I am working on a long-term research project studying changes in urban patterns in 59 of the largest metropolitan areas in the U.S. from 1950 to 2010. The research uses data on numbers of housing units by census tract. These data are used to delineate urban and exurban portions of the metropolitan areas for each census year and to study patterns and changes within those areas.
This page has links for downloading pdf documents related to this research. The papers are the more formal, complete pieces presenting the results in inquiries into various questions. The notes are informal descriptions of the data and examinations of issues arising in the course of the research.
Density of Large Urban Areas in the U.S., 1950–2010
Density is a fundamental, defining characteristic of urban areas that has important implications for many other aspects of urban life. Using census tract data for 1950 to 2010, the extent of the built-up urban areas is delineated in a consistent manner for 59 of the largest metropolitan regions in the United States. Contrary to common expectations of nearly universal decline in urban densities, many areas showed relatively stable densities or even significant increases over the period. The areas with stable or increasing densities were located in the South and, especially for increases in density, in the West. The larger declines in densities occurred in areas in the Northeast and Midwest. Density levels and changes in density were associated with the sizes of areas, prior densities, rates of growth, and the presence of barriers to urban expansion.
The Negative Exponential Decline of Density in Large Urban Areas in the U.S., 1950–2010
The monocentric model predicts the negative exponential decline of density with distance from the center, but employment in urban areas has become increasingly dispersed in multiple employment centers. Using census tract data from 1950 to 2010, the parameters of the negative exponential model are estimated for 43 large urban areas. Density gradients have declined consistently. Overall, central densities likewise declined, with exceptions for some areas that have seen more rapid growth. The average fit of the model across the areas, measured by R2, fell by nearly half after 1970, consistent with more polycentric employment patterns. Nevertheless, even for areas with extremely poor fit, negative exponential parameter estimates continued to be reasonable.
The Monocentric Model with Polycentric Employment: Ring versus Tract Estimates of the Negative Exponential Decline of Density
The increase in employment away from Central Business Districts raises questions about the continued applicability of the monocentric model and its prediction of the negative decline of density, yet the model continues to be used and produces reasonable results. This paper argues that while the development of multiple employment subcenters produces variation in density patterns resulting in declining goodness-of-fit of the negative exponential model when estimated using data for small areas, the overall pattern continues to be a general decline of density with distance. The negative exponential model is estimated using data on densities both for census tracts and concentric rings around the center for 43 large urban areas in the United States from 1950 to 2010. The R2 values for the estimates using the tract data decline steadily after 1970, while the ring estimates show only small decreases. It is further hypothesized that since more general measures of accessibility to employment may now better predict density at the tract level, distance to the center as a proxy incorporates increasing error, resulting in attenuation bias in the estimates of the density gradients, which was shown by comparing the tract and ring estimates.
The Degree of Centralization in Large Urban Areas in the U.S., 1950–2010
Levels of centralization of population and housing and the phenomenon of decentralization are an important aspect of large urban areas. A measure of centralization called the centralization ratio is developed that reflects the proportional reduction in the mean distance housing units are located from the center compared to a uniform distribution in the urban area. Values for this measure are computed using data on numbers of housing units by census tracts for 59 large urban areas defined for each census from 1950 to 2010. The results show that mean levels of centralization have declined steadily and significantly over the period. This decline was not universal, however, with 14 areas showing increases. Centralization varied by region of the country, highest in the Northeast and lowest in the South. Mean levels of centralization were also higher for the largest urban areas.
Negative Exponential Model Parameters and Centralization in Large Urban Areas in the U.S., 1950–2010
The change in the negative exponential density gradient has often been used as a measure of urban decentralization, with the gradient itself also being taken as a measure of the degree of centralization for comparing urban areas. Changes and levels of estimated negative exponential model parameters for 43 areas from 1950 to 2010 are compared with a “pure” measure of centralization, the centralization ratio. The proportional change in the density gradient is indeed significantly related to the change in the centralization ratio, while the relationship of the change in central density to centralization is inconsistent. However, the level of the density gradient is not significantly related to the level of centralization, except that controlling for the size of the urban area produces a significant relationship. The central density is related to the level of centralization.
Negative Exponential Model Parameters and the Size of Large Urban Areas in the U.S., 1950–2010
The density of urban development tends toward a negative exponential decline with distance from the center. The density gradient has been observed to be inversely related to the size of the urban area, while the central density is directly related. If the negative exponential density decline holds, the size of the urban area, the density gradient, and the central density are necessarily mathematically related. This relationship is derived, and a simplified approximation is compared with the sizes of large urban areas and the estimated density gradients and central densities. The results generally confirm the expectations, although the coefficient for the central density is larger than expected, possibly because of the use of gross rather than net residential density in estimating the parameters for the negative exponential model.
On the Choice of Combined Statistical Areas
Some Metropolitan Statistical Areas (MSAs) fail to encompass the full extent of metropolitan areas. Combined Statistical Areas (CSAs), combinations of Core-Based Statistical Areas, are larger and may be more a more appropriate choice for certain analyses. Differences between MSAs and CSAs (and some MSAs are not even included in CSAs) range from minor to the combination of large MSAs, with population increases ranging from a few percent more than doubling. The sharing of transportation infrastructure in the form of commuter rail service and shared airports demonstrates the integration of areas combined into CSAs. In addition, the extent of the MSAs defined for the 2000 census are comparable to current CSAs, which arise from a subsequent change in how metropolitan areas are defined.
Defining Exurban Areas for the Analysis of Urban Patterns Over Time
This paper addresses the issue of defining exurban areas around 59 large urban areas from 1950 to 2010. The ideal definition would include contiguous census tracts meeting a minimum density threshold and showing integration with the urban area based on commuting. Since data on the latter are not available throughout the period, only a density criterion could be used. A density minimum was selected such that the areas of contiguous exurban density in 2010 would be largely contained within the urban area’s metropolitan area boundaries, indicating a likelihood of integration with the urban area. An assessment of the resulting exurban areas shows a high degree of containment for metropolitan areas. A brief examination of the 2010 exurban areas shows they vary greatly in terms of size.
Exurban Areas Around Large Urban Areas in the U.S. in 2010
Exurban areas are defined as contiguous census tracts having a density above a minimum surrounding 59 large urban areas. The sizes of exurban areas in terms of both land area and number of housing units varied widely in 2010. Absolute size is related to the size of the urban area. When the ratios to the urban area sizes are taken as the measures of exurban development, this changes to a modest negative relationship, with smaller urban areas having relatively larger exurban areas. Exurban areas are larger in the Northeast and South and smaller in the West. Areas where urban and exurban expansion is limited, as by an arid climate, have smaller exurban areas. Areas vary considerably in the amount of development at urban densities. Simple regression models do well in predicting exurban land area and housing units. Changes in exurban size from 2000 to 2010 ranged from significant declines to large increases and were not related to urban size and change and only weakly related to region. Changes were lower for areas located on large bodies of water.
Exurban Areas Around Large Urban Areas in the U.S., 1950–2010
Exurban areas are defined as contiguous census tracts having a density above a minimum surrounding 59 large urban areas and have been delineated for each census year from 1950 to 2010. In every year, the sizes of exurban areas in terms of both land area and number of housing units varied widely. Most dramatic was the increase in the sizes of the exurban areas over that period, with both mean land area and mean housing units over 6 times larger by 2010. Exurban area size is related to the size of the urban areas, but exurban areas have grown more rapidly. The size of exurban areas relative to their urban areas as measured by the ratios of exurban to urban land area and housing units increased steadily. These mean relative sizes varied by region with the Northeast by far the highest in 1950, but with mean exurban-urban ratios in the South catching up by 2010. Areas in the West have consistently low exurban area sizes relative to their urban areas, with one factor being arid climate for some of these areas limiting exurban expansion.
Developing Multiple Measures of Urban Patterns
Four measures of urban patterns are identified to describe the distributions of housing units in 59 large urban areas in the United States from 1950 to 2010. These measures include density; variation in density using the index of dissimilarity; centralization measuring the proportional reduction in distance to the center; and clustering using Moran’s I, a measure of spatial autocorrelation. An empirical assessment of the suitability of these measures was undertaken. All showed sufficient variation throughout the period. The measures were significantly correlated with one another, which was expected, but each retained significant uncorrelated variation as well. Principal components analysis showed that most of the variation in these measures could be captured in 3 independent factors, which were density, a mixture of variation and centralization, and clustering with some relationship to centralization.
Measures of Urban Patterns in Large Urban Areas in the U.S., 1950–2010
Patterns of housing unit distributions in 59 large urban areas in the United States from 1950 to 2010 were evaluated using 4 measures: density, the index of dissimilarity for variation in density, the centralization ratio, and Moran’s I for clustering. The mean values for the first 3 measures consistently declined over the period, but wide variation was observed among the urban areas with both large increases as well as large decreases. The measures were correlated with one another as expected. Simple multivariate analysis showed centralization and clustering to be strongly related to variation with weak or no direct relationship with density. Larger urban areas exhibited greater complexity, tending to have higher values for all 4 measures. Average values varied by region, with areas in the Northeast generally having the highest values while those in the South were consistently lowest. However, a significant shift occurred with urban areas in the West changing from having below-average densities in 1950 to the highest densities in 2010. Cluster analysis was used to develop a typology of urban areas in 2010, classifying them into 6 groups.
On Population-Weighted Density
Population-weighted density is the mean of the densities of subareas of a larger area weighted by the populations of those subareas. It is an alternative to the conventional density measure, total population divided by total area. This paper shows that population-weighted density is equal to conventional density plus the variance in density across the subareas divided by the conventional density. This density alternative is very dependent on the size and configuration of the subareas, an issue that has not been adequately addressed by most users. Urban sprawl is associated with lower densities, and the choice of the appropriate density measure is dependent upon the negative consequences of sprawl being considered. Comparison of conventional and population-weighted densities show the latter to be more highly skewed and to sometimes rank urban area densities very differently. Population-weighted density is more strongly related to the size of the urban area, especially size in earlier years, demonstrating the effect of the timing of urban growth on density.
Urban Patterns Dataset Description
This note is provides a description and documentation of the data used for the Urban Patterns dataset and the methods used to delineate urban and exurban areas for each census year.
Year-Built Estimates Analaysis
The Urban Patterns dataset has estimates of the numbers of housing units in census tracts for the earlier years derived from the Census data on housing units by year-built, primarily from the 1970 census. This note provides estimates of the error associated with this estimation.
Urbanized Area Comparison
The delineation of the urban areas in the Urban Patterns dataset was modeled on the procedures currently used by the Census for delineating Urbanized Areas. This note is a comparison of the urban areas in the dataset with the Urbanized Areas.
The Effect of the Changed Definition of Metropolitan Statistical Areas
A greatly changed metropolitan area definition was first used to delineate areas in 2003. In many cases, areas considered to be single metropolitan areas in 2000 were split into multiple Metropolitan Statistical Areas in 2003. This note compared the extent of the 2000 areas with the 2003 areas to examine the effect of the change in the definition.
Problems with the Urban and Metropolitan Area Definitions
The previous note showed how changes in the metropolitan area definition resulted Metropolitan Statistical Areas in 2003 that were frequently much smaller then before. This note examines the changes to the urban and metropolitan area definitions that caused this, finding that these had become fundamentally circular definitions. For 2010, the Census Bureau compounded the problem by making the inexusable decision to freeze the set of Urbanized Areas as they were delineated for 2000. This note concludes with some initial ideas on better approaches for defining these areas.
The Monocentric Model with Polycentric Employment Revisted: Employment Accessibility, Density Gradient Attenuation, and Negative Exponential Model Performance
The paper The Monocentric Model with Polycentric Employment: Ring versus Tract Estimates of the Negative Exponential Decline of Density hypothesized and showed that if generalized accessibility to employment were a better predictor of tract density than distance to the center, the error in using distance to the center to predict density would result in the attenuation of the estimates of the density gradient. I have now added the hypthesis that if the error in using distance as a proxy for accessibility is indeed the result of greater development of outlying employment centers, the degree of attenuation should be related to the performance of the negative exponential model in predicting density. This note provides the confirmation.