It became apparent that analytical techniques were not well-suited to examine this particular research question, due to the high degree of spatial interdependencies and induced spatial heterogeneity that these externalities imply. As a complement to an initial analytical model, I developed a cellular automaton, agent-based model to represent the key components of the system. This model meets the definition of a cellular automaton in the sense that each cells contains a single, identical, immobile decision maker, and the rules available to decision makers are identical. Each agent/cell is potentially impacted by a spatial externality generated by only immediately neighboring cells. However, the model meets the definition of an agent-based model in the sense that the decision rules used by each agent consist of an intelligent decision-making process, whereby agents use a traditional profit maximization algorithm to choose between two possible land uses. A key feature of this model is an endogenous price for the outpur from one land use (designed to represent a niche market). This endogeneity provides sufficient structure to the model so that both land uses are represented in any economic equilibrium, and the assumption was appropriate for the particular case study for which the model was designed. I have used this model to demonstrate that stable inefficient patterns of land use are possible in an unregulated free-market setting, and that initial conditions influence the final outcome. Further, I have used the model to demonstrate key interactions between transportation costs (an agglomeration mechanism) and negative spatial externalities (a dispersal mechanism). The model and results are described in Parker 1999. The model was create in Mathematica, and the code is available on request. A slightly refined version of this paper, and a discussion of empirical analysis on the locations and patterns of production of certified organic farming operations, are presented in Parker 2000.

Recently, I have used an expanded version of the same model to explore the relationship between economic processes and landscape pattern, with the goal of identifying landscape pattern as a possible emergent outcome in explicitly spatial models of landscape processes. The model has been expanded to include representation of a more flexible range of spatial externalities. In its current form, either of two possible land uses can generate both positive and negative externalities to either or both uses. I have also updated the model to produce a set of landscape metrics that measure pattern outcomes. A paper based on this model [Parker et al. 2001] was presented at this year's Society for Computational Economics annual meetings.

Since January, 2001, I have been involved as a Participating Scientist in a National Science Foundation grant funded under the ``Biocomplexity in the Environment'' initiative: ``Biocomplexity in Linked Bioecological-Human Systems: Agent-Based Models of Land-Use Decisions and Emergent Land Use Patterns in Forested Regions of the American Midwest and the Brazilian Amazon.'' (A participants list is available at http://www.cipec.org/research/biocomplexity/participants.html.) The goal of this project is to create an integrated socioeconomic and biophysical model of rural land use in South-Central Indiana. An agent-based model is being developed to represent the land-use decisions of rural land-owner households. Through a geographic information system, this decision-making model will be linked to a biophysical forest growth model, information on topography, hydrology, transportation network, soil conditions, and other relevant biophysical and infrastructure factors. Thus, interactions between the socioeconomic and biophysical systems will be endogenized. We are developing historical GIS layers that will be used to validate model performance. Concurrently to developing the agent-based model, an econometric model of the region is being developed. This model will both inform development of the agent-based model and allow for a comparison between the two modeling techniques. Further, we also plan a series of related economic experiments, which will test our assumptions regarding agents' decision-making processes and further inform model development.

Our agent-based model is designed to compare a series of preference specifications, information processing abilities, decision-making strategies, and learning models. A preference specification will be used to evaluate agent well-being for any decision-making strategy. This specification is based on a modified economic household decision framework, and consists of a definition of goods (for our model: intertemporal leisure, consumption, residential housing, aesthetic and recreational benefits from land use); a particular mathematical functional form that may reflect risk preferences; constraints on available labor, land, and the household's budget; influences of other agents (ie, altruism, spatial spillovers, etc); and exogenous factors such as production and price parameters. Agents will vary in their ability to process information in two dimensions. Their time horizon may vary from completely myopic to infinitely forward looking. They may also vary in their ability to discern information, from receiving a very noisy signal to perfectly receiving information signals. Agents may use a variety of decision strategies: the pure mathematical optimization of Homo Economicus, boundedly rational optimizing search strategies, and heuristic rule-based decision strategies. We also plan to compare a variety of learning models, including Bayesian learning, neural network models, reinforcement learning, and genetic algorithm models

While substantial endogeneity will be build into our model, certain factors, such as climate, will always be taken as exogenous. Initially, political factors and demographic influences may be exogenous. However, we are exploring possible approaches to modeling the endogenous development of institutions. Within the economic module, prices and wages will be modeled as exogenous. However, modeling of endogenous land markets is a high priority. A vegetation growth model will reflect interactions between agent decision making and the biophysical state of the landscape.

We have developed a list of key questions that our modeling efforts will address:

1. How do individuals make labor allocation, production, consumption, and investment decisions in risky, multi-asset environments?
2. What factors affect individual preferences and actions related to land use?
3. What is the impact of landowner actions on the landscape?
4. How do socioeconomic landscape patterns and ecological landscape patterns interact?
5. How does a change in land use in one location influence the probability of a change in land use at a neighboring location?
6. What is the role of scale in the observed changes in land use in southern Indiana?
7. What are some key ways of testing our theoretical models? How do initial assumptions impact model outcomes? Can differing assumptions lead to observationally equivalent outcomes?

Questions of model platform, accessability, and software remain open at this writing.

References

[ Parker 1999]

Parker, D. C. (1999, July). Landscape Outcomes in a Model of Edge-Effect Externalities: A Computational Economics Approach. Santa Fe Institute Working Paper 99-07-051 E.

[ Parker 2000]

Parker, D. C. (2000, September). Edge-effect Externalities: Theoretical and Empirical Implications of Spatial Heterogeneity. Ph. D. thesis, University of California at Davis.

[ Parker, Evans, and Meretsky 2001]

Parker, D. C., T. P. Evans, and V. Meretsky (2001, June). Measuring emergent properties of agent-based landuse / landcover models using spatial metrics. Seventh Annual Conference of the International Society for Computational Economics.

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