the relative influences of land-owner and landscape heterogeneity in an agent-based model of...

Ecological Economics 70 (2011) 1075–1087

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Ecological Economics

j ourna l homepage: www.e lsev ie r.com/ locate /eco lecon

Analysis

The relative influences of land-owner and landscape heterogeneity in an agent-basedmodel of land-use

Hugh Kelley a,⁎, Tom Evans b

a Department of Economics, National University of Ireland, Cairns School of Business and Economics, Galway, Irelandb Department of Geography, Indiana University, Bloomington, IN 47401, USA

⁎ Corresponding author. Tel.: +353 91 49 5087; fax:E-mail addresses: [email protected] (H. Kell

(T. Evans).

0921-8009/$ – see front matter © 2011 Elsevier B.V. Aldoi:10.1016/j.ecolecon.2010.12.009

a b s t r a c t
a r t i c l e i n f o
Article history:Received 22 June 2010Received in revised form 8 December 2010Accepted 8 December 2010Available online 15 February 2011

JEL classification:C60D81Q15

Keywords:Agent-basedLand-usePortfolio-theorySpatial

The purpose of this work is to explore the extent to which landowners' land-use decisions are influenced byheterogeneous land-use preferences, spatial externalities, and unique suitability features? We develop andcalibrate a heterogeneous-agent portfolio-theory model to the historical Southern Indiana land-use history.Calibration exercises demonstrate that our spatially-explicit approach provides an accurate description oflandowners in our study area, with the most descriptive model explaining 70% of land-use variation acrosstime and space. Comparative statics simulations indicate that landowners' heterogeneous calibratedpreference parameters marginally influence the landscape more than suitability and externality parameters.Policy simulations demonstrate that weaker multi-policy management strategies simultaneously targetingheterogeneities and spatial interactions can provide 1–6% more forest that is 1–3% less fragmented comparedto alternative strong single-policy approaches.

+353 91 52 4130.ey), [email protected]

l rights reserved.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

A feature of land-use decision making that is difficult to explainis the observation of heterogeneous land-uses on similar land. Evanset al. (2001) describe how this diversity of uses observation isparticularly evident within and across parcels in our 1940 to 1993Indiana study area.

Many researchers have suggested heterogeneous parcel ownerpreferences as one possible explanation; owners facing similar payoffsignals from suitability features may still have different land-useresponses due to subjective preferences. The idea that heterogeneousagent preferences may play an important role in agents' land-usedecision making has been explored by Wu et al. (2004), Irwin (2002),Deller et al. (2001), Morton and Podolny (2002), Inman et al. (2002),and Barbier (2001). These studies respectively suggest housinglocation or land-use choice is importantly affected by unique agentpreferences over climate, land amenities (including the presence offorests), water amenities, recreation infrastructure, the type ofagricultural production or crops previously produced, and the amountof agricultural infrastructure.

Another possible source of the diversity of uses outcome is thatagents may experience or perceive particular patterns of spatial

externality which modify the payoff signal they receive for alternativeland-uses see Marshall (2004). Spatial econometrics approaches, suchas those of Nelson and Hellerstein (1997) and Irwin and Bockstael(2001), consider the roles that road placement and fragmentation costsor agglomeration bonuses may have in the location of forests. In thesestudies there are clearly identified influences of spatial externalities.However, as summarized by Anselin (2001) and previously addressedby Nelson and Hellerstein (1997), there are a number of crucial spatialeconometric problems concerned with spatial dependence and spatialheteroscedasticity which impair researchers' ability to draw economet-ric inferences about externality influences.

This study takes a novel, agent-based modeling approach toexplore the relative influence of land suitability, agent preferences,and spatial externalities while dealing with the aforementionedstatistical problems. Our simulation approach allows us to avoidcrucial problems with parameter identification and spatial hetero-scedasticity since inferences about individual agent parameters ormicro level effects are not made. Rather, the sensitivity of the overalllandscape to perturbations of individual calibrated parameters is thefocus. Further, spatial dependence is controlled for with a latticeapproach whereby a distance weighted variable representing land-use spatial externality influences from adjacent land cells isintroduced directly into the agents' utility structure and decisionproblem. To emphasize that our agent-based model predictions avoidspatial dependence problemswe reproduce relevantmodel predictiveperformance tests described in Nelson and Hellerstein (1997).

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1076 H. Kelley, T. Evans / Ecological Economics 70 (2011) 1075–1087

There are three objectives of this analysis, onemethodological, onequantitative, and the last policy oriented. The methodologicalobjective is to construct and calibrate a spatially explicit agent-based variation of a land portfolio allocation model which integrateslandscape suitability, preference for land-use, and externality features(see Balmann (1997), Mathevet et al. (2003) and Blank (2001) forrelated modeling work). Within this objective guided calibrationexercises similar to Plantinga (1996), using observed historical land-use decisions as a target, allow us to calibrate individual agentparameters for alternative land-use drivers. Our quantitative objec-tive employs the calibrated model to address the research question,what are the relative influences of preferences, suitability, and spatialexternalities for influencing the organization of the landscape.Simulations similar to Stavins and Jaffe (1990) and landscape levelland-use comparisons allow us to identify the sensitivity of thelandscape to perturbations of individuals' calibrated parameters. Ourpolicy objective is to address a second research question asking howeffective are strong single policy management approaches in affectingthe organization of forest on the landscape given the presence ofagent heterogeneities. And further, might there be weaker multi-policy approaches that could harness preferences and spatial inter-actions to more effectively achieve spatially contiguous reforestation.

2. Theoretical Structure

We present a static spatially-explicit agent-based portfolio-theorymodel of land-use. In such a model, an agent's objective is tomaximize utility derived from a particular portfolio of labor and land-uses for a particular year. The basic underlying hypothesis of portfoliotheory (PT) is that an agent may be better able to manage risk andrespond tomarket and environmental shocks by producing a portfolioof outputs or having a diversity of uses of their inputs (land cells andlabor hours), rather than producing a single output. In the unrestrict-ed version of the theory employed here, an agent may choose todiversify or to alternatively produce a single output. Although not amajor focus of our work, our by-agent land use predictions inform usabout the extent to which agents find it optimal to diversity the use oftheir inputs, thereby providing evidence about the validity of thishypothesis.

DeLong et al. (1990), and many other authors, have shown that atraditional representation of agent k's expected utility in a PTframework can be:

Uek = αk ⋅ πe

k−RA⋅σ2πk π2

k pe;Y2� ��

ð1Þ

where superscript e represents the expectations operator, Uk is therisk adjusted utility derived from applying their labor and land, αk

represents agent k's vector of preference weights, πk represents thepayoff for k's particular portfolio of activities, RA is a risk aversionparameter (zero for risk neutral, positive for risk averse, followingParks (1995)), and σ2

πk is the variance of payoffs for k's portfolio,which is a function of commodity prices and squared output; thelatter is a function of squared labor allocated to a particular activity.This model has been shown to be an appropriate representation ofportfolio managers when the number of options within a portfolio issmall, and when the returns from the portfolio are small compared toan agent's total wealth; both of these features are present in thiscontext. Specifically, the numbers of labor and land-use options aresmall and the returns from a portfolio are small relative to an agent'stotal wealth as represented by their land value.

In a traditional model researchers might assume a representativeagent. However, in this agent-based application the parcel-leveloptimization problem will be solved for each individual agent giventheir unique context. In this case one agent is assumed to govern thedecisions of one parcel of land as defined by ownership boundaries. A

further modification we make is to include in the agent's payoffspecification non-pecuniary payoffs from land-uses including prefer-ences for use and externality effects.

Based upon contextual information describing activities for ourarea (Evans et al., 2001), we assume agents can supply labor inputs tofour activities respectively: growing crops (farm), harvesting trees(tree), growing trees (aesthetic), or working off the farm in a non-agricultural sector (off farm). Similar to Benjamin (1992) our modelassumes that land can be used for four activities: growing crops(farm), growing trees (aesthetic), harvesting trees (tree), or fallowingthe land (graze). Similar land options were also included in themodels of Hosier (1988), Stavins (1999), and Etienne et al. (2003).Each decision period (year), agents observe the new set of exogenousand endogenous features of their environment and re-optimize theirfactor allocations. Details of the theoretical structure are provided inAppendix A.

For a variety of reasons, and in particular due to data availabilityconstraints, the land suitability features included in this study arerestricted to slope and soil quality. First, slope has been identified as akey driver in numerous ecological studies (Lansing and Kremer, 1994;Turner et al., 1996; Mathevet et al., 2003; Etienne et al., 2003), andactual topological data is used for this exogenous driver.

The remaining suitability drivers are endogenous simulationoutcome variables whose levels are not directly based upon fielddata. Although soil plays a key role in influencing agents productiondecisions, we do not have the disaggregated soil data for each agents'50 m2 cell from 1940 to 1993 that we would need to base thissuitability measure completely on field data. Instead, based on theextant literature, we posit functional relations among land use andsoil quality which allows us to vary the soil value from an initiallyhomogeneous landscape in 1940 in response to each agents land usedecisions. As a result, the calibrated suitability parameter described inthe results section refers only to the role of slope, and parameters forthe following outcome variables cannot be provided. However, theoutcome variables below are endogenous drivers of land use decisionsthrough their impact on productivity/technology, see Eq. (A.2). Lal(2003) identifies the importance of soil quality for land-use decisionmaking, and the functional relationship between land-use and soilquality is based upon field data. The importance of land-useexternalities has been documented in both the agent-based andland-use modeling literatures respectively (Robinson et al. (2002);Mokma and Sietz (1992)). Also, age and percent cover features offorest have been shown to be relevant for determining timber output(Faustmann (1849); Etienne et al. (2003)). The values for the latterthree variables are initialized based upon the actual 1940 land-usepattern, and then evolve within the simulation. Finally, in line withHosier (1988) and Stavins (1999), forward looking opportunity costsusing expected market prices allow agents to compare discountedpayoffs for alternative future uses of the land. Additional field dataincluded but de-emphasized for this particular application includewage rates for alternative non-agricultural employment opportunitiesand income taxation rates.

Additional drivers of land cover change identified in previousstudies of other areas, but excluded from the utility structure of thisstudy, include: parcel size and shape, absolute elevation, distance toroad, distance to market, population density, transport costs,household size and composition, commodity and labor marketscharacteristics, irrigation structures, property rights, macroeconomicand trade policy conditions, general and sector-specific technologicallevels, selective cutting in a multi-species forest, variations in localinput prices, property rights differences, and household taxation ratedifferences.

The stylized model we employ is designed to be representative ofour context, but must also be simplified in order to provide insightsabout our particular research questions. We therefore do not claimthat it perfectly represents all dynamics present upon our landscape.

Table 1Historical landscape distribution of forest by slope and historical composition andpattern metric values.

Panel A. Historical landscape distribution of land use at 1993

Land use class Low slopes Moderate slopes Steep slopes

Sb4° 4°≤S≥10° 10°bS

Agriculture/pasture 38.3 18.3 6.5Forest 41.8 69.3 84.6Other

Residential 11.7 9.0 7.0Commercial 8.0 3.4 1.8Water 0.3 0.1 0.1

Panel B. Historical landscape percent forest and forest edge 1940–93

Year Percent forest Edge(m)

1940 43.9 1,403,6001958 53.1 1,597,1001967 53.3 1,573,2001975 54.7 1,613,3001980 55.1 1,611,5501987 57.7 1,629,5501993 59.2 1,638,200

1077H. Kelley, T. Evans / Ecological Economics 70 (2011) 1075–1087

In the absence of specific econometric data for our study area, weimpose Cobb–Douglas production functions with equal degrees offactor input substitutability. This assumption allows us to identifyunique and maximal solutions for each agent and each time period(see Appendix B). The calibrated preference parameters we obtaincapture preferences for land-use, but may also capture the effects ofother unobserved drivers. Importantly, we believe that our choice of aprimarily agricultural study area limits the potential influences ofthese, in particular urban, unobserved preference drivers; see thepercentage of ‘Other’ land classifications in Table 1 Panel A. Further,although stylized, our model is based upon elements from earlierresearch within the land-use cover change literature and augmentsthese elements with a small number of additional preference,externality, and agent-based methodological elements. This incre-mental approach is employed to maintain comparability with existingresearch while still providing insights relevant to the literature.

The key aspects of this theoretical environment are that: (1) thereare multiple potentially heterogeneous agents who can differ in thequality and quantity of land owned, in their preferences, and inperceptions about the productivity effects of land suitability andexternalities; (2) agents make parcel-level labor then cell-by-cell landallocation decisions each year; (3) agents' calibrated parameters areconstant across multiple years; (4) agents interact with one anothervia spatial production cost or aesthetic benefit land-use externalities;(5) agents are aware of the functions that describe the output, costs,and profits they can expect from the various activities; (6) there aredynamic endogenous interactions among geophysical features con-ditional upon previous land-uses, and finally, (7) similar to Ahn et al.(1981) the planning horizon is one year, and each period agents uselagged beginning-of-the-year information for decision-making inorder to avoid across-agent sequence effects.

3. Agent Decision Making

The final modification we introduce in this paper is a two stagecell- and parcel-level decision process for agents. Both these levels arecritical for characterizing an agent's decision. The parcel level gives usan aggregate decision unit which allows calibrated parameters andmeasures of goodness of fit. The cell level critically allows us to predictthe land-use pattern within an agent's parcel. The parcel levelaggregate is determined by the cross sectional variation of the celllevel. This dynamic, across time and space, cell-level variation allows

us to calibrate agent parameters by comparing the observed andpredicted patterns of land use. Thus, in much the same way a marketprice is the result of individual participants' goods demands, a parcel'sspatial metric value is the result of an agent's multiple decisions abouthow to use each of their cells each period. Additionally, an agents'portfolio is defined by their group of cells, with each cell having one ofthe possible set of uses. Finally, the landscape level outcome, which isthe focus of the later experiments, is the sum of the parcel-leveloutcomes.

The first stage of the decision problem is to solve a parcel-leveloptimization problem which yields a portfolio of labor allocationsconditional upon the average geophysical characteristics of the parceland market conditions. The second stage is to identify upon whichindividual cells of their land to apply this labor, thereby determining aparticular cell's land-use. This is implemented by applying the payoffstructure described in Appendix A on both the parcel-level in stage 1,and on the cell level using a particular cell's characteristics in stage 2.

3.1. Parcel-level Labor Allocation

Combining the components described by Appendix A Eqs. (A.1)–(A.6), and dropping the agent subscript k, yields the constrainedexpected utility expression (2). The agent's first decision is to choosethe portfolio of labor that maximizes this Lagrange expressionrepresenting the one year planning horizon problem.

maxLi Λ = U Li jMi;α;γ;Ω;σ2πi;RA

� �+ λ⋅ L−∑iLið Þ ð2Þ

Define λ as the Lagrangemultiplier on an agent's labor constraint, L(hours) as the total available labor hours, Li as the labor allocated toactivity i,M (number of 50 m2 cells) as the total available land, andMi

as the beginning-of-period land available for i. U refers to the totalparcel-level utility from a portfolio potentially including all activities.Alternatively, Ui is the total utility derived from activity i across allcells on a parcel. α represents the preference scaling factor for variousactivities, γ represents potential externality effects, and Ω representsthe set of dynamic biophysical features of the land. σ2

πi represents thevariance of payoff stream, which is a function of Yi2 and commodityprice variability, and RA reflects agents' sensitivity to this risk.Crucially, all parameters (α, γ) and geophysical characteristics (M,Ω) are unique to a particular agent/parcel. However, total labor(L=2000 h or 50 weeks×40 h/week) and risk preferences (RA) inaddition to market prices and variances are assumed common acrossagents. Intuitively, agents derive utility from a composite of pecuniaryand non-pecuniary payoffs; however, they dislike variance in thismeasure.

Each agent's labor allocation decision is an approximation of a utility-maximization approach. An agent's maximal parcel-level labor alloca-tion is that which satisfies the first order and Kuhn–Tucker conditions(see Finnoff and Tschirhart (2003); Puu (1997); Berliant and Fujita(1992); and Ahn et al. (1981)):

∂Λ∂Lf

= 0;∂Λ∂Lt

= 0;∂Λ∂Laes

= 0;∂Λ∂Lof

= 0;∂Λ∂λ = 0 ð3Þ

λ≥0;∂Λ∂λ≥0; λ⋅ ∂Λ∂λ = 0: ð4Þ

By design, the stylized structure assumed for the technologyparameters, the Cobb–Douglas production function, and linear profitand labor constraint allows this simple system to reduce to oneequation with one unknown, the Lagrangian λ. This is numericallyestimated to solve Eqs. (3) and (4) for each agent and period. The λ⁎that provides the solution to Eqs. (3) and (4) for each agent and yearoccurs within each run of the parameter estimation procedure for the


free parameters αi and γi. In other words, conditional upon each set ofpreference, externality and suitability parameters chosen by the useror the parameter search algorithm, a nested non-linear estimationprocedure is used to solve for λ⁎ for each agent and period. This yieldsan agent's maximal parcel-level and across activity labor allocation,Li⁎= f(αi, γi, Mi, L, Ω, RA, σ2

πi, λ⁎), which must be distributed acrosscells.

3.2. Cell-level Land Allocation

The second step of the agent's decision process involves optimallyallocating the total allocated labor per activity, Li⁎, to obtain an optimalland-use at each location j, that is Mij

⁎. The labor applied to any cell ofland for a given activity is determined by the equal allocation rulelij=max(1, Li⁎/Mi) hours/cell, where lijmay differ by activity i, but for agiven i not by location j. Introducing a minimum of one hour/cell ismotivated by informal surveys of local farmers who indicated theyspent 1 to 2.5h/50 m2 cell of their land in a season.

Let Uij refer to the utility obtained from applying labor for activity ito a cell at location j; note that the agent subscript k is dropped forclarity. The following conditions must hold if activity i is conductedat j:

Uij Mij j lij;αi;γij;Ωj

� �≥U

i′ j Mi′ j j li′ j;αi′ ;γi′ j;Ωj

� �

≥Uij′ M

ij′ j lij′ ;αi;γij′ ;Ωj′

� �:

ð5Þ

The first inequality at Eq. (5) states that for a decision to conductactivity i at location j to occur, it must be the case that the conductingof any other activity i′≠ i at location j yields at most equal utility. Thesecond condition states that for a decision to be made to conduct i at jit must be the case that pursuing i at any other location j′ yields atmost equal utility. Together, these conditions indicate that a decisionto apply labor and use a cell for an activity only occurs if it is the bestcombination of activity and location compared to all other owned cellsand their potential uses. The agent then allocates all land and labor,choosing the best activity-location pairs, until all labor is employedyielding Umax(Li*,Mij*).

Simulating this model with a particular set of parameters providesa 53 year sequence of labor and land-uses for each agent and eachowned cell. These land-use predictions can then be compared to thehistorical sequence of land-use decisions in order to calibrateparameters and to gain insights about general validity of thefunctional forms chosen within our model.

4. Study Area

The physical land-use setting to which we apply our model is theIndiana Creek township of Monroe County in Southern Indiana, from1940 to 1993. This region is approximately a 40 mi2 (100 km2) area,with 190 parcel owners as defined by the 1958 Monroe Countyownership records.We chose the 1958 date for ownership boundariesfor simplicity since it represents a midpoint in the monotonicallyincreasing fragmentation process observed for land ownership in ourarea. In our sample period owners utilized their land primarily forgrowing wheat and soy crops, fallowing the land for grazing and soilregeneration, or allowing re-growth of pine, maple, and oak forests(Evans, et al. (2001)).

In order to account for the history of land usage we summarize thespatial stylized facts of the landscape via spatial metric statistics.Calculation of these metrics is performed using a raster data structurein a geographical information system (GIS). A raster data structure is acell-based structure where a series of rows and columns is placed overthe landscape in regular intervals with a cell representing anindividual row-column combination. A key feature of this data, andspatial modeling in general, is the choice of the size of an agent's land-

use decision unit, henceforth referred to as a cell (see Mathevet et al.(2003)). Larger cells aggregate and generalize landscapes and alsointroduce error. Smaller cells introduce less error but increaseprocessing time and data storage requirements. Earlier work byEvans and Kelley (2004) explores the implications of modeling acrossa variety of scales from 30 m2 to 480 m2 and suggests our choice of50 m2 resolution provides an appropriate balance of land-usevariation, error, and processing time.

A historical time series of land cover, ownership, and slope datawas developed by visual interpretation of historical aerial photogra-phy from the following dates: 1940; 1958; 1967; 1975; 1980; 1987;and 1993. These seven validation years are then used as a comparisonto the land-uses predicted by the simulation model. We generatemetrics at the township (henceforth landscape) and household (i.e.parcel) levels in order to provide a multi-scale characterization of thestudy area. In this research we use both composition and patternmetrics to characterize the actual and simulated landscapes. Earlierapproaches have also employed these two classes of metrics as acomprehensive description of the landscape (e.g. Wear and Flamm(1993)).

Landscape composition describes the proportion of differentlandscape components within a defined geographic unit. Percentforest area (PF) is a compositional metric that represents the total landin a forest cover classification on a landscape with R×C rows andcolumns. arc equals 1 if a cell at location r×c is forest, zero otherwise.

PF = ΣRr = 1Σ

Cc = 1

arcR + C

ð6Þ

Landscape pattern describes the spatial arrangement of alternativeuses of the land. The indicator of pattern utilized is Forest Edge (FE),which measures the total length of forest boundaries in a parcel orlandscape. For example, for a forest cell surrounded by a field, theamount of edge in the landscape is the perimeter of the forest patch.Forest edge for our 50 m2 resolution data is calculated as:

FE = ΣRr = 1Σ

Cc = 1erc⋅50: ð7Þ

Here erc is an indicator for forest land-use that takes a value of 1 ifcell erc≠erc±1 or erc≠er±1c and zero otherwise, i.e. if any non-diagonal neighboring cell is different, this represents an edge to beadded up.

Table 1 Panel A summarizes the diversity of uses observation, andPanel B provides landscape and by-parcel metric values across time. Inthis study we measured suitability by land slope, and in Panel A ofTable 1 we see that diverse activities occur on similarly sloped land.For instance, low sloped land would be deemed particularly suitablefor agriculture (Blank (2001)), yet only 38% of such land is used foragriculture while 42% is used as forest. The fact that there is adistribution across the three broad suitability classifications, ratherthan closer to an all-or-nothing outcome, is the direct representationof our diversity of uses observation. Additionally, based upon themetrics reported in Panel B, there are two other stylized facts that oursimulation model aims to reproduce: that there has been a monotonicre-growth of forest on the overall landscape, beginning at 43.9% forestcomposition in 1940 and ending at 59% by 1993; and that landscapeforest edge has increased non-monotonically during this period.

5. Empirical Methodology

Results from four types of analyses summarize the empiricalfeatures of this agent-based model. First, we identify if spatial effectsare important for the spatially explicit land use data that is the focus ofour simulation work. The presence of such effects justifies theinclusion of spatial externality influences in agents' decision structure.Next, we conduct a by-parcel calibration exercise exploring the extent


to which our agents can be parameterized to reproduce the actualhistory of land-use. Third we assess our model's predictive perfor-mance using approaches similar to those described in Nelson andHellerstein (1997). Finally, simulation experiments explore how thespatial organization of the landscape responds to calibrated param-eter perturbations; this allows us to address our research questionsregarding the relative influence of preferences, suitability andexternalities for explaining the diversity of uses observation andgives insight into the potential effectiveness of policy. By using thisdiverse set of analysis methods we can better demonstrate therobustness of our results.

5.1. Spatial Effects

In order to construct and calibrate spatially explicit land-usemodels it is important to address spatial effects including spatialdependence and spatial heteroscedasticity (see Anselin (2001)).Spatial autocorrelation is akin to time series dependent variableautocorrelation, but refers to dependence across space. Spatialheteroscedasticity reflects variability in structural relations amongbehavioral or geophysical variables across space. For a strictlyeconometric study, in contrast to this work, failing to address theseproblems would create biases in estimated parameters and predictionerrors.

Nevertheless, to determine if these effects may be present in ourdata we calculate Moran's I statistic for our historical land cover datafor the seven dates we used as targets for parameter calibrations. Thisstatistic ranges from −1 to 1 for a standardized data set with zerorepresenting the absence of the effect. Allowing eight adjacentneighbors for each cell, and averaging across time, I=0.51 for the214,302 space–time observations in our sample. This value suggeststhat spatial effects are likely to be influencing our data, justifying ourinclusion of a spatial effects variable in agents' utility structure.

Even though our approach is not econometric, we take a number ofsteps to mitigate the potential problems associated with these effects.First, we do not perform a strict econometric estimation to determinecorrelation coefficients for specific predictor variables with our data.In fact this would be impossible because our ‘predictor variables’ arein fact dynamic and spatially interactive processes rather thanindividual independent variables. Rather, we conduct simulationswith a guided calibration technique in order to uncover generalrelations influencing parcels and the landscape. Second, we do notconduct inference tests with the parcel-level parameters whichwouldrequire strict measures of significance and comparisons of magni-tudes. Finally, given that earlier literature suggests spatial interactionsare likely to be important for studying forest change (Baskent (1999);Spies et al. (1994); Nelson and Hellerstein (1997)), and the high valueof the I statistic, we include a weighted-lattice spatial-externalityvariable directly into agents' utility structure. In the results describedbelow this simulation variable with calibrated parameter allowsspatial effects to be distinguished from land-use preference andsuitability influences.

5.2. Calibration

We calibrate key agent decision parameters in order to reproducethe actual history of land use for each agent. Agents' calibratedparameters are constant for each 53 year simulation and include theagricultural and timber growing land-use preferences αfarm and αaes;the spatial externality weights for farming, tree harvesting, andreforestation, respectively γe,farm and γe,tree, =γe,aes; and finally, theland suitability weight, γslope (see Appendix A). Note that othersuitability drivers such as soil are present and operating in the model,but because we do not have the detail of data necessary to calibratethe model to these drivers, parameters are not estimated for theseinfluences. We focus on these five parameters (two are equal) for two

reasons: first, they summarize agents' motivations for pursuing theprimary land-uses in this area, farming and forest activities. Second,earlier econometric and theoretical work has identified thesecomponents as important determinants of land cover change (Hosier(1988); Turner et al. (1996)).

Because our time series is limited we are not able to calibrate indetail all model parameters. As a result a set of baseline parametersdeemed to be of lesser importance were only subjected to apreliminary analysis with the simulation model where we attemptedto find values that resulted in balance/equal magnitudes for allcalibrated and non-calibrated utility influences. From this ‘marginal’position, parameter calibration was able to proceed allowing smallparameter changes to lead to dominating utility effects and land usechanges. The alternative would be a situation where utility influenceswere of dramatically different magnitudes producing large areas ofparameter space where parameter changes produced no utilitydominance and therefore no land use changes.

Our calibration approach is a variation of the non-linear calibrationtechnique described in Plantinga (1996). Importantly, our methodol-ogy would not be described as a traditional econometric analysislinking a dependant variable to a set of independent predictorvariables. Instead we attempt to generally match our simulationhistory to the actual history of land-use by calibrating key agentparameters. As a result, issues of parameter identification have lessmeaning and applicability to our problem. Specifically, we are notinterested in comparing parameter magnitudes across agents, nor inmeasuring the statistical distinction of these parameters from zero,nor in making inferences across individual parcels. Nevertheless,within a parcel we do need a reference for parameter magnitude, thuswe compare calibrated parameters to our baseline parameters.Importantly, in all cases our calibrated parameters are larger inabsolute value than the baseline values, indicating that the sign of ourparameters clearly identifies the direction of effects on utility.

The parameters are chosen to maximize an individual parcelgoodness of fit incorporating our spatial metrics denoted Null_R2. Thismeasure, unique to our work, compares the across-time deviationbetween simulated and actual parcel metric values (based on thecross sectional variation across cells) relative to the variation of theactual historical parcel from the base year 1940. This measure is avariation of Granger and Newbold (1986), and is calculated as:

NullPR2 = 1− SSESimSSENull

ð8Þ

SSESim = ∑7t=1 ActMetrict−SimMetrictð Þ2 ð9Þ

SSENull = ∑7t=1 ActMetrict−ActMetrict=1ð Þ2: ð10Þ

For this measure SSESim represents the sum of the across-timesquared deviations of a particular metric value for the actuallandscape ActMetric, from the metric value for the simulationprediction, SimMetric. SSENull represents the overall variation in theactual landscape across time relative to the cover at (t=1), i.e. thenull model. The second term in Eq. (10), ActMetrict=1, represents theactual metric value for the cover in the first year for which we havedata. For the R2 described in Granger and Newbold (1986), the secondterm in Eq. (10) would be the mean value for the metric over the timeperiod. However, in the land cover change literature, one commonmeans to compare the accuracy of a land-use prediction model isrelative to what no model, or a null model, would provide. A nullmodel uses the landscape metric value at the first time period (t=1)to predict all future dates, and then calculates the resulting SSE giventhe actual history; this is a random walk assumption. To remainconsistent with this literature our null prediction error, SSENull, playsthe role of total sum of squared error in our pseudo R2. Null_R2N0indicates our model does better than assuming random walk.

Table 2Calibrated parameter summary statistics.

Calibration targets

Percent forest Forest edge PF and edge index

Number of agents 73 73 73Number of parameters per agent 5 5 5Number of target obs per agent 7 7 7Median target R2 across agents 0.70 0.62 0.39Max target R2 0.94 0.98 0.94

Calibrated parameters (medians)

αfarm 176.1 129.8 181.9αaesthetic 156.0 144.7 166.0γext,farm 131.8 126.3 135.8γext,aes 149.8 117.2 173.2γslope 91.0 103.9 82.7


Null_R2b0 indicates insufficient variance in the dependent variableand would be equivalent to failure of parameter identification in aneconometric study.

5.3. ABM Experiments

5.3.1. Comparative StaticsAfter calibration our first set of simulation experiments explores

the relative importance of land use drivers by perturbing agents'calibrated driver parameters by multiplying each by 0, by 0.5, and by2, holding the other fitted parameters at their calibrated values. Thisanalysis is a variation on the Nelson and Hellerstein (1997) marginalbeta analysis. There, the authors investigated landscape effectsresulting from variations in the predictor variables given constantparameters. For our application it is more appropriate to considervariations in the organization of the landscape arising from changes inparameters given constant predictors such as slope. This allows us toexplore the extent to which preferences, land suitability, andexternalities marginally influence the landscape. Parameter perturba-tions that lead to large landscape effects are likely to be associatedwith important drivers; while parameters that lead to no effects areless likely to be important. For each change in the parameter relativeto its calibrated value, we report the total landscape percent forest,forest edge, and error in these metrics relative to the calibratedsimulated history.

Note that although we simulate all 190 agents on the landscape,we only have calibrated parameters for a subset of these agents whowere either very large-parcel agents or agents whose parcels changedby more than eighty 50 m2 cells in our sample. For the remaining 117smaller or no-change agents we impose and perturb the medianparameters from those who were estimated, a weak representativeagent hypothesis. This is necessary due to the lack of across-time oracross-space land use variation to use as a calibration target. Theprimary implication of this necessary simplification is that some of thesmaller or no-change agents, who would not have reorganized theirparcels, will be given preferences to produce some change (i.e.deforestation). This will manifest as a deviation from the predictedforest cover trend characterizing our study area. Because we observeda primary trend of reforestation, agents who may not have reducedforest cover may be parameterized to do so. This most likely willmanifest as underestimation of the actual level of reforestation sincethe stable agents maintaining their forest may now be somewhatreducing forest cover.

5.3.2. Homogeneity CounterfactualA key way to assess the underlying assumptions and predictive

power of our model is to focus on the relevance of our heterogeneousagent assumption. We can do this by comparing our heterogeneousagent calibrated simulation to a homogeneous agent counterfactualsimulation. For this counterfactual simulation we impose the mediansof the by-agent calibrated parameters upon all 190 agents on thelandscape and consider the effects on the spatial organization of thelandscape.

5.3.3. Alternative Accuracy AssessmentsA final way to measure predictive performance is to use a

prediction matrix. Our simulation provides a predicted category foreach locationwhich can be compared to the actual historical use.Withthese, a prediction matrix can be calculated where rows showlocations actually in a category and columns the number of locationspredicted to be in a category. For our data we can directly distinguishagricultural land from forest. This allows us to construct a 2×2prediction matrix where the diagonal represents locations correctlypredicted. From this matrix four derivative measures can beconstructed: average, producer, and user accuracy, and kappa.Average accuracy is the percentage of correct predictions across the

entire landscape. Producer accuracy is the probability that the actualvalue is predicted correctly and user accuracy is the probability aprediction is correct. Kappa is similar to average accuracy and is anoverall indicator of accuracy (Nelson and Hellerstein (1997)).

6. Results

6.1. Model Calibration

Table 2 reports pseudo R2s for three versions of the calibrationexercise conducted for our model. The first version calibratesparameters by attempting to match the by-parcel time series of thepercent forest composition metric. Version 2 attempts to match thetime series of forest patch edge, and version 3 attempts to match anequal weight index of composition and pattern metrics. In the tablewe only report the R2 for the metric target of interest. Although inprincipal it is possible to calculate an R2 for the other metric targets,because the calibration routine is not taking these targets intoaccount, the values are necessarily lower than the value reported forthe actual target. Thus the table only reports one R2 for each version ofthe model. Our results indicate that the magnitudes of medianparameters and the pseudo R2s vary depending uponwhichmetric weuse as a target. In general the calibrated model predicts agents'historical land-uses quite well. Calibrating to the percent forest targetproduces the best overall predictions, with a median Null_R2 of 0.70.Calibrating to the edge target alone produces slightly less accurate fits,0.62, and targeting the index of the two metrics produces the lowestmedian value of 0.39. This indicates that simultaneously explainingcomposition and edge characteristics represents a more difficult task.For all calibration versions the maximal Null_R2s are quite high, e.g.≥0.94. These results generally indicate that our stylized structure andchosen parameters are descriptive of actual history.

The magnitudes of the parameters reported at Table 2 can givesome insights into the drivers of trends in these two metrics. Thecomposition metric appears most sensitive to the preference forfarming, followed by the preference for reforestation. For the patternmetric this is reversed, suggesting forest edge features are moresensitive to the preference for reforestation than for farming andassociated clearing. Interestingly, this pattern is not observed whentargeting the composition and pattern edge index. There, preferencefor farming appears most important but perceived reforestation/timber harvesting externality is second most important. This suggeststhat trends in a multi-metric index including pattern are sensitive toexternality effects slightly more than preferences for reforestation. Inall cases the metrics are least sensitive to slope.

We also calculate across-time prediction errors for our calibratedmodel. These can give insights about any prediction bias that may beresulting from our chosen parameters. The errors represent the across

Table 3Predicted landscape distribution of land-use by slope and predicted landscapecomposition and pattern metric values.

Panel A. Predicted landscape distribution of land-use at 1993

Land use class Low slopes Moderate slopes Steep slopes

Sb4° 4°≤S≥10° 10°bS

Agriculture/pasture 68.7 42.0 15.4Forest 31.3 58.0 84.6

Panel B. Predicted landscape percent forest and forest edge 1940–93

Year Percent forest Edge(m)

1940 44.8 1,419,7001958 48.0 1,609,4001967 50.8 1,724,9001975 50.8 1,742,3001980 50.6 1,742,6001987 51.6 1,756,9001993 52.2 1,760,000

Table 4Calibrated parameter experiments.

Sensitivityanalysissimulations

Landscapepercentforest at1993a

Percentforest sumsquared error(1940–93)

Landscapeedge at1993 (m)1

Edge (m)sum squarederror(1940–93)

Calibrated parametersαi × 1.0 52% 0 1,760,000 0

Panel Aαfarm × 0.0 74%⁎⁎ 2088.4 1,860,000⁎⁎ 17.4e+10

Policy 1 0.5 53%⁎ 6.3 1,790,000⁎ 0.2e+102.0 50%⁎ 2.7 1,730,000⁎ 0.4e+10

Panel Bαaesthetic × 0.0 41%⁎ 476.4 1,440,000⁎ 50.7e+10

0.5 51%⁎ 4.2 1,740,000⁎ 0.3e+10Policy 2 2.0 54%⁎ 15 1,790,000⁎ 0.3e+10

Panel Cγext,farm × 0.0 54%⁎ 40.2 1,801,700⁎ 0.2e+10

0.5 54%⁎ 263 1,800,300⁎ 0.4e+102.0 52% 0.3 1,737,200⁎ 0.3e+10

Panel Dγext tree × 0.0 48%⁎ 47.8 1,520,000⁎ 27.8e+10

0.5 54%⁎ 23.5 1,731,200⁎ 0.3e+10Policy 3 2.0 55%⁎ 51.5 1,815,800⁎ 1.3e+10

Panel Eγslope × 0.0 55%⁎ 31.8 1,600,000⁎ 17.3e+10

0.5 52% 2.7 1,756,000 0.1e+10Policy 4 2.0 50%⁎ 13.2 1,703,100⁎ 2.7e+10

Homogeneous agent parametersαi=median(αi) 45%⁎ 280.4 1,645,600⁎ 6.3e+10γi=median(γi)

Combined Pigou. and input taxγext tr × Policy 5 1.5 56%⁎ 98.6 1,777,200 0.2e+10γslope × 1.5

*(**) indicates 5% (7%) significance for rejecting the null hypothesis that the perturbed-parameter simulations have the same landscape across-time mean metric value as thecalibrated simulation.

a Values reported obtain from simulations using the percent forest metric as thetarget for maximizing Null_R2 when comparing simulated and actual landscapes.Importantly, results from parameters obtained using the edge or weighted average ofmetrics as the targets produce similar results.


time composition and pattern prediction errors associated withcalibrating toward percent forest and forest edge targets. The meansof the percent forest and edge error distributions are −0.1% (150 m),the standard deviations are 0.2%2 (1772 m2), and kurtoses are 2.5%3

(14 m3) respectively. The results clearly indicate that the distributionsof errors are centered on zero with few outliers, providing furthersupport for the descriptiveness of our model and relevance of theheterogeneous calibrated parameters.

Our calibrated model also reproduces the historical landscapestylized facts summarized in Table 1. Table 3 Panel A provides thecorresponding predicted values for our simulated landscape. For thesmaller set of land-use categories predicted by ourmodel we do not seean all-or-nothing prediction by suitability category. Thus, we generallyreproduce the diversity of uses/portfolio allocation outcome with ourassumed theoretical structure. Panel B indicates that we nearlyreproduce the monotonic increase in composition across time but wehave difficulty reproducing the non-monotonic increase of forest edge.

Given the assumed theoretical structure we can also interpret thesigns of our calibrated parameters. Median preference parameters arerevealed positive, indicating that the productive aspects of thelandscape these parameters represent enter positively in utility. Themarginal direction of effect of these parameters on percent forest andforest edge metrics is summarized later in Table 4. The medianexternality parameters are positive, indicating that there are costreducing externalities associated with proximate agricultural produc-tion and timber cutting. Similarly, the estimates for γe,aes are positive,indicating positive externalities may exist for the non-pecuniary utilityderived from the presence of contiguous forests. Finally, the medianslope parameter is greater than zero. Given the way slope enters thetechnology Eq. (A.2), this indicates that higher slope is associated withreduced agricultural and timberharvesting landproductivity andutility.This echoes earlier work by Mokma and Sietz (1992). Importantly, thissuitability parameter only reflects to role of slope, for which we havetime series data for all agents' cells. The other suitability drivers, inparticular soil, are present but are underlying and endogenous dynamicmodel processes. Because we have no disaggregated time series sourcedata for these drivers, we cannot calibrate suitability parameters forthem individually. Nevertheless these drivers do impact agents'decisions though the assumed production structure and their effect onproductivity and therefore expected returns.

6.2. Assessments of Predictive Performance

6.2.1. Comparative StaticsTable 4 Panel A results describe simulation experiments perturbing

the parameters obtained when calibrating toward the percent forest

target. Other simulations not reported perturb the parameters obtainedfrom targeting the edge and weighted average targets, and the resultsare comparable. The results indicate that as we increase the preferencefor farming fromzero, there is a decreasing amount of forest on the1993landscape and it becomesmore contiguous. As a result of this parameterchangewe observe a 24% decrease in the amount of forest and a decreaseof almost 130,000 m of forest edge. This is consistent with Hosier, 1988and others citing that agricultural land-use, and a preference for this, ispositively related to deforestation.

Panel B describes the effect of varying the agents' preferences forgrowing trees from zero. As we increase the preference forreforestation we observe a 13% increase in the amount of forest andan increase of roughly 350,000 m of forest edge. This indicates thathigher reforestation preferences lead to more forest on the landscape,but forest that becomes spatially distributed.

Panel C describes the effect of increasing the strength of theagricultural externality parameter from zero. We observe a 2% decreasein percent forest and a decrease of 64,500 m of forest patch edge on thelandscape in this case. This indicates that promoting agriculture viaexternality-based incentives will slightly reduce forest cover and forestedge, and that this approach will have the smallest effect compared toour other alternatives.

Panel D describes the effect of varying the forest externalityparameter that is associated with spatially proximate forest. Weobserve that increasing the strength of the tree harvesting/growingspatial externality from zero leads to a 7% increase in the amount offorest cover. At the same time this leads to an increase in the forestpatch edge of 295,000 m. This implies again that forest cover on the


landscape can be increased, but as this happens the resulting forestmay be non-contiguous.

Finally, Panel E describes the effect of varying the strengthof the landslope effect for agricultural and timber output.We observe a 5% decreasein the amount of forest cover and a 103,100 meter increase in theamount of forest edge as the role of suitability is increased from zero.This is counter-intuitive, but is produced by agents being forced to seekout the most suitable land for agriculture, and removing any treespresent, since un-forested but less suitable land is no longer profitable.

In summary, variations in all parameters produced reorganizationsof the landscape. The largest effects are produced by variations in thepreference parameters, followed by the forest externality parameters,the slope/suitability parameters, and lastly by the agriculturalexternality parameter. This suggests preference effects appear atleast as important as suitability influences.

6.2.2. Homogeneity CounterfactualThe lower part of Table 4 provides the results from the assumed

homogeneity simulation. We observe large variations in the compo-sition and pattern measures, as well as substantial increases inprediction error. These results suggest the assumption of homoge-

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Alpha_farmmedian = 176.1

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Slope Dependencemedian = 91.0

Fig. 1. Histograms of by-parcel calibrated parameters and Null_R2s target

neous agents is far from innocuous, and this supports our assumptionof heterogeneous agents.

Finally, as further evidence regarding the importance of hetero-geneity, Fig. 1 provides histograms of the by-parcel calibratedparameters and Null_R2s to give a sense of the revealed across-parcelheterogeneity. The figure reports results for the most accuratecalibration version, targeting percent forest only. In general, thisfigure indicates that in order for our model to most accuratelyreproduce each parcel's sequence of land-use change, agents requireparcel-specific parameters. Although performing across-agent com-parisons would be statistically inappropriate, the histograms indicateheterogeneity is important and may account for the error increasesprovided by the homogeneous agent simulations.

6.2.3. Alternative Accuracy AssessmentsTable 5 reports values for predictionmatrix measures. The producer

and user statistics indicate ourmodel is better at predicting agriculturalthan forest (0.69 versus 0.43 and 0.65 versus 0.46 respectively),although the measures differ by only a small amount. The averageaccuracy is moderate at 0.59, and exceeds the values reported in manyearlier studies. Considering that only 73 of the 190 agents are actually

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Externality_farmmedian = 131.8

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ing Percent Forest when comparing actual and simulated landscapes.

Table 5Alternate accuracy assessments.

Land use category Producer accuracy User accuracy

Agriculture/pasture 0.69 0.65Forest 0.43 0.46Average accuracy 0.59κ 0.12


calibrated, this indicates that the median parameters have some abilityto generalize to other agents where we may have little information.Finally, the kappa value of 0.12 is quite low. However it is alsocomparable, but lower, to the values reported in earlier work.

In summary, using pseudo R2 or the prediction matrix and relatedstatistics suggests the model's overall predictive performance ismoderate to good. The model is best able to predict agriculture, andslightly less able to predict forest. Importantly, the alternative accuracyassessment values reported are comparable to those reported in otherstudies of other areas, in particular to those of Nelson and Hellerstein(1997).

6.3. Management Simulations

Our last set of agent-based simulations compares the ability of thiscalibrated model to inform us about the potential effects of policymanipulations in the presence of agent heterogeneity. Although themenu of policies available to managers is broad, here we focus on asmall set of five options that can be represented with parameterperturbations from our comparative statics described in Table 4. Ourchosen policy goal is to achieve the conflicting outcomes of moreforest cover with little or no more forest edge; in other words thelarge contiguous forest described by McGarigal and Cushman (2002).We first describe the effects of strong single-policy manipulations.Then we investigate whether a weaker management strategy mayexist that uses smaller but simultaneous parameter perturbations toachieve the same goal.

Policy 1 is described as an agricultural production disincentive andis implemented by multiplying αfarm×0.5, effectively halving theutility one derives from agricultural income. Since the benefit fromagriculture in this setting is purely monetary, reducing αfarm can beinterpreted as an agricultural output tax disincentive. This policyslightly increases the amount of forest cover and the edge associatedwith forest patches. Policy 2 is described as a reforestation incentiveand is implemented by multiplying αaes×2.0, effectively increasingthe utility from forest. Given the dual monetary and non-monetarynature assumed for forest, one can either think of this as a policydesigned to promote the social norm of reforestation, or simplyreflecting payments to individual agents who chose to reforest. Thispolicy also results in slightly more forest and associated edge. Policy 3is described as a Pigouvian forest policy which is implemented bymultiplying γext tree×2.0, effectively doubling the tree growing andtree harvesting utility from forest externalities. This is akin to aPigouvian credit for pursuing similar and proximate forest uses. Thispolicy results in the largest increase in forest cover, and at the sametime we see the largest increase in forest patch edge. More forestresults from the increased aesthetic benefit at proximate forest sites,while more edge results from the fact that the parameter also appliesto proximate timber harvesting resulting in less forest around harvestsites; the net effect is more but patchier forest. Policy 4 is described asan input tax and is implemented by multiplying γslope×2.0, effectivelydoubling the cost-increasing effect of poor land suitability. An inputtax can be thought of as a tax that binds when purchasing largeamounts of inputs. In the field the typical response to poor landsuitability, such as steep slope, is to purchase additional inputs inorder to enhance productivity. In this case, increasing γslope is akin toincreasing the cost of productivity-enhancing inputs, thereby raising

marginal costs and the importance of slope. Intuitively this shouldcause agents to employ only the most suitable land for each purpose.This policy (akin to a fertilizer nitrate directive) slightly reduces cover,and substantially reduces forest edge.

Our final policy manipulation Policy 5, reported at the bottom ofTable 4, attempts to adapt from the previous simulations in order toidentify a weaker multi-policy manipulation that can achieve oursame goal. Earlier we observed that the Pigouvian forest externalitypolicy produces the largest increase in forest cover, but at the cost oftoo much edge, while, the input tax has essentially no effect on forestcover, but substantially reduces edge. Combining weaker versionsof these policies, implemented by multiplying γext tree×1.5 andγslope×1.5, we observe the largest increase in forest cover; in factmore reforestation than either policy in isolation. This also predictsthe smallest increase in forest edge.

7. Discussion

We set out to achieve three primary objectives with our micro-level approach to this land-use problem. First, our methodologicalobjective was to construct and calibrate an individual householdagent-based variant of a portfolio theory model of land-useintegrating suitability, preference and externality features and adiversity of geophysical, socioeconomic, and political data. Second,our quantitative objective was to perform comparative statics withour calibrated model in order to answer our research question: whatare the relative influences of suitability, preferences for land-use, andexternalities for predicting the diversity of land-uses observation?Our final policy objective was to address a research questioninvestigating the effectiveness of policy by simulating the extent towhich heterogeneous preferences or spatial effects mitigate ormagnify land-use response to management policy.

First, our calibrated agent-based simulations produce dynamicsconsistent with landscape-level stylized facts describing Indiana. Atthe aggregate level we do predict the gradual trend of reforestationduring our sample period. However, all of our simulations underes-timate the total extent of reforestation. This is because we can onlycalibrate a subset of the agents on the landscape, and we impose themedian of calibrated parameters to those agents with insufficientvariation. This essentially gives agents who may have had preferencesfor no change, preferences to produce some change. Second, we haddifficulty reproducing the other regularity, the non-monotonicevolution of forest edge as forest monotonically increases. Impor-tantly, our model reproduces the diversity of uses observation for ourarea, and elements critical for this prediction includes heterogeneousagents' land-use preferences and spatial interactions. Thus, our resultsalso demonstrate support for the diversification hypothesis that iscentral to portfolio theory. That is, none of our agents produces asingle output portfolio.

The primary result of our agent-based simulations is theobservation that land owners' heterogeneous preferences appear atleast as important as variations in land suitability and perceivedexternalities in accounting for land-use decisions and the organizationof the landscape. We employ a numerical comparative staticstechnique which applies equal percentage perturbations to theagents' calibrated parameters in order to observe the marginalchanges on the landscape. This analysis finds that preferenceparameter changes produce 3 to 5 times larger landscape level effectscompared to changes in the agent's calibrated suitability parameters;and 2 to 8 times larger effects compared to externality parameterchanges. This suggests that the diversity of uses observation may berelated to subjective preferences for particular land-uses. Regardingspecific drivers of land-use we observed that the majority of agents'calibrated externality parameters are revealed to positively influencetheir likelihood of pursuing proximate agricultural, timber harvesting,or reforestation activities; this indicates agglomeration bonuses are


more common than costs. Also, for most parcels land slope is observedto reduce the likelihood of pursuing agricultural or timber harvestinguses.

Calibrated parameters and pseudo R2s showed differencesdepending upon which metric is used as a basis to measure modelpredictive accuracy. This suggests that if one seeks a comprehensiveaccount of landscape dynamics, researchers should consider at leastthese two metric classes when summarizing the landscape. Next, theassumption of homogeneous agents was observed to producesignificantly larger prediction errors in simulations. And finally, animportant policy implication of this work is that a manager may beable to harness revealed heterogeneities and spatial interactions inorder to design more effective location specific policy. We observedthat a weak composite policy tool, integrating an input tax andPigouvian externality reforestation credit, proved more effective thanstrong versions of any other policy in isolation.

As with many other studies, these particular results should beviewed with caution. First, although the selection of study area andchoice of land-use drivers attempted to reduce the effects ofunobserved variation, this problem can never be fully eliminatedfrom studies inferring unobserved characteristics from observedactions. As a result we do not focus on econometric features, butrather general landscape interaction effects. Possible sources ofunobserved variation that may be affecting our preference parametersinclude other household demographic features, ownership dynamics,and marginal production cost differences. Second, we chose aparticularly simple theoretical structure for agents' land-use andproduction problems to ensure unique solutions for each agent andtime period. Although this structure is not exactly accurate, thedescriptiveness of the model was nevertheless quite good. Third, wemade a number of other assumptions regarding the spatial structureof the landscape, namely that ownership boundaries remained staticand calibrated preference parameters remained constant over theentire time sample. These assumptions are also not exactly accurate.However, they do not overly detract from our basic conclusions. Giventhese limitations, a weaker statement of our results would be thatpreferences combinedwith other sources of unobserved variation are atleast as important as land suitability features for predicting land-use forthe potential multiple owners of individual parcels in our area and timesample. Importantly, although this implies our resultsmay beweaker, itdoes not detract from our main hypothesis that suitability features tellan incomplete story about land-use and that heterogeneous preferencesand perceived spatial effects appear to account for this limitation.

A final comment concerns the potential for future work. In thisanalysis we assumed that agents employ utility maximizationdecision making. However, it may be the case that a non-deductivedecision making assumption may be more descriptive. Future workcompares alternative inductive decision strategies to the maximiza-tion approach for the same Indiana study area and for an abstractspatially-explicit land-use laboratory experiment.

Acknowledgements

The authors would like to thank Jerome Busemeyer, JamesWalker,Elinor Ostrom, the seminar participants at IUPUI and UtrechtUniversity for helpful comments, and National Science FoundationNSF: SES008351 for financial support.

Appendix A. Theoretical Structure of Agents'Constrained-optimization Labor Allocation

Output

In calculating their labor allocation, agents first consider theproduction relationship between land and labor inputs and the outputproduced. Similar to Benjamin, 1992 and many others, a Cobb–

Douglas production function is used as an approximate description ofthe historical production environment facing owners. The parcel orcell output generated by applying labor L and land M is:

Yi = Ai⋅Lβi ⋅Μ

βi : ðA:1Þ

In Eq. (A.1), β=0.5 and Yi can be Yfarm, Ytree, Yfallow, Yaes and Yoff farmwhich are respectively, crop output, timber output, fallowed land, theoutput of aesthetic forest amenity, and the supply of non-agricultural‘output’. Li includes Lfarm, Ltree, Laes, Loff farm, which represent the hoursof labor devoted to farming, tree harvesting, tree growing, or off farmwage activities. Similarly,Mi includesMfarm,Mfallow, andMtree inclusiveof (Maes, Mtree), which is the amount of land available for farming,fallow, or forest classification. The values for the Ys, Ls, and Ms are allsimulation outputs of the model. Note the off farm productionfunction has one input, labor, with a coefficient and technologyparameter of 1.

Technology

In Eq. (A.1) the Ais are composites of several indices representingdynamic productivity enhancing inputs, and will be referred to as‘technology’ for simplicity. As shown in Eq. (A.2), these As incorporateboth endogenous and exogenous biophysical aspects of the environ-ment, and variables with subscript t evolve across time and withagents' previous land-use decisions. The dynamic endogeneitiesrepresented by these variables preclude a present value equilibriumsolution given the many potential interacting spatial configurationson the landscape. The ability to model such interactions is a keybenefit of the agent-based approach. Based upon the land-use andcover change literature we posit the general functional relationships:

Afarm; t = soilt = 1 + γslope⋅slope� �

Αtree;t = aget⋅pcovertð Þ= 1 + γslope⋅slope� �h i

Αaes;t = aget⋅ 1 + pcovertð Þ⋅γaes⋅exaes½ �:ðA:2Þ

In Afarm, soilt is a soil quality index that lies between 0 and 1 foreach cell on the parcel. Since soil appears in the numerator of Afarm ahigher index value for soil implies higher productivity and thereforemore output for a given cell, and it evolves endogenously with respectto a simulated agent's land-use decisions. Based upon the landscapeecology literature, we assume that soil quality regenerates fromallowing forest re-growth or fallowing and degrades based upon thelength of time a particular cell of land has been under farming usage inthe absence of any other inputs Lal (2003). Erosion research suggeststhat in the absence of other inputs there is a negative relationshipbetween a cell's surface slope and agricultural output Mokma andSietz (1992). Therefore, (1+γslope·slope) is present in the denomi-nator of the agricultural technology variable, and γslope represents anagent's belief about the extent to which slope affects productivity.slope is based on actual topographical data and is normalized between0 (flat) and 1 (landscape maximum).

For the timber harvesting technology, the expression Atree includesthe forest stand aget, normalized to [0,1] by assuming a maximumstand age of 50 years. Given limited historical data for tree ages in ourstudy area, we assumed that initial ages are common for eachsimulation and are randomly distributed about the recorded 1940mean age of 20 years. Next, pcovert represents a binary variable takinga value of 1 if trees of at least the minimum harvest age of twentyyears are present on a cell or 0 otherwise. The variable also enters thenumerator implying that if tree cover is present timber output may bepositive on a cell; otherwise timber output will be zero. (1+γslope·slope) also enters this expression and indicates that eachagent perceives a relationship between timber output and the slope

1 Chicago Board of Trade (CBOT), Bureau of Labor Statistics (BLS), and Departmentof Agriculture (DOA).


of the land; with γslope again representing the perceived strength ofthis effect.

Next, the most complex technology variable is Aaes whichrepresents several pecuniary and non-pecuniary factors which definethe incentive for growing trees. For non-pecuniary factors, survey datasuggest that the level of aesthetic enjoyment or output a forested cellyields is important. Furthermore, this output is increasing in thecurrent aget of the trees, i.e. people prefer larger, older trees. Similarly,previous work suggests aesthetic pleasure is increasing in the forestcover level. As a result, aget and (1+pcovert) both enter with apositive effect. This term also captures the effect that agents derivesome minimum amount of utility from immature forest, i.e., ifpcovert=0. Finally, the presence of exaes implies that the aestheticoutput generated by a forested cell surrounded by other forested cellswill differ from the output that that cell would generate in isolation.Note that all other externality effects are introduced as productioncost externalities in the Eq. (A.3) function. However, since we do notinclude a direct cost function for tree growing, the externality effectneeds to be introduced here. This variable is normalized to liebetween 0 and 1, with 1 indicating that the current cell is surroundedby the maximum of 4 directly adjacent (non-diagonal) similarlyforested cells. This lattice variable is a composite of a weights matrixwhich takes a value of 1 for adjacent cells, zero otherwise, and a useindicator which equals one for similar uses of a neighboring cell, zerootherwise. γe,aes is a parameter describing the agent's subjectiveperception regarding the strength, and sign, of this aestheticexternality effect. If this parameter is positive it implies that theaesthetic output from contiguous forest will be larger than that from adispersed forest. The notion that externalities are generated byproximate contiguous forest is supported by research demonstratingthe effects of forest fragmentation for wildlife McGarigal and Cush-man (2002). Finally, the technology for fallow, Afallow, and off farmlabor, Aoff farm, is constant across all agents, and since they are not afocus of this work they are not discussed.

Costs and Externalities

We next assume that agents are aware of the simple linear costfunctions associatedwith their production activities.We focus only onmarginal operating and externality costs since fixed setup costs in ourstudy area had mostly been incurred 40 to 90 years prior to oursample at farm inception. Marginal operating costs represent materialinputs such as fuel, seeds, and transport. Since we do not havehistorical data on these farmers' marginal costs, we simply assumethey receive a margin of 20% over costs which, given our field pricedata, makes marginal cost 80% of the per unit price. This is, of course, asubjective choice and any heterogeneities in marginal costs acrossfarms may be picked up as heterogeneities in our estimatedpreference parameters. However, we believe this is a reasonablesimplification given no documentation of marginal cost differencesacross farms in this 100 km2 area.

Rashford et al. (2003) also suggest there may be positive marginalcost externalities across parcels due to equipment and infrastructuresharing, land renting, sharecropping, and greater access to physicaland financial support in agricultural clusters. Others documentnegative externalities related to mutually exclusive productiontechniques such as chemical spraying on traditional farms that areproximate to organic producers. We argue that such externalityeffects occur within and across agents' parcels among groups of cellsand make no restrictions about the sign of effect. For the activitiesi= farm or tree harvesting, we have a common total cost function withci representing marginal operating cost of production and exi thespatial spillovers.

Ci = ci−γi⋅exið Þ⋅Yi ðA:3Þ

The lattice variable exi ranges from 0 (no adjacent similar use cells)to 1 (the maximum of 4 adjacent same use cells) and represents thealtered marginal cost of production obtained if one pursues similaractivities in proximity to one another. γi represents agents' constantperceived sign and strength of these effects; positive indicatesagglomeration bonus while negative indicates agglomeration cost.

Pecuniary Utility

Output price indices, off farm labor wages, and fallowing subsidypayments are based on CBOT, BLS, and DOA field data.1 Also, researchindicating that commodity prices follow a random walk Deaton andLaroque (1992) allow us to define expectations of output prices orwages as pet,i=pt−1,i. Commodity prices are equal weighted indicesfor the timber or crop species relevant to the study area, see Section 4.Dropping the agent subscript k for clarity we can then write thepreference-weighted, expected profit for use i summing across cells jas,

πet;i = pet;i⋅Yt;i−Ct;i ct;i; ext;i;Yt;i

� �+ e−ρ⋅ T−tð Þ⋅πe

T;i′ YT;i′ A

T;i′ ;MT;i′ ; LT ;i′� �

; peT;i′� ��

ðA:4Þ

πeT ;i′ = peT;i′ ⋅YT ;i′−C

T ;i′ cT;i′ ; exT ;i′ ;YT;i′

� �ðA:5Þ

Uet = ∑

5

i=1αi⋅ πe

t;i−RA⋅σ2π π2

t;i pet;i;Y2t;i

� �� : ðA:6Þ

In Eq. (A.4) total costs are shown to be a function of marginal costs,externality effects and output. The last part of Eq. (A.4) representseither: the forward looking farming value of harvesting timber oncurrently forested cell in order to farm it in one year (T− t=1); or thefuture timber harvest value of converting a currently farm or fallowcell to forest and discounting for the time it takes to reach itsminimum harvest age (T− t=20), see Hosier (1988). These forwardlooking opportunity costs or alternative payoffs are explicitly definedin Eq. (A.5). Importantly, the agent reevaluates any reforestationdecision each year until the harvest date. e−ρ(T− t) represents theprofit discount factor for the years remaining before forest is farmableor timber on farmland has reached its minimum harvesting age. Thenotation πeT.i′ represents the fact that profit for alternative usage i′ isexpected to be realized at a future date T, conditional upon takingaction i at time t; this structure allows forward looking opportunitycosts to influence current decisions. Eq. (A.6) indicates that pecuniaryprofits are then scaled by the preference weights α and the riskassociated with an activity in order to form utility, and further that anagents' total utility from their portfolio is the sum of preference andrisk scaled utilities for all activities i. Importantly, risk is a function ofcommodity price variance and squared profits, the latter being afunction of squared output, which is defined at Eq. (A.1), and isultimately a function of the labor allocated to an activity.

Lastly, the across use covariance terms for alternative uses withinσ are assumed to be zero, only variances are considered. We believethis to be a reasonable assumption, in contrast to the Blank (2001)structure, due to the broad definition of crop versus timber versussubsidy versus off farm alternative land and labor uses. While covariances among wheat and soy prices may be non-zero, co variancesamong crop and timber indices more likely reflect low or no covariation.


Appendix B. Uniqueness of Agents' Constrained Optimization Labor Allocation Solution

The excerpt fromMathematica code below indicates that, using the theoretical structure described in Appendix A and summarized in Eq. (2)Lagrangian combined with the median parameter values from the calibrated model reported in Table 2, that the principal minor determinants ofthe bordered Hessian representing this problem alternate positive and negative. Line 136 describes the determinant of the 2×2 subset of the 5×5bordered Hessian being less than zero. Line 138 describes the determinant of the 3×3 subset of the 5×5 bordered Hessian being greater thanzero. Line 140 describes the determinant of the 4×4 subset of the 5×5 bordered Hessian being less than zero. Finally, line 141 indicates that thedeterminant of the full 5×5 bordered Hessian is greater than zero. These results indicate the identification of a regular maximum for the agents'decision problem for this representative parameterization.

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