theory, data, methods: developing spatially explicit ... ecosystems and environment 85 (2001) 7–23...

Agriculture, Ecosystems and Environment 85 (2001) 7–23

Theory, data, methods: developing spatially explicit economicmodels of land use change

Elena G. Irwin a,∗, Jacqueline Geoghegan b,1

a Agricultural, Environmental, and Development Economics, Ohio State University, 2120 Fyffe Rd., Columbus, OH 43210, USAb Department of Economics and George Perkins Marsh Institute, Clark University, 950 Main St., Worcester, MA 01760, USA

Abstract

Questions of land use/land cover change have attracted interest among a wide variety of researchers concerned with modelingthe spatial and temporal patterns of land conversion and understanding the causes and consequences of these changes. Amongthese, geographers and natural scientists have taken the lead in developing spatially explicit models of land use change athighly disaggregate scales (i.e. individual land parcels or cells of the landscape). However, less attention has been given inthe development of these models to understanding the economic process — namely, the human behavioral component —that underlies land use change. To the extent that researchers are interested in explaining the causal relationships betweenindividual choices and land use change outcomes, more fully articulated economic models of land use change are necessary.

This paper reviews some of the advances that have been made by geographers and natural scientists in developing thesemodels of spatial land use change, focusing on their modeling of the economic process associated with land use change. Fromthis vantage point, it is argued that these models are primarily “ad hoc,” developed without an economic theoretical framework,and therefore are susceptible to certain conceptual and estimation problems. Next, a brief review of traditional economicmodels of land use determination is given. Although these models are developed within a rigorous economic framework, theyare of limited use in developing spatially disaggregate and explicit models of land use change. Recent contributions fromeconomists to the development of spatially explicit models are then discussed, in which an economic structural model of theland use decision is developed within a spatially explicit framework and from which an estimable model of land use changeis derived. The advantages of this approach in terms of simulating policy scenarios and addressing econometric issues ofspatial dependency and endogeneity are discussed. We use some specific examples from ongoing research in the PatuxentWatershed, Maryland, USA to illustrate our points. The paper concludes with some summary remarks and suggestions forfurther research. © 2001 Elsevier Science B.V. All rights reserved.

Keywords: Land use change; Spatial economic models

1. Introduction

Questions of land use/land cover change have at-tracted interest among a wide variety of researchers

∗ Corresponding author. Tel.: +1-614-292-6449;fax: +1-614-292-0078.E-mail addresses: [email protected] (E.G. Irwin),[email protected] (J. Geoghegan).

1 Tel.: +1-508-751-4626; fax: +1-508-751-4600.

concerned with modeling the spatial and temporal pat-terns of land conversion and understanding the causesand consequences of these changes. Among these,geographers and natural scientists have taken the leadin developing spatially explicit models of land usechange at highly disaggregate scales (i.e. individualland parcels or cells of the landscape). Significantprogress has been made in acquiring spatial data setsfrom remotely sensed data (e.g. satellite imagery of

0167-8809/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved.PII: S0 1 6 7 -8 8 09 (01 )00200 -6

8 E.G. Irwin, J. Geoghegan / Agriculture, Ecosystems and Environment 85 (2001) 7–23

land cover), conceptualizing the basic geographic andenvironmental processes that are associated with landuse change, and developing spatial models that fit thespatial process of land use change reasonably well.

Less attention has been given in the developmentof these models to understanding the economic pro-cess — namely, the human behavioral component —that underlies land use change. To the extent thatresearchers are interested in explaining the causalrelationships between individual choices and land usechange outcomes, more fully articulated economicmodels of land use change are necessary. These mod-els usually begin from the viewpoint of individuallandowners who make land use decisions, either tomaximize expected returns or utility derived from theland. Economic theory is used to guide the modeldevelopment, including choice of functional formand explanatory variables. This approach goes be-yond non-behavioral models that have sought to fitthe spatial process of land use change by developingan underlying structural model that seeks to explainthe human behavior that generates these patterns. Incontrast, the non-behavioral models use an ad hocapproach to identifying physical variables that repre-sent the outcomes of economic and social processes,e.g. the location of roads and urban centers, withoutany underlying economic theory to guide the choiceof variables.

The distinction is illustrated in the next section, inwhich the difference between underlying structuralequations, derived from a conceptual economic modelof a landowner’s land use decision, and the result-ing reduced form estimating equations is illustratedusing a simple example. The rest of the paper is thenoriented towards a fuller discussion of non-economicand economic models of land use change. First, theadvances that have been made by geographers andnatural scientists in developing cell-based models ofspatial land use change are reviewed. This review isnot meant to be exhaustive, but rather illustrative ofthe existing approaches. While there are many contri-butions that these models have made to the researchon land use/cover modeling, we consider them onlyin terms of their treatment of the economic processassociated with land use change. Next, traditional eco-nomic models of land use determination are brieflyreviewed. These models are developed within a rigo-rous economic framework, but, for reasons that we

discuss, are of limited use in developing spatiallydisaggregate and explicit models of land use change.Finally, recent contributions from economists to thedevelopment of spatially explicit models are dis-cussed, in which an economic structural model of theland use decision is developed within a spatially ex-plicit framework and from which an estimable modelof land use change is derived. The paper concludeswith some summary remarks and suggestions forfurther research.

2. Structural economic models

Modeling the economic structural process that un-derlies land use change has several benefits. First, bymodeling the human behavior directly, rather than theoutcome of human behavior, the underlying spatialand temporal dynamic process associated with theeconomic agent can be made explicit. This allowsfor consideration of the cumulative effect of factorsover time on an individual’s land use decisions and ofpotential spatial interactions among economic agents.For example, if an individual’s land use decision isinfluenced by the land use decisions of those aroundhim/her, then this process can be explicitly modeledas a spatial lag.

Secondly, and perhaps most importantly, issues ofendogeneity can be addressed using a structural mod-eling approach. For example, if the location of roadsand land use decisions are jointly determined, thenthis endogeneity can be explicitly modeled using asystem of simultaneous equations that includes equa-tions explaining both land use change and the locationof road-building and improvements. Such an approachis necessary for consistent parameter estimation anddrawing correct policy implications.

As an example, consider the following to illustratethe estimation problem that arises with endogenousvariables and the distinction that economists gener-ally make between “structural” and “reduced form”models. Consider a county that experiences high pop-ulation growth and increases their property tax ratein order to accommodate the increased demand forthe local government’s public services. If householdsmigrating to the county take account of the tax ratein their location decision, then population changesand tax rates may be jointly determined. In order to

E.G. Irwin, J. Geoghegan / Agriculture, Ecosystems and Environment 85 (2001) 7–23 9

represent this process, a structural model with interre-lated equations representing migration and local gov-ernment expenditures and revenues is needed. Fromthis structural model, which will contain endogenousvariables as explanatory variables, a reduced formmodel can be derived that can be estimated, in whichall explanatory variables are exogenous. For example,let the following two interdependent equations rep-resent a highly simplified structural model 2 of theserelationships:

POPit = β1 EMPit + β2 TAXit

+β3 PUBSit + ε1it (1)

TAXit = γ1 POPit + γ2 PUBSit

+γ3 INCit + ε2it (2)

where POPit is the total population of county i inperiod t, EMPit the employment level within county iin period t, TAXit the property tax rate of county i inperiod t, PUBSit the measure of the quantity and qual-ity of public services in county i in period t, INCit theper capita income of households in county i in periodt, ε1itand ε2it are error terms, and β1, β2, β3,γ 1, γ 2,and γ 3 are parameters to be estimated.

Note that based on the above specification, POPit

and TAXit are jointly determined and therefore areendogenous, whereas EMPit , PUBSit , and INCit

are exogenous variables. Because POPit and TAXit

are endogenous variables, they will be correlated withthe error terms and therefore the parameter estimatesfrom this model will be inconsistent.

An approach to obtaining consistent estimates is toestimate the reduced form model and try to recoverthe structural parameters from these estimates. Forexample, a reduced form model can be derived fromstructural equations (1) and (2) via substitution to yield

POPit = π1 EMPit + π2 PUBSit

+π3 INCit + µ1it (3)

TAXit = π4 EMPit + π5 PUBSit

+π6 INCit + µ2it (4)

2 We include this example simply as an illustration of structuraland reduced form models and not as a serious model of migrationand taxation. For example, in a more rigorously specified model,the endogeneity of both employment and public service levelswould have to be considered.

where

π1 = β1

1 − β2γ1, π2 = β2γ2 + β3

1 − β2γ1, π3 = β2γ3

1 − β2γ1,

π4 = γ1β1

1 − β2γ1, π5 = γ2 + γ1

β2γ2 + β3

1 − β2γ1,

π6 = γ3 + γ1β2γ3

1 − β2γ1, µ1it = β2ε2 + ε1

1 − β2γ1, and

µ2it = ε2 + γ1β2ε2 + ε1

1 − β2γ1

As in the example above, parameter estimates fromthe reduced form model are a combination of theparameters from the underlying structural equations.In order to understand the correct policy implicationsof a property tax increase on population change, forexample, the parameter estimates from the structuralmodel (in this case, the estimate for β2) must be re-covered from the estimated parameters of the reducedform model. In some cases it is possible to recoverstructural parameters from the reduced form param-eter estimates using algebraic manipulation and byimposing constraints on the parameter values basedon theory. In other cases, this is not possible andan alternative estimation strategy, such as indirectleast-squares or an instrumental variables estimationmethod, must be used. 3

3. Spatially explicit, non-economic models of landuse change

Geographers and natural scientists have taken thelead in developing spatially explicit models of landuse change. Numerous spatially disaggregate andheterogeneous land use change models exist in theenvironmental science and geography literatures,spurred by the vast amount of spatially disaggregateland use/cover data that are now available (Andersen,1996; Batty et al., 1989; Berry et al., 1996; Clarkeet al., 1997; Flamm and Turner, 1994; Hazen andBerry, 1997; LaGro and DeGloria, 1992; Ludeke et al.,1990; Mertens and Lambin, 1997; White and Engelen,1993; White et al., 1997; Wu and Webster, 1998;Veldkamp and Fresco, 1996, 1997a,b). This body ofwork has contributed substantially to the development

3 See Greene (2000) for a full discussion of simultaneous-equations models and estimation methods.


of spatially explicit land use/cover change modeling.In what follows, we briefly review these models,focusing on how they have sought to incorporate eco-nomic considerations into the modeling framework.The spatially explicit land use/cover change modelscan be placed in three broad categories: simulation,estimation, and a hybrid approach that includes es-timated parameters with simulation. Because manyof the simulation models are based on a cellularautomata approach, the general form of cellular au-tomata is briefly discussed, followed by a discussionof the specifics of particular models and methods.

3.1. Cellular automata

Cellular automata are a class of mathematicalmodels in which the behavior of a system is gener-ated by a set of deterministic or probabilistic rulesthat determine the discrete state of a cell based onthe states of neighboring cells. States of individualcells are updated based on the values of neighboringcells in the previous time period. This locality ofthe interactions between a cell and its neighbors is adefining characteristic of cellular automata. Despitethe simplicity of the transition rules, these modelswhen simulated over many times periods often yieldcomplex and highly structured patterns. This is dueto the recursive interactions among cells: the state inperiod t + 1 is determined by the state in period t, butnot vice versa. Because these models are explicitlyspatial, they have been used to model a variety of spa-tial processes mainly in the physical and biologicalsciences, e.g. chemical turbulence, spatial diffusionof chemical reactions, evolution of spiral galaxies,and the development of patterns in the growth oforganisms (Wolfram, 1986).

Much of the literature on cellular automata is con-cerned with identifying local and global properties ofa cellular automaton, defined by a given set of tran-sition rules, by quantifying the resulting pattern. Forexample, long-range spatial correlations between thesystem’s states in different time periods are shownto generate structure and pattern (Wolfram, 1986).These correlations can be quantified and compared toa random configuration of the same dimension andpossible states to yield a measure of the relative orderin a system. For example, a statistical comparison ofa configuration generated by a cellular automaton vs.

a random configuration can be used to illustrate theself-organizing characteristic of cellular automata,which is one of their main features.

3.2. Simulation models of urban growth

Some researchers, mainly geographers, have usedcellular automata models to analyze the process ofurban growth (Wu and Webster, 1998; Clarke etal., 1997; White et al., 1997; White and Engelen,1993; Batty et al., 1989). In contrast to the stan-dard economic models of urban structure, in whichcomplex patterns are generated by imposing externalconditions, these models demonstrate how complexstructure arises internally from the interaction amongindividual cells. When compared to actual data fromUS cities, researchers argue that these models yield agood representation of actual urban form.

These models are instructive and offer a practicalapproach to understanding of how interaction amongindividual agents “aggregate up” over space to de-termine regional patterns of urbanization. However,conclusions about their explanatory power should notbe overstated. By demonstrating a correspondencebetween a hypothesized interaction effect and theresulting spatial evolution of land use pattern, thisapproach establishes that the hypothesized interac-tion among cells is a possible explanation of theobserved land use patterns. But these models are notestimated using actual data. Instead, “growth rules”are assigned that govern the land use transitions ofcells based on the cell’s attributes and the states ofsurrounding cells. In reality, a whole host of featuresthat create extensive spatial heterogeneity across thelandscape will drive actual changes in land use pat-tern and therefore, conclusive statements about theinteraction causing the changes in actual urban formare misleading. To test the hypothesized growth rules,an empirical model is needed which deals with theidentification problem that arises in distinguishing theinteraction effects from other landscape heterogeneity,e.g. zoning, employment centers, and environmentalfeatures. Instead, these cellular automata models ofurban growth are developed with the assumption ofa simple spatial landscape and therefore are unableto differentiate the interaction effect from the varietyof exogenously determined variables that may alsogenerate the same patterns of development.


An additional shortcoming of many of these mod-els of urban growth is the absence of an economicfoundation. Rather than modeling the interaction ef-fect as a function of economic factors, the interactioneffects are imposed by the researcher. This is donewith little economic rationale or empirical evidenceof the hypothesized effects. Contrary to some claimsmade by these researchers, this limits the useful-ness of these models for planning and policymakingpurposes. Predictions of how land use patterns willchange under alternative policy scenarios requiresan understanding of how individual landowners willreact under these different policy regimes. To do sorequires more explicit modeling of the underlyingeconomic spatial process of land use change.

3.3. Empirical models of land use/cover change

Geographers have also taken the lead in estimatingspatially explicit empirical models using remotelysensed data on land use/cover change. Examples fromthis literature include Mertens and Lambin (1997),Andersen (1996), LaGro and DeGloria (1992), andLudeke et al. (1990). Each of these examples focuseson some aspect of deforestation that is derived fromthe remotely sensed data for the dependent variable.These models include explanatory variables that canbe “seen” from the remotely sensed data and calcu-lated using GIS, such as, distance measures, otherspatial biophysical variables (e.g. soil, slope and eleva-tion), and occasionally socio-economic “drivers,” suchas population or gross domestic product measures.

In many cases, these models fit the spatial processand land use change outcome reasonably well. How-ever, like the urban growth models discussed above,they are less successful at explaining the humanbehavior that leads to the spatial process/outcome ofland use change. This is not to say that these modelsare devoid of economic considerations. On the con-trary, these models usually include some variablesthat capture economic effects. For example, distanceto urban center and variables that reflect the biophys-ical heterogeneity of the landscape are commonlyincluded for economic reasons. Distance to the urbancenter matters because of accessibility to markets (i.e.transportation costs), whereas biophysical features ofthe landscape, e.g. certain soils are preferred for agri-cultural use, will affect the choices of individual land

managers. However, there are many other featuresthat affect choice concerning land use change. Thesemight be characteristics of the individual land man-ager such as family size, off-farm income, educationlevel, wealth and ability to bear risk. Such considera-tions are largely overlooked in these models since thechoice of economic variables is “ad hoc,” rather thanbeing derived from a set of structural models that at-tempt to more fully explain the underlying economicprocess.

Clearly temporal dynamics are an important con-sideration in modeling land use/cover change. Thereare many external features that change over time (andnot necessarily space), including variables that af-fect the economic returns to different land uses, e.g.agricultural and timber prices, subsidies, land tenurerules, etc., that will affect individual choices. Suchconsiderations are often omitted from these models ofland use change, most likely due to data constraints,but failure to control for temporal dynamics can biasestimation results. As discussed earlier, the presenceof endogenous variables (i.e. variables that changeover time due to changes in land use) can lead to in-consistent parameter estimates and misleading policyconclusions. Without an underlying structural modelthat could make these interrelationships explicit, theseempirical models are unable to address this issueof endogeneity.

A final shortcoming of these models from an eco-nomics perspective is that the unit of analysis is eitheran individual pixel or some aggregation of landscapeunits, rather than the individual decision-maker. Inmodeling land use change from an economics per-spective, the individual is the unit of observationrather than a landscape pixel. For this reason, havinginformation on the boundaries of individually ownedland parcels, rather than just the boundaries betweentwo dissimilar land use pixels, is greatly preferred. Forexample, individuals owning large land parcels mayreact differently to a policy than those with small landparcels. Distinguishing the effects of a policy changeamong large and small landowners is important andonly possible if ownership boundaries are known. 4

4 This issue could potentially be more relevant in a developedcountry context, where property rights are well established, thanin a developing country context, where land use change can be aform of gaining land tenure at the agricultural frontier.


3.4. Hybrid models of land use/cover change

Hybrid models of land use/cover change begin withan estimation model, as discussed in the previoussection, but continue with the addition of a simulationmodel. The simulation models use the parametersfrom the estimation model to predict the spatial pat-tern of land use/cover change that could occur underdifferent exogenously imposed scenarios.

Landscape ecologists were also early developersof spatially explicit models of land use change usedto predict changes in spatial patterns of the landscape(Ives et al., 1998). The early models were simple grid-based Markov models that merely calculated the per-cent change of each land cover type during a timeperiod and predicted future changes by assuming thatthese proportionate changes remained constant overtime. More sophisticated Markov models were thendeveloped that estimated these changes as a functionof other explanatory variables and not just simply afunction of previous land use changes. While manyof these models have sophisticated treatment of eco-logical relationships that affect or a result of landuse/cover change, they are very simple with respect tohuman behavior (for a review of these early models,see Baker, 1989).

Recent examples of these hybrid models from thenatural sciences include the LUCAS model (Berryet al., 1996; Flamm and Turner, 1994; Hazen andBerry, 1997) and the CLUE model (Veldkamp andFresco, 1996, 1997a,b). Both of these models estimatethe effects of such explanatory variables as slope, soil,elevation, aspect, location, and population measures,on different types of land use/cover change. Usingthe estimated models, both groups of researchers thensimulate the effect of different scenarios on land usechange. For example, the LUCAS model is used tosimulate the effect on future land use change of amoratorium on logging or road-building; the CLUEmodel is used to simulate the effects of urbanization,abolition of national parks extension of national parkssoil erosion crop disease at certain elevations andvolcanic eruption.

From an economics perspective, these models arelimited for the same reasons as those discussed in theprevious section. In addition, the only simulations thatcan be performed in these models are changes thatare imposed on the explicit features of the landscape,

such as a moratorium on road-building or certainland uses, or changes to other features of the land-scape, such as soil erosion or crop disease at certainelevations. Because the underlying decision-makingbehavior is imposed, it is not possible to model abehavioral response to a change in any variable in-cluded in the models. For example, the impact of anagricultural policy change (e.g. a subsidy change)on a farmer’s decision to farm his land cannot bepredicted. The only way to simulate such a policywith these models would be to assume the land usedecision of the farmer in response to the policy.

4. Economic models of land use change

4.1. Non-spatially explicit models

Traditional economic models that describe urbanspatial patterns of land use can be broadly classifiedas either microeconomic models that describe equi-librium land use patterns within an urban area or re-gional economic models that describe the equilibriumflows of population, employment, or other economicfactors across regions. For various reasons that weoutline below, most of these models do not offer a sat-isfactory approach to explaining the spatial economicprocess of land use change at the parcel level. 5

The traditional urban economic model of land usepattern is the bid-rent model (or monocentric model),which presumes the location of an exogenous cen-tral business district to which households commute(Alonso, 1964; Muth, 1969; Mills, 1967). All otherfeatures of the landscape are ignored, so that distanceto the center is the underlying determinant of landuse change. Individual households optimize their lo-cation by trading off accessibility to the urban centerand land rents, which are bid up higher for locationscloser to the center. In its simplest form, the resultingequilibrium pattern of land use is described by con-centric rings of residential development around theurban center and decreasing residential density as dis-tance from the urban center increases. More sophisti-cated versions of the model have been developed, but

5 For a more detailed review of these models and the spatiallyexplicit economic models discussed in the following section, seeBockstael and Irwin (2000).


nonetheless, the model’s ability to explain spatiallydisaggregate land use patterns is limited. In com-paring the model’s predictions with actual land usepatterns, the model fails to explain the complexity ofthe spatial and temporal patterns of urban growth (seeAnas et al., 1998, for a recent discussion).

The limitation of the monocentric model is partlydue to its treatment of space, which is assumed to bea “featureless plane” and is reduced to a simple mea-sure of distance from the urban center. Within thiscontext it is not possible to represent all the heteroge-neous landscape features that exist in reality and thatdo influence land use decisions. The Ricardian tradi-tion explains differences in land rents due to differ-ences in land quality that arise from a heterogeneouslandscape, but abstracts from any notion of relativelocation leading to spatial structure. Many models thattry to explain land values (namely, hedonic pricingmodels 6 ) combine the two approaches by includingvariables that measure the distance to urban center(s)as well as specific locational features of the land par-cel. However, these types of models, in general, havenot been used in the land use change literature, exceptfor Bockstael (1996) (discussed below).

More recent urban economic models have focusedon explaining the formation of urban spatial struc-ture as an endogenous process that is the result of“interactions” among individual economic agents dis-tributed in space (Fujita et al., 1999; Krugman, 1991,1996; Anas and Kim, 1996; Zhang, 1993; Arthur,1988). These models, which are part of the new eco-nomic geography literature, hypothesize an interde-pendence among individual households and/or firmsthat leads to the location decisions of one individualaffecting the location decision of others. Such inter-dependence can arise due to a variety of factors, e.g.demand and supply linkages between customers andfirms, knowledge spillovers among firms, or conges-tion effects among residential land uses. Depending

6 The hedonistic pricing model is a method for estimating the im-plicit prices of characteristics of a heterogeneous good, in whichthe price of the good is estimated as a function of a vector ofattributes that describe the good. For example, housing is a differ-entiated good defined by a host of structural, neighborhood, andlocational attributes. A hedonic pricing model can be used to esti-mate the marginal value of these individual housing characteristicsby estimating housing price as a function of these attributes. SeeFreeman (1993) for further details

on the type and magnitude of these interactions, amonocentric, polycentric, or fully dispersed land usepattern may result. Because these models explain theemergence of agglomerations and urban spatial struc-ture, they are much more robust than the traditionalbid-rent models. However, in order to solve the modelfor an equilibrium solution that describes the urbanspatial structure, much of the actual heterogeneity ofthe landscape is ignored. As such, these models offera fairly abstract description of land use pattern basedon equilibrium conditions. Nonetheless, because theyare models based on individual agents spatially dis-tributed within a landscape, they offer potential forincorporating the effects of spatial heterogeneity at adisaggregate scale. Some economists have developedagent-based simulation models of this sort applied toland use change and we review some of this researchin a subsequent section.

An alternative approach to modeling urban spatialstructure is given by regional economic models thatdescribe population and other economic flows acrossregions (see Wegener, 1994, for a review). The urbanregion is represented as a limited number of discretezones, in which each zone is described by an aggre-gate number of households and industries, and zonesare connected via a transportation network. Basedon the relative distance between zones and the loca-tion preferences of individuals, these models seek todescribe the equilibrium flows of people across thesediscrete zones. While many of these models haveproven quite useful for transportation planning andother regional planning applications, their spatial res-olution is too coarse to capture the heterogeneity ofthe landscape at a parcel level.

4.2. Spatially explicit models

Recent work in environmental economics hasfocused on developing economic models of theindividual landowner’s decision within a spatiallyexplicit framework. This work is noteworthy becauseof the link between the resulting empirical model andthe underlying theoretical motivation for the model.In what follows, we review some of these recentcontributions. 7

7 See Bockstael and Irwin (2000) for a fuller review of thesemodels.


Much of the economic work in land use change hasfocused on deforestation in lesser-developed coun-tries. For example, Chomitz and Gray (1996) developa simple model of deforestation in which landownersmaximize expected profits, so that the optimal use isdetermined by the use with the highest rents, using re-motely sensed data and other spatial (GIS) data. Rentsin an agricultural use are equal to returns minus costsof production, where production is a function of soilquality. The likelihood of forest conversion to agricul-ture is modeled as a function of soil quality and inputand output prices at any given location. Accessibilityto markets is used as a proxy for the spatial variation inprices, based on the argument that prices will vary atany given location depending on transportation coststo market centers. Chomitz and Gray recognize thepotential endogeneity problem associated with theaccessibility measure, since road location may be in-fluenced by the location of agricultural production. Intesting for this possibility, evidence of the endogene-ity of roads is found, which suggests that the estimateof the influence of accessibility on deforestation isoverstated.

Other examples of economic models of deforesta-tion using remotely sensed data and GIS includePfaff (1999) and Nelson and Hellerstein (1997). LikeChomitz and Gray, these studies demonstrate howeconomic theory can be applied to motivating thevariables that are included in the land use conversionmodel and identifying potential endogeneity prob-lems. For example, Pfaff (1999) points out that pop-ulation may be endogenous to forest conversion, dueto unobserved government policies that encouragedevelopment of targeted areas, or that population maybe collinear with government policies. If the former isthe case, then including population as an exogenous‘driver’ of land use change would produce a biasedestimate and lead to misleading policy conclusions.If the latter is the case, then the estimates wouldbe unbiased, but inefficient, leading to a potentialfalse interpretation of the significance of variables inexplaining deforestation. To address these issues, heuses a temporally lagged value of population in theregression analysis.

A spatially explicit and spatially disaggregate landuse change model from the urban planning literatureis found in Landis (1995) and Landis and Zhang(1998a,b). The unit of observation in this model is

a 1 ha cell of the landscape, and they use a discretechoice approach to model development and redevel-opment in an urban setting. The choice of explana-tory variables is motivated using economic theoryand includes initial site use, variables to capturedemand pressures, distance/accessibility measures,costs of development, returns to alternative uses, andnon-conforming uses. The economic process is mod-eled, so that the impact of different policies that affectthe returns to different land uses can be predictedfrom the model. However, there is no explicit modelof price formation and the policies that most directlyaffect land uses, such as zoning and impact fees, arenot included in the model, so only indirect policiescan be simulated. The unit of observation is a cellof the landscape, rather than the land manager, andtherefore there is no direct link between the unit ofobservation and the decision-maker. Lastly, becausethe model is estimated with only one time change, itis does not capture how changes in other variablesaffect land use change over a longer time horizon. Forexample, the influence of cumulative developmentpressures over time is not considered.

While these models clearly demonstrate the benefitsof incorporating economic theory into land use changemodels, they do not go beyond estimating a land useconversion model to predicting resulting changes inthe spatial pattern of the landscape. To do so requiresa dynamic model of land use change and one in whichindividual, spatially distributed land use decisions canbe aggregated to describe the resulting changes inregional pattern. Examples of a dynamic land usechange model and one in which changes in land usepatterns are simulated over time in order to predict re-gional outcomes are discussed in the following section.

5. Examples from the Patuxent RiverWatershed project

In this section we offer examples of economicspatially explicit modeling of land use change from on-going research at the University of Maryland to furtherillustrate some of the benefits of a spatially explicit,economic modeling approach. This research projectis an extensive effort aimed at modeling the spatialdynamic changes of land use and land use changewithin the counties of the Patuxent River Watershed


Fig. 1. Central Maryland region.

and furthering an understanding of some of the eco-nomic and ecological consequences of these changes.The Patuxent area, located in central Maryland, USA,has witnessed tremendous growth in residential landuse and changes in land use patterns in recent years(see Fig. 1). Between 1973 and 1994, population in

this seven county region increased from approximately1.79 million to 2.44 million, an increase of 36%. Theamount of low-density residential land use in the studyarea increased from approximately 92 000 acres toalmost 188 000 acres during the same time period, anincrease of 119%. Particularly in the urban–rural


Fig. 2. Land use changes in Calvert County, Maryland, 1981–1997.

fringe areas of the region (e.g. Calvert and CharlesCounties), the high conversion and population growthrates have led to an increasingly fragmented land usepattern. Fig. 2 illustrates the change in the patternof development that has occurred in Calvert County,which is located within the study area and was one ofthe fastest growing counties in Maryland in the 1990s.These rapid changes have sparked concerns about thecosts of providing public services, the preservationof open space, and the protection of environmentalresources.

5.1. Economic spatial models of land use conversion

Because most of the land use changes occurring inthis area are from previously undeveloped land to res-idential use, much of the work to date has focused onthis residential urbanization process, in which land inagriculture, forest, or a natural state is converted to aresidential use. Similar to other microeconomic mod-els of the land use conversion decision, the underlyingmotivation for landowners to convert land to a devel-oped use is assumed to be maximization of expected

returns over an infinite time horizon. Based on thistheoretical framework, a simple structural model de-scribing the individual’s discrete choice of land usecan be developed. The simplest characterization basedon profit maximization is one in which parcel j, whichis currently in state u, will be converted to state r intime t if

Wjrt|u − Cjrt|u ≥ Wjmt|u − Cjmt|ufor all land uses m = 1, . . . , a, . . . , M (5)

where Wjrt |u is defined as the present value of thefuture stream of returns to parcel j in state r at timet, given that the parcel was in state u in time t − 1and Cjrt |u is defined as the cost of converting parcelj from state u to state r in period t (Bockstael, 1996).

Given that not all factors that affect W and C areobservable, this statement can be rewritten in terms ofthe probability the parcel j is converted from state u tor in time t, in which the systematic (or observed) andrandom portions of W and C are explicitly modeled,

Prob(Vjrt|u − ηjrt|u ≥ Vjmt|u − ηjmt|u) (6)


where V represents the systematic portion of W − C

and η the random portion, which is unobserved tothe researcher. Given a distribution for the error termsand a functional form for the systematic portion, thismodel can be rewritten and estimated using discretechoice modeling techniques (see Bockstael, 1996 formore details).

The first step in incorporating spatial heterogeneityof the landscape is accomplished by recognizing thatthe returns to converting land to a residential use, W,and the costs of conversion, C, will both be influencedby a host of spatially heterogeneous variables. In earlywork, Bockstael (1996) develops a two-stage approachto modeling residential land use change. A spatiallyexplicit hedonic 8 model of residential land values isfirst estimated as a function of spatially varying land-scape features, including lot size, accessibility mea-sures, neighborhood zoning, and percentages of landin different uses. The estimated model of residentialland values is then used to predict the value is residen-tial use of all “developable” land in the region. Thispredicted residential land value is used as an exoge-nous variable, along with other variables representingthe costs of development and the value of the land inagricultural use (estimated from a separate model) ina binary discrete choice model of land use conversion,in which the land may either be in an undeveloped orresidential use. This model is estimated using observa-tions on actual residential land use conversions and isthen used to predict the probability of development ofeach cell for a future round of development. The out-put of this type of model is a probability map (Fig. 3shows an example for the southern region of the studyarea) that shows the likelihood of future developmentof each spatially differentiated land parcel that is yetundeveloped. A limitation of this model is that it onlypredicts the spatial distribution of conversion probabil-ities and does not explain the amount of developmentthat might occur in any given period. In addition, thismodel is limited to a “snapshot” representation of landuse change and does not seek to explain the dynamicevolution of land use patterns over time.

This modeling approach can be used to predict theeffects of different land use policies. For example,Bockstael and Bell (1998) analyze the effects of anumber of alternative land use policies including the

8 See Freeman (1993) for a review of hedonic pricing models.

effects of different regulations concerning minimumlot size, used in land use zoning. They find that dif-ferential zoning across counties deflects developmentfrom one county to another and that the amount of in-creased nitrogen loadings from a constant amount ofnew development varies from 4 to 12%, depending onthe degree of difference across counties’ minimum lotsize zoning.

Further development of the data and model ofBockstael (1996) is found in Irwin and Bockstael(2001) and Geoghegan and Bockstael (2000). In thesepapers, a dynamic model of rural–urban fringe devel-opment that is both spatially disaggregate and spatiallyexplicit, is developed in which land use and land usechange over both time and space are modeled. Thetemporal dimension is explicitly considered by posingthe land use conversion decision as an optimal timingdecision in which the landowner seeks to maximizeexpected profits by choosing the optimal time t = T ,in which the present discounted value of expectedreturns from converting the parcel to residential useare maximized. In this case, the underlying dynamicstructural model can be written as follows (Irwin andBockstael, 2001). The landowner will choose to con-vert his/her parcel to residential use in the first periodin which the following conditions hold:

WjrT|u − CCjrT|u −∞∑

t=0

Ajut+T δT +t > 0 (7)

and

WjrT|u − CjrT|u − AjuT > δ(WjrT+1|u − CjrT+1|u) (8)

where W and C are defined above, δ is the discountrate, and A the one period returns from the land in itsundeveloped use, so that the last term in (7) representsthe present value of forgone returns from the land inits undeveloped use. In words, Eq. (7) states that theagent will convert his/her parcel when the net returnsfrom development, W −C, is greater than the forgonereturns from keeping the land in an undeveloped useover an infinite horizon. Eq. (8) states that the agentwill convert given that the expected returns from con-verting in period T, net the one period opportunitycost of conversion A, is greater than the discountednet returns from converting in period T + 1. Theagent is hypothesized to develop his/her land in thefirst period that both of these conditions are true.


Fig. 3. Predicted probability of development.

As in the simpler model outlined in (5) and (6),the spatial characteristics of the parcel and its rela-tive location in space are expected to influence W,C, and A. In both Irwin and Bockstael (2001) andGeoghegan and Bockstael (2000), historical data overtime is used that tracks the conversion of land parcelsfrom an undeveloped parcel (e.g. farm) to subdividedresidential lots. This provides a direct link betweenthe unit of observation and the land manager, whomakes the land use conversion decision. The struc-tural model outlined in (7) and (8) is operationalizedusing a duration model, in which the conditionalprobability that a parcel is developed in period t is

estimated, conditional on the parcel still being in anundeveloped use in period t − 1.

Geoghegan and Bockstael (2000) use this modelingapproach to explore the effects of different land useregulations on the location and timing, of residentialdevelopment and how these changes respond to landuse regulations. The model includes land use policyinstruments that have the potential to affect the patternof development, such as zoning, development impactfees, adequate public facilities moratoria and provisionof public sewer and water. Because the major land useregulations that affect the location of residential devel-opment are incorporated in the model, relevant policy


simulations can be performed that illustrate the pre-dicted effects of these growth control tools on land usechange patterns. Given changes in one or more of theexogenous variables of the model, the model is ableto predict both the spatial location of residential de-velopment and the timing of residential development.This allows for the effect of different land use policieson land use pattern to ultimately be tested.

This spatially explicit approach to identifying thevariables that are significant in land use change canalso provide insight into the spatial and temporaldynamics of land use change. Drawing upon theagent-based interaction models that have recentlybeen developed in the new economic geography lit-erature to explain urban spatial structure, Irwin andBockstael (2001) develop a model in which exoge-nous features create attracting effects (e.g. centralcity, road, public services) among developed landparcels and interactions among land use agents createnet repelling effects. They demonstrate that such amodel offers a viable explanation of the fragmentedresidential development pattern found in many USurban–rural fringe areas. Assuming the presence ofexogenous growth pressure effects that increase thelikelihood of conversion over time, the time dimen-sion is explicitly modeled by estimating a durationmodel of residential land use conversion. The con-version decision is treated as a function of both ex-ogenous landscape features and a temporally laggedinteraction effect among neighboring agents making aresidential conversion decisions. Empirical evidenceof a negative interaction effect among land parcels ina residential use is econometrically identified.

Irwin and Bockstael (2001) use a spatial simulationmodel to predict patterns of land use change in an urba-nizing area, in which the transition probabilities areestimated as functions of a variety of exogenous vari-ables and an interaction term that captures the effectof neighboring land use conversions. Given estimatedparameters from a model of land use conversion, tran-sition probabilities are calculated for yet undevelopedparcels and then updated with each round of develop-ment. The spatial simulation model is used to demon-strate that negative interaction effects result in theevolution of a more fragmented land use pattern thatis qualitatively much more similar to the observed pat-tern of development than the pattern that is predictedby a more naive model in which these interactions are

ignored. Fig. 4 illustrates the result of this simulationexercise for the northeast portion of Charles County,one of the exurban counties located within the studyarea. The actual pattern of development in this areabetween 1990 and 1997 is compared with the pre-dicted pattern of development from a restricted model,in which the spatial interaction effects are ignored,vs. the full model, in which the negative interactioneffects are shown to generate a much more scatteredpattern of development. Comparison of nearest neigh-bor spatial statistics from these two different predictedpatterns vs. the actual pattern show that the patterngenerated by the full model is qualitatively muchmore similar to the pattern of actual development.

5.2. Spatial data issues

In any modeling approach that uses spatial data,there are two related issues to using these data: howto use the data “creatively” and how to use the data“correctly.” The former refers to developing ways ofcreating variables from spatial data that can be used ina model; the latter refers to issues of spatial economet-rics. The question of using data creatively relates tofinding ways in which the power of the spatial data canbe used in a model to better estimate the spatial pro-cess. For example, in many of the traditional land usemodels, “space” is often reduced to a uni-dimensionalmeasure of distance to city representing transportationcosts to and from a central market. But the importanceof location in land values and land use determinationis not restricted to market accessibility. The pattern oflandscape features and land uses that surround a parcelof land are likely to have a major influence on its valueand use, for example, a negative influence on a resi-dential land value that is caused by surrounding indus-trial land uses, and a positive influence as a result of anearby park. That is, individuals value the pattern ofland uses surrounding a parcel. In order to test this hy-pothesis for the Patuxent Watershed, Geoghegan et al.(1997) create spatial indices on land use fragmentationand diversity, borrowed from the landscape ecologyliterature that were calculated for each residential landparcel at different scales in a model of residential landvalues. These variables were found to be statisticallysignificant in the different empirical specifications ofthe model. By using these spatial landscape indices,an improved model of land values was developed


Fig. 4. Northeast Charles County, Maryland. Actual vs. predicted development.

by capturing how individual value the diversity andfragmentation of the land uses around their homes.

The second modeling issue, spatial econometrics,deals with the methodological concerns that followfrom explicit consideration of spatial effects in econo-metric models (Anselin, 1988). Such effects may takethe form of spatial dependence, in which the values ofobservations in space are functional related, or spatialheterogeneity, in which model parameters are not sta-ble across location. Spatial dependence may arise dueto data measurement errors or omitted variables, lead-ing to spatial error autocorrelation, or from spatial in-teraction, which implies a structural interdependenceamong observations. Analyzing a problem that is es-sentially location-based while ignoring the potential ofinteractions among the location of the observations isanalogous to analyzing a time series problem withoutknowing the chronological order of the observations.Just as the chronological relationship of one obser-vation to another is critical in time series analysis,so is the spatial relationship among observations inlocation-related problems, such as land use questions.

All of the interesting statistical/econometric compli-cations one encounters in time series analysis, suchas autocorrelation, temporal dynamics, and structuralchange, have analogues, sometimes of greater com-plexity, in spatial analysis. Because of these, applyingstandard statistical/econometric techniques to spatialdata in the presence of spatial dependence will gener-ate inconsistent and/or inefficient estimates and leadto false conclusions regarding hypothesis tests.

Spatial dependence can result from a structuralspatial relationship across dependent variables or aspatial dependence across error terms. If either form ofspatial dependence occurs, specialized spatial econo-metric techniques can be used, where the pattern ofthe spatial dependence is assumed. The practice thathas developed in the spatial econometrics literatureuses spatial weight matrices, based either on conti-guity or distance between observations, to assign thespatial structure needed to correctly estimate thesemodels (for further details see Anselin, 1988).

Bell and Bockstael (2000) illustrate the importanceof controlling for spatial error autocorrelation in a


model of residential land values. Recognizing thata hedonic model of residential land values is likelyto suffer from an omitted variables problem that, ina spatial setting, will lead to spatial autocorrelation,they use two different estimation methods to estimatea spatial error model. Parameter and standard errorestimates from this model, in which the autocorrelatederror structure is corrected using a spatial weightsmatrix that specifies the spatial dependent structure,are compared to estimates from a standard ordinaryleast-squares (OLS) model of residential land values.The results show that the significance of some of theexplanatory variables changes with the spatial auto-correlation correction. In addition, the authors findthat the results are dependent on the particular spec-ification of the spatial weights matrix, e.g. whetherthe spatial weights are defined using a contiguityvs. distance-decay rule and the particular maximumdistance cut-off that is used to delineate neighbors.

An example of spatial dependence caused by spatialinteraction is found in Irwin and Bockstael (2001), inwhich the probability that an individual will converthis/her land parcel to a residential use is posited tobe a function of the neighboring parcels’ land uses.Evidence of a negative spatial interaction among de-veloped parcels is found, implying that a developedland parcel “repels” neighboring development due tonegative spatial externalities that are generated fromdevelopment, e.g. congestion effects. The presence ofsuch an effect implies that, ceteris paribus, a parcel’sprobability of development decreases as the amountof existing neighboring development increases. In thiscase, Irwin and Bockstael reasoned that this spatiallag is also temporally lagged, so that neighboringland uses in period t were hypothesized to influence aparcel’s land use in period t +1. The authors also dis-cuss an econometric identification problem that arisesin this situation. Given the presence of unobservedspatial heterogeneity that is time invariant, temporallylagged neighboring land use states will be correlatedwith the error term and will introduce a positive bias inthe estimated spatial interaction parameter. If this un-observed spatial correlation is not accounted for, thenevidence of a positive spatial interaction effect couldbe found even if no spatial interaction existed in reality.

Geoghegan et al. (1997) test for the presence ofspatial heterogeneity with the use of a varying para-meters model (also known as a spatial expansion

model), in which the coefficients on some of the ex-planatory variables were allowed to vary over space.Results show that for such variables as access toroads and lot size, the value of an additional unit onresidential price did vary significantly with distancefrom the central business district, so that these did notremain stable with location.

6. Conclusions and further research

In order to improve our understanding and mod-eling of spatially explicit and spatially disaggregateland use change, improved datasets, improved meth-ods, and improved theory are needed. All three ofthese issues are closely linked. As has been arguedelsewhere (Geoghegan et al., 1998), the historicallack of spatially explicit social science data con-strained spatial modeling of human behavior. As aresult, interest in spatial issues in the social sciencesbeyond the field of geography has been limited. But,with the increasing availability of spatial social sci-ence data, there has been a renewed interest in spatialissues among other social sciences. In a recent dis-cussion of future research issues in natural resourceand environmental economics, Deacon et al. (1998)comment, “the spatial dimension of resource use mayturn out to be as important as the exhaustively studiedtemporal dimension in many contexts.” Therefore,having spatially explicit data on a decision-makerbasis should result in more sophisticated modeling ofspatial human behavior and hypotheses testing. 9

However, obtaining better data that can be used totest more sophisticated theories of spatial behavior ne-cessitates improved empirical methods, such as thosebeing developed within the field of spatial economet-rics. As argued above, not taking into account spatialdependence or spatial heterogeneity when estimatinga model can lead to biased or inconsistent estimatesand false conclusions regarding the sign and signifi-cance of parameter estimates. While many advanceshave been made in the field of spatial econometrics,it is still in its infancy when compared to its dynamic

9 The need for improved spatial data beyond the developmentof remotely sensed datasets, has been documented in LUCC Re-port Series No. 3 “LUCC Data Requirements Workshop: Surveyof Needs, Gaps, and Priorities on Data for Land-use/Land-coverChange Research”, November 1997.


counterpart, time series econometrics. A particularneed for land use and land cover change modeling isthe application of spatial econometric techniques todiscrete choice models, since these models are par-ticularly useful in modeling land use and land coverchanges. To date, a rigorous methodology has not yetbeen developed that would allow for the treatment ofspatial effects in a discrete choice framework, althoughsome limited cases have been developed in the litera-ture (for more details, see Anselin and Florax, 1995).

Lastly, the development of better economic modelsof land use/cover change rests on advances in thespatial economic theory of urban spatial structure thatcan better explain the spatial and temporal patternsof migration, employment growth, government ac-tions, and resulting land use changes. As discussedin Bockstael and Irwin (2000), a primary challengeis in understanding how individual choices that arespatially distributed can be aggregated up to regionalmarket outcomes, i.e. the issue of crossing from onescale of analysis to another. In general, the definingfactor for economists in aggregating from individ-uals to markets is the distinction between what isendogenous and what is exogenous at each scale. Butonce spatial heterogeneity is introduced, aggregatingindividual land use choices to spatially articulatedmarket outcomes becomes much more complicated.As reviewed above, new theories about the evolutionof urban land use patterns have begun to take holdin the urban and regional economics literature, butthis research remains almost all theoretical. Morehypotheses from these new theories need to be identi-fied and empirically tested to gauge the robustness ofthese theories.

Land use/cover change research requires an inter-disciplinary approach, as has been argued in theLUCC Science Plan and Implementation Plan 10 andas has been proven on the ground in many researchprojects. However, until recently economists have notbeen active participants in the international LUCCcommunity. We hope that this discussion paper and theexamples that it includes, demonstrates some of the

10 IGBP Report 35-IHDP Report 7, 1995. Land-use and Land-cover Change, Science/Research Plan, Stockholm and Geneva.IGBP Report 48-IHDP Report 10, 1999. Land-use and Land-coverChange, Implementation Plan, Stockholm and Bonn.

ways that economics can contribute to, and advancethe interdisciplinary field of land use/change research.

Acknowledgements

We gratefully acknowledge support for the PatuxentRiver Watershed project from the EnvironmentalProtection Agency under Cooperative AgreementCR-821925010; EPA Grant #R825309; MarylandAgricultural Experiment Station grant MD-AREC-96-62; NASA New Investigator Program # NAG5-8559and the MacArthur Foundation.

References

Alonso, W., 1964. Location and Land Use. Harvard UniversityPress, Cambridge.

Anas, A., Kim, I., 1996. General equilibrium models of polycen-tric urban land use with endogenous congestion and jobagglomeration. J. Urban Econ. 40, 232–256.

Anas, A., Arnott, R., Small, K., 1998. Urban spatial structure. J.Econ. Lit. 36, 1426–1464.

Andersen, L.E., 1996. The causes of deforestation in the BrazilianAmazon. J. Environ. Dev. 5, 309–328.

Anselin, L., 1988. Spatial Econometrics: Methods and Models.Kluwer Academic Publishers, Dordrecht, The Netherlands.

Anselin, L., Florax, R. (Eds.), 1995. New Directions in SpatialEconometrics. Springer, Berlin.

Arthur, W.B., 1988. Urban systems and historical path dependence.In: Ausubel, J., Herman, R. (Eds.), Cities and Their VitalSystems. National Academy Press, Washington, DC, pp. 85–97.

Baker, W., 1989. A review of models of landscape change. Land-scape Ecol. 2, 111–133.

Batty, M., Longley, P., Fotheringham, S., 1989. Urban growthand form: scaling, fractal geometry, and diffusion-limitedaggregation. Environ. Plann. A 21, 1447–1472.

Bell, K.P., Bockstael, N.E., 2000. Applying the generalizedmoments estimation approach to spatial problems involvingmicro-level data. Rev. Econ. Statist. 82, 72–82.

Berry, M., Hazen, B., MacIntyre, R.L., Flamm, R., 1996. LUCAS:a system for modeling land-use change. IEEE Comput. Sci.Eng. 3, 24–35.

Bockstael, N.E., 1996. Modeling economics and ecology: theimportance of a spatial perspective. Am. J. Agr. Econ. 78,1168–1180.

Bockstael, N.E., Bell, K.P., 1998. Land use patterns and waterquality: the effect of differential land management controls.In: Just, R., Netanyahu, S. (Eds.), International Water andResource Economics Consortium, Conflict and Cooperation onTrans-boundary Water Resources. Kluwer Academic Publishers,Norwell, MA, pp. 169–191.


Bockstael, N.E., Irwin, E.G., 2000. Economics and the landuse-environment link. In: Folmer, H., Tietenberg, T. (Eds.),The International Yearbook of Environmental and ResourceEconomics 1999/2000. Edward Elgar Publishing, Northampton,MA, pp. 1–54.

Chomitz, K., Gray, D., 1996. Roads, land use and deforestation:a spatial model applied to Belize. World Bank Econ. Rev. 10,487–512.

Clarke, K.C., Hoppen, S., Gaydos, L., 1997. A self-modifyingcellular automaton model of historical urbanization in the SanFrancisco Bay area. Environ. Plann. B 24, 247–261.

Deacon, R., Brookshire, D., Fisher, A., Kneese, A., Kolstad, C.,Scrogin, D., Smith, V.K., Ward, M., Wilen, J., 1998. Researchtrends and opportunities in environmental and natural resourceeconomics. Environ. Resour. Econ. 11, 383–397.

Flamm, R., Turner, M., 1994. Alternative model formulations fora stochastic simulation of landscape change. Landscape Ecol.9, 37–46.

Freeman, M., 1993. The Measurement of Environmental andResource Values. Resources for the Future, Washington, DC.

Fujita, M., Krugman, P., Venables, A.J., 1999. The Spatial Eco-nomy: Cities, Regions and International Trade. MIT Press,Cambridge, MA.

Geoghegan, J., Bockstael, N.E., 2000. Smart growth and the supplyof sprawl. Paper presented at the Association of Environmentaland Resource Economists Workshop, La Jolla, CA.

Geoghegan, J., Wainger, L., Bockstael, N., 1997. Spatial landscapeindices in a hedonic framework: an ecological economicsanalysis using GIS. Ecol. Econ. 23, 251–264.

Geoghegan, J., Pritchard Jr., L., Ogneva-Himmelberger, Y., RoyChowdhury, R., Sanderson, S., Turner II, B.L., 1998. Socializingthe pixel and pixelizing the social in land-use and land-coverchange. In: Liverman, D., Moran, E., Rindfuss, R., Stern,P. (Eds.), Committee on the Human Dimensions of GlobalEnvironmental Change. National Research Council. People andPixels: Linking Remote Sensing and Social Science. NationalAcademy of Science Press, Washington, DC, pp. 51–69.

Greene, W., 2000. Econometric Analysis, 4th Edition. Prentice-Hall, Upper Saddle River, NJ.

Hazen, B.C., Berry, M.W., 1997. The simulation of land-coverchange using a distributed computing environment. Simulat.Pract. Theory 5, 489–514.

Irwin, E.G., Bockstael, N.E., 2001. Interacting agents, spatialexternalities, and the endogenous evolution of residential landuse patterns, Department of Agricultural, Environmental, andDevelopment Economics Working Paper AEDE-WP-0010-01,The Ohio State University.

Ives, A.R., Turner, M.G., Pearson, S.M., 1998. Local explanationsof landscape patterns: can analytical approaches approximatesimulation models of spatial processes? Ecosystems 1,35–51.

Krugman, P., 1991. Increasing returns and economic geography.J. Polit. Econ. 99, 438–499.

Krugman, P., 1996. The Self-organizing Economy. BlackwellPublishers, Cambridge, MA.

LaGro, J.A., DeGloria, S.D., 1992. Land use dynamics within anurbanizing non-metropolitan county in New York state (USA).Landscape Ecol. 7, 275–289.

Landis, J., 1995. Imagining land use futures: applying the Cali-fornia urban futures model. J. Am. Plann. Assoc. 61, 438–457.

Landis, J., Zhang, M., 1998a. The second generation of theCalifornia urban futures model. Part 1: model logic and theory.Environ. Plann. A 25, 657–666.

Landis, J., Zhang, M., 1998b. The second generation of theCalifornia urban futures model. Part 2: specification andcalibration results of the land-use change submodel. Environ.Plann. A 25, 795–824.

Ludeke, A.K., Maggio, R.C., Reid, L.M., 1990. An analysis ofanthropogenic deforestation using logistic regression and GIS.J. Environ. Manage. 32, 247–259.

Mertens, B., Lambin, E., 1997. Spatial modeling of deforestationin southern Cameroon. Appl. Geogr. 17, 143–162.

Mills, E.S., 1967. An aggregative model of resource allocation ina metropolitan area. Am. Econ. Rev. 57, 197–210.

Muth, R., 1969. Cities and Housing. University of Chicago Press,Chicago.

Nelson, G., Hellerstein, D., 1997. Do roads cause deforestation?Using satellite images in econometric analysis of land use. Am.J. Agr. Econ. 79, 80–88.

Pfaff, A., 1999. What drives deforestation in the BrazilianAmazon? J. Environ. Econ. Manage. 37, 26–43.

Veldkamp, A., Fresco, L., 1996. CLUE-CR: an integrated multi-scale model to simulate land use change scenarios in CostaRica. Ecol. Model. 91, 231–248.

Veldkamp, A., Fresco, L., 1997a. Exploring land use scenarios:an alternative approach based on actual land use. Agric. Syst.55, 1–17.

Veldkamp, A., Fresco, L., 1997b. Reconstructing land use driversand their spatial scale dependence for Costa Rica (1973 and1984). Agric. Syst. 55, 19–43.

Wegener, M., 1994. Operational urban models: state of the art. J.Am. Plann. Assoc. 60, 17–29.

White, R., Engelen, G., 1993. Cellular automata and fractal urbanform: a cellular modelling approach to the evolution of urbanland use patterns. Environ. Plann. A 25, 1175–1199.

White, R., Engelen, G., Uljee, I., 1997. The use of constrainedcellular automata for high-resolution modelling of urbanland-use dynamics. Environ. Plann. B 24, 323–343.

Wolfram, S., 1986. Theory and Applications of Cellular Automata.World Scientific Publishing, Singapore.

Wu, F., Webster, C.J., 1998. Simulation of land developmentthrough the integration of cellular automata and multicriteriaevaluation. Environ. Plann. B 25, 103–126.

Zhang, W., 1993. Location choice and land use in an isolatedstate: endogenous capital and knowledge accumulation. Ann.Reg. Sci. 27, 23–39.

theory, data, methods: developing spatially explicit ... ecosystems and environment 85 (2001) 7–23...

Documents