The Hoover Index of Population Concentration and the Demographic Components of Change

Abstract

The Hoover Index is the most widely used measure for assessing the concentration or deconcentration tendencies of a country’s evolving population distribution. In this article, the authors propose alternative variants of the index designed to explore the influences of the various demographic components of change (birth, deaths, net domestic, and net international migration) on settlement dynamics. These decompositions can also be applied to examine the differential contributions of various race and ethnicity groups to overall trends. Using U.S. Census Bureau county population estimates, the authors deploy their approaches to examine the nature of deconcentration trends evidenced for the decadal periods 1990–1999 and 2000–2009.

Keywords

demographics migration human spatial structure spatial structure population and employment distribution demographic analysis methods spatial analysis

Dedication

This article is dedicated to the memory of our colleague, mentor, and friend, Andrew M. Isserman. In his mentoring and collegial roles, he did much to spark our own interests in novel methods for regional demographic analysis.

We, along with Paul Beaumont, were privileged to have worked with Andy building the ECESIS economic/demographic population projection model at the U.S. Census Bureau during the period 1979–81. That venture—an ambitious investigation of the issues connected with building a combined economic/demographic model—was Andy’s project as an American Statistical Association/National Science Foundation/Census Fellow. Among the publications reporting on the results of that project was a book Andy edited, Population Change and the Economy: Social Science Theories and Models (Isserman 1986) and, on the migration component on which we primarily worked, an article in the Journal of the American Statistical Association titled: “Forecasting Interstate Migration with Limited Data: A Demographic Economic Approach” (Isserman et al. 1985). A 1982 article reviewing the then extant sources of federal migration data (Isserman, Plane, and McMillen 1982) would rank among Andy’s most well-cited works.

A major focus of Andy’s far-reaching and multifaceted research interests was the shedding of light on the dynamics of U.S. population trends. Late on one of many long nights we spent at the Census Bureau kicking around ideas about the ECESIS project, Andy told us that when he had been a kid he was always the boy out on the field or basketball court who tried to persuade the others that it really was not too dark to keep playing. Andy had an infectious enthusiasm, a passion for big ideas, a persuasive vision of how academic research could motivate public policies to better the human condition, and a caring commitment to the people with whom he came in contact. His light continues to shine, reminding us that it is never too dark to keep working, questioning, and questing.

Introduction

Demographers, population geographers, and regional scientists have long been interested in the spatial concentration of population. Population densities vary widely from place to place at any given time. In addition, the tendency for people to cluster in some counties, states, or regions more than in others may vary over time, and it is of interest to characterize and understand this variability.

The components of population change can exert differing levels of influence on population concentration. Although we may tend to think of population concentration changing only through the redistribution of population brought about by internal migration, in fact the spatial distributions of other components of change—births, death, and international migration—may be quite important as well.

In addition, various subsets of the population may exhibit differing degrees of population concentration. To understand changes in population concentration over time, it is necessary to understand the changing importance of these subsets. Thus if, for example, Hispanics are more spatially concentrated than the rest of the population, the fact that this group is a growing share of the total population will—even absent a change in the distribution of the group itself—lead to an increase in measures of overall population concentration.

In this article, we use the Hoover Index (Hoover 1941) to examine the changes in population concentration in the United States from 1990 to 2010. We carry this out at several spatial scales, and we investigate the contributions to changes in concentration made by components of population change and by changing racial/ethnic distributions.

The Hoover Index and its Decomposition by the Components of Population Change

The Hoover Index as a Measure of Population Concentration

The degree of population concentration in a region of the earth, such as a country, that is disaggregated into a set of subregions (for instance, states, counties, or census tracts) is most commonly measured using the Hoover Index (Hoover 1941). The index can range from a low of 0 to a high that approaches 100, with larger values indicating greater degrees of concentration. The value of the index can be interpreted as the percentage of the total population that would need to be redistributed across subregions to achieve equal population densities in all subregions. The index is calculated as follows:

H = 50 \sum_{i = 1}^{n} | p_{i} - a_{i} |,

where p_i and a_i denote subregion i’s shares of total population and area, respectively, and where there are n subregions. The maximal value of the index is equal to 100 (1 − a_S), where a_s is the proportion of total area that is occupied by the smallest subregion. This value would be obtained if the entire population were to reside in that smallest subregion.

Alternatively, the Hoover Index may be found from a Lorenz Curve (Figure 1). The curve is constructed by first calculating each region’s percentage of total area and total population. The regions are then ordered in terms of increasing population density, and cumulative percentage areas and populations are found and plotted—first for the region with lowest density (point A in the figure), then for the two regions with lowest density (point B), followed by the three regions with lowest density (point C), and so on. The Hoover Index is simply the maximum vertical distance between the forty-five degree line and the Lorenz Curve (i.e., the length of segment EB in the figure). Alonso-Villar (2011) focuses on alternative decompositions of the Lorenz curve.

Figure 1

The Lorenz curve and the Hoover Index.

In his seminal 1941 article, Hoover noted that his procedure for gauging population concentration and deconcentration trends had already been used in the context of measuring the localization of manufacturing industries in Great Britain by Florence and Wensley (1939), and he recognized antecedents of the ideas in the work of Wright (1937).

The index is identical in concept to the Index of Dissimilarity used in studies of segregation (where the value of the index indicates the percentage of the population of one of the two groups that would have to be redistributed to achieve perfect integration, i.e., to obtain identical percentage allocations of majority and minority population in each subregion’s population). Although Duncan and Duncan (1955) are properly given credit for the term Index of Dissimilarity (as well as its conventional notation, D), the suggestion of this as a measure of segregation was made earlier by Jahn, Schmid, and Schrag (1947), and in fact Duncan and Duncan cite this earlier work.

Vining (1975) and Johnson and Vining (1976) have examined the Hoover Index within the context of long-term population trends. Specifically, they calculate the index associated with the long-term equilibrium spatial distribution that is implied by current population trends. Monitoring changes in this index is equivalent to tracking the long-term level of concentration toward which the population is currently headed.

Viewed over a long-time period, the US population has increasingly concentrated in urban areas while deconcentrating at the broadest spatial scales: away from the densely populated northeast and toward the less populated south and west. Beyond these well-known long-term trends, more subtle and less obvious counter trends have emerged in certain recent time periods. The so-called metropolitan/nonmetropolitan “turnaround” during the 1970s, termed by some as clean break with past trends, was convincingly demonstrated by Vining and Strauss (1977) using the Hoover Index. They showed that the Hoover Index decreased during that decade regardless of what spatial scale was used to disaggregate the country’s land area. During the 1980s, however, counties in metro areas once again began to grow more rapidly than nonmetro counties, before a second “turnaround,” with a resurgence of faster nonmetropolitan population growth, was noted to have occurred in the early 1990s (Long and Nucci 1997).

Recent Changes in the Hoover Index

Table 1 displays the Hoover Index as calculated at various geographic scales from US Census Bureau annual population estimates, for each year during the period 1990–2009. Recall the interpretation of the index: these numbers indicate that roughly 66 percent of the population would have to be redistributed between counties of residence in order for all counties to have equal population densities.

Table 1.

Hoover Index for U.S. Counties, States, Divisions, and Regions: 1990–2009

Year	Counties	States	Divisions	Regions
1990	65.49	46.07	36.86	28.27
1991	65.51	45.99	36.69	28.10
1992	65.52	45.87	36.51	27.93
1993	65.49	45.72	36.37	27.82
1994	65.47	45.54	36.24	27.73
1995	65.43	45.38	36.12	27.64
1996	65.43	45.25	35.99	27.54
1997	65.46	45.14	35.82	27.39
1998	65.51	45.04	35.66	27.25
1999	65.57	44.96	35.52	27.13

2000	65.64	44.80	35.46	27.07
2001	65.77	44.79	35.34	26.94
2002	65.86	44.76	35.23	26.84
2003	65.93	44.74	35.14	26.75
2004	65.99	44.69	35.04	26.67
2005	66.06	44.63	34.94	26.58
2006	66.11	44.52	34.84	26.49
2007	66.16	44.45	34.68	26.42
2008	66.23	44.40	34.51	26.33
2009	66.32	44.37	34.34	26.24

Examining the annual trend, we find, similar to Long and Nucci (1997), evidence for a slight deconcentration at the county scale during the early 1990s. Although their period of study ends in 1995, our calculations show the index continuing to decline through 1996. The index dropped from 65.49 in 1990 to 65.43 in 1995 and 1996.¹ Beginning in 1997, county-scale population concentration increased, and the index increased slowly and steadily throughout the remainder of the 1990s and into the 2000s. Thus, at the county scale, the US population was again concentrating during the first decade following the millennium. Although these changes might appear small at first glance, even fractional percentage point changes represent substantial changes in the location of people across counties since the index is a summary for a national population distribution of hundreds of millions.

Table 1 also shows that at scales larger than the county (i.e., states, census divisions, and census regions), deconcentration occurred throughout the twenty-year period. Note too that the value of the index declines with increasing scale: only a relatively small percentage of the population would have to change their census region of residence to ensure equal population densities across the four census regions. A general property of the Hoover Index for nested geographies is that the index value for a higher scale set of units cannot exceed that for a set with finer spatial disaggregation.

Effects of the Components of Population Change on the Hoover Index

In his original application to the measurement of population concentration, Hoover (1941) was keenly aware of the fact that all of the components of population change, and not just internal migration, contributed to the changes in the index. A lack of migration data prevented him from analyzing the effects of the individual components of change on trends in the index of concentration:

… the method lends itself to a comparison of the same distribution at two different dates, thus showing the net shift or redistribution occurring between two dates. Such a “redistribution coefficient” does not attempt, of course, to measure either migration or mobility. No adequate statistics exist for the accurate estimation for either of these, save in quite recent years; nor is it possible to trace accurately the effects of differential fertility and mortality upon redistribution. For these reasons, and because for many practical purposes the net total result of birth–death differentials and migration is the important thing, the measurement of redistribution seems worthy of serious attention. (Hoover, p. 201)

The availability of migration data has improved markedly since Hoover’s original study in 1941, and we now turn to an examination of the individual components of change, and their relation to the index. To carry out this analysis, we make use of decennial census data for 1990 and 2000, and the US Census Bureau’s annual postcensal estimates for 1991–1999 and 2001–2009. Our methodology is analogous to the three techniques proposed in Plane (2011) to decompose shifts in another summary measure of population distribution: the mean center of population.

Table 2 categorizes rates of birth, death, and migration, according to whether the county was one that had a share of the national population that was greater than, or less than, its share of land area in 2000. The denominators of these rates use an interpolated midperiod population for each decade. Since the length of the period runs from the time of the census (April 1, 1990 and 2000) to the time of the estimates for July 1, 1999, and July 1, 2009, the middle of these periods occur in mid-November of 1994 and 2004.

Table 2.

Components of Change in High and Low Population Density Areas

Population share	Number of counties	Crude birth rate	Crude death rate	Domestic mig. rate	International migration rate
1990–1999
Greater than share of area	1,001	141.524	76.374	−10.045	32.041
Less than share of area	2,139	126.100	91.580	48.864	9.571
All	3,140	138.894	78.967	—	28.209
2000–2009
Greater than share of area	995	132.159	73.346	−2.197	34.198
Less than share of area	2,148	121.515	92.229	11.212	11.073
All	3,143	130.415	76.440	—	30.409

Note from the table that the domestic net migration rate is positive for the subset of counties that have relatively low population shares and that there is net outmigration from the subset of counties with population shares that are large relative to their area. This is in keeping with the idea that the population is deconcentrating due to the effects of domestic migration; people are, on balance, moving from high population density areas to areas of lower population density.

Also, note that the crude birthrate is relatively higher for those counties that have relatively high population shares; this implies that births act to counteract the effect of domestic migration on population deconcentration.

The crude death rate is higher in those counties with population shares that are low relative to their area. This is at least in part due to the relatively older age structures that characterize these areas. During the decade, the death rate differential acted in the same way as birthrates: to concentrate population share even further, and thus widen the disparities in population density. Furthermore, the difference in crude rates between the two areas is substantially higher for deaths than it is for births. Finally, international migration also acts in this same direction, and the effect of international migration alone would be to increase concentration, since the rate into high-density areas is greater than the rate into low-density areas.

Figure 2 depicts both the spatial distribution of birthrates and population density. The darkest gray and cross-hatched areas constitute places of higher than average population density, and white and light gray are used for places with lower than average population density. The darkest gray areas have higher than average crude birthrates, and since these are in high population density areas, they contribute to concentration. Similarly, crude birthrates are lower than average in the white areas—they also contribute to increasing concentration since they represent counties with low population density. The large number of rural counties in the Midwest with low crude birthrates (white), combined with a smaller set of highly urbanized counties with high crude birthrates (the dark gray areas, including, e.g., Chicago and southern California), give rise to the finding that the distribution of births is acting to increase population concentration.

Figure 2

Population density (2005) and crude birthrate, 2000–2009.

Figure 3 is similar, but now the spatial distributions of death rates and population density are being shown. The darkest gray and cross-hatched areas again constitute places of higher than average population density, and white and light gray are again used for places with lower than average density. Dark gray areas have lower than average crude death rates, and since these are in high population density areas, they contribute to concentration. Crude death rates are higher than average in the white areas—they contribute to increasing concentration since they represent counties with low population density. The combination of many rural counties in the Midwest with relatively high crude death rates (reflecting in part the relatively old age structure of this region) and a sizable number of urban areas with low crude death rates (the dark red areas, including New York City, Southern California, and parts of Florida) combine to cause the distribution of death to contribute to increasing population concentration. The low crude death rates in these regions are at least partially attributable to relatively young age structures, and the age structure is in turn affected by the migration patterns of both the young and the elderly.

Figure 3

Population density (2005) and crude death rate (2000–2009).

Table 3 illustrates the second of the three perspectives we propose on demographic decomposition of changes in the Hoover Index. It was constructed by using county shares of national births and deaths, and by comparing those shares with shares of land area. It shows that (1) the spatial distribution of births is more concentrated than the spatial distribution of deaths, (2) the spatial distribution of both births and deaths have levels of concentration that are not too different from that for total population, and (3) there was little change in the Hoover Index for both births and deaths throughout the decade.

Table 3.

Hoover Index for Births and Deaths

	Births	Deaths
1990–1991	67.43	63.41
1991–1992	67.45	63.39
1992–1993	67.48	63.38
1993–1994	67.54	63.30
1994–1995	67.43	63.40
1995–1996	67.30	63.17
1996–1997	67.23	63.14
1997–1998	67.10	63.00
1998–1999	67.13	62.97
2000–2001	67.47	63.19
2001–2002	67.54	63.08
2002–2003	67.59	63.02
2003–2004	67.56	62.99
2004–2005	67.47	63.01
2005–2006	67.46	63.00
2006–2007	67.33	62.95
2007–2008	67.34	63.23
2008–2009	67.24	63.27

This index is of course “global”—it is a single number that captures the extent of spatial concentration. Thus, although the index is similar for deaths and population, the detailed geographic distributions of population and death across counties differ (e.g., we have seen from the previous table that the death rate is higher in counties with lower population densities).

One may also ask how the Hoover Index would change if only a single component acted upon population. Table 4 depicts the results of this third approach to examining the influence of individual components of change on concentration. We term the quantities shown here “Effect-Alone” Hoover Indexes. For example, the values shown in the “Births” column for 1991 to 1999 were calculated by adding to the 1990 populations of each county the number of births recorded for the county between July 1 of the year listed and the 1990 Census April 1 base date to obtain a hypothetical “birth effect-alone” population. Similarly, the 2001–2009 numbers were calculated for the sums of births and the counties' Census 2000 base populations.

Table 4.

Effect-Alone Hoover Index Values for Components of Population Change

Year	Births (P₀₀ + B)	Deaths (P₀₀ − D)	International migration (P₀₀ + IM)	Combined (P₀₀ + B_t − D_t+ IM_t)	Domestic migration (P₀₀ + DM)
1990	65.49	65.49	65.49	65.49	65.49
1991	65.51	65.50	65.51	65.57	65.39
1992	65.53	65.52	65.55	65.66	65.29
1993	65.56	65.55	65.59	65.75	65.15
1994	65.58	65.58	65.62	65.83	65.02
1995	65.60	65.60	65.66	65.91	64.89
1996	65.62	65.63	65.70	65.99	64.80
1997	65.64	65.66	65.73	66.07	64.74
1998	65.66	65.69	65.77	66.15	64.70
1999	65.67	65.73	65.80	66.23	64.67

2000	65.64	65.64	65.64	65.64	65.64
2001	65.66	65.66	65.69	65.75	65.66
2002	65.68	65.69	65.74	65.84	65.65
2003	65.70	65.72	65.77	65.92	65.62
2004	65.72	65.75	65.81	66.01	65.58
2005	65.74	65.78	65.84	66.08	65.55
2006	65.76	65.81	65.88	66.16	65.51
2007	65.78	65.84	65.91	66.24	65.48
2008	65.80	65.86	65.94	66.31	65.47
2009	65.81	65.89	65.97	66.38	65.49

Examining the time-series index values in Table 4, we can see that the separate effects of births and deaths, if left to act alone on population change, would have been to cause small, yet steady increases in population concentration throughout the decade. Similarly, the effects of international migration were also in the direction of increased population concentration; there was more net migration into the counties that already had higher than average population density.

The “combined” column shows the joint effect of birth, death, and international migration on the Hoover Index, and reveals the increase in population concentration that would have occurred in the absence of domestic migration. The final column shows the effects of domestic migration alone. Here we see that, in the absence of the other components of change, there would have been a small amount of population deconcentration. The other components served effectively to mask the effect of internal migration trends on deconcentration.

The Hoover Index Decomposed by Race and Hispanic Origin

The overall concentration or deconcentration trends exhibited by the US population can also be thought to be composed of the trends in population change for various race and ethnic groups. As shown in Table 5 , the values of the Hoover Index and the changes in the index from 2000 to 2010 are rather different when computed separately for settlement patterns of different race/ethnicity groups. Because annual subnational population estimates by race and Hispanic origin are less reliable than those for the components of change, and because a different race categorization was adopted in 2000 than had been in use previously, here we restrict our analysis to the subpopulations of selected groups as enumerated on the 2000 and 2010 censuses.

Table 5.

Hoover Indexes of Population Concentration, 2000–2010, by Hispanic Origin and Race

	Tract scale			County scale			State scale
	2000	2010	Change	2000	2010	Change	2000	2010	Change
Total population	77.10	77.45	0.36	65.64	66.16	0.52	44.85	44.42	−0.42
Hispanic	90.00	89.03	−0.97	79.85	78.58	−1.27	59.79	56.38	−3.41
Non-Hispanic	76.14	76.22	0.08	65.20	65.54	0.34	45.97	45.12	−0.84
White	75.48	75.49	0.02	64.19	64.22	0.02	43.62	42.68	−0.94
Non-Hispanic white	76.14	76.22	0.08	63.95	63.90	−0.05	44.56	43.62	−0.94
Black	89.16	88.95	−0.22	80.25	80.04	−0.21	58.72	57.47	−1.25
Am. Indian, AK Native	77.96	78.17	0.21	62.93	63.26	0.33	39.38	38.07	−1.31
Asian	93.96	93.25	−0.72	85.63	85.15	−0.49	62.32	59.64	−2.69
Native HI, Pac. Islander	92.63	92.10	−0.53	82.11	81.60	−0.51	62.07	57.25	−4.82
Some other race	90.85	89.73	−1.12	80.50	78.88	−1.62	59.58	55.03	−4.54
Two or more races	85.44	84.16	−1.28	74.22	72.46	−1.76	49.87	46.62	−3.25

There are also interesting differences in concentration or deconcentration depending on the geographic units used to calculate the index. Whereas our analysis of the effects of the components of change used annual estimates data, which permit analysis only down to the county level, race and Hispanic origin are “complete count” items on the decennial censuses, and thus we can examine the index at the scale of census tracts as well for counties and states.² Because census tract boundaries do not cross county lines, it is possible to compare across three sets of units that exhibit nesting relationships. As was noted in discussing Table 1, one of the properties of the Hoover Index for nested geographies is that the values cannot be smaller for the more spatially disaggregated units.

Note that the Hoover Index for total population increased from 2000 to 2010 when calculated for either census tracts or counties, revealing a trend toward more concentrated settlement. When calculated for states, however, the index value went down, indicative of a broader scale trend toward overall population deconcentration.

When calculated separately for each of the race/Hispanic origin groups, the Hoover Index discloses relative levels of concentration. Across all three scales of geography, and for both time periods, the highest values, indicative of the highest levels of spatial concentration, are those calculated for Asians. The lowest values, meaning the most dispersed pattern of settlement, are those for whites and American Indians and Alaskan Natives.

At the state scale, for every race and Hispanic origin group examined there was a trend toward deconcentration of population: lower Hoover Index values were found for 2010 than for 2000. At the county and census tracts levels, however, overall population became more concentrated. The overall increase in concentration is reflective of the differential population growth dynamics across the race/Hispanic origin groups. The numbers illustrate an important point about comparing the changes in the Hoover Index for subpopulations having differential rates of growth to the change in the index for total population. Let us consider, for instance, the trends for two groups: non-Hispanic whites and Hispanics.

At the tract level, a concentrating pattern of non-Hispanic whites—when compared to the non-Hispanic white distribution in 2000—can be noted. A further factor, however, is shown in Table 6 : non-Hispanic whites accounted for a lower proportion of the total population in 2010 than in 2000. As a group that continued to be more deconcentrated than the population overall, their declining share vis-à-vis other more spatially concentrated groups was an additional factor contributing to more concentrated overall population.

Table 6.

Changing Percentage Shares of National Population for Hispanic Origin and Race Groups, 2000–2010

	2000 (percent)	2010 (percent)	Change (percent)
Hispanic	12.55	16.35	3.80
Non-Hispanic	87.45	83.65	−3.80
White	75.14	72.41	−2.73
Non-Hispanic white	69.13	63.75	−5.38
Black	12.32	12.61	0.29
Am. Indian, AK Native	0.88	0.95	0.07
Asian	3.64	4.75	1.11
Native HI, Pac. Islander	0.14	0.17	0.03
Some other race	5.46	6.19	0.73
Two or more races	2.43	2.92	0.49

At the county scale, Hispanics in 2010 were less concentrated than were Hispanics in 2000. Hispanics, however, continued to exhibit substantially above-average levels of concentration and had well above the national rate of population growth over the decade (see Table 6). Thus, Hispanics contributed more to the Hoover Index value for 2010 than for 2000. Their increased proportion of the population was a factor in the greater overall concentration of the US population at the county level—even though the group itself was becoming more dispersed!

The Effect-Alone method discussed in the earlier section of the article can be applied to help provide a more explicit perspective on the influence of the settlement trends of Hispanics, non-Hispanic whites, and the various race groups on the overall concentrating or deconcentrating tendencies of the American population. Table 7 shows calculated values of the Hoover Index for hypothetical distributions of 2010 population if it were to be assumed that the only change occurring in the system was the changed distribution of the specified group. So, for example, the tract-level index value for Hispanics, 77.44 percent, was obtained based on adding the change in the number of Hispanics residing in each tract to the tract’s base (Census 2000) total population to obtain a 2010 “Hispanic Effect-Alone” population:

P_{H i s p E A, 2010} = P_{T o t a l, 2000} + (P_{H i s p .2010} - P_{H i s p, 2000}) .

Such Effect-Alone Hoover Index values can then be compared to the 2000 Hoover Index value for total population to assess the extent to which any specific group’s changed distribution contributed to overall change in the index. Thus, at the tract scale, the increased concentration of population can be seen to have been due first and foremost to the rapid growth and redistribution of Hispanics. Blacks and Asians also contributed significantly to greater concentration at the tract scale, whereas non-Hispanic whites represented a countervailing—deconcentrating—influence.

Table 7.

Effect-Alone Hoover Indexes of Population Concentration for 2010, by Hispanic Origin and Race, with Differences from 2000 Index Value for Total Population

	Tract scale			County scale			State scale
	2000	2010	Difference	2000	2010	Difference	2000	2010	Difference
Total Population	77.10	77.45	0.36	65.64	66.16	0.52	44.85	44.42	−0.42
Hispanic		77.44	0.34		65.97	0.32		44.90	0.05
Non-Hispanic		77.09	−0.01		65.87	0.22		44.37	−0.47
White		76.97	−0.12		65.65	0.00		44.41	−0.44
Non-Hispanic white		76.73	−0.37		65.47	−0.18		44.31	−0.54
Black		77.27	0.18		65.88	0.23		44.91	0.06
Am. Indian, AK Native		77.09	−0.01		65.63	−0.02		44.81	−0.04
Asian		77.24	0.15		65.86	0.21		44.94	0.09
Native HI, Pac. Islander		77.10	0.00		65.65	0.00		44.84	−0.01
Some other race		77.18	0.08		65.74	0.10		44.80	−0.04
Two or more races		77.10	0.00		65.66	0.01		44.79	−0.06

The main difference between what took place at the county scale and at the tract level was that the changed distribution of non-Hispanic whites represented less of a deconcentrating influence at the county scale. Hispanics, blacks, and Asians all exerted significant concentrating effects. Note, too, that many persons of Hispanic origin choose to self-enumerate in the Census Bureau category of “Some Other Race,” and across all our findings the “Some Other Race” and “Hispanic origin” index values tend to be quite similar.

At the state scale, at which the overall Hoover Index discloses population deconcentration, it is non-Hispanic whites who account for most of the lowered value, as an already below-average-concentration group further deconcentrates. Hispanics at the state scale have been redistributing away from the traditional Mexican American border regions into other portions of the country, but given their above-average concentration their more dispersed settlement pattern across the states represents a relatively insignificant influence on changing the overall index. Similarly, blacks, Asians, and a number of the other groups show more muted effects at the state scale than at the tract and county scales.

We have thus now examined the influences on the Hoover Index of concentration of population change broken down both by the demographic components of change and by broad race/ethnicity groups. In principle, it would be possible to take the analysis one step further to examine an even more disaggregated picture of distributional change by breaking out each of the components by race/ethnicity. Thus, one could examine, say, the effects of Hispanic fertility and non-Hispanic white internal migration. While births and deaths by race and Hispanic origin are obtainable down to the county scale (if not the tract level), internal migration and immigration/emigration data are much more problematic. While the Census Bureau in preparing its annual county estimates by race and Hispanic origin disaggregates domestic and foreign in- and out-migration,³ the numbers are generated for internal use only and, at present, are not publically released.

Summary and Discussion

In this article, we have described the changes that have occurred in population concentration in the United States during the past two decades. Population concentration at the county scale is attributable to the spatial pattern of births, deaths, and international migration; the effects of internal migration alone were in the opposite direction and would, on their own, have led to population deconcentration. At larger spatial scales (i.e., states and census divisions and regions), the population continued its long-term trend of deconcentration. Although not studied here, these national trends exhibit spatial heterogeneity that would be interesting to examine further. For example, during the most recent decade, regions in the central and Rocky Mountain portions of the country exhibited population concentration at the county scale, while counties in New England and near the Pacific coast exhibited deconcentration at this scale.

Changes in the population concentration are also affected by both the changing distribution of particular racial/ethnic groups and the changing share of these groups, relative to the total population. Thus, at the county scale, although the Hispanic population became less concentrated during the most recent decade, this subpopulation actually contributed to the increase in concentration observed for the total population, by virtue of the facts that (1) the Hispanic population is more concentrated than the rest of the population and (2) the Hispanic population constituted an increasing share of the overall population as the decade progressed.

The Hoover Index, as a measure of population concentration, is straightforward to calculate and easy to interpret. It provides a single summary measure that allows for the study of change over time. Changes in population concentration, however, are the result of changes in the concentration of various components or subgroups of that population. Study of the contributions that each of these components and subgroups make to changing population concentration can shed light on the characteristics of population processes.

Footnotes

Acknowledgments

The authors acknowledge the assistance of Drew Trgovac and Peter Kedron with the production of the figures.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

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