Economics of spatial-dynamic processes.

I am honored to have the opportunity to give the AAEA Fellows Address this year. I would like to talk about a class of problems that are becoming more prevalent and yet have not received much attention by economists. These problems are a frontier area for economists--good topics for students looking for thesis topics and for the rest of us looking for new research questions. This class of problems poses challenges at the conceptual level, for empirical analysis, and at the policy design level.

Spatial-Dynamic Processes

The problems I would like to talk about I call "spatial-dynamic" problems, situations for which there is some (generally biophysical) process that generates potentially predictable patterns that evolve over space and time. The system generating such patterns may be largely exogenous. For example, the pattern of coastal area inundation around the world that we are about to witness as sea surface rises due to global warming is essentially exogenous. The biophysical forces generating the pattern are already in play, and the process is unfolding and inexorable. Alternatively, many spatial-dynamic processes are endogenous in the sense that they are influenced by individual decisions at points in space/time. A good example is a forest fire. A forest fire spreads over space in a manner influenced by some biophysical processes (e.g., wind direction and speed), but the pattern is clearly also influenced by decisions made by individuals in the landscape. Firefighters are the most obvious agents of influence. The spatial-dynamic pattern of a fire is influenced by backfires in front of the advancing front, bulldozed firebreaks, and fire retardant dropped by firefighters. In addition, however, the inhabitants of areas potentially influenced by fire also affect the pattern of spread. Most importantly, individuals who do (or do not) invest in "defensible space" around their homes influence the spatial-dynamics of fires once started.

Aside from simply being interesting systems, these kinds of processes often pose challenging economic and policy questions. Some are predictive questions such as: how will a rise in sea surface height affect individuals in low-lying coastal areas? How will various policies (e.g., dikes) alter or mitigate some of the potential impacts? How do homeowners in fire-prone areas react behaviorally to the prospect of fires? Do actions taken in a fire-prone area influence the prospective patterns of fires? Other questions raised by these kinds of processes are prescriptive or normative. How should we control a spatial dynamic process? Can we influence this process, and how many economic resources should we invest? Can we mitigate impacts? If so, how much should we spend? Is it worth building dikes all around the edge of San Francisco Bay to protect that land value in the face of rising sea surface? What parts of the areas around New Orleans should be rebuilt, and what kinds of land uses should be allowed, given the possibility of future spatial-dynamic flood processes affecting the Mississippi watershed?

One can think of many examples whereby spatial-dynamic processes link economic actors over space and time. Water in aquifers moves from areas of high to low density in a manner mediated by soil porosity. When aquifers are tapped by wells, the natural equilibrium is disturbed; water withdrawal creates "cones of depression" around the wells, which further influence relative densities and subsequent water flows. If contaminants are introduced into the groundwater system, they also flow from high-to low-density sites and are influenced by pumping rates and the spacing and depth of wells in the subsurface system. Bio-invasions are another example of spatial-dynamic processes for which patterns may be influenced by both exogenous and exogenous factors. The spread of such different organisms as the star thistle plant, the honey bee mite, and the sudden oak death causing fungus are among the kinds of bio-invasions currently experienced in the West. Each has its own propagation source, means of introduction, opportunity for establishment, and pattern of spatial-dynamics, generally mediated in some way by human activities.

Other examples of spatial-dynamic processes are the various mechanisms that link so-called metapopulations. The notion of metapopulations is a recent and important paradigm shift in biology, away from a view that depicted populations as homogeneously distributed over species' ranges to a new view of discrete subpopulations that are connected. For example, marine populations are now seen as inhabiting discrete patches or distinct aggregations (Sanchirico and Wilen 1999). These are linked with each other via adult movement, larval flow, winds, and currents. The ebb and flow of any particular sub-population is thus driven by patch-specific factors interacting with systemwide determinants of patch connectivity.

Another spatial-dynamic process of importance is that governing human and animal disease. For example, if one looks at the pattern of flu cases in a country like the United States each year, one finds a bell-shaped incidence pattern, peaking in February and flattening throughout the fall and winter, only to reappear again the next year in the same pattern. (1) Other countries experience similar patterns, with different peaks and different distributions of flu strains. If one looked only at country-specific data, it would be tempting to see these patterns as purely dynamic "local" processes. However, as epidemiologists have discovered, each country's seasonal dynamic pattern is itself part of a larger global spatial-dynamic process. In particular, virtually every annual cycle of flu originates in southeastern Asia, in high human density regions of China in proximity to domestic and wild birds and animals (Viboud et al. 2006). The source of the flu is then transmitted in a manner that reflects the dominant flow of humans along major airline routes, from China to major cities in the United States and elsewhere around the world, to regional centers and then to less-dense rural areas.

Patterns of the spread of flu are a good example of why it is important to fully understand spatial-dynamic processes. If one examines flu from a local scale, one is led to an incorrect perception that what is being observed is a dynamic phenomenon, much like technology saturation. But if one steps back and takes a global view, it is apparent that each year's local pattern is itself part of a process with a single source that then feeds multiple "sinks" around the world. The policy implications of each view are dramatically different. If one believes the local story, then one is led to reactive policies that are initiated each year once the flu strain is discovered and typed. But if one believes the global story, it is obvious that other, much more efficient policies might be envisioned. The global view leads naturally to thinking about the global public good aspects of epidemics and institutions that might be able to tackle the problem at a different scale. For example, one might envision a global fund to which potential receptor countries contribute, and that acts earlier in the flu season to quarantine early carriers before they can spread the disease globally.

These kinds of problems are especially interesting for at least two reasons. First, they are becoming more prevalent. Globalization, in particular, is a force that is linking more systems and hence increasing the opportunities for epidemic and invasion-style processes to proliferate. Second, there has been a knowledge explosion about spatial processes in the sciences, driven by new technologies such as remote sensing, GIS, and computational improvements. These technologies, remote sensing in particular, are generating vast amounts of new data on spatial patterns in the biosphere, patterns not seen before and that beg explanation. The sciences are devoting a considerable amount of attention to understanding the patterns that are newly revealed, in some cases completely revamping old concepts to focus on important spatial processes.

Despite the challenges and despite the attention that spatial-dynamic processes are attracting in the hard sciences, economists have not paid much attention to these kinds of problems. We have dynamic theories, such as the elegant analytical structures of capital theory, or the theories of renewable and non-renewable resource use that form the core of natural resource economics. And we have spatial theories, such as those espoused by von Thunen (Hall 1966), Losch (1954) and Tiebout (1956). But we have very few spatial-dynamic theories of systems whereby integrated processes drive patterns over space and time. The exceptions are work by Bhat, Huffaker, and Lenhart (1993; 1996) and Lenhart and Bhat (1999) on terrestrial pests; modeling of metapopulations I have done with my colleagues Jim Sanchirico (1999, 2005) and Marty Smith (2003); recent conceptual analysis of the optimal control of diffusion systems by Brock and Xepapadeas (2006); modeling of aquifers by Brozovik, Sunding, and Zilberman (2006); and some work on foot and mouth disease by Rich (2005) and Rich, Winter-Nelson, and Brozovik (2005).

Deconstructing Spatial-Dynamic Processes