G.,1995, “Searching for the elusive aggregation effect: evidence from statistical simulations”, Environment and Planning A, 27, pp. 105-119.

Anselin, L. ,1999, “The alchemy of statistics, or creating data where no data exist”, Annals of the Association of American Geographers, 89, pp. 586-592.

Arbia, G., 2001, “Modelling the geography of economic activities on a continuous space”, Papers is Regional Science, 80, pp. 411-424

Bach, L., 1981, “The problem of aggregation and distance for analyses of accessibility and access opportunity in location-allocation models”, Environment and Planning A, 13, pp. 955-978.

Batty, M.–Sikdar, P. K., 1982, “Spatial aggregation in gravity models: 4. Generalisations and large-scale applications”, Environment and Planning A, 14, pp. 795-822.

Brunsdon, C.–Fotheringham, A. S.–Charlton, M., 2002, “Geographically weighted summary statistics – a framework for localised exploratory data analysis”, Computers, Environment and Urban Systems, 26, pp. 501-524.

Davis, J. A.–Houson, C.–Spaeth, J. L., 1961, “A technique for analysing the effects of groups composition”, American Sociological Review, 26, pp. 215-225.

Duncan, O. D.–Davis, B., 1953, “An Alternative to Ecological Correlation”, American Sociological Review, 18, pp. 665-666.

Duranton, G.–Overman, H. G., 2002, “Testing for Localisation Using Micro-Geographic Data”, CEPR Discussion Paper No. 3379

Flanigan, W. H.–Zingale, N. H., 1986, “Rejoinder to Dykstra and Kousser”, Social Science History, 10, pp. 87-90.

Fotheringham, A. S.–Densham, P. J.–Curtis, A., 1995, “The zone definition problem in location-allocation modeling”, Geographical Analysis, 27, pp. 60-77.

Fotheringham, A. S.–Rogerson, P. A., 1993, “GIS and spatial analytical problems”, International Journal of Geographic Information Systems, 7, pp. 3-19.

Gehlke, C. E.–Biehl, K., 1934, “Certain Effects of Grouping Upon the Size of the Correlation Coefficient in Census Tract Material”, Proceedings of the American Statistical Journal New Series, March pp. 169-170.

Goodman, L. A., 1953, “Ecological regression and behavior of individuals”, American Sociological Review, 18, pp. 663-664.

Hayek, F. A., 1935, Prices and Production, Routledge & Kegan Paul, London

Hayek, F. A., 1967, “The theory of complex phenomena”, In: Studies in Philosophy, Politics and Economics. Routledge and Kegan Paul, London pp. 22-42.

Hayek, F. A., 1984, “The pretence of Knowledge”, In: The essence of Hayek. Edited by C. Nishiyama, K. R. Leube, Hoover Institution Press, Stanford, pp. 266-277.

Jelinski, D. E.–Wu, J., 1996, “The modifiable areal unit problem and implications for landscape ecology”, Landscape Ecology, 11, pp. 129-140.

King, G., 1997, A solution to the ecological inference problem: reconstructing individual behavior from aggregate data. Princeton University Press, Princeton

Lazarsfeld, P. F.–Menzel, H., 1970, “On the relation between individual and collective properties”, In: A sociological reader on complex organizations. Edited by A. Etzioni London, Sidney, New York pp. 499-516.

Menger, C., 1994, Principles of economics, Libertarian Press, Grove City

Neprash, J. A., 1934, “Some problems in the correlation of spatially distributed variables”, Proceedings of the American Statistical Journal New Series, March pp. 167-168.

Openshaw, S., 1977, “A geographical solution to scale and aggregation problems in region-building, partitioning and spatial modelling”, Transactions of the Institute of British Geographers, 2, pp. 459-472.

Openshaw, S., 1984a, “Ecological fallacies and the analysis of areal census data”, Environment and Planning A, 16, pp. 17-31.

Openshaw, S., 1984b, The modifiable areal unit problem, Concepts and Techniques in Modern Geography, Number 38, Geo Books, Norwich

Qi, Y.–Wu, J., 1996, “Effects of changing spatial resolution on the results of landscape pattern analysis using spatial autocorrelation indices”, Landscape Ecology, 11, pp. 39-49.

Reynolds, H. D., 1998, The modifiable areal unit problem: empirical analysis by statistical simulation. Doctoral Thesis, University of Toronto

Robinson, W. S., 1950, “Ecological correlations and the behavior of individuals”, American Sociological Review, 15, pp. 351-356.

Spadaro, L. M., 1956, “Averages and Aggregates in Economics”, In: On freedom and free enterprise. Edited by M. Sennholz, D. van Nostrand Company, Princeton, pp. 140-160.

Steinnes, D. N., 1980, “Aggregation, gerrymandering, and spatial econometrics”, Regional Science and Urban Economics, 10, pp. 561-569.

Stephan, F. F., 1934, “Sampling errors and interpretations of social data ordered in time and space”, Proceedings of the American Statistical Journal New Series, March pp. 165-166.

Stoker, T. M., 1993, “Empirical Approaches to the problem of Aggregation Over Individuals”, Journal of Economic Literature, 31, pp. 1827-1874.

Theil, H., 1954, Linear aggregation of economic relations, North-Holland Publishing Company, Amsterdam

Haut de page


The basic data was in Excel file format. In worksheet “data” in column A are the code of settlement, in column B are X coordinates in meter, in column C are Y coordinates in meter, in column D are the income per capita, in column E are the cars per inhabitant. The locations of Hungarian settlements are in Cartesian coordinates. (The difference between Cartesian and spherical distance is neglibigle in the case of Hungary, but the computation is made easier with Cartesian coordinates.)
The autocorrelation and moving correlation have been calculated by help of a Visual Basic program designed by the author. The following program gives the order matrix (the first 253 neighbours of each settlement):
Sub order()

t = 2
Do While t < 3066
s = 2
Cells(1, 3).Value = Cells(t, 1).Value
Cells(1, 4).Value = t
Cells(1, 2).Value = 1
Cells(2, 2).Value = 2
Selection.AutoFill Destination:=Range("B1:B3065")
Do While s < 3066
Cells(s, 3).Value = Sqr((Worksheets("data").Cells(t, 2).Value - Worksheets("data").Cells(s, 2).Value) ^ 2 + (Worksheets("data").Cells(t, 3).Value - Worksheets("data").Cells(s, 3).Value) ^ 2)
s = s + 1
Selection.Sort Key1:=Range("c2"), Order1:=xlAscending, Header:=xlGuess, _
OrderCustom:=1, MatchCase:=False, Orientation:=xlTopToBottom
For i = 2 To 254
Cells(t, i + 2).Value = Cells(i, 2).Value
t = t + 1

End Sub

The data needed to calculate moving correlation can be calculated by the following programs:

Sub average()

s = 2
t = 2
Do While t < 3066
Cells(1, 2).Value = t
n = 0
p = 0
u = 1
Do While u < 51
s = Worksheets("order").Cells(t, u + 2)
n = n + Cells(s, 4).Value
p = p + Cells(s, 5).Value

u = u + 1
Cells(t, 24).Value = n / 25
Cells(t, 25).Value = p / 25

t = t + 1
End Sub

Sub dx2dy2dxdy()

t = 2
s = 2
Do While t < 3066
Cells(1, 2).Value = t
n = 0
p = 0
s = 1
u = 1
np = 1
Do While u < 51
s = Worksheets("order").Cells(t, u + 2)

n = n + (Cells(t, 24).Value - Cells(s, 4).Value) ^ 2
p = p + (Cells(t, 25).Value - Cells(s, 5).Value) ^ 2
np = np + (Cells(t, 24).Value - Cells(s, 4).Value) * (Cells(t, 25).Value - Cells(s, 5).Value)

u = u + 1

Cells(t, 26).Value = n
Cells(t, 27).Value = p
Cells(t, 28).Value = np

t = t + 1
End Sub

Haut de page

Table des illustrations

Fichier image/jpeg, 36k
Fichier image/jpeg, 372k
Fichier image/png, 537k
Fichier image/jpeg, 284k
Fichier image/jpeg, 348k
Fichier image/jpeg, 396k
Fichier image/jpeg, 176k
Titre Figure 6 : Correlation between the income per capita and cars per 1000 inhabitants at settlement level (in each small region)
Fichier image/jpeg, 156k
Titre Figure 7: Spatial moving correlation between the income per capita and cars per 1000 inhabitant at settlement level (the first 50 neighbours at each settlement)
Fichier image/jpeg, 352k
Fichier image/jpeg, 287k
Haut de page

Pour citer cet article

Référence électronique

Tamás Dusek, « Spatially aggregated data and variables in empirical analysis and model building for economics », Cybergeo: European Journal of Geography [En ligne], Dossiers, document 285, mis en ligne le 09 septembre 2004, consulté le 05 juillet 2022. URL : ; DOI :

Haut de page


Tamás Dusek

Széchenyi István University, 9022 Győr, Egyetem tér 1, Hungary

Haut de page

Droits d’auteur

Licence Creative Commons
La revue Cybergeo est mise à disposition selon les termes de la Licence Creative Commons Attribution 4.0 International.

Haut de page
Rechercher dans OpenEdition Search

Vous allez être redirigé vers OpenEdition Search