Urban Growth Models Research Paper

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An urban model is a statement about the interrelationships between parts of an urban system, which not only describes these interactions, but makes possible the prediction of the effects of some kinds of changes in the system or in its environment. This is the essence of any scientific theory.

Viewed as a part of a scientific discipline, urban models provide an organizing framework for bringing together many aspects of knowledge about urban life, for testing subsidiary theories, and for identifying gaps in knowledge and guiding future research. Viewed as an aid to professional practice in urban planning or engineering, a model which is operational at a relevant level of detail can provide insights into the future results of new policies, and guidance in their formulation and improvement. To serve these two divergent purposes, a model must be understandable and acceptable to both the scientist and the professional.

Prior to the mid-1950s, many disciplines and professions engaged in disjointed efforts to analyze urban affairs. In Geography and Sociology, there were efforts to achieve an overall view in largely descriptive terms. Examples include Burgess (1927), Hoyt (1939), and Harris and Ullman (1945). Starting in a period of optimism about scientific management, the last 50 years have seen substantial growth in urban modeling, but there are still many imperfections in current models, and obstacles to their filling their dual role. We will try to expose the bare bones of both the progress and the difficulties as they have developed over five decades.

1. Basic Considerations

An urban metropolitan area comprises a set of organized activities and residential spaces, occupying land and buildings, and using infrastructure. These activities and their containers are at higher densities than their nonurban surroundings, and are more closely connected with each other than with their ambient environment. Their existence and development require the proper functioning of markets or allocation methods for land, for housing, offices, and factories, for labor, and for public and private services, including those of the transport and communications systems which knit these other functions together.

Because of the paramount importance of resource allocation, and the role of real or artificial markets, these interrelationships are largely governed by economic considerations—but with many differences from received economic dogma. There is a division of decision-making between the private and public sectors, necessitated in part by economies of scale and indivisibilities. In the ultimate political sense, economic efficiency is only one of several means to a bundle of humanistic ends. In analyzing behavior, especially that of households and their members, economic forces are greatly influenced and modified by social and psychological ones. Economic analysis depending on equilibrium tendencies ignores or belittles the lags in personal and organizational adjustment to change, and the durability of investment in infrastructure, buildings, and human capital.

There is another and fundamental schism between economic descriptions of ‘rational’ behavior and the realities of urban life. This divergence has led to two trends in urban modeling which are only now being resolved. In economics, similar actors in similar conditions make similar decisions—people shop at the nearest center, traffic follows the shortest route, and employees seek out the nearest jobs. In reality, some actors make long trips, and roundabout ones (but with diminishing frequency) for the same purposes which might be pursued using shorter and more direct trips. The ‘rational’ behavior is defined in economic models of optimizing choices, while diverse behavior is described, but not explained, in a number of ways by ‘gravity models’, ‘entropy maximization’, and ‘discrete choice’—three very similar approaches.

By far the most important issue in model development has been this antinomy between an economic view that posits uniform behavior and a humanistic view which posits diversity. These two views underlie different lines of model development, and we will follow their reconciliation, though a recognition of ignorance—a reconciliation which clears the way for the resolution of other but less important difficulties.

2. Inventing A Paradigmatic Model

In the early 1950s a number of factors favoring the discovery of a new paradigm in urban modeling came together: on the ground, through the suburban redirection of American urbanism, and planning and building urban expressways; in technique, through the optimism of instrumental rationalism, seen in Operations Research and Management Science and buttressed by the commercial availability of computers; and in planning, through the widespread influence of the University of Chicago Program. In the middle of the decade, urban land planning began a slow movement in the direction of modeling (see Voorhees 1959), and the Chicago Area Transportation Study (CATS 1959) developed an innovative approach, drawing on many sources, which in retrospect must be considered a new paradigm for urban modeling.

A new paradigm in scientific or professional matters involves a framework for studying phenomena and defining their relationships. The importance of such innovation does not imply perfection; implementing and extending the paradigm and overcoming its imperfections may require decades. The essential novelty of this paradigm for analyzing the critical aspects of urban settlement systems extends far beyond transportation itself, and embodies the following elements:

(a) Examine the system in all relevant detail, with massive data collection and thorough analysis of user behavior and system responses. (This was done in transportation studies by large-scale sampling of travel behavior and traffic conditions.)

(b) Simulate user behavior over the entire system or subsystem, together with the system response, and with feedback in which the system response influences the user behavior. (The simulations in CATS were inventive and completely novel.)

(c) Draw heavily on other disciplines that can contribute to the accuracy and realism of the simulations; use exact formulations wherever possible, and implement data management and simulation through computers where this is necessary and relevant. (CATS employed sociologists, planners, economists, engineers, and computer experts—and used computers for its most advanced innovations.)

Similar simulations could be imagined, and indeed have been undertaken, for the housing market, the labor market, the location of economic activity and public services, and the environment. Clearly, these subsystems are mutually interdependent, and in the final analysis their simulations would have to interact.

Despite its seminal influence, the CATS study has often been denied its paradigmatic role because of its shortcomings, most obviously inadequate attention to transit and failure to take into account the reaction of land uses to transportation. It shares many other problems with land-use modeling, as we will see in exploring them. It also embodied the schism between economics and behavior: in connecting residences and workplaces by trips it used a gravity model of dispersed behavior, but in assigning trips to the highway system it used the deterministic idea of taking only shortest routes. As a paradigm for transport analysis, it has been and is being reworked; in principle its methods can be traced even in divergent but related urban models.

3. Residential Models: Two Directions And Their Linkages

The major steps in land-use modeling are easily summarized. A series of theoretical models, initially of residential location, were generated by Wingo (1961), Alonso (1964), and Mills (1972)—with other contributions. These models all assumed a monocentric city (having a single employment center), which produced rings of settlement, each occupied by a single residential income class. Density declined and income rose with distance from the center. Residents were trading off commuting costs against space, under the constraints of their income. Mills’s model dealt with zones in a linear programming framework, while the other models used continuous space.

The rigor and simplicity of these models inspired efforts to make them operational, hindered by their restrictive assumptions. Herbert and Stevens (1960) developed very early the idea of bid-rents (i.e., specifications of willingness to pay for various types of housing in various locations), and postulated a multicentered city with competition for land in a linear programming format. They did not operationalize the measures of preferences that would underlie a bidding process, or the connection between place of residence and place of work. The National Bureau of Economic Research (Ingram et al. 1972) extended this work in a larger operational form, with actual employment centers, a diversity of choice of spatially distributed housing submarkets, and a final determination of residency by linear programming based on the cost of work-to-home travel. Building, remodeling, and redeveloping housing was in a separate supply model.

The alternative route of replicating consumer choice in housing and shopping through the use of a gravity model (that specified a declining probability of choice with increasing distance) was more realistic and more appealing to planning practitioners, but was initiated at the cost of disregarding some economic realities. The Lowry Model (Lowry 1964) thus gave the appearance of modeling the behavior of all locators (including residents and their choices), and gave room for diversity through a gravity model. The same approach was widely adopted; for a review, see Goldner (1971). It was popularized by Putman (1982) in the USA, and in structure planning and by Echenique in the UK (reviewed in Echenique and Owers 1994). Most of these efforts went beyond modeling residential choice to consider other locational trends, and other improvements were introduced to make the Lowry Model still more realistic. This model was thus a major contribution to the paradigm shift, by its introduction of a partially unified system of activity location.

The stage was set for a new type of advance that tended to bring these two trends much closer together. The necessity for multicentered models in applied analysis was firmly established. The NBER had introduced a certain amount of diversity through a probabilistic choice of housing markets. Echenique had realized the necessity for constraints on residential location, and began to introduce rents as an incentive for supply and a brake on choice in the face of income limitations. Three important events in the 1970s solidified these advances. In Geography, Wilson (1970) explained the gravity model by analogy with entropy (or constrained randomness) in physics. In Economics, MacFadden (1973) formalized the idea of ‘discrete choice’, which made diverse behavior acceptable to economists; the gravity model became a special case of this accepted theory. Independently, Anas (1975) showed in a seminal paper that interaction under a gravity model could be constrained by ability to pay in a competitive housing market, leading to an economic equilibrium solution, with market clearing.

All three models—gravity, discrete choice, and maximum entropy—can produce mathematically identical results. There is a common recognition that there are aspects of behavior which are not represented in models, and which contribute to a kind of statistical error in any deterministic explanation. The degree of error varies, and may or may not be susceptible to resolution by further analysis.

4. Complete Models

While residential choice models are the most important and perhaps the most interesting, a complete model as described at the outset would be a model suite containing numerous submodels. First, land development and its uses are determined by way of locational decisions that in turn are strongly influenced by transport considerations. Putman and Echenique have taken the lead over the last three decades in driving this lesson home—at least to the transport planning community. We will assume that any complete land-use model will embody or interface with an appropriate transportation model and use a forecast of transportation system changes. Second, even the most advanced residential models suffer from some of the general difficulties discussed below, and in particular, models of residential housing supply are weaker than those of demand. Third, models are needed for all land uses, most particularly manufacturing industry and trade and services. With the increasing shift in the overall economy toward business and consumer services, these sectors and their representation in models need thorough review.

There is a modest number of complete model suites publicly available worldwide (see Wegener 1994 for a review). Putman’s ITLUP and EMPAL models have been extended to METROPOLIS, which is widely used, and maintains the Lowry tradition of noneconomic constraints. Its employment location is somewhat descriptive in style. Echenique has developed an elaborate input–output framework to generate goods traffic as well as personal trips, with extensive economic constraints. Anas (1987) is continuing to develop a range of economically rigorous and ambitious models, most recently for the New York Metropolitan Transportation Commission (in progress). New work is being undertaken which we cannot elaborate here, but special mention must be made of de la Barra, who follows Echenique in the Americas, and Waddell (2000), who is approaching residential location from a microeconomic viewpoint in direct collaboration with state planning and transportation studies. Most model sets are provided on a made-to-order basis, which raises their cost and severely limits their availability.

In our judgment, the characteristic nonresidential models have various weaknesses in almost all model sets. The manufacturing sector is undergoing changes that are not yet fully understood and which may upset conventional wisdom. Business services have barely begun to be studied in the locational literature, let alone embodied in models. Retail trade is the best understood of these three fields, but inadequate use is being made of existing knowledge.

5. Comments On The State Of The Art

It is apparent that considerable advances have been made in urban models, but that results are still short of what might be desired. There are still no established scholarly standards in the field, nor is there a clear link between research and practice. Limited tests of models on the same or similar data sets show little unanimity in their conclusions.

There are many social and equity issues being newly faced in planning of all sorts. Some of these have appeared in the USA in the implementation of the clean air act and its amendments, and related issues in transport planning have been litigated. It appears that there is inadequate disaggregation in most models, so that the behavior of minority groups and their reactions to policy inputs could be studied, while some aspects of disaggregation affect the evaluation of transport and planning policy. These needs conflict with the needs for simplicity, transparency, and speedy computation which arise in public discourse.

With increased computer capabilities, microsimulation is appearing as a possible approach to the disaggregation problem, but its relation to the speed of computation must be studied. Indications in the transportation planning field are that it will extend greatly the time required for analysis—and even today transportation models are the biggest bottleneck in operational land-use models.

The growth of urban modeling is linked closely with the expansion of computational power through both mainframe and personal computers. The first steps in modeling were conceptual, and computationally limited in their demands. Growing computer power has made it possible to develop and implement more accurate and more elaborate models. Computing for planning has been decentralized to the desks of planners and administrators. Computer users have readier access to large data sets, now organized in Geographic Information Systems. Research workers of all types have greatly increased power to investigate localized and sectoral phenomena, having better access to computation, data, and modeling methods. All of these investigations contribute to a web of knowledge that expands understanding of urban phenomena, and undergirds improved modeling. Examples include, the work of Anas and Waddell discussed above, as well as of specialists like Landis, Cevero et al. (1999), and Shen (2000).

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