An Introduction to Regional Economics
Edgar M. Hoover and Frank Giarratani


What is a region? A voluminous and somewhat turgid literature has been devoted to this question, with a variety of answers. One irreverent suggestion is that a region means an area which a regional economist gets a grant to study. Be that as it may, it is clear that the most appropriate and useful definition depends on the particular purpose to be served.

Common to all definitions of a region is the idea of a geographical area constituting an entity, so that significant statements can be made about the area as a whole. Aggregation into regions is useful in connection with description, because it means that fewer separate numbers or other facts need to be handled and perceived. Thus for many purposes, totals and averages for a Census tract or a county are just as informative and much easier to handle and present than stacks of individual Census returns would be, even if one had access to them. Similarly, aggregation is obviously economical in connection with analysis of information; and it is particularly important if there is a good deal of interdependence of units or activities within the area, so that the whole really is more than merely the sum of its parts. Finally, and for similar reasons, aggregation is necessary for administration and for the formulation and implementation of plans and public policies. From this standpoint at least, the most useful regional groupings are those which follow the boundaries of administrative jurisdictions.

A normal attribute of a region is general consciousness of a common regional interest; this is fortunate because it makes possible some rational collective efforts to improve regional welfare. The commonality of interests may be reflected in numerous ways, but basic to this idea is a high degree of correlation of economic experiences of the region’s subareas and interest groups. Since this correlation can reflect either of two quite distinct features of internal structure, we distinguish two different types of regions: the homogeneous and the functional.

A homogeneous region is demarcated on the basis of internal uniformity. The winter wheat belt in the central part of the United States is a homogeneous agricultural region because all its parts grow the same main crop in the same way. Some external change, such as a new farm price support or loan program, a series of drought years, or a change in the world demand for wheat, will affect all of the region in a similar way; what is true of one part of the region is true of other parts, and the various parts resemble one another more than they resemble areas outside the region. The distinctive land-use zones of the von Thünen model, discussed in Chapter 6, can be regarded as homogeneous regions. America’s Appalachia and Italy’s Mezzogiorno are regions defined on the basis of a common syndrome of poverty, arrested economic development, and limited human opportunity. On a microscale, a homogeneous zone or neighborhood within an urban area (such as a ghetto or other ethnic area, a wholesaling district, or a wealthy suburb) might for some purposes be regarded as a homogeneous region.

The set of nonmetropolitan State Economic Areas, established by the U.S. Bureau of the Census for tabulation of various kinds of data such as migration, presents still another example. Those State Economic Areas that do not simply coincide with Metropolitan Statistical Areas are made up by grouping contiguous counties within a state. The grouping is systematically worked out by computer so that (with respect to a large number of characteristics such as income level, racial mix, and principal economic activity) the counties within any one State Economic Area are highly similar but the different State Economic Areas are highly dissimilar. The Regional Economics Division of the U.S. Department of Commerce has similarly developed a breakdown of the whole United States into eight relatively homogeneous groups of contiguous states (see Figure 9-1).

The alternative principle of regionalization is based on functional integration rather than homogeneity. Here, the region is composed of areas that exhibit more interaction with one another than with outside areas: It is the extent of economic interdependence that serves as a criterion for regional demarcation. Among functional regions one particular type, the nodal region, is of special interest. The structure of a nodal region resembles that of a living cell or an atom: There is a nucleus and a complementary peripheral area. The distinction between nodal and non-nodal functional regions has been clearly described by Lawrence A. Brown and John Holmes:

A nodal region is seen as a special case of a functional region which has a single focal point and in which the notion of dominance or order is introduced. If a grouping of locational entities is based on the criterion that within-group interaction is greater than interaction between groups, without considering the role of each entity in the interaction pattern, a functional region maintains [sic]. If, on the other hand, grouping is based upon both interactions between locational entities and the rank or order of one locational entity to another, and a single locational entity is identified as dominating all others, a nodal region maintains.1

From earlier chapters we have gained some understanding of the ways in which different activities, in the proximity and interdependence associated with sharing a regional location, affect one another’s development. Thus within any region, particularly a functional one, there is a vast amount of transference of goods and services among activities. A furniture factory buys locally its electricity, labor services, public services, and at least some of its materials and supplies. A wholesale firm supplies retailers in the region and gets its labor, public services, and some of its other inputs from inside the region. Nearly everyone in a region is in fact both a buyer from and a seller to someone else in the region and thus helps to support the presence of various other activities.

In addition to this interdependence through local purchases and sales of goods and services, regional activities affect one another by competing for space and other scarce local resources, such as water. Some of these relationships were explored in Chapter 6.

In Chapter 5 we examined other ways in which activities in a region affect one another by mutually creating external economies of agglomeration, and in Chapter 8 we saw how agglomerative forces give rise to urban concentrations of various sizes and functional characteristics.

A city and its surrounding commuting and trading area make a nodal region. The parts with the main concentration of business and employment are in sharp contrast to the residential areas, especially to the "bedroom suburbs," but they are tightly linked to them by flows of commuters, migrants, goods and services, and payments. Thus the region is usefully considered as a unit in its reaction to changed conditions affecting economic growth and well-being. Neither core nor periphery can flourish without the other.

Figure 9-2aand Figure 9-2b shows regions designated as Standard Metropolitan Statistical Areas (SMSAs), which are demarcated on a nodal basis, using such criteria as commuter flows and circulation areas of metropolitan newspapers. Recently, the term "Standard Metropolitan Statistical Area" has been shortened to "Metropolitan Statistical Area." Each designated area must have a nucleus consisting of at least one "central city," defined to have a population of at least 50,000 or an urbanized area of at least 50,000 with a total metropolitan population of at least 100,000. Large areas with a population of one million or more, also satisfying criteria for economic integration, may qualify as Primary Metropolitan Statistical Areas (PMSAs). Still larger Consolidated Metropolitan Statistical Areas, comprising two or more PMSA’s, are also designated.

At a more macro level, the concept of functional integration can be used to identify regions made up of a number of nodal subregions. Again, it is the intensity of economic interaction that is critical. Movements of goods and services, labor and money flows, the frequency of telephone calls, or other measures of transactions among areas, each of which may include one or more cities, can be used as a basis for recognizing the boundaries of larger spatial entities.

In the establishment of planning or administrative "regions," "subregions," "districts," or other areas, considerations of homogeneity and functional integration are both relevant, and so are a variety of special factors in particular cases. Consider, for example, the cases of river-basin planning, flood control, defense, sewage disposal, school district administration, fire and police protection, services in aid of disadvantaged or minority groups, judicial districts, and the proportionality constraints and gerrymandering temptations involved in demarcating electoral districts.

In a large country such as the United States, virtually all national government agencies are "decentralized" to the extent of working through a set of regional areas, each with its administrative center. Each agency is subject to its own set of efficiency considerations and political pressures in regard to the set of regional areas and centers to be used; but problems of administrative coordination and economy can become serious if the sets are all different, as they would tend to be in the absence of any overall constraint. In 1969, the President announced the establishment of a set of Standard Federal Regions and centers, shown in Figure 9-3, in order to promote greater uniformity in the location and geographic jurisdiction of federal field offices. As of 1981, thirteen departments and agencies were using these administrative regions. However, some thirty-three others had their own nonconforming sets of regions and centers,2  even though the mandate requires that exemption from the use of the Standard Federal Regions be granted only by petition. This fact reflects the extent of differences in the geographic distributions of the clienteles served by various components of the federal government.

Though both homogeneous and functional regions make sense as useful groupings, they play different roles in the spatial organization of society. This is particularly evident in regard to the flow of trade, when homogeneous and nodal regions are compared. The usual basis for a homogeneous region is a common exportable output: The whole region is a surplus supply area for such an output, and consequently its various parts have little or no reason to trade extensively with one another. By contrast, in the nodal region, internal exchange of goods and services is the very raison d’être of the region. Typically, there is a single main nucleus (the principal city of the region), perhaps some subordinate centers, and the rural remainder of the territory. These two or three specialized parts of the organism complement one another and are linked by internal transfer media.

Our main concern in this chapter is with functional regions and, in particular, nodal regions. We shall begin by presenting a simple example of the kind of statistical analysis often used to identify functional regions. Next, we shall look more closely into the nature of the interdependence relationships that link up a region’s activities. These relationships will provide a basis for explorations in later chapters as to (1) how regions develop and acquire their distinctive characteristics; and (2) how a region interacts with other areas in terms of trade, investment, migration, and other flows and influences.


As mentioned above, movements of goods and services, people and money flows, and the frequency of telephone calls are among the best indicators of functional integration. For this reason, empirical studies rely on these measures in efforts to delimit regions.

Table 9-1 presents hypothetical data on dollar values of trade flows during a year among six areas, which might be thought of as counties of a state or other subareas of a larger whole. The numbers shown give a picture of economic interdependence among the six areas as measured in this single dimension (trade). Our task is to group these areas into functional regions in such a way that trade flows among areas within each region are relatively strong, while flows between regions are relatively weak.

Clearly we should not group areas together simply on the basis of the absolute amount of trade between them. We can get a more meaningful measure of interarea trade linkage by subjecting our data to "double standardization"—that is, expressing the actual trade between two areas (in) and (n) in relation to the total external trade (exports and imports) of both areas.3  Perhaps the simplest linkage measure incorporating double standardization would be

Lmn=Lnm=2(Smn + Snm) / (Em + En + Im + In)

where Smn and Snm are trade flows from (m) to (n) and from (n) to (m)

respectively; Em and En are the total exports from (m) and (n) respectively; and Im and In are the total imports into (m) and (n) respectively.


The standardized linkages for the present example are shown in Table 9-2. Note that it is necessary to present only one such linkage for each pair of areas, since Lmn is equivalent to Lnm.

The linkages in Table 9-2 can be used to group the six areas into regions. The five largest Ls fully characterize the strength of trade interactions among the six areas. In order to demonstrate this, the five largest Ls (L62 =.366, L51 =.351, L31 =.333, L42 =.272, and L52 =.216) are used to generate the hierarchical display known as a tree diagram (dendrogram), which is shown in Figure 9-4.

Areas 6 and 2 are joined at a linkage of .366 (L62 =.366) by connecting the lines or "branches" associated with these areas. Similarly, the branch associated with area 4 is connected with areas 6 and 2 at a linkage of .272, because of the degree of interdependence represented by the standardized linkage L42 (=.272). Continuing in this manner, we find that the branches of areas 5 and 1 are joined at a linkage of .351 and that this pair is joined by the branch associated with area 3 at a linkage of .333.

The data reveal two groups of areas that fit the definition of a functional region. The linkages among areas 6, 2, and 4 and those among areas 5, 1, and 3 are relatively strong; each group constitutes a region. Further, we find that these regions are joined at a linkage of .216 (L52 =.216). Thus we have relatively strong linkages among members of each region, but the linkage among regions is somewhat weaker.4

One characteristic of the clusters identified by this grouping method is that not all areas within a given region need have strong pairwise linkages. For example, the second group (areas 5, 1, and 3) has strong pairwise linkages between area 5 and area 1 (L51 =.351) and between area 3 and area 1 (L31 =.333). However, even though the direct linkage between area 5 and area 3 is relatively weak (L53 =.199) these areas are placed into the same cluster because each has strong linkage to area 1. Not all clustering techniques have this characteristic. More restrictive groupings based on the strength of all pairwise linkages can be applied.5

This example has served to illustrate the application of a particularly simple grouping method that can be used to delimit regions, given data on trade, money, migration, or commuting flows among a set of areas.6  As the complexity of these techniques grows, they become capable of identifying more subtle characteristics of spatial interaction, including nodality.7


While the previous section focused on the analysis of trade flows, functional integration really depends on a variety of complex interdependencies. A simple classification of relationships will be helpful here. We shall consider separately (1) vertical relationships, (2) horizontal relationships, and (3) complementary relationships. As has been brought out in previous discussion, the locational relation between two activities can involve either mutual attraction (sometimes called a positive linkage) or mutual repulsion.

9.3.1 Vertical Relationships

When outputs of one activity are inputs to another activity, transfer costs are reduced by proximity of the two activities, and the presence of either of these activities in a region enhances to some degree the region’s attractiveness as a location for the other activity. Thus vertical linkages normally imply mutual attraction.

Rarely, however, is such attraction equal in both directions. We can distinguish between cases in which the linkage is predominantly "backward" and cases in which it is predominantly "forward."

Backward linkage means that the mutual attraction is important mainly to the supplying activity. In other words, a market-oriented activity is attracted by the presence of an activity to which it can sell. This is called backward linkage because it involves transmission of an effect to an activity further back in the sequence of operations that transforms such primary inputs as natural resources and labor into products for final consumption.

An example of backward linkage is the case of a Pittsburgh printing firm specializing in the production of annual reports for large corporations. In 1968 a number of large corporations with national headquarters in Pittsburgh were merged into firms with headquarters in other cities, so that Pittsburgh lost its position as the third-largest center of corporate headquarters activity. As a result, the printing firm is reported to have lost a number of its larger contracts. Corporations prefer to have their annual reports printed locally if possible (in other words, the business of printing annual reports is rather closely oriented to corporate headquarters locations).

Backward linkage is extremely common because so much of the activity in any region is, in fact, producing for and oriented to the regional market. The larger the region (in terms of total area, population.. or employment), the greater the relative importance of the internal market is likely to be. The residentiary activities in a region (including nearly all retail and most wholesale trade, most consumer and business services, local government services, public utilities, construction, and the manufacturing of such perishable or bulky products as ice cream, bread, newspapers, soft drinks, gravel, and cement blocks) are likely to be stimulated by any increase in aggregate regional employment and income, and thus are the recipient of backward linkage effects.

Forward linkage means that an impact of change is transmitted to an activity further along in the sequence of operations. The activity affected by a forward linkage must be locationally sensitive to the price or supply of its inputs (that is, input-oriented). One class of forward linkage involves activities that use by-products of other activities in the same region: for example, glue or fertilizer factories or tanneries in areas where there is a large amount of activity in fish canning, freezing, or meat packing. The supply of by-products from coke ovens is similarly an inducement to establish a considerable range of chemical processes in steel-making centers—sometimes, but not necessarily, by the same firm that operates the coke ovens. The presence of steel rolling and finishing facilities is usually regarded as a significant factor in the choice of location for heavy metal-fabricating industries, since it means cheaper steel and probably quicker service.

In addition, many of the external economies of agglomeration, discussed in Chapter 5, involve the locational advantages of a local supply of some inputs—such as materials, supplies, equipment repair or rental services, or last but not least, specialized manpower. The importance of a good local supply of business services for regional growth, and particularly for the establishment of new lines of activity in a region, has become increasingly recognized in recent years.8  There has also been marked emphasis on the vital role of infrastructure (the supply of basic public facilities and services) in the development of backward, low-income regions, both in the United States and overseas. In all these situations, forward linkages are the key factors.

9.3.2 Horizontal Relationships

The role of horizontal relationships has already been discussed in some detail in Chapter 4. These relationships involve the competition of activities, or units of activity, for either markets or inputs. The locational effect is basically one of mutual repulsion, in contrast to the mutual attraction implied in vertical linkages.

Particularly significant for regional growth and development is the rivalry of different activities for scarce and not easily expansible local resources (such as particular varieties of labor, sites on riverbanks or with a view, clean and cool water, or clean air). The entrance of a new activity using such local resources tends to raise their costs and may thus hamper or even preclude other activities requiring the same resources. The region as a whole has much at stake in this rivalry. A relevant and important question of regional policy, for example, is whether to let the region’s water and waterside sites be preempted and polluted by water-using industries or to reserve them in part for residential institutional, or recreational use. Again, should regional efforts to enhance employment opportunities take the form of trying to attract new activities with the largest number of jobs, regardless of character, or should priority be given to new activities that pay high wages, provide opportunities for individual learning and advancement, and attract a superior grade of in-migrants? Should a community’s last remaining tract of vacant level land be given over to an airport, a strip-mining operation, a high-class low-density suburban development, a low-income housing project, a missile-launching site, or an industrial park? How much smoke is the community willing to tolerate for the sake of the income earned by the smoke producers and the taxes they pay? These are all familiar issues that must be faced by citizens, responsible authorities, and planners of a city or larger region; and they all arise because of horizontal linkage in the form of competition for scarce local resources. Regional objectives and policy are the subject of Chapter 12.

9.3.3 Complementary Relationships

We have already noted, in previous chapters, complementary relationships among activities in a region, particularly in connection with external economies in Chapter 5. The locational effect is mutual attraction—that is, an increase of one activity in a region encourages the growth of a complementary activity.

Mutual Attraction Among Suppliers of Complementary Products. Examples of this attraction are found in fashion goods and other shopping goods industries. As additional producers come into a region, they help those already there by building up the region’s status as a Mecca for buyers of those products or services, because the buyer is looking for a variety of offerings and a chance to compare and shop around. The manufacture of sportswear in some large cities in California and Texas in recent years has developed largely on this basis.

This is really a two-step linkage, which can be broken down into (1) a forward linkage effect, whereby the coming of an additional producer attracts to the region more buyers of the product, and (2) a backward linkage effect, whereby the greater demand from those buyers enhances the attractiveness of the region for still more producers.

Such effects are, however, not entirely restricted to shopping goods. Still another example from the Pittsburgh region is pertinent here. In the 1960s, various civic leaders urged Pittsburgh to aim for major league status as a designer and producer of urban transit systems to meet the projected growing demand from large urban areas in the United States and other countries. A wide variety of inputs is needed to feed into this line of activity: the manufacture of components and supplies, designers knowledgeable in transport technology and urban planning, urban and regional economists, and specialized research facilities and consultants. Had the main effort been successful and had Pittsburgh firms received more orders for transit systems, local suppliers of the various inputs cited above would have flourished and multiplied, and their availability and expertise would have enhanced further the capabilities and reputation of the prime contractors.

Mutual Attraction Among Users of Jointly Supplied Products. This second kind of complementary linkage (also with an effect of mutual locational attraction) is basically the converse of the complementary linkage just discussed. Many activities (perhaps most) turn out not one but several different products, those of lesser importance or value being called by-products. A regional activity that furnishes a market for one or more by-products helps the supplying activity, and this can make the supplier’s other outputs more easily or cheaply available to some third activity which uses them. All three of the activities are then in a situation of mutual assistance and attraction.

There are many examples of this effect in the chemical industries, which by their nature usually turn out combinations of products. Producers of coke for blast furnaces also turn out gas and a variety of hydrocarbon chemicals that can serve as building blocks for a still wider range of products, such as synthetic rubber, synthetic gasoline, dyestuffs, and pharmaceuticals. The presence in the same region of industries using any of the first-stage outputs of the coal distillation process enhances the returns of the coke producer and may even be a significant factor in its decisions to expand or relocate. If it does expand output, this means a still larger (and perhaps cheaper and more dependable) regional supply of other coal distillation products, which in turn makes the region more attractive as a location for industries using these products.

Like the complementary linkage among sellers of jointly demanded products, discussed earlier, this complementary linkage can be broken down into two separate links. There is a backward linkage effect if additional demand from a new synthetic rubber producer, for example, leads coke producers to expand their output. Then there is a forward linkage if the resulting increased regional supply of coal distillation products from the ovens attracts still other users of these products (for example, producers of pharmaceuticals or dyestuffs) to the region.

In case the reader is by now a bit bemused with the nomenclature of linkages, some surcease is provided in Figure 9-5, where the linkages are all schematically diagrammed and illustrated.

The complementary linkages we have described are, of course, valid regardless of whether the complementary processes are engaged in by separate firms or within the same firm. In the case of the steel producer and its coke ovens, for example, the firm may elect to process its distillation outputs for one or more additional stages or even down to the final consumer product, rather than selling them to other firms.

Complementary Linkages and the Economies of Scale and Agglomeration. The external economies of agglomeration, discussed in Chapter 5, represent in part complementary linkages among users of jointly supplied products. Manufacturers of fashion garments and many other typical external-economy industries identified by Lichtenberg (see Section 5.3.3 above) have a strong tendency to cluster because they draw on both kinds of complementary linkage: among suppliers of complementary products and among users of jointly supplied products. For example, fashion garment manufacturers find a clustered location pattern profitable (1) because such clustering gives the location the advantage of variety of offerings, which attracts buyers, and (2) because in such a cluster many kinds of inputs can be secured quickly and cheaply from specialized suppliers who could not economically exist without the volume supported by a large cluster. We see, then, that external economies of agglomeration can be broken down into internal economies of scale plus two kinds of complementary linkage; each of which, in turn, can be broken down into backward and forward linkages.


The growth of a region and the kinds of opportunities it provides for its residents depend to a large extent on the region’s mix of activities. We can characterize regions as being more or less narrowly specialized in a limited range of activities, or as being more or less diversified or "well rounded."

9.4.1 A Classification of U.S. Metropolitan Regions

To illustrate this differentiation, let us consider the metropolitan areas of the United States as separate urban regions. Table 9-3 shows a structural grouping made by the U.S. Department of Commerce on the basis of the sources of income of residents of each SMSA in 1966. "Manufacturing" SMSAs (there were 97 in all) were defined as those in which earnings from manufacturing employment accounted for a relatively high fraction of total personal income. In each of the 28 SMSAs in the "manufacturing-intensive" category, this fraction was 40 percent or higher. Nearly all of those 28 are in the Mideast and Great Lakes regions.9

SMSAs with at least 20 percent of personal income derived from government (compared with 12.4 percent for all SMSAs) were put in the "government" category. In 26 of these, military payrolls bulked large (at least 10 percent of personal income); in the other 21, government civilian payrolls were relatively more important.

There were 10 SMSAs classified as agricultural, since each had at least 10 percent of its personal income (that is, more than the average for all nonmetropolitan areas!) derived from agriculture. This classification reflects the fact that SMSAs, being generally made up of whole counties, contain substantial amounts of rural farm territory, usually intensively developed.

In 5 SMSAs, mining was a major source of personal income. In 4 of these—in Texas, Oklahoma, and Louisiana—the specialization was in oil and natural gas production, and property incomes also bulked large in their sources of income; the fifth was the Duluth-Superior SMSA, specializing in iron ore mining.

Recreational and retirement SMSAs (there were 4 of each) were characterized by low proportions of income derived from manufacturing, rather high proportions derived from property, and (in the case of the retirement SMSAs such as Tampa-St. Petersburg and Tucson) high proportions of income derived from transfer payments, principally pensions.

There were 16 SMSAs classed as regional or national centers because an above-average share of their incomes was derived from typically residentiary types of activity. This reflects the fact that in such areas, some of the typical residentiary activities such as transportation, communications, finance, trade, and services are really export activities serving an unusually far-flung region. The 4 national centers were New York, Los Angeles, Chicago, and San Francisco, ranking first, second, third, and sixth in population in 1966. It is interesting to observe that Philadelphia and Boston (ranking fourth and fifth in size) did not appear as national centers; because they are so close to New York, their areas of influence are curtailed.

The residual group of 40 "mixed" SMSAs comprises those lacking any of the marked specializations of structure that characterize the other categories.

In similar fashion, larger geographical areas such as states or multistate regions exhibit different specializations of function and structure. Regional specialization in some specific activity generally implies that the region is a net exporter of the product of that activity, although in some cases it can reflect instead a distinctive pattern of demand in the region itself. Thus Michigan’s specialization in motor vehicle production and the District of Columbia’s specialization in government are associated with heavy exports of cars and government services from those areas; but the unusually high proportions of health and recreational service activities in retirement areas are primarily accounted for by the local demand.

9.4.2 Some Quantitative Measures of Specialization and Concentration

The location quotient has already been introduced in Appendix 8-2 and further discussed above in section 9.4.1. As we have seen, (1) the same quotient measures both the degree of an area’s specialization in an activity and the degree of concentration of the activity in the area; (2) the quotient can be calculated in three ways, with identical results; and (3) the quotient can be based on either just one variable, such as employment, in the areas and activities involved, or on two different variables, such as earnings in a given activity and total employment, population, or income.

In still other applications, we might want to compare the location quotient for the same activity and area at two different dates in order to measure change in specialization or concentration. Finally, we can apply the quotient not to an activity but to some other measurable characteristic of an area (such as the size of a specified ethnic group, number of motorcycles registered, or number of dog licenses issued) as related to some different characteristic of activity such as population or employment.

The coefficient of specialization, a broader type of measure, can be used to gauge the degree to which the mix of a region’s economy differs from some standard, such as the mix in the national economy or the mix in the same region at an earlier date. The calculation of this measure is illustrated in Table 9-4.

The first two columns of numbers are the percentage distributions of value added by manufacture in 1978 according to broad industry groups in the United States and New England respectively, and the last two columns contain the differences between the national and the New England percentages. If the industrial mix in New England were identical to the national mix (that is, if New England had just the same share of the national total in every industry group), all these differences would be zero.

The sum of the-differences is in any case zero, since the pluses exactly offset the minuses. But if we add up just the positive differences (or just the negative ones, which would give the same sum) we have a measure of the degree to which the New England mix differs from the national. This is the coefficient of specialization. A coefficient of zero indicates no specialization at all, with the region’s mix just matching the national or other standard mix. The maximum value of the coefficient would be close to 100 percent and would correspond to a situation in which the region in question is devoted entirely to one industry not present in any other region.

This coefficient, too, has a fairly wide range of applications. For example, we could use it to determine which areas most nearly have a cross section of the national population in terms of age groups or ethnic categories; or whether a given region’s employment pattern diverges more from the national pattern in years of recession than in prosperous years; or whether two areas are more like each other than either is like some third area (which might be useful in aggregating areas into regions on the basis of homogeneity).

Finally, one other closely related measure should be mentioned: the coefficient of concentration, which measures how closely one locational distribution (for example, that of population, income, or employment in a specific activity) matches another locational distribution (for example, that of total employment or land area). Thus if the distribution of population by counties in the United States just matched the distribution of land area among counties, we should say that the population was evenly distributed (at the county level); while if the location pattern of the rubber industry is radically different from that of population or total employment, we can say that the rubber industry is spatially concentrated.

The coefficient of concentration is calculated in much the same way as the coefficient of specialization, except that we line up two columns of figures representing location patterns (that is, each is a percentage distribution by areas), take all the positive or all the negative differences, and add.

Although location quotients and coefficients of concentration and specialization are handy summary measures, their limitations must be kept in mind. In particular, their values depend partly on the arbitrary decisions we make regarding demarcation of both activities and areas. The measures all become larger if we use smaller geographical units (for example, states instead of Census divisions, or counties instead of states, or Census tracts instead of cities), and they become larger also if we employ a more detailed classification of activities. Consequently, any two coefficients of the same type are comparable only if they are based on the same classifications.


A region is an area that is usefully considered as an entity for purposes of description, analysis, administration, planning, or policy. It can be demarcated on the basis of internal homogeneity or functional integration. Nodal regions are those where the character of functional integration is such that a single specialized urban nucleus can be identified. Homogeneity and nodality are basic even when political, historical, military, or other considerations are importantly involved in regional demarcation.

Functional regions may be delimited by various statistical techniques. Some of these rely on data concerning commodity, service, financial, migration, or commuting flows among regions in order to identify the strength of interdependencies between and within regions.

Activities within a region interact in various ways. Horizontal linkages involve basically competition among similar units and are expressed in mutual spatial repulsion, with formation of market areas and/or supply areas. Vertical linkages (between the two parties in a transaction, such as seller and buyer) involve spatial attraction to save transfer costs. If it is primarily the buyers who are attracted toward the sellers, a vertical linkage is called forward; whereas backward linkage means that the sellers are attracted toward the buyers. Complementary linkages, more complex in nature, entail mutual attraction among (1) suppliers of complementary products or (2) users of jointly supplied products. Such complementary linkages are basic to the external economies of agglomeration discussed in Chapter 5.

Not only homogeneous regions but also functional ones tend to develop distinctive specializations of activities or other characteristics. The nature and degree of specialization can be gauged by such statistical measures as the location quotient and the coefficients of (area) specialization and (activity) concentration.



Homogeneous region

Residentiary activities

Functional integration

Forward linkage

Functional region


Nodal region

Horizontal linkage

Positive linkage

Complementary linkage

Vertical linkage

Coefficient of specialization

Backward linkage

Coefficient of concentration


Lawrence A. Brown and John Holmes, "The Delimitation of Functional Regions, Nodal Regions, and Hierarchies by Functional Distance Approaches," Journal of Regional Science, 11, 1 (April 1971), 57-72.

Beverly Duncan and Stanley Lieberson, Metropolis and Region in Transition (Beverly Hills, Calif.: Sage Publications, 1970).

Otis Dudley Duncan et al., Metropolis and Region (Baltimore: Johns Hopkins University Press, 1960).

David L. Huff, "The Delineation of a National System of Planning Regions on the Basis of Urban Spheres of Influence," Regional Studies, 7, 3 (September 1973), 323-329.

W. F. Lever, "Industrial Movement, Spatial Association, and Functional Linkages," Regional Studies, 6, 4 (December 1972), 371-384.

Harry W. Richardson, Regional Economics (Urbana: University of Illinois Press, 1978), Chapter 1.



1. Lawrence A. Brown and John Holmes, "The Delimitation of Functional Regions, Nodal Regions, and Hierarchies by Functional Distance Approaches," Journal of Regional Science, 11, 1 (April 1971), p. 58.

2. See General Services Agency, Office of the Federal Register, The United States Directory of Federal Regional Structure, 1981/1982 (Washington, D.C.: Government Printing Office, 1981).

3. Standardization can be accomplished by any of several techniques. For example, Paul B. Slater has developed a technique that constrains each row and each column total to unity or some other number. The resultant matrix of flows is thus doubly standardized by one transformation. See P. B. Slater and H. P. M. Winchester, "Clustering and Scaling of Transaction Flow Tables: A French Interdepartmental Migration Example," IEEE Transactions on Systems, Man, and Cybernetics, SMC-8 (August 1978), 635-640; and P. B. Slater and Wolfgang Schwarz, "Global Trade Patterns: Scaling and Clustering Analysis," IEEE Transactions on Systems, Man, and Cybernetics, SMC-9 (July 1979), 381-387. The algorithm used in these studies is available in SAS (Statistical Analysis System) Supplemental Library Users Guide (Cary, N.C.: SAS Institute, 1980) under the name IPFPHC.

4. When clustering methods of the sort described in the example are applied to actual data, areas that have rather diffuse linkages (those that interact with most other areas in a uniform manner) often stand out as being isolated or unconnected to any particular group in a clear way. Paradoxically, areas of this sort tend to be either very remote (like Alaska in the U.S.) or high-order central places (like Paris, France). In the first instance, difficulty of access and in the second, centrality results in dispersed interactions with other areas.

5. For an excellent survey of related statistical techniques, see Michael R. Anderberg, Cluster Analysis for Applications (New York: Academic Press, 1973). The interested reader will also find a number of computer programs, which have been developed for this type of data analysis, in the same source.

6. Migration data are used frequently for this purpose because of the availability of regularly published information on place-to-place movements. However, while migration between two areas is certainly indicative of labor market interactions, the areas in question may have very limited linkages in other dimensions (trade, for example). Indeed, as we shall find in Chapter 10, the fact that there is substantial migration between two areas may result from the fact that the two economies are quite diverse, reacting to different stimuli or being affected differently by the same stimuli, so that the correlation in their behavior may actually be negative.

7. Applying quite different methods from the one described above, a number of researchers have devised sophisticated techniques for carving up a country into "optimum" sets of nodal regions on the basis of weighted factors of spatial linkage. The formula can be adjusted to produce demarcations of any desired fineness or coarseness. For such demarcations, dividing the United States successively into 72, 292, and 347 areas, see David L. Huff, "The Delineation of a National System of Planning Regions on the Basis of Urban Spheres of Influence," Regional Studies, 7, 3 (September 1973), 323-329. See also the discussion in section 12.6.3 concerning the work of Karl Fox and Brian Berry in demarcating efficient regions for planning, development, and administrative purposes.

8. See Benjamin Chinitz, "Contrasts in Agglomeration: New York and Pittsburgh," Papers and Proceedings of the American Economic Association, 51 (May 1961), 279-289. Chinitz argues that a center such as Pittsburgh, heavily specialized in a few industries and dominated by large plants and firms, is likely to be deficient in various business services needed by small and new firms, because the dominant firms are big enough to provide such services internally for themselves.

9. The basis on which SMSAs were characterized according to the primary specialization for Table 9-3 will be recognized as essentially the same as the location quotient procedure already described in Appendix 8-2. For example, if in a given SMSA the fraction of total personal income derived from manufacturing employment was notably large compared to that fraction for all SMSAs, that SMSA’s location quotient was much greater than 1 in manufacturing. Other location quotients for the same SMSA would measure its degree of specialization in other kinds of activity; and the SMSA could be categorized according to the activity in which it had the highest location quotient, It will be observed that the calculations here were in terms of earnings as related to income, whereas in the application of location quotients described in Appendix 8-2, they were in terms of employment as related to employment.

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