Some tests of alternative urban population density functions

The purpose of this study is to test the usefulness of some alternative gross population density functions for urbanized areas. Two evaluation criteria are used; maximum explanatory power in standard regression analysis and accuracy in predicting total population in the urbanized area. It is concluded that the explanatory power of the negative exponential function can be improved upon in some cases by adding a quadratic distance term, but that population can be predicted more accurately if the quadratic term is omitted. Also, it is found that constraining the negative exponential function to predict population exactly reduces explanatory power by an insignificant amount.     

A bias in estimating urban population density functions

This paper demonstrates that because of the rules used to delineate census tracts, unweighted estimation of an urban population density function using census tract observations leads to a severe upward bias in the estimated function. A weighted estimation procedure which leads to an unbiased estimate is proposed. The paper also points out that if one computes the integral of an unbiased estimate of a density function over the area of a city, that integral is not necessarily an unbiased estimate of total population. The paper thus explains the “disturbing” empirical results concerning density functions reported by McDonald and Bowman.     

Simulating urban population density with a gravity-based model

Theoretical justifications for the negative exponential urban density function were first proposed by urban economists, although some of their foundations have been criticized. From the geographer's perspective, the gravity-based model reported in this research uses a well-known concept (the “potential”) to offer an alternative explanation. Using numerical analysis techniques, the model simulates various urban density patterns. By varying the model's parameters (the distance friction coefficient β and the city size), the numerical simulations do confirm two important empirical findings: the flattening of density gradients over time owing to transportation improvements, and flatter gradients in larger cities. The observed relationship between the β value and the urban density gradient, as established by this research, opens an avenue for empirical testing.     

Modelling urban population density in a multi-centered city

Modelling the geographic distribution of urban population densities has been attempted in several ways. Recently a controversy emerged in the Journal of Urban Economics regarding whether or not calibrations of these models render unbiased parameter estimates. Three sources of bias were dealt with in these discussions, namely (1) model specification error, (2) the estimation procedure employed, and (3) the definition of areal unit observation size. Additional sources of bias overlooked in this controversy include the presence of multiple centers in a city, and the existence of externalities. This paper explores these additional sources, from both a conceptual and an empirical point of view.     

Econometric issues in interpreting Mills' estimates of urban density gradients

Mills has estimated a first order, autoregressive distributed lag model of the process of adaptation of urban density gradients. The error term in such equations estimated by ordinary least squares is likely autocorrelated, biasing upward the estimated coefficient of the lagged dependent variable. A specification error may be concealed, with autocorrelation in the error term resulting in overestimates of the length of the adjusted lag. Longer time series samples will be required if the nature of the lagged adjustment processes and the error term are to be simultaneously estimated.     

Structural shifts in urban population density gradients: an empirical investigation

This study investigates the structural shifts in urban population density gradients by first using the shifting regression technique of Farley, Hinich, and McGuire to detect the possible change in the structure of an urban area. Secondly, a generalized random coefficient technique is used to simultaneously detect the possible structural change and stochastic behavior of density gradients. Data for 50 United States SMSA's are used to do the empirical analyses.     

How good are two-point estimates of urban density gradients and central densities?

Some researchers have estimated urban density gradients and central densities using only information on the population and area of the inner city and the outer ring of suburbs. The statistical properties of these two-point estimates have not been previously analyzed. This paper shows the difficulties in providing a definitive analysis of these properties and provides, as an alternative, some Monte Carlo experiments. It appears that the two-point density gradients are mildly biased downward (toward zero), while the bias on the central density depends on the underlying error structure. Two-point estimates are compared with OLS and nonlinear least-squares estimates. Some results for actual cities are also provided.     

Estimation and recent behavior of urban population and employment density gradients

The monocentric model of urban structure predicts that urban population density declines with distance from the central business district. Using the negative exponential function to approximate the decline, Mills (E. S. Mills, “Studies in the Structure of the Urban Economy,” Johns Hopkins Press, Baltimore, Md. (1972)) estimated population and employment density gradients from 1948 to 1963 for a sample of 18 SMSAs. This paper updates Mills' estimates and examines recent patterns in population and employment suburbanization. The updated series estimated here is obtained using a “corrected” version of Mills' method. The original procedure incorporated a bias which Mills noted and later corrected (E. Mills and K. Ohta, in “Asia's New Giant” (Patrick and Rosovsky, Eds.), The Brookings Institution, Washington, D.C. (1976)). The comparability of the series begun by Mills and extended here is not interrupted, however, because, as Mills suspected, the bias is indeed small provided SMSA data are used. On the other hand, Urbanized Area definitions of metropolitan areas cause the original and corrected versions to yield significantly different results. This finding has implications for the appropriate choice of data for urban studies.     

乡村运动:城市功能的外溢——新农村建设与城市化进程的内在逻辑

通过总结在城市化进程不同阶段中农村经济社会发展的基本特征,对比分析邻国日本、韩国乡村的发展经验,对我国的农村发展问题进行了深入研究。提出新农村建设策略应该是以建立在区域差异性基础上的城市化水平为轴线,通过区域功能分工实现城市功能延续,逐步推进新农村建设,最终达到城乡一体化发展的境界。     

Joint estimation of population density functions and the location of the central business district

"In this paper we [propose] a new procedure for estimating population density functions under conditions that the exact location of the CBD [central business district] is unknown or uncertain. As such it can also be utilized as a method for identifying the location of the CBD....[We apply] this method to cross-sectional data from Tel-Aviv-Yafo [Israel] during 1961 through 1990...."     

Metropolitan density functions : A Further exploration

The application of mathematical functions to population density data within metropolitan areas has become a well-established analytical procedure. The more important functions that have been previously employed in this connection are reviewed, and two additional functional forms are suggested. The proposed functions, together with the earlier ones, are evaluated in terms of their ability to describe actual density patterns, as well as their accuracy in characterizing certain features of metropolitan spatial structure. The evaluation is undertaken in relation to two metropolitan areas of the United Kingdom. While these both possess certain distinctive features, they conform in many respects to metropolitan areas in other western nations.     

Capital-land substitution in urban housing: A survey of empirical estimates

Recent empirical studies of capital-land substitution in urban housing are examined to determine the best estimate of the elasticity of substitution parameter σ. Studies based upon a cross section of metropolitan areas produce a rather narrow range for σ. Studies of individual metropolitan areas produce a wide range of estimates for σ, suggesting that a may vary across metropolitan areas. However, all estimates of σ are probably biased toward zero by errors in the measurement of land values.     

Estimation of symmetric functions of a finite population

Summary Estimation of symmetric functions under the assumptions of noninformativeness of labels in a finite population of distinguishable units has been examined. The primitive strategies of srs, sample mean, sample variance etc. are found to play important roles.