Using an economic agent-based urban model to evaluate land preservation policies
I. Introduction
Urban development patterns depend on a complicated mix of market forces, government land use policy, and physical features of landscapes. In urban fringe locations, the interplay between market factors – preferences of consumers, productivity of farmland, profit motives of landowners and developers – and local government zoning and other regulations is a key determinant of land use outcomes. A good understanding of this interplay is central to understanding which parcels are converted to development, the density of that development, and the timing of development.
Most existing models of urban development fall short in one way or another when it comes to adequately capturing all of these features of land markets. Most structural economic models do a good job of describing the behavior of economic agents such as farmers and homeowners and often adequately describe the incentive effects of regulations such as zoning. However, they usually fail to capture the spatial aspects of development and cannot sufficiently handle market dynamics. This is because their central assumption is one of equilibrium. As pointed out by Irwin (2009), while this assumption facilitates the modeling of land markets, it creates a roadblock in addressing the dynamics and spatial characteristics of land use patterns. Models used by landscape ecologists focus on describing spatial heterogeneity but usually lack an adequate description of the role played by economics in determining land use outcomes.
In this paper, we develop a model of land use in a growing ex-urban jurisdiction in which we account for both the spatial and temporal heterogeneity of the development process as land goes from rural to urban uses, and we incorporate agent optimizing behavior, market interactions among agents, and uncertainty. The model is an agent-based model of the housing and land markets that includes as agents farmers, developers, and consumers who purchase housing. We use the model to describe the spatial patterns of development that take place over time in a hypothetical region as a result of economic forces such as commuter transportation costs, the value of land in farming, and household income levels. In a case study, we assume that zoning constraints are imposed on the landscape and assess the development patterns that occur as a result.
The paper advances the literature in two regards. First, it advances the nascent agent-based economics literature on land use. Like Parker and Filatova (2008), for example, we model the conversion of farmland to development, but unlike those authors, we also model the density of development. This allows us to study the impacts of zoning, which is our second contribution to the literature. Large lot zoning is an instrument used frequently by local governments in ex-urban locales to protect open space and deter development of farmland. It has been criticized in some quarters, however, for contributing to sprawl by simply leading to more land consumed for a given amount of residential development. We are able to address these claims with our model and assess the transitional dynamics and spatial outcomes with and without a zoning policy.
Our work sheds light on the dynamics and spatial aspects of development and our zoning case study develops some intriguing findings about both the pace and degree of farmland conversion and the patterns of development density across the landscape. But we hasten to point out that the analysis is very much a work in progress. Most importantly, sensitivity analyses of several parameters in the model are important work for the future to better understand our results. Agent-based models, while having much to recommend them, are highly complex with many underlying assumptions and rules. This often makes it difficult to identify the key factors that lead to particular outcomes, making sensitivity analyses perhaps even more important than in other models. In addition, possible changes to model assumptions such as the number of housing types, the size and number of farms, and the overall size of the geographic area could change results.
Section II contains our review of the literature on structural models of land use, with an emphasis on those models that consider zoning. Section III describes the model structure, outlining the features of the consumer, farmer/landowner, and developer modules. Section IV shows results of our baseline scenario, without zoning. Section V shows results with zoning density limits imposed in one geographical area. Section VI offers some concluding remarks and plans for future research.
II. Literature Review
The urban economic literature has attempted to explain the patterns of development within the monocentric city framework using dynamic equilibrium models of cities. In deterministic models of growing urban areas, land is developed when rent in the urban use is equal to the opportunity cost of development – the sum of agricultural land rent and the opportunity cost of capital. However, when uncertainty about the future path of urban land rent is introduced, this result no longer holds and development at the urban fringe is postponed because of uncertainty in future rents. The seminal paper showing this result is Capozza and Helsley (1990). These authors show that irreversibility of development and future uncertainty of land rents leads to the price of land at an urban area boundary being higher than its opportunity cost in other uses. Moreover, the presence of uncertainty tends to reduce equilibrium city size and imparts option value on agricultural land prices.
While this analysis greatly advanced the ability to understand the dynamics of urban land development, many realistic features of urban development cannot be explained within this framework. One such feature is leapfrogging, i.e. discontinuous development of land in an urban area where vacant plots are surrounded by developed plots. Another is that heterogeneity of both agents and goods (farmers, consumers, housing types and farm land productivity) are very hard to represent in a monocentric-type growth model.
Another way to model land use change is to estimate an econometric model of land conversion and other phenomena using micro-data and then simulating alternative outcomes. Examples include Irwin and Bockstael (2002), Irwin et al. (2003), and Towe et al. (2008). As outlined by (Irwin 2009), this method allows for the inclusion of substantial spatial heterogeneity, but data requirements are often restrictive and methodological issues such as spatial dependence, endogenous regressors, spatial instability of parameters, and selection biases can arise. Furthermore, econometric modeling is limited in its ability to represent land use dynamics (Parker et. al., 2003). Econometric parameters ineffectively capture feedbacks that occur over multiple spatial and temporal scales that often drive land use change dynamics (Irwin, 2009).
Spatial equilibrium models are foundational to urban economics (Glaeser, 2008). They are based on the assumption that given a sufficiently long period of time, mobile consumers will locate across a spatially heterogeneous landscape so that utility is equal for all consumers and location disamenities are perfectly offset by prices. The spatial structure of these models is often rooted in the monocentric city model with travel costs to the central business district accounting for spatial variations (see Bento et al. (2006), for example). Alternative versions of these models abandon the monocentricity assumption (Epple and Sieg, 1999; Walsh, 2007). The spatial equilibrium assumption provides analytical tractability for modeling urban land use patterns and captures the capitalization process (Irwin, 2009). However, these models quickly become complex when adding the spatial detail often necessary to analyze land use policies such as zoning, transferable development rights, impact fees, and the like. And the equilibrium requirement does not allow for an explicit representation of land use change dynamics in the model, which makes the integration of economic and ecological models extremely difficult (Irwin et. al., 2007). Furthermore, in reality, cities tend not to be in spatial equilibrium. The importance of out-of-equilibrium market dynamics has gained growing recognition among economists (Arthur, 2006).
Driven by these limitations, the use of agent-based models (ABMs) for land markets has grown rapidly (e.g. Arthur, Durlauf, and Lane, 1997; Epstein and Axtell, 1996; Kirman and Vriend, 2001; LeBaron, 2006; Lux, 1998; Tesfatsion, 2006). ABMs offer several advantages over traditional economic models because they can explicitly represent causal drivers of land market dynamics. These advantages are outlined in Parker and Filatova (2008) and we summarize them here:
1) Heterogeneous goods can be traded by heterogeneous agents. Unique attributes of land (productivity, neighborhood characteristics, etc.) can be represented explicitly, as well as attributes of agents. For example, farmers selling their land have heterogeneous agricultural returns derived from their land’s productivity and operating costs, and they may have different heuristics for decision-making (prediction models and preferences for farming versus selling). Developers differ in their costs and the housing demands they face based on the zones in which they operate. Consumers differ in preferences and income.
2) Spatial and agent-agent interactions are explicitly represented. Location-specific land uses and option values affect the use and value of surrounding land through spatial externalities. The dynamics of these uses and values are driven by competition between agents’ bid and asking prices and future price expectations. Heterogeneous consumers value living in specific locations differently. ABMs capture these differences by modeling competing consumer bids for a specific location, therefore explicitly modeling the emergence of neighborhood effects. Furthermore, transitional dynamics of that location will be dependent on which consumers value that location more in the future. Thus, feedbacks emerging from consumer competition for spatially unique land uses are preserved locally and dynamically adjusted.
3) By modeling agent-agent and agent-environment interactions, market non-equilibrium outcomes can be represented. Land markets are rarely in equilibrium and typically display such complex behaviors as cyclical growth and decline and bubbles (Arthur, 2006). Land markets and associated urban growth patterns tend to be path-dependent and driven in large part by out-of-equilibrium dynamics (Arthur, 2006; Tesfatsion, 2006). ABMs allow these dynamics to emerge rather than exclude them through abstract market adjustments.
ABMs have some drawbacks. Many of the models developed and used to analyze land use dynamics and spatial outcomes, for example, are highly complex and detailed – the UrbanSim model, for example (Waddell, 2002) – making it difficult to understand model results and attribute those results to particular factors. In addition, the models can generate multiple plausible outcomes and developing rules for choosing among them can be difficult and sometimes seem arbitrary. However, land use change and urban growth are spatially complex and path-dependent phenomena; ABM modeling provides the necessary flexibility and richness to address such challenges without the traditional spatial equilibrium and representative agent simplifications needed for analytical tractability.
Agent based models have provide an excellent opportunity to assess the timing and effects of density restrictions on land markets over time. In the US zoning is one nearly ubiquitous method of land use control. Historically, it has been used as a means of protecting property owners from negative externalities that arise when incompatible land uses are located in close proximity to one another. Increasingly, it is also described as a policy tool that is useful for controlling urban growth (Fischel 1990). Minimum lot size restrictions, the most common provisions of most residential zoning ordinances, are often cited as a growth control tool. However, both theory and empirical evidence are unclear about the direction of the relationship between lot size restrictions and land use change. Some claim that minimum lot size zoning restrictions actually exacerbate sprawl development (Field 2001).
Several theoretical models were developed to study the effect of zoning while capturing the dynamics of the development process (e.g. Fujita 1982, Turnbull 1988; Tegene, Wiebe, and Kuhn 1999). These models attempt to account for the long-term nature of the land use decisions explicitly. Such models show that zoning could delay development at some sites while inducing leap-frog development in others, while neither of those phenomena would occur under absence of zoning.
III. Description of Model
The model is an agent-based model with farmers, developers and consumers all represented as heterogeneous economic agents in the model. The decisions they make are based on underlying economic conditions for each agent. A growing exurban area is represented in which land is converted from farming to development over time. Farmers compare the returns to farming to expected profit from selling to developers. Farmers differ in how they form expectations about future prices, and they adapt those expectations according to the success of past predictions. Farmers interact with developers in the land market, and the market power of each group is represented and can change over time. Developers determine the profitability of different types of housing that varies by both structure and lot size. They sell to consumers who are differentiated by both income and preferences over different housing types. The model tracks development over time; it allows for path dependence in spatial development patterns and for dispersed and even leapfrog development. A schematic of how agents in the model behave and the market interactions are shown in Figure 1.
Figure 1. Agents and Markets
III.A. Basics of the Model
The model is designed to depict an ex-urban area that is developing at the fringe of an existing “city” or established residential area.[1] This established area is already developed, and is shown as the dark blue half-moon shaped region at the top of Figure 2. This urban area includes a variety of housing types including ¼, ½ acre, 1 acre and 2 acre lots. The initial city is surrounded by 50 farms, as shown by the different colored areas in Figure 2. Total region size is 6,400 acres (80 acres square), or 10 square miles.
We assume that there is exogenous population growth of 10 percent per year. As new households move to the region, they demand housing; developers respond by buying land from farmers and building houses. Thus farmland is gradually converted to developed uses over time. The model tracks growth over a 20-year period. The areas surrounding the initial suburban area are assumed to have no zoning restrictions in the baseline model. We introduce zoning in the next section as a policy case study.