Alex Anas

Dynamics of urban residential growth

Abstract This paper develops a dynamic model of the urban residential market. Under specific assumptions about market behavior on both the supply and the demand sides it is shown that cities grow by attaining a sequence of short run equilibria. A set of recursive equations is derived and through these the impact of growth on the structure of rents, densities, and consumer welfare is analyzed. The dynamic model explains the decay of the central locations in large old American cities. Housing obsolescence and abandonment arises under special conditions and is reflected in positively sloped rent gradients in central locations. The well-known static result of declining densities with distance from the center is shown to occur only under special conditions such as rising income levels. Directions for further analyzing urban growth, by expanding this dynamic approach, are pointed out.

A REGIONAL ECONOMY, LAND USE, AND TRANSPORTATION MODEL (RELU‐TRAN©): FORMULATION, ALGORITHM DESIGN, AND TESTING

RELU is a dynamic general equilibrium model of a metropolitan economy and its land use, derived by unifying in a theoretically valid way, models developed by one of the authors [Anas (1982), Anas-Arnott (1991, 1997), Anas-Kim (1996), Anas-Xu (1999)]. RELU equilibrates floor space, land and labor markets, and the market for the products of industries, treating development (construction and demolition), spatial interindustry linkages, commuting, and discretionary travel. Mode choices and equilibrium congestion on the highway network are treated by unifying RELU with the TRAN algorithm of stochastic user equilibrium [Anas-Kim (1990)]. The RELU-TRAN algorithms performance for a stationary state is demonstrated for a prototype consisting of 4-building, 4-industry, 4-labor-type, 15-land-use-zone, 68-link-highway-network version of the Chicago MSA. The algorithm solves 656 equations in a special block-recursive convergent procedure by iterations nested within loops and loops within cycles. Runs show excellent and smooth convergence from different starting points, so that the number of loops within successive cycles continually decreases. The tests also imply a numerically ascertained unique stationary equilibrium solution of the unified model for the calibrated parameters. Copyright Blackwell Publishing, Inc. 2007

Reducing Urban Road Transportation Externalities: Road Pricing in Theory and in Practice

Urban road transportation creates several externalities, the most important of which are congestion (time delay and extra fuel consumption), accidents, pollution, and greenhouse gas emissions. Road pricing is widely promoted as a tool to reduce these externalities. Based on a review of theory as well as experience with existing schemes, this article draws four conclusions about urban road pricing: (1) the benefits of road pricing exceed the costs; (2) the benefits of congestion relief are larger than the benefits of improvements in environmental quality; (3) success depends in part, but only to a limited extent, on the presence of public transit and on how service is adjusted; and (4) the distributional effects and public acceptance of road pricing pose important challenges for policy design.

Theories of systems of cities

Economic theories of systems of cities explain why production and consumption activities are concentrated in a number of urban areas of different sizes and industrial composition rather than uniformly distributed in space. These theories have been successively influenced by four paradigms: (i) conventional urban economics emphasizing the tension between economies due to the spatial concentration of activity and diseconomies arising from that concentration; (ii) the theory of industrial organization as it relates to inter-industry linkages and to product differentiation; (iii) the New Economic Geography which ignores land markets but emphasizes trade among cities, fixed agricultural hinterlands and the endogenous emergence of geography; (iv) the theory of endogenous economic growth. Among the issues examined are specialization versus diversification of cities in systems of cities, how city systems contribute to increasing returns in national and the global economies, the factors that determine skill distribution and income disparity between cities, the impacts of income disparity on welfare, whether population growth should cause economic activity to become more or less concentrated in urban areas, and how resources should be allocated efficiently in a system of cities. Related to the last issue, we consider models where cities are organized by local planners or developers as well as cities that self-organize by atomistic actions. A conclusion of the theoretical study of city systems is that markets fail in efficiently allocating resources across cities when certain intercity interactions are present and that a role for central planning may be necessary.

On the birth and growth of cities:: Laissez-faire and planning compared

Abstract In a growing laissez-faire economy, the optimal time when the large cities should be decentralized into new settlements is missed because such timing requires collective migration to the same place by many self-interested agents. New cities are born at stochastically determined times when existing cities are larger than their optimal sizes and unstable. With negligible migration costs, such city births are associated with panic-migrations and related economic shocks. Thus, laissez-faire city systems develop in cycles of booms and busts. The planned timing of settlements smooths these cycles by rounding the tops and raising the troughs in the per capita utility profile over time.Efficient growth requires alternating cycles of laissez-faire and planning. Planning establishes each new city at the optimal time and nurses it through an initial period of instability. As the economy grows large, the duration of the necessary planning periods vanishes asymptotically. In a declining laissez-faire economy, cities are abandoned at deterministic times and at smaller sizes than the sizes at which they would be born during growth. The decline path cannot be obtained by reversing the growth path, and a hysteresis effect is present.

Taste heterogeneity and urban spatial structure: The logit model and monocentric theory reconciled

Abstract A model of urban spatial structure for a linear and closed monocentric city is formulated by allowing the presence of randomly distributed idiosyncratic tastes for location in an otherwise uniform household population. Land use equilibrium conditions are shown to have a stochastic representation which depends on the distribution of the idiosyncratic tastes over the population of households. A special case in which the multinomial logit model gives the representative households locational choice probability is derived and examined for a logarithmic utility function. It is shown that the stochastic equilibrium can also be obtained as the solution of a welfare optimum problem, either by maximizing total social welfare (primal) or by minimizing total opportunity cost (dual). Either formulation gives the equilibrium allocations and associated decentralizing land prices. Some comparative statics analysis is undertaken to show that while most results are like those of the Alonso-Mills-Muth model, increasing taste heterogeneity decentralizes the linear urban form, “flattening” the rent and population density gradients. The Alonso-Mills-Muth solution is obtained as an asymptotically limiting case which provides an upper bound on the “steepness” of the rent and population density gradients and a lower bound on the length of the linear city and the welfare level of the representative consumer.

Mode choice, transport structure and urban land use

Abstract A theoretical model of the urban land market is solved to examine the impact of bimodal passenger transportation on equilibrium residential land use. In this model travel to the central business district occurs on a dense system of radial roads or bus routes and a competing system or radial expressways or mass transit lines fed by a subsidiary system of densely spread access streets. Under rational behavior assumptions for households, it is shown that various basic urban forms can result depending on the relative generalized cost characteristics of the competing dense and sparse radial networks. The basic urban forms yield fundamental shapes, differing as to the relative geometry and position of the market areas for the two modes. The standard Alonso-Muth model of unimodal travel and circular urban form is found to result as a special case in several of these cases. American urbanized areas of various sizes and modal mix provide plausible examples for each of the basic forms. The paper concludes with a discussion of the models implications as a framework for examining optimum urban transport structure and the proliferation of transport routes as a function of urban size.

Discrete choice models and the housing price and travel to work elasticities of location demand

Abstract Multinomial logit and nested logit models of mode choice in travel to work and housing location choice are estimated from 1970 U.S. census data aggregated to small zones of the Chicago SMSA. The estimated models are then used to derive the “housing rent,” “travel time,” and “travel cost” elasticities of location demand. The effects of sampling variation, sample size, attribute inclusion, model specification, and estimation method on the estimated elasticities are evaluated and found to be important. The elasticities are also compared and found to agree with those obtained from other discrete choice models and, in the case of “housing rent,” with estimates obtained from models based on other theoretical structure.

Dynamic housing market equilibrium with taste heterogeneity, idiosyncratic perfect foresight, and stock conversions*

A discrete-time, nonstationary dynamic equilibrium model of the housing market is developed in which consumers exhibit taste heterogeneity and investors act with perfect foresight subject to idiosyncratic uncertainty in costs. Housing is treated as a discrete, durable, and differentiated good which is indivisible in consumption and a convertible asset in investment. The dynamic market equilibrium determines the allocation of each consumer type among the housing types, the rent and vacancies of each housing type, the asset prices of housing and land, and the conversions between land and housing and among the stocks of housing of each type. The model relies on probabilistic discrete choice theory, whereby the investors and consumers choice probabilities are given the multinomial logit specification. An algorithm is developed which solves for dynamic equilibrium by assuming a relationship between rents and asset prices in the terminal period. The computable model is used to examine the “filtering hypothesis”: that technological progress or government subsidies targeted to the construction of high-quality housing eventually benefit the poor. While this hypothesis is correct when subsidies do not induce stock conversions, it is false if investors demolish sufficient numbers of low-quality housing units in order to construct high-quality housing.

Intercity trade and the industrial diversification of cities

Abstract The industrial diversification of cities is explained without imposing linkages among industries. In each of two city-industries, a manufacture is produced competitively as the final good using labor and industry-specific differentiated services. Manufacturers import the services of their industry from all cities that produce them, since their technology favors variety. In specialized cities, the city-industry is large and many services are locally available but the two manufactures have to be traded among cities. In diversified cities, the two manufactures are produced in the same city, and each industry crowds out half the local services of the other, but manufactures need not be imported. A lower cost of trading manufactures (e.g., railroads and intercity highways) favors a system of specialized cities, while a lower cost of trading services (e.g., telephone, the Internet) favors a system of diversified cities since the latter cities rely more on imported services, having fewer locally. A larger cost-share of services favors specialization, and high intra-city commuting cost and population growth favor diversification.