Measuring Happenstance
David Rusk's City Elasticity Hypothesis


From a review of the nation's metropolitan areas, David Rusk, a former mayor of Albuquerque, develops the hypothesis that metropolitan areas in which central cities have been able to expand (annex) have experienced more favorable social and economic results than those in which annexation is limited. His book, Cities without Suburbs(1) concludes from this analysis that local government consolidation (metropolitan government) and regional tax base sharing should be encouraged and that regulations should be implemented to severely limit suburbanization. Rusk has been retained to apply his principles to individual metropolitan areas around the nation, and his work has given new life to efforts to regionalize governments and tax bases.

The City Elasticity Hypothesis

Rusk's conclusion that metropolitan health is driven by central city elasticity rests largely on an analysis 117 metropolitan areas containing central cities with populations of more than 100,000 in 1990. He classifies these areas into five categories (quintiles) of "relative elasticity," based upon the percentage increase in central city land area expansion from 1950 to 1990.

Rusk generally concludes that:

  • Metropolitan areas with more "elastic" central cities have higher rates of job creation than metropolitan areas with less elastic central cities.

  • Metropolitan areas with more "elastic" central cities have higher average incomes than metropolitan areas with less elastic central cities.

  • Metropolitan areas with more "elastic" central cities have higher population growth than metropolitan areas with less elastic central cities.

  • Metropolitan areas with more "elastic" central cities have smaller central city-suburb income gaps and smaller concentrations of poverty than metropolitan areas with less elastic central cities.

  • Metropolitan areas with more "elastic" central cities have less residential racial segregation than metropolitan areas with less elastic central cities.

According to Myron Orfield,

    ...David Rusk showed that areas that had created metropolitan governments by consolidation or annexation were less segregated by race and class, more fiscally sound, and economically healthier.(2)


The core areas of American (not to mention European) metropolitan areas have been losing population for decades, as people have moved first to the outer reaches of the central cities and more recently, to the suburbs beyond the borders of the central cities. There are a number of reasons for this, both market and non-market. Examples of market factors are falling household sizes, which has increased the demand for housing increased affluence and the democratization of automobility. Examples of non-market factors are higher central city crime rates, substandard education and higher central city taxes. As a result, virtually all central cities that have not expanded their boundaries have lost population (except where their boundaries included large tracts of undeveloped land). Even within the central cities that have expanded their boundaries, population losses have been sustained in their cores. Rusk thus correctly observes that central cities can generally increase their population only if they annex, because population density (population per square mile) is generally falling. However, the associations between central city elasticity and favorable metropolitan performance that Rusk asserts are largely happenstance, arising from wholly unrelated factors.

1. The Quintiles Reflect a Strong Regional Bias: Rusk's five elasticity categories exhibit strong regional characteristics. Generally, the lower elasticity categories are populated by Eastern and Midwestern ("Rust Belt") metropolitan areas, while the higher elasticity categories are largely populated by Southern and Western ("Sun Belt") metropolitan areas (Table #1).

  • All but one of the 23 "zero elasticity" (Quintile 1) metropolitan areas is in the older industrial areas of the East and Midwest. The two lowest elasticity quintiles (1 and 2) contain 33 metropolitan areas from the East and Midwest and 12 from the South and West.

  • All 25 of the hyper elasticity (Quintile 5) metropolitan areas is in the South and West. The two highest elasticity quintiles (4 and 5) contain 43 metropolitan areas from the South and West and five from the East and Midwest.
Table #1
Rusk City Elasticity Sample by Region
Rust Belt/Sun Belt BEA Region Elasticity Quintile
Quintile 1
Low Quintile 2 Medium Quintile 3 High Quintile 4 Hyper Quintile 5
East & Midwest (Rust Belt) Northeast 5 2 0 0 0
Mid East 12 3 0 0 0
Great Lakes 3 6 8 3 0
Plains 2 0 3 2 0
South & West (Sun Belt) Southeast 0 5 7 7 11
Southwest 0 0 1 5 7
Rocky Mountains 0 0 1 0 1
Far West 1 6 4 6 6
EAST & MIDWEST 22 11 11 5 0
SOUTH & WEST 1 11 13 18 25
TOTAL 23 22 24 23 25
% IN SOUTH & WEST 4.3% 50.0% 54.2% 78.3% 100.0%

Since World War II, there has been a substantial transfer of population and economic activity from the East and Midwest to the South and West.

  • From 1950 to 1990, 72 percent of population growth was in the Sun Belt.

  • From 1950 to 1990, 58 percent of economic growth was in the Sun Belt, as the area increased from 37 percent to 53 percent of economic activity.

It is therefore to be expected that any classification of metropolitan areas that reflects a strong Rust Belt versus Sun Belt composition will also reflect the regional demographic and economic dynamics.

  • A regional analysis of employment growth yields results similar to Rusk's. When regional employment growth percentage is substituted for the individual metropolitan area elasticity data, the zero elasticity metropolitan (Quintile 1!) areas score 49.8 percent below the average employment growth, compared to Rusk's minus 54.0 percent. The hyper elasticity (Quintile 5) metropolitan areas score 40.6 percent above the average in the regional analysis, compared to 42.0 percent in the Rusk analysis. Indeed, the similarity is evident at the Rust Belt-Sun Belt level. Substitution of the broader Rust Belt and Rust Belt employment growth averages for the metropolitan elasticity data yields strikingly similar results (Table #2).(3)

Table #2
Change in Employment: Variation From Mean

Quintile Elasticity Quintile Rusk 1973-88 Substitute Regional Values 1970-90 Substitute Rust Belt/ Sun Belt Values 1970-90
1 Zero Elasticity -54.0% -48.5% -49.8%
2 Low Elasticity -22.0% -11.0% -10.3%
3 Medium Elasticity 14.0% -3.9% -2.5%
4 High Elasticity 20.0% 22.8% 21.7%
5 Hyper Elasticity 42.0% 40.6% 41.0%
Range 96.0% 89.1% 90.8%
Calculated from Rusk & Census Bureau data.
  • A regional analysis of average income growth yields results similar to Rusk's. When regional income growth is substituted for the individual metropolitan area data, the zero elasticity (Quintile 1) metropolitan areas score 4.4 percent below the average employment growth, compared to Rusk's minus 2.5 percent. The hyper elasticity (Quintile 5) metropolitan areas score 13.9 percent above the average in the regional analysis, compared to 12.6 percent in the Rusk analysis. And again, the similarity carries through to the Rust Belt-Sun Belt indicators. (Table #3).(4)
Table #3
Change in Per Family/Household Income: Variation from Mean
Quintile Elasticity


Rusk 1949-89 Substitute Regional Values 1949-89 Substitute Rust Belt/ Sun Belt Values 1949-89
1 Zero Elasticity -2.5% -4.4% -7.4%
2 Low Elasticity -14.4% -3.4% -2.7
3 Medium Elasticity 0.6% -2.5% -0.2%
4 High Elasticity 6.2% 0.9% 3.9%
5 Hyper Elasticity 10.1% 9.5% 6.4%
Range 12.6% 13.9% 13.8%
Calculated from Rusk & Census Bureau data.

The metropolitan areas in Rusk's classification represented 56 percent of the nation's population in 1990. Yet substitution of regional data for specific metropolitan data yields similar results for 100 percent of the population.

Factors other than annexation policy have been more important in propelling the post-war job and economic growth gap between the Rust Belt and the Sun Belt, such as:

  • The nation has become more homogeneous, as the interstate highway system, jet airline service, telecommunications and other factors have made previously remote areas more competitive.

  • Air conditioning has made the hot and humid summers in the South more bearable. As a result, the South has competed more successfully as a region in which to work, live and retire.

  • Taxes are generally lower in the Sun Belt. In 1996, state and local taxes per capita were 26 percent higher in the Rust Belt. The regional bias of the Rusk quintiles is evident in the tax data. Application of the regional state and local tax rates to Rusk's quintiles demonstrates that the heavily Rust Belt lower elasticity categories (Quintiles 1 and 2) have significantly higher taxation than the higher elasticity categories (Quintiles 4 and 5). The difference is even greater with respect to non-consumption taxes, especially individual and corporate income taxes. High income taxes particularly discourage business relocation, and have made the South and West generally more attractive than the East and Midwest.

  • More businesses have been attracted to and established in the Sun Belt, where there is room to build more spacious modern plants, and where labor costs are lower. For example, only seven percent of Rust Belt employment was in right-to-work (voluntary unionism) states, compared to 59 percent in Sun Belt states (James Bennett has found disposable income and employment growth to be greater in right to work states).(5)

  • In addition to losing firms to the Sun Belt, the industrial base of Rust Belt metropolitan areas has been challenged, as older, "smokestack" industries have fallen into decline due to international competition and high labor costs.
Table #4
State and Local Taxation per Capita by Region: 1996


All Taxes

Non-Consumption Taxes
Per Capita Variation from Mean Per Capita Variation from Mean
1 Zero Elasticity $3,100 19.4% $2,029 38.6%
2 Low Elasticity $2,680 3.2% $1,567 7.0%
3 Medium Elasticity $2,444 -5.9% $1,344 -8.2%
4 High Elasticity $2,390 -8.0% $1,203 -17.8%
5 Hyper Elasticity $2,287 -12.0% $1,070 -26.9%
Range   31.3%   65.5%

There are other factors as well. For example, Katharine L. Bradbury, Anthony Downs and Kenneth A. Small concluded in a 1980s study that factors such as climate (severity of winter) and the presence of a state capital helped to determine metropolitan growth rates.(6)

With respect to economic growth, the central city elasticity hypothesis is holds only if it can be shown that the Rust Belt to Sun Belt economic and population migration occurred as a result of annexation policy. It must also be plausible that had the situation had been reversed, with high central city elasticity in the East and Midwest and low in the South and West, that the growth that has occurred over the past half century in the Sun Belt would have instead occurred in the Rust Belt. This seems highly unlikely. The similarity between the central city elasticity results and the regional and Rust Belt/Sun Belt analysis suggests that Rusk's categories simply reflect underlying regional differences with respect to employment and income growth.

2. The Quintiles Reflect a Strong Metropolitan Size Bias: In addition to a regional imbalance, the Rusk sample reflects a size imbalance. Only 46 of Rusk's 117 metropolitan areas had populations of above 500,000 in 1950. Metropolitan areas in the zero and low elasticity quintiles were overwhelmingly above 500,000 population in Rusk's base year of 1950 (Table #5). All 17 zero-elasticity (Quintile 1) metropolitan areas were above 500,000 population, while 15 of 29 high elasticity (Quintile 2) areas had populations of more than 500,000. At the same time, a large percentage of metropolitan areas in the high and hyper elasticity quintiles were under 500,000 in 1950. Out of 38 hyper elasticity (Quintile 5) areas, 24 were below 500,000 in 1950, while 14 of 33 high elasticity (Quintile 4) areas were below 500,000. Since 1950, population growth (and job growth) have been much higher in the smaller metropolitan areas, with metropolitan areas with high and hyper elasticity central cities growing between 1.5 and six times as fast as metropolitan areas with zero or low elasticity central cities. Smaller metropolitan areas have grown faster than larger ones, and as a result have exhibited greater employment growth. And, as was shown above, the greater economic growth has produced lower measures of residential segregation. Rusk's results reflect much more about the characteristics of metropolitan size and growth than annexation policy.

Table #5
1950 Metropolitan Population


Elasticity Quintile
Metropolitan Population
>1,000,000 500,000-999,999 250,000-499,999 <250,000
1 Zero Elasticity 14 8 1 0
2 Low Elasticity 3 7 10 2
3 Medium Elasticity 0 4 8 12
4 High Elasticity 0 8 5 10
5 Hyper Elasticity 0 2 9 14
Total 17 29 33 38
1950-90 Average Growth 48.6% 94.2% 143.2% 305.4%
From Rusk & calculated from Census Bureau data.

3. The Quintile Segregation Results Reflect Variances in Housing Turnover: Using the Census Bureau's Black segregation index (based upon census tracts), Rusk finds that metropolitan areas with elastic central cities tend to be less segregated. But again, there is a more plausible explanation. It was not until the late 1960s, that legal racial barriers to housing were eliminated in the United States. In 1990, many people continued to live in the same residences that they had lived in when the 1970 census was conducted. Generally, metropolitan areas in the Rust Belt had larger percentages of longer term residents than in Sun Belt metropolitan areas. In fact, a regression analysis found a strong correlation between the 1990 percentage of people living in their 1970 residences and the 1990 Census Bureau segregation index.(7)

Similar results are found when comparing the segregation indexes of the elasticity quintiles with the corresponding concentration of people still living in their 1970 residences (Table #6). In addition to the statistical results, the residential tenure-segregation index relationship seems plausible, because residential integration is likely to proceed at a greater rate where there is greater economic growth, because there is greater turnover in the housing stock. This has occurred in the newer, faster growing Sun Belt metropolitan areas as opposed to the older, slower growing Rust Belt metropolitan areas. In residential segregation The cause of Rusk's segregation results does not appear to be annexation practice, it is rather differences in housing turnover that are a function of economic growth.

Table #6
Segregation and Housing Tenure
Quintile Elasticity
Black Segregation Index Percentage of People Sill Occupying 1970 Residence
1 Zero Elasticity 0.653 21.5%
2 Low Elasticity 0.575 19.6%
3 Medium Elasticity 0.579 17.9%
4 High Elasticity 0.514 15.0%
5 Hyper Elasticity 0.457 12.7%
Low Value Compared to High 69.9% 59.1%
Calculated from US Census Bureau data.

4. The Rusk Poverty and Segregation Results Derive from Data Masking: Broadly published census reports do not provide data for components of municipalities. Where cities are smaller (generally inelastic), much more localized data is readily available than where cities are larger (generally elastic). As a result, in elastic cities there is the greater potential for masking the social and economic characteristics that are typical of core areas.

Poverty: Rusk finds lower income disparity in metropolitan areas with greater central city elasticity, noting that the gap between average income in the central cities and suburbs is less in metropolitan areas with more elastic central cities.

But a closer examination of the data indicates the income disparity data is simply masked in the elastic cities. As was noted above, the core areas of virtually all major cities have declined in population over the past half century. As more Americans have achieved sufficient affluence to buy their own homes, whether in the suburbs or the identical suburban-looking neighborhoods in elastic central cities, the core neighborhoods they left behind were populated by lower income people. This has occurred in both elastic and inelastic central cities. To test the income disparity thesis, two Rusk "peer group" pairs were analyzed in detail: Elastic Nashville, which Rusk compares with inelastic Louisville, and elastic Indianapolis, which Rusk compared to inelastic Milwaukee.

  • In 1989, per capita income in the city of Indianapolis was 10 percent less than in its suburbs, while per capita income in the city of Milwaukee was 38 percent below that of its suburbs. But the Indianapolis data masks the fact that, within the 1950 boundaries of the city, income disparity in 1989 was much greater --- 42 percent below that of the central city and suburbs outside the 1950 boundaries. Indeed, the income disparity between the 1950 core and the subsequently annexed portions of the city was a nearly equal 41 percent.

  • In 1989, per capita income in the city of Nashville was two percent less than in its suburbs, while per capita income in the city of Louisville was 22 percent below that of its suburbs. But the Nashville data masks the fact that, within the 1950 boundaries of the city, income disparity in 1989 was much greater --- 29 percent below that of the central city and suburbs outside the 1950 boundaries. As in the case of Indianapolis, average income within the 1950 city boundaries is well below that of annexed portions of the city, at minus 26 percent.

Masking and Residential Segregation: Further, Rusk's observation that elastic metropolitan areas have less segregated central cities is a function of masking within the larger elastic cities.

  • In 1990, the city of Indianapolis had a 22 percent Black population, compared to Milwaukee's 30 percent. Yet, within its 1950 boundaries, 41 percent of the Indianapolis population was Black.

  • In 1990, the city of Nashville had a 24 percent Black population, compared to Louisville's 30 percent. Yet, within its 1950 boundaries, 54 percent of the Nashville population was Black.

This masking of core area income and ethnic data is typical of US central cities. Both Indianapolis and Nashville have annexed significantly through city-county consolidations and experienced strong population gains from 1950 to 1990. But over the same period, each has lost approximately 40 percent of the population that lived within the 1950 boundaries --- a loss of a magnitude similar to that of well known population losers Detroit and Cleveland (both approximately 45 percent). A similar dynamic has occurred in other US central cities --- whether elastic or inelastic, population and income in the core has been dropping. The reality is the same, even though the nature of census data publication makes it is less apparent to demographers.

Central City Data: Finally, Rusk's conclusions that poverty and racial segregation are greater in inelastic central cities than in elastic central cities is just another manifestation of data masking. Poverty appears to be greater in inelastic central cities because they have fewer more affluent households to skew average income higher. The concentration of minority population is greater, because fewer non-minority households are included in the average. But the situation are virtually the same --- core area poverty and segregation tends to be greater in both elastic and inelastic central cities

5. The Quintiles include Subcomponents of Metropolitan Areas: Early on, Rusk advises that "the real city is the total metropolitan area --- city and suburb." Yet Rusk proceeds to base his analysis on metropolitan subareas, not entire metropolitan areas. The Census Bureau classifies metropolitan areas as "metropolitan areas" and "consolidated metropolitan areas," (CMAs) the latter of which is comprised of two or more "primary metropolitan areas." Rusk's analysis is based upon metropolitan areas and primary metropolitan areas (PMA), not CMAs. As a result Rusk separates the Jersey City area --- barely a mile from Manhattan --- from the New York metropolitan area, Orange County, California is considered separate from Los Angeles and the East Bay suburbs are separate from metropolitan San Francisco. In fact, four of the component parts of the New York consolidated metropolitan area are included among the 23 areas with zero elasticity central cities. This failure to analyze the entire metropolitan area (CMA) skews the data against the larger and older metropolitan areas, because their suburban PMAs tend to have more favorable economic and social indicators, not least because they are newer.

6. Rusk's "New Home Buyers" Characterization is Flawed: Rusk calculates the number of "new home buyers" from 1950 to 1990 (a more accurate term would be "new dwelling occupiers"). For metropolitan areas with central cities that have grown, Rusk defines the number of new home buyers as the net increase in population. But for metropolitan areas in which the central city has lost population, Rusk defines the number of home buyers as the gain in suburban (non-central city) population plus the number of people that have left the central city. Rusk indicates that "For an inelastic area, new homes must be provided for newcomers to the metro area and for current residents moving to the city from the suburbs." Rusk's "new home buyers" indicator is simplistic and misleading. It assumes that residents in elastic central cities do not move. This is, of course, absurd. Census data indicates that 63 percent of US households moved between 1980 and 1990. For example, in the hyper-elastic central city of Phoenix, approximately 225,000 households occupied new dwelling units between 1980 and 1990, while the number of households increased by only 100,000. Presumably someone had to move out of the 125,000 dwellings that were occupied by Phoenix "new home buyers" who lived in Phoenix in 1980.

7. Small Elastic Cities Could Not be So Influential. If it were true that city elasticity produced superior economic and social results, then it would seem reasonable to believe that the best performance would be achieved in metropolitan areas where the central cities accounted for a higher percentage of the population. Yet six of the top eleven metropolitan areas in job creation from 1973 to 1988 had central cities with 25 percent or less of their metropolitan population (Orlando, Dallas-Fort Worth, Tampa-St. Petersburg, Raleigh-Durham, Sacramento and Atlanta). It frankly seems implausible that central cities of such small comparative size could have such significant impacts on their much larger suburbs and metropolitan areas,

8. Business Relocation Decisions do not Generally Consider Annexation Policy. Another flaw in the central city elasticity hypothesis is that annexation policy simply does not emerge in the literature as a factor of significance considered by corporations that are relocating or establishing new facilities. It seems, for example, unlikely that the Walt Disney company concerned itself with annexation policy when it made its 1960s decision to locate Disney World, and set off an unprecedented rate of urbanization that made Orlando one of the top markets in employment growth. It seems even more implausible that Orlando's superior economic and social performance arises from the annexation policies of its hyper elastic central city, which today contains barely 15 percent of the metropolitan population.

9. There is a Lack of Statistical Rigor: There is also a lack of analytical rigor in Rusk's survey. No attempt is made to examine the rate of growth of metropolitan areas with elastic central cities before and after major annexations, despite the fact that the annexations studied occurred over the entire 40 year period. No analysis is provided that would eliminate alternative causes of the phenomenon Rusk identifies, such as the regional and metropolitan size sample biases identified above. At one point, Rusk indicates that the elasticity quintiles have "about the same number of new-home buyers" yet the data described in the subject table (page 57) exhibits a nearly 70 percent range (from 484,703 to 818,853), well beyond the limits of similarity.


Accepting the Rusk thesis requires a childlike faith that the Rust Belt to Sun Belt migration of the past half century was driven by municipal annexation policy. In fact, other factors, such as economic growth, business cost differentials, weather and air conditioning, have driven the changing economic and social fortunes of US metropolitan areas. That the comparatively prospering metropolitan areas happen to be located in states with more liberal annexation laws has no more driven their success than that their state speed limits have been generally higher. Overall, southern and western metropolitan areas have done better than eastern and Midwestern areas. Rusk's policy prescriptions of government consolidation, regional tax base sharing and anti-suburban policies are inappropriate, not least because his diagnosis is flawed.

There is no dispute with Rusk's contention that the city is the entire metropolitan area, though he himself fails to apply this principle. But the geographical boundaries of urban development are not the optimal size for local governing units or local taxing districts. In his The Wealth and Poverty of Nations, David Landes points out that innovation during the industrial revolution occurred outside the reach of the existing municipalities, whose guilds would have stifled it --- and did where annexation was permitted. It is a lesson we should not soon forget.

6 February 2000


1. David Rusk, Cities without Suburbs (Washington: Woodrow Wilson Center Press), 1995 (second edition).

2. Myron Orfield, Metropolitics: A Regional Agenda for Community and Stability (Washington: Brookings Institution Press and Cambridge: Lincoln Institute of Land Policy), 1997, p. 100.

3. Rusk uses change in employment from 1973 to 1988. This analysis uses change in employment from 1970 to 1990. If the central city elasticity hypothesis is valid, the use of different years should produce similar results.

4. Rusk uses average family income from 1949 to 1989. This analysis uses a similar measure, average household income from 1949 to 1989.

5. James T. Bennett, A Higher Standard of Living in Right to Work States, (Springfield, VA: National Institute for Labor Research), 1990.

6. Katharine L. Bradbury, Anthony Downs and Kenneth Small, Urban Decline and the Future of American Cities, Brookings Institution (Washington: 1982), pp. 89-97.

7. The regression produced an r-squared of 0.267, which is at the 99 percent level of statistical significance for a sample of 94 metropolitan areas (primary metropolitan statistical areas were included in their corresponding metropolitan statistical areas). The resulting factors were: Constant: +0.364 and variable +0.416. The independent variable was the percentage of people living in their residence in 1970 or before and the dependent variable was the Census Bureau Black segregation index.

(c) 2001 --- Wendell Cox Consultancy --- Permission granted to use with attribution.
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