A Spatial Econometric Analysis of Land-Use 

Change With Land Cover Trends Data: An 

Application to the Pacific Northwest

David J. Lewis and Ralph J. Alig

DEPAR TMENT OF AGRICULT URE

United States Department of Agriculture

Forest 

Service

Pacific Northwest 

Research Station

Research Paper

PNW-RP-600 

September 

2014
Authors

David J. Lewis is an associate professor, Department of Applied Economics, 

Oregon State University, 200A Ballard Ext. Hall, Corvallis, OR 97331; Ralph 

J. Alig is a research forester emeritus, U.S. Department of Agriculture, Forest 

Service, Pacific Northwest Research Station, 3200 SW Jefferson Way, Corvallis, 

OR 97331.

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Abstract

Lewis, David J.; Alig, Ralph J. 2014. A spatial econometric analysis of land-use 

change with land cover trends data: an application to the Pacific Northwest. 

Res. Pap. PNW-RP-600 Portland, OR: U.S. Department of Agriculture, Forest 

Service, Pacific Northwest Research Station. 44 p.

This paper develops a plot-level spatial econometric land-use model and estimates 

it with U.S. Geological Survey Land Cover Trends (LCT) geographic information 

system panel data for the western halves of the states of Oregon and Washington. 

The discrete-choice framework we use models plot-scale choices of the three 

dominant land uses in this region: forest, agriculture, and urban development. 

The results provide a technical foundation for developing larger scale models 

from the LCT database. In particular, we develop a random-effects estimation 

method for dealing with the spatially clustered sample design underlying the 

LCT. We also exploit the increased spatial information content available in the 

LCT by exploring the estimation of a fully spatial multinomial discrete-choice 

land-use model by including measures of land-use agglomeration economies as 

independent variables in estimation. Estimation of the spatial econometric model 

includes a novel combination of panel-data random parameters logit estimation 

with instrumental variables implemented within the recently developed control 

function approach. The estimated econometric model is used to project landscape 

change in the presence of alternative assumptions regarding future urban returns. 

Our results indicate that variation in urban returns on the order of what was 

experienced in the housing boom and bust of the 2000s generates a wide range of 

predicted future land-use shares in developed uses. The Puget Lowland ecoregion 

has by far the most sensitive landscape projections in response to wide swings in 

urban returns.

Keywords: Land use, spatial modeling, econometric, resource economics, 

land development.
Summary

Empirical models of land-use change have long been used in environmental and 

resource economics for policy analysis of the effects of land-use change on the 

forest land base, including analyses of urban sprawl and ecosystem services. This 

paper estimates a new regional-level econometric land-use model at the plot scale 

from the U.S. Geological Survey’s Land Cover Trends (LCT) database, a spatially 

detailed panel dataset covering the contiguous 48 states. The model is estimated 

for the western halves of the states of Oregon and Washington from 1980 to 

2000 and focuses on transitions among the three major land uses in the region: 

forest, agriculture, and urban development. The empirical data used to condition 

plot-level probabilities of land-use transition include county-level measures of net 

returns to land and plot-level measures of soil quality, distance to cities and roads, 

and measures of land-use agglomeration economies. The inclusion of detailed 

spatial independent variables provides an advance over prior large-scale models 

estimated from land-use surveys that do not disclose the exact location of surveyed land plots. We provide several novel additions to the empirical economics 

literature on land use, including (1) a method for dealing with the clustered sampling strategy implicit in the LCT design, (2) an approach for estimating spatial 

econometric discrete-choice model in a multinomial setting, and (3) providing 

empirically based land-use projections for the Pacific Northwest under alternative 

assumptions regarding the level of future returns to urban development. The model 

development also provides a technical foundation for developing future nationalscale model econometric models from the LCT data.
Contents

1 Introduction

4 Land Use Modeling by the USDA Forest Service

5 Basic Econometric Framework and Database Construction

5 Conceptual Model

6 Land-Use Dataset Used for Estimation

9 Sampling of Plots for Estimation

9 Comparing Development Probabilities Across the LCT and NRI

11 Data for Independent Variables Used in Econometric Estimation

13 Accounting for the LCT’s Clustered Landscape Block Sampling Strategy

16 Estimation Technique—Maximum Simulated Likelihood

18	 Alternative Specifications and Parameter Estimates

18 Model 1: Base Random Parameters Logit (RPL)

20 Model 2: RPL With Agglomeration Economies

21 Identification Strategy With Agglomeration Economies

23 Evaluating the Instruments in the Control Function Approach

25 Model 2 Results

25 Marginal Effects

34	 Landscape Projections and Out-of-Sample Forecast Test

38 Conclusion and Suggestions for Future Research

42 References

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A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

Introduction

Plot-level empirical land-use models are widely used in environmental and resource 

economics for policy analysis of the effects of land-use change on urban sprawl, forest land loss, ecosystem services, and biological diversity. Many of these analyses 

can be classified according to the scale with which they are estimated and applied. 

The first category can be labeled small-scale models and are generally estimated at 

the scale of a single county or smaller (e.g., Butsic et al. 2011, Irwin and Bockstael 

2002, Lewis et al. 2009, Newburn et al. 2006, Towe et al. 2008). These studies are 

typically estimated from parcel map data provided by local or regional planning or 

assessor authorities. The strength of these studies is their being extremely detailed 

in their spatial information content; their weakness is that their small scale limits 

any broader applicability. The second category can be labeled large-scale models, 

and includes land-use models that are estimated at regional (e.g., multistate) or 

national levels (e.g., Langpap and Wu 2011, Lewis and Plantinga 2007, Lubowski et 

al. 2006). These studies are typically estimated from land-use surveys such as the 

U.S. Department of Agriculture (USDA) National Resources Inventory (NRI) or 

Forest Inventory and Analysis (FIA) conducted by the USDA Forest Service. Largescale models have the strength of being much more broadly applicable with the ability to analyze larger scale environmental problems and policies. The weakness of 

large-scale models is the lack of detail in their information content, which leads to a 

spatial specificity that is generally far inferior to small-scale models. This weakness 

is particularly important for large-scale analyses of the many environmental goods 

whose provision depends on fine-scale spatial patterns.

The purpose of this paper is to improve on the specification of large-scale 

land-use models by developing a multistate empirical land-use model from a 

publicly available spatial panel dataset that has far more spatial information than 

land-use surveys such as the NRI or FIA. The discrete-choice framework we use 

models plot-scale choices of the three dominant land uses in the western half of the 

Pacific Northwest: forest, agriculture, and urban development. The model is estimated for the western halves of the states of Oregon and Washington using micro 

spatial panel data from the U.S. Geological Survey (USGS) Land Cover Trends 

(LCT) dataset from 1980 to 2000. The LCT dataset includes four snapshots of the 

landscape, corresponding to three separate land-use transition periods. The study 

region includes two states with large urban centers (e.g., Seattle, Portland, etc.) and 

significant amounts of undeveloped agricultural and forest land. The empirical data 

used to construct independent variables include plot-level measures of soil quality, 

distance to cities and roads, and measures of land-use agglomeration economies. 

The data also include temporal variation in county-level measures of the net returns 

of an acre (hectare) of land to urban, agricultural, and forest uses of land.
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RESEARCH PAPER PNW-RP-600

The inclusion of spatial independent variables representing the distance of plots 

from cities and roads has been absent in many large-scale plot-level econometric 

analyses of land-use change. This absence has been driven by the fact that the 

national land-use surveys—such as the NRI—do not disclose the exact location 

of sample plots. However, the LCT provides an alternative land-use dataset to the 

NRI that potentially can be used as the basis for a national-scale econometric model 

similar to Lubowski et al.’s (2006) NRI-based model. The LCT is a nationwide 

geographic information system (GIS) panel database derived from manually edited 

satellite images, aerial photography, and topographic maps. A primary advantage of 

the LCT over the NRI is the spatial information content—the exact location of plots 

can be observed and corresponding information can be included as independent 

variables in econometric estimation. Further, while land use/land cover datasets 

derived from automated interpretation of satellite imagery have been found to 

underrepresent low-density development (Irwin and Bockstael 2007, Kline et al. 

2009), we provide a comparison of urban development probabilities generated from 

the LCT and NRI that suggests minimal differences for this region. Similar to many 

land-use analyses, we use the LCT’s Anderson level I land cover classification as a 

good proxy for land use.

Using the LCT for estimation brings up multiple research possibilities and 

challenges that do not arise in models estimated from land-use surveys. First, 

unlike the NRI, the LCT does not provide a random sample of plots within counties. Rather the LCT provides a time-series of GIS 10- by 10-km maps randomly 

sampled within U.S. ecoregions, and we sample plots within each LCT block for a 

computationally feasible estimation. However, as we show formally, this process 

generates spatial correlation in the model unobservables—plots within a block will 

be affected by a different set of unobservables than plots from a separate block. 

Second, the observation of land use within each block brings up the possibility 

of estimating a fully spatial model that includes variables representing spatial 

externalities induced by neighboring land use. For example, Irwin and Bockstael 

(2002) found evidence of negative spatial externalities resulting from urban land on 

the development probability of neighboring lands, while Lewis et al. (2011) found 

evidence of positive spatial externalities resulting from organic dairy farms on 

the decision of neighboring conventional farmers to convert to organic. These two 

papers are binary models with only two land-use choices. A primary challenge is 

how to estimate similar spatial effects in a multinomial discrete-choice model of 

three land-use choices when the spatial lag is endogenous.

The econometric analysis in this paper features several novel additions to the 

empirical economics literature on land use. First, we develop the first large-scale 

econometric land-use change model estimated from the LCT and explore a method 
3

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

for dealing with the LCT’s clustered sampling properties in estimation. The method 

amounts to including landscape block random effects in a random parameters logit 

(RPL) framework that accounts for spatially correlated unobservables induced by 

the LCT’s sampling strategy. We provide Monte Carlo evidence on the method’s 

ability to yield consistent parameter estimates. Accounting for landscape-block 

unobservables with a random effect is preferred to fixed effects in our nonlinear 

model because fixed effects would generate inconsistent estimates owing to the 

incidental parameters problem.

Second, we develop a novel approach for estimating a full spatial econometric 

discrete-choice land-use model in a multinomial setting that is estimable with 

standard maximum simulated likelihood techniques. In addition to modeling 

spatially correlated unobservables, the spatial properties of the model include a 

type of spatial lag—the inclusion of the share of a plot’s neighboring landscape in 

various land uses—as a way to explicitly model and test for spatial agglomeration 

economies in land-use change. Our approach accounts for the endogeneity of the 

spatial lag with the recently developed control function approach for including 

instruments in multinomial discrete-choice models (see Train 2009: chap. 13). We 

use exogenous land-quality indexes at the landscape-block level for instruments. To 

date, fully spatial multinomial discrete-choice econometric models have been little 

used owing to computational constraints (see LeSage and Pace 2009). However, the 

combination of the LCT’s clustered sample of discrete landscape blocks, along with 

panel data and control-function RPL techniques, provides an alternative framework 

for incorporating both a spatial lag and spatial errors.

Third, we use the estimated land-use econometric model to provide empirically 

based landscape projections for the Pacific Northwest under alternative assumptions regarding the level of future urban returns. The landscape projections indicate 

substantial urban growth and loss of forest and farmlands in the Puget Lowland and 

Willamette Valley ecoregions, with minimal changes in the Coast Range, Cascades, 

and North Cascades regions. Our results demonstrate that landscape projections in 

the Puget Lowland ecoregion are extremely sensitive to the assumed level of future 

urban returns that was witnessed in the decade of the 2000s. In particular, the 

share of the Puget Lowland ecoregion projected to be developed is between 12 and 

14 percentage points higher if the level of real urban returns remains at the levels 

observed in 2006 as compared to if real urban returns remain at the more modest 

levels observed in 2012. Variation in the projected development share of the Puget 

Lowland ecoregion between 12 and 14 percentage points presents major challenges 

for managing a landscape for ecosystem service provision, as 12 percent of a 1.8 

million ha region is approximately 0.2 million ha of land.
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RESEARCH PAPER PNW-RP-600

Finally, this analysis serves as a pilot study for the potential creation of a 

national-scale econometric land-use model based on LCT data. The Forest Service 

extensively used Lubowski et al.’s (2006) NRI-based national model for Resource 

Planning Assessment (RPA) and climate change analyses. However, changes in the 

NRI sampling scheme after 1997 has created a need for a new data source for future 

national-scale models. This paper develops the technical foundation necessary to 

estimate a large-scale econometric land-use model with LCT data.

Land-Use Modeling by the USDA Forest Service

The Forest Service (e.g., Adams and Haynes 2007) has conducted national and 

regional assessments of the forest and rangeland land base for many decades. A 

land-base assessment (e.g., Alig et al. 2010) is a key part of such natural resource 

assessments, given the importance of land and land-use changes for forest and 

agricultural products, living space, and ecosystem services provided by forest 

ecosystems. With a broad range of economic, ecological, and biophysical phenomena of interest in such assessments, considerable uncertainty exists about future 

projections of outcomes, particularly projections that look forward 50 years with the 

added pressures of climate change. Past land-base assessments by the Forest Service 

have typically focused on one “business-as-usual” future, although there have been 

variations in this approach in analyzing additional scenarios. For example, varying 

assumptions about future population have been used to create high, medium, and 

low trajectories of supply and demand. Now with the growing interest in markets 

for carbon as an ecosystem service, analysts can compare results to those of other 

studies that explicitly include carbon price scenarios (e.g., Alig et al. 2010).

Land-base assessments provide information that can help shape perceptions 

about whether we can sustain both increasing consumption of forest products, forest 

resource conditions, and ecosystem services, and how to best adapt to and mitigate 

climate change. Related data illustrate the dynamics of our Nation’s land base and 

how adjustments are likely to continue in the future. Land-use change projectons 

can also provide inputs into a larger system of models that project forest resource 

conditions and harvests, wildlife habitat, climate change, and other natural resource 

conditions. Current debates about sustainability and concerns about climate change 

involve both physical notions of sustainability and competing socioeconomic goals 

for public and private land management. The fixed land base necessitates viewing 

“sustainability” across the entire land base and across sectors.

Methods and data sources used in land-base assessments have changed materially over the last several decades. In general, since around 1980, land-use projections have moved from reliance on expert opinions (e.g., Wall 1981) to systematic 
5

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

models involving systems of land-use equations. Early land-use models relied on 

FIA data (e.g., Alig 1986), with initial models estimated for the Southern United 

States, which has a significant amount of the Nation’s private timberland as well as 

some of the larger forestry datasets. The first cross section of NRI data was used to 

create urban-area models (Alig and Healy 1987) for use in land-base assessments. 

Panels of NRI data were later used to create subsequent land-use models used in 

RPAs (e.g., Alig and Plantinga 2004, Alig et al. 2010). With the availability of spatial or georeferenced data, models were developed at a regional or subregional level 

(e.g., Kline and Alig 2005; Kline et al. 2003) to complement larger scale aspatial 

land-use models, especially to help improve finer scale ecological investigations 

(e.g., Lewis and Plantinga 2007). In addition, other analyses by the Forest Service 

and others used U.S. Census Bureau data on housing densities combined with 

spatial land cover data (e.g., National Land Cover Database) at a watershed level to 

investigate pressures on U.S. private forests from housing developments, referred to 

as “Forests on the Edge” studies (e.g., Stein et al. 2005).

Basic Econometric Framework and 

Database Construction

Conceptual Model

The econometric framework begins with the assumption that landowners allocate a 

plot of homogeneous quality land to the use that maximizes the present discounted 

value of expected net returns less any costs of converting land. Expectations of net 

returns are assumed static and depend on current and historical net returns, thereby 

generating the decision rule that the landowner chooses the use generating the 

greatest annualized net return less conversion cost (Plantinga 1996). Although the 

landowner is assumed to observe the net returns to alternative uses in each decision 

period, this information is not perfectly available to the researcher. As such, the 

annualized net return to land can be specified as a function of both deterministic 

and random components (Lewis and Plantinga 2007, Lubowski et al. 2006). For plot

i that begins period t in use j and ends in use k, the real annualized net return (Rikt) 

net of annualized conversion costs (rCijkt) are:

Rikt – rCijkt = αjk + β0jk RC(i)kt + β1jk LQikRC(i)kt + [ωik + φB(i)k + εijkt] (1)

for all uses k = 1,....K and time periods t = 1,....,T, where the unobservable in the 

square bracket of the right hand side of (1) is an unobservable term composed of a 

time-invariant plot/use random effect (ωik), a random effect specific to the landscape 

block B that contains plot i (φB(i)k

), and an IID unobservable (εijkt). The variable 

RC(i)kt is the average net return from use k at time t in the county C that contains 
6

RESEARCH PAPER PNW-RP-600

parcel i, and LQik is the land quality of parcel i in use k. Land quality is represented 

as soil quality when k = agriculture or forest, and land quality is represented as 

distance to cities and roads when k = urban. The interaction of RC(i)kt and LQik

allows the deterministic parcel return to deviate from the county average owing to 

observable measures of land quality. Finally, the land-use specific constants αjk are 

assumed to account for real annualized costs of converting from use j to use k.

If the IID unobservable εijkt is distributed type i Extreme Value, then equation 

(1) is the latent equation version of an error components random parameters logit 

model (Train 2009: chap. 6). This flexible error components structure allows for 

unobserved correlation that is specific to the spatial-temporal nature of the panel 

data used in estimation. First, because the land-use choice for each parcel i is 

observed repeatedly, ωik captures time-invariant parcel unobservable determinants 

of i’s return to use k. For example, the parcel’s distance to a river does not change 

over time and might affect the return to developing the parcel. Second, because we 

observe parcels in landscape blocks B, then φB(i)k captures block-specific determinants of i’s return to use k. For example, the Pacific Northwest has many microclimates that affect the tree species that can be grown (e.g., the commercially valuable 

Sitka spruce in the far west Coast Range). This flexible error structure allows for 

temporally correlated unobservables with ωik, and spatially correlated unobservables with φB(i)k.

Land Use Dataset Used for Estimation

This project uses spatial panel data from the LCTs project funded by the USGS. 

The LCT is a national dataset derived from manually edited satellite images, aerial 

photography, and topographic maps that classifies land cover into 11 categories 

for five periods in time: 1973, 1980, 1986, 1992, and 2000. Owing to the lack of 

available data on the net returns to land prior to 1978, we exclude the 1973 to 1980 

transition period in our analysis. Importantly, the LCT is not derived solely from an 

automated algorithm run on satellite data. Rather, accuracy is improved by combining satellite data with manual editing from aerial photographs and topographic 

maps. This long panel provides both spatial and temporal variation in land use, 

allowing the researcher to observe changes in land use over multiple periods of 

time. Table 1 indicates the classification system used in the LCT.

The LCT data are collected by first stratifying the continental United States 

into Envirnomental Protection Agency (EPA) level III ecoregions, and then randomly selecting a sample of 10- by 10-km blocks from each ecoregion. Satellite 

images of each block are then placed into 60- by 60-m pixels and assigned one of 

the land cover classes from table 1. Figure 1 shows a map of the study region, 

Oregon and Washington west of the Cascade crest, including the privately owned 
7

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

Table 1— Land Cover Classifications in the Land Cover Trends data

Land Cover 

Classification	 Description

Water Areas persistently covered with water, such as streams, canals, lakes, 

 reservoirs, bays, or oceans.

Urban Areas of intensive use with much of the land covered with structures or 

 anthropogenic impervious surfaces (e.g., high-density residential, 

 commercial, industrial, roads, etc.) or less intensive uses where the 

 land cover includes both vegetation and structures (e.g., low-density 

 residential, recreational facilities, cemeteries, parking lots, utility 

 corridors, etc.), including any land functionally related to urban or 

 suburban environments (e.g., parks, golf courses, etc.)

Mechanically Land in an altered and often unvegetated state that, owing to 

 disturbed disturbances by mechanical means, is in transition from one cover 

 type to another. Mechanical disturbances include forest clear-cutting, 

 earthmoving, scraping, chaining, reservoir drawdown, and other 

 similar human-induced changes.

Mining Areas with extractive mining activities and directly related land uses.

Barren Land comprised of naturally occurring soils, sand, or rocks where less 

 than 10 percent of the area is vegetated.

Forest Tree-covered land where the tree cover density is greater than 10 

 percent. Note that cleared forest land (i.e., clearcuts) is mapped 

 according to current cover (e.g., mechanically disturbed).

Grass/shrub Land predominately covered with grasses or shrubs. The vegetated 

 cover must comprise at least 10 percent of the area. 

Agriculture Land in either a vegetated or an unvegetated state used for the 

 production of food and fiber. This includes cultivated and uncultivated 

 croplands, hay lands, pasture, orchards, vineyards, and confined 

 livestock operations. Note that forest plantations are considered forests 

 regardless of the use of the wood products.

Wetland Land where water saturation is the determining factor in soil 

 characteristics, vegetation types, and animal communities. Wetlands 

 usually contain both water and vegetated cover.

Nonmechanically Land in an altered and often unvegetated state that, owing to 

 disturbed disturbances by nonmechanical means, is in transition from one 

 cover type to another. Nonmechanical disturbances are caused by 

 fire, wind, floods, animals, and other similar phenomena.

Ice/snow Land where the accumulation of snow and ice does not completely melt 

 during the summer period (e.g., alpine glaciers and snowfields).

Source: Land Cover Trends Project, http://landcovertrends.usgs.gov/main/classification.html.

portion of the sampled LCT blocks. Because the econometric model is motivated as 

a model of private decisionmaking, public land pixels are identified and removed. 

The data used for estimation include the five EPA level III ecoregions in western 

Oregon and Washington: Willamette Valley, Cascades, Puget Lowland, Coast 

Range, and North Cascades.
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RESEARCH PAPER PNW-RP-600

The region is dominated by the top three land uses of forest, agriculture, and 

urban lands. The distribution of land-use change by transition period is presented in 

table 2. The most common transitions between land covers are forest to mechanically disturbed, and mechanically disturbed to forest. Importantly, the forest to 

mechanically disturbed transition is typically clearcut forestry in this region, while 

mechanically disturbed to forest transitions are regrowth after clearcut (see Sleeter 

et al. 2012). As such, transitions between forest and mechanically disturbed are 

treated as changes in land cover but not as a change in land use. Therefore, the most 

Figure 1—Map of the sample Land Cover Trends blocks used in analysis for western Oregon and Washington.
9

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

common land-use transitions in this region involve the development of forest and 

agricultural lands into an urban use (see Sleeter et al. 2012). As shown in table 2, 

for private lands, the development of forested and agricultural lands is much more 

common than conversions between agriculture and forest.

Sampling of Plots for Estimation

The full LCT dataset in this region consists of over 3 million pixels, a number that 

is far too much for the maximum simulated likelihood techniques that will be used 

in econometric estimation. Therefore, we sample 5,000 unique pixels and observe 

their land-use classifications over all LCT change periods. To ensure that we capture enough variation in land-use change, we oversample change pixels. Following 

the sampling analysis of LCT data conducted by Chambers (2010), we divide the 

data into two separate strata: “change pixels” and “nonchange pixels.” The “change 

pixels” are pixels that change land use (transitions between forest and mechanically 

disturbed are not considered a change—see above) at some point during the LCT 

time period. The “nonchange pixels” are pixels that do not change land use during 

the LCT time period. The LCT population of private pixels has a probability of 

choosing a change pixel at 27 percent, while our oversample of change pixels has a 

probability of a change pixel equal to 35 percent. Standard Logit estimation off this 

“choice-based” sample generates consistent estimates of all parameters except the 

alternative-specific constants, which can be adjusted in a straightforward manner 

(Train 2009). We discuss the adjustment of the alternative-specific constants in the 

“Landscape Projections and Out-of-Sample Forecast Text” section.

Comparing Development Probabilities Across the LCT and NRI

Land-use datasets derived from automated interpretation of satellite imagery have 

been found to underrepresent low-density development (Irwin and Bockstael 2007, 

Kline et al. 2009). Irwin and Bockstael (2007) compared the widely used National 

Land Cover Dataset (NLCD) to local parcel maps available from local planning 

agencies and found widespread misclassification of exurban development. Likewise, 

Table 2—Distribution of Pacific Northwest land use change by land 

cover trend transition period for private land

1980–1986 1986–1992 1992–2000

 Percent

Forest → forest 98.96 98.55 98.16

Forest → agriculture 0.28 0.36 0.15

Forest → urban 0.76 1.09 1.68

Agriculture → agriculture 98.14 97.98 98.07

Agriculture → forest 0.27 0.56 0.39

Agriculture → urban 1.59 1.46 1.54
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RESEARCH PAPER PNW-RP-600

Kline et al. (2009) compared auto-interpreted satellite data of land cover for western 

Washington to survey-based FIA plots and also found common misclassification 

of low-density development as nondevelopment. In contrast to the satellite-derived 

datasets considered by Irwin and Bockstael and Kline et al., the LCT does not 

simply use an automated interpretation from satellite imagery. Although Landsat 

satellite imagery is the primary source for the LCT maps, a variety of ancillary 

sources are used to improve classification (see Sleeter et al. 2012: app. 4). In particular, all classifications were manual and combined the base satellite imagery 

with aerial photographs, topographic maps, and Google Earth1

 imagery. Because 

we are aware of no formal tests of the LCT in determining urban development, we 

compare land-use change probabilities generated from the LCT with those same 

probabilities generated by the survey-based NRI in table 3. The LCT probabilities 

are calculated from private land parcels, while the NRI probabilities are calculated 

from nonfederal lands. Both probabilities are annualized to account for the different 

time period lengths in the two datasets and to provide an apples-to-apples comparison. Results suggest minimal differences for this region. In particular, results 

1 The use of firm or trade names in this publication is for reader information and does not 

imply endorsement by the U.S. Department of Agriculture of any product or service.

Table 3—Annualized land-use change probabilities for the Land Cover Trends (LCT) and 

Natural Resources Inventory (NRI) for Oregon and Washington west of the Cascades

Period 1	 Period 2	 Period 3

NRI—1982 to 1987 NRI—1987 to 1992 NRI—1992 to 1997

LCT—1980 to 1986	 LCT—1986 to 1992	 LCT—1992 to 2000

Forest to forest:

 NRI 0.9997 0.9994 0.9996

 LCT 0.9979 0.9971 0.9974

Forest to agriculture:

 NRI 0.0002 0.0005 0.0003

 LCT 0.0006 0.0007 0.0002

Forest to urban:

 NRI 0.0001 0.0001 0.0001

 LCT 0.0015 0.0022 0.0024

Agriculture to forest:

 NRI 0.0052 0.0050 0.0020

 LCT 0.0005 0.0011 0.0006

Agriculture to agriculture:

 NRI 0.9937 0.9935 0.9941

 LCT 0.9963 0.9959 0.9972

Agriculture to urban:

 NRI 0.0011 0.0015 0.0038

 LCT 0.0032 0.0029 0.0022
11

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

in table 3 provide no evidence that the LCT systematically underrepresents urban 

development compared to the NRI. This result is in contrast to Irwin and Bockstael 

(2009) and Kline et al.’s (2009) analyses of land-use datasets solely derived by 

automated interpretation of satellite imagery alone and provides confidence in the 

LCT as a data source for econometric modeling.

Data for Independent Variables Used in Econometric Estimation

County-level net return variables come from Lubowski’s (2002) national-level 

dataset of annual per-acre net returns to crops, pasture, range, and urban land uses 

from 1978 to 1997. Landowners are assumed to form expectations of net returns 

based on average returns from the 3-year period preceding each transition period. 

Because the LCT bundles crop and pasture lands together as agriculture, average 

agricultural net returns are constructed as a weighted average of crop and pasture 

returns, with the weights derived from the NRI. All net returns are adjusted to 1990 

dollars using the consumer price index. The net returns are linked to each sample 

plot by identifying the county in which each parcel resides using a GIS overlay of 

a county layer and the sample LCT plots. Table 4 presents average county-level 

returns for the three time periods used to construct the average returns used in 

estimation. Urban returns have generally climbed over time, agricultural returns 

have fallen, and timber returns were flat over the first two periods and significantly 

higher during the final period. The significantly higher level of forest returns in the 

final period was likely influenced by the large-scale reductions in federal timber 

harvests from public lands resulting from the spotted owl restrictions (Wear and 

Murray 2004).

Data on plot-level soil quality comes from the Soil Survey Geographic Database (SSURGO from the USDA National Resources Conservation Service). The 

SSURGO data categorize soil quality into eight nonirrigated Land Capability 

Classes (LCC) corresponding to land productivity (1 is highest, 8 is lowest). A GIS 

map of LCC is overlaid to the sample of LCT plots to determine the soil quality of 

each plot. Soil quality is a strong determinant of crop and timber yields, and so is 

used as an interaction with agricultural and forest returns in econometric estimation 

to account for observable plot soil characteristics. The LCC is widely used as a soil 

indicator in econometric land-use models.

Table 4—Average county-level real per-acre net 

returns for western Oregon and Washington

Years Urban Forest Agriculture

 Dollars

1978–1980 3,965 15 134

1984–1986 4,362 14 26

1990–1992 5,803 55 41
12

RESEARCH PAPER PNW-RP-600

The Euclidian distance of each plot to the nearest city of greater than 10,000 

people and the distance to a major road are included as interactions with urban 

returns in econometric estimation to account for observable location characteristics 

that influence plot-level development probabilities. Data on city populations come 

from GIS datasets provided by the Oregon Geospatial Enterprise Office (OGE) and 

the Washington Office of Financial Management (WA OFM). Data on roads come 

from the U.S. Census Bureau, and we include the distance to the nearest major 

road, where major roads are defined by the Census Bureau as interstate, U.S., state, 

or county routes. Figure 2 presents histograms of the distance of LCT sample plots 

to cities and roads. As expected, forest plots are generally farther from both cities 

and roads than agricultural plots, representing the fact that Northwest forest lands 

tend to be located in the mountains where few live, while agriculture tends to be in 

the valleys closer to cities.

A. Distance of agricultural plots to cities B. Distance of agricultural plots to roads

C. Distance of forest plots to cities D. Distance of forest plots to roads

0.00

0.05

0.10

0.15

0.20

0.25

1 11 21 31 41 51

Percent

Distance to nearest cty (km)

0.00

0.05

0.10

0.15

0.20

0.25

0.5 3 5.5 8 10.5 13 15.5 18 20.5

Percent

Distance to nearest road (km)

0.00

0.05

0.10

0.15

0.20

1 11 21 31 41 51 61

Percent

Distance to nearest city (km)

0.00

0.02

0.04

0.06

0.08

0.10

0.5

3

5.5

8

10.5

13

15.5

18

20.5

Percent

Distance to nearest road (km)

Figure 2—Distribution of the distance of sample Land Cover Trends plots to cities and roads. 
13

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

Accounting for the LCT’s Clustered Landscape Block 

Sampling Strategy 

The LCT data are collected by first stratifying the continental United States into 

EPA level III ecoregions, and then randomly selecting a sample of 10- by 10-km 

blocks from each ecoregion. This brings up the issue of how to account for this 

clustered sampling technique in econometric estimation. We present a simple 

Monte Carlo exercise that illustrates properties of econometric estimation with 

a simple random sample of plots from counties, and compare that to a clustered 

sample similar to the LCT design. Results confirm that the LCT’s sampling design 

creates a block-level unobservable that induces bias in estimation by generating 

spatial correlation in the error component of the econometric model. Results also 

confirm that consistent estimation can be achieved by including a block-level 

random effect in estimation. For simplicity, our results are illustrated with a binary 

plot-level model to develop or not.

A random sample of plots from counties—

This section describes a process for generating data used in the Monte Carlo exercise. The computer-generated data are developed to mimic properties of the LCT 

data. For plot i that begins period t in an undeveloped use u and ends period t in an 

undeveloped use, real annualized net value of the land is:

Riuut = αuu + βuuRc(i)ut + εiuut (2)

Real annualized net returns less conversion costs for developing parcel i into 

use d during period t are:

Riudt – rCiudt = αud + βud Rc(i)dt + εiudt (3)

For all uses k = 1,2,.....,K and time periods t = 1,....,T, where αjk and β0jk are 

parameters, RC(i)kt is the county average return to use k, and εijkt is a standard 

normal unobservable. For simplicity, we have no land quality information for plot i, 

though that could be easily introduced. The plot will be developed if the net value 

of conversion (3) – (2) is positive:

(Riudt – rCiudt) – Riuut = (αud – αuu) + βud Rc(i)dt – βuu Rc(i)ut + (εiudt–εiuut) > 0 (4)

For simulation purposes, assume that the scale of (2) and (3) is such that both 

are plot-specific net returns written as deviations from the county average return. 

This is accomplished with αuu = αud = 0, and βuu = βud = 1:

(Riudt – rCiudt) – Riuut = Rc(i)dt – Rc(i)ut + (εiudt–εiuut) (5)
14

RESEARCH PAPER PNW-RP-600

So, given a random sample of plots within each county, we can estimate a probit 

model of (5):

Prob(yit = 1|Rc(i)dt – Rc(i)ut) = Prob[(εiudt – εiuut) < β(Rc(i)dt – Rc(i)ut)] (6)

Consistent estimation should yield a sampling distribution of the estimate of β

that is centered at one, the population parameter value of β.

Monte Carlo simulation steps for random sampling from counties—

1. Draw 100 county average net returns to conversion (Rc(i)dt – Rc(i)ut) from a 

U[0,1] distribution.2

2. Draw 30 plots per county, with (εiudt – εiuut) being drawn from a N(0,1). This 

establishes (5) as a probit model.

3. Create the dependent variable yit to be equal to one if (5) is positive, and 

zero otherwise.

4. Estimate (6) as a probit model with one variable, the net county returns to 

conversion (Rc(i)dt – Rc(i)ut).

5. Repeat steps 1 through 4 many times.

Monte Carlo results—

Given the setup of the Monte Carlo simulation, the estimate of β should be equal to 

one when averaged over 1,000 independent simulations, where the 1,000 simulations approximate β

^

’s sampling distribution. Results confirm that (1/S)∑S

s=1 β

^s = 1, 

where S = 1,000, indicating that a random sample of plots from each county can be 

used to provide consistent parameter estimates of this land-conversion model.

A random sample of plots from clustered blocks within counties—

The LCT dataset consists of a sample of 10- by 10-km blocks randomly sampled 

within ecoregions. Many counties have multiple blocks within them, and a block 

can straddle multiple counties. Importantly, sampling plots from LCT blocks no 

longer comprise a random sample from counties, so we explore the implications of 

such a sampling design for econometric estimation.

Begin by rewriting (5) as the plot-specific deviation from the block-specific 

average return to conversion, where b indexes blocks:

(Riudt – rCiudt) – Riuut = (Rc(i)dt + ωb(i)dt) – (Rc(i)ut + ωb(i)ut) + (εiudt – εiuut) (7)

Where (Rc(i)dt + ωb(i)dt) is the average developed return for block b, which contains plot 

i, and (Rc(i)ut + ωb(i)ut) is the average undeveloped return for block b, which contains 

plot i. Equation (7) can be arranged into the relevant latent form used for estimation:

(Riudt – rCiudt) – Riuut = (Rc(i)dt – Rc(i)ut) + (ωw(i)dt – ωw(i)ut) + (εiudt–εiuut) (8)

2 A uniform distribution is standard for drawing values of independent variables in Monte 

Carlo analyses, though results are not contingent on this distribution.
15

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

Equation (8) highlights that the additional term (ωb(i)dt – ωb(i)ut) generates an 

unobservable that will be correlated across all plots within block b. All plots within 

block b share this same unobservable. Failure to account for such correlation could 

lead to inconsistent parameter estimates arising from a standard probit model. This 

econometric complication arises entirely from the fact that sampling plots from 

LCT blocks generates a random sample of plots within blocks, but not a random 

sample of plots within counties. Consistent estimation can be achieved by including 

a block-specific random effect to account for (ωb(i)dt – ωb(i)ut). A random effect can 

be used because (ωb(i)dt – ωb(i)ut) can be reasonably assumed to be independent of 

(Rc(i)dt – Rc(i)ut) since the LCT randomly samples blocks within ecoregions. Given a 

random sample of plots within each block, a probit model of the latent equation (8) is:

Prob(yit=1|Rc(i)dt–Rc(i)ut)=Prob[(εiudt – εiuut) <β(Rc(i)dt –Rc(i)ut) +ωb(i)dt – ωb(i)ut] (9)

Consistent estimation should again yield a sampling distribution of β

^

 that is 

centered at one, the population parameter value of β.

Monte Carlo simulation steps for random sampling from landscape blocks—

1. Draw 100 county average net returns to conversion (Rc(i)dt – Rc(i)ut) from a 

U[0,1] distribution (see footnote 2).

2. Draw 100 block deviations from the county average net returns to conversion (ωb(i)dt – ωb(i)ut) from a U[-a, a] distribution, where parameter a will 

be varied over different scenarios. This step implicitly assumes that each 

county has one block.

3. Draw 30 plots per county, with (εiudt – εiuut) being drawn from a N(0,1) distribution. This establishes (8) as a probit model.

4. Create the dependent variable yit to be equal to one if (8) is positive, and 

zero otherwise.

5. Estimate (9) as a probit model with one variable, the net county returns to conversion (Rc(i)dt – Rc(i)ut). This should generate inconsistent parameter estimates.

6. Estimate (9) as a probit model with one variable, the net county returns to 

conversion (Rc(i)dt – Rc(i)ut), and a block random effect. This should generate 

consistent parameter estimates by accounting for correlated unobservables 

across all plots within a block.

7. Repeat steps 1 through 6 many times.

Given the setup of the Monte Carlo simulation, the estimate of β should be 

equal to one when averaged over 1,000 independent simulations. Again, the 1,000 

independent simulations form an approximation of β

^

’s sampling distribution. 

Results confirm that (1/S) ∑S

s=1 β

^s = 1 for the random effects model, indicating 

that a random sample of plots from each block can be used to provide consistent 
16

RESEARCH PAPER PNW-RP-600

parameter estimates of this land-conversion model. However, failure to include a 

random effect generates inconsistent estimates, which are worse as the |a| value is 

larger, where 2a is the length of the interval through which the block unobservable 

was uniformly drawn. Intuitively, |a| is larger when block-specific mean returns to 

conversion are further from the county mean. Results from different values of a are 

found in table 5, and probit estimates without a random effect become increasingly 

biased away from the true value of one as the block average return to conversion 

becomes increasingly different from the county average return. Including block 

random effects generates consistent estimates. This Monte Carlo analysis supports 

the inclusion of LCT block random effects in the primary econometric model from 

equation (1). 

Estimation Technique—Maximum Simulated Likelihood

There are three sets of fixed (not random) parameter vectors to be estimated in the 

basic econometric model of equation (1): a set of alternative specific constants for 

the transition from land-use j to k (αjk), a set of parameters on the average returns 

to use k in time t for the county that contains parcel i (β0jk), and a set of parameters 

on the interaction of county returns with observable land quality for parcel i in 

use k (β1jk). One alternative specific constant must be normalized to zero, and so 

we always normalize the alternative specific constant on the starting use (αjj = 0), 

which gives the other constants the interpretation as a conversion cost. A fully 

specified model also must make distributional assumptions regarding the random 

parcel and block effects (ωik and φB(i)k, respectively). We assume both are normally 

distributed with zero mean. The parcel effects have standard deviation σ1jk, and 

the block effects have standard deviation σ2jk. Because we have three separate land 

uses (agriculture, forest, urban), there are three separate parcel effects and three 

separate block effects. Given our use of panel data, there is no need to normalize 

one transition-specific random effect to zero (Walker et al. 2007). Finally, assuming 

Table 5—Monte Carlo simulation results of including block random effects to 

account for the Land Cover Trend’s clustered sampling approach

Average probit 

Average Average probit estimate using 

probit estimate estimate using county mean 

Block deviation using block county mean returns with block 

(-a to a)	 mean returns	 returns	 random effects

-0.25 to 0.25 1.001 0.989 1.002

-0.5 to 0.5 1.001 0.963 0.992

-0.75 to 0.75 1.001 0.914 1.006

-1 to 1 1.001 0.862 1.018

-1.25 to 1.25 1.001 0.809 1.001

-1.5 to 1.5 1.002 0.74 1.035
17

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

that εijkt is an iid type I extreme value unobservable, then the probability that parcel

i changes from use j to use k in time t is:

Pijkt = ∫ ∫ Lijkt (αjk, β0jk β1jk, σ1jk, σ2jk)f(θik)f(μB(i)k

)dθik dμB(i)k (10)

where

Lijkt(αjk, β0jk β1jk, σ1jk, σ2jk ) =

eαjk + β0jk RC(i)kt + β1jk LQik RC(i)kt + σ1jk θik + σ2jk μB(i)k

∑keαjk + β0jk RC(i)kt + β1jk LQik RC(i)kt + σ1jk θik + σ2jk μB(i)k

(11)

And where θik and μB(i)k are standard normal random variables. The probability in 

(10) is known as a mixed logit, or random parameters logit probability (Train 2009). 

The integrals in (10) do not have a closed form solution, and so parameters must be 

estimated via simulation of the log likelihood function. Such maximum simulated 

likelihood estimation employs the assumption that the parcel (ωik) and block (φB(i)k

) 

random effects are independent and normally distributed, which allows us to solve 

(10) by repeatedly drawing from standard normal distributions for θik and μB(i)k, 

calculating (11), and averaging. Following this logic, and denoting DB as the full set 

of observed land-use decisions in block B, the probability of the observed land-use 

decisions on parcel i at time t conditional on draws from θik

and μB(i)k is simply (11); the probability of the sequence of land-use choices in DB

is thus:

Pr(DB) = ∏i∈B ∏t ∏k

eαjk + β0jk RC(i)kt + β1jk LQik RC(i)kt + σ1jk θik + σ2jk μB(i)k

∑keαjk + β0jk RC(i)kt + β1jk LQik RC(i)kt + σ1jk θik + σ2jk μB(i)k

yijkt

(12)

where yijkt equals one if plot i converts from use j to use k during time t, and zero 

otherwise. The likelihood of the observed land-use behavior in block B can be 

simulated by drawing randomly from the independent standard normal distributions 

of θ and μ. Taking R sets of draws, with each set r denoting a single draw for each 

observation generates the approximated likelihood function:

PrSim (DB ) = 1

–

R ∑R

r=1Pr(DrB) (13)

The full simulated log-likelihood function over all BT blocks in the study region is 

defined as 

∑Bt

b=1log[PrSim(DB)] (14)

Maximizing the function in (14) over the parameter set (αjk, β0jk β1jk, σ1jk, σ2jk) 

generates the estimated parameters for the land-use model. Two hundred independent Halton draws are used to draw from the random effect distributions. All 

estimation is done with original code written in Matlab.
18

RESEARCH PAPER PNW-RP-600

Alternative Specifications and Parameter Estimates

Model 1: Base Random Parameters Logit (RPL)

We estimate the model for plots starting in agriculture separately from those 

plots starting in a forested use. Plots starting in urban do not change, so we do 

not estimate a model for those plots beginning in urban. For the agriculture-toagriculture transition, the land quality variable is the LCC measure of the plot, 

and LCC categories are grouped as three dummies representing classes 1 and 2, 

classes 3 and 4, and classes 5 and above. The dummy representing classes 1 and 

2 is omitted as the base category. For the agriculture-to-forest transition, LCC 

categories 5 through 8 are the base category, with a dummy for classes 1 through 

4 included. For the forest-to-agriculture transition, the LCC categories 1 through 

4 are the base category, and a dummy for LCC categories 5 through 8 is included. 

For the forest-to-forest transition, LCC categories 5 through 8 are the base category, 

with separate dummies for LCC 1 and 2 and LCC 3 and 4 included. This specification with grouped LCC categories reflects the lack of variation in transitions within 

these grouped categories. All LCC dummies are interacted with their respective 

county-average forest or agricultural returns. For both the agriculture-to-urban and 

the forest-to-urban transitions, land quality is included as two variables representing distance of the plot to the nearest city with 10,000+ people, and distance of the 

plot to the nearest road. Both distances are interacted with county-average urban 

returns and measured in thousands of kilometers.3

 One other specification note is 

that all block random effects are interacted with two time-dummies representing 

the 1986–1992 transition period and the 1992–2000 transition period, allowing us to 

test for temporal variation in the standard deviation of the block random effects.

The dataset includes 3,789 transition opportunities for plots that begin in 

agriculture and 7,489 transition opportunities for plots that begin in forest. Plots that 

never leave agriculture between 1980 and 2000 are included three times in the dataset for each of the three transition periods. Those that transition at some point before 

the final transition period are dropped in subsequent periods. Plots that convert to 

agriculture or forest after 1980 can also have fewer than three observations in the 

data. The same principles hold for plots that begin in forest. Of those observations 

that begin in agriculture, there are 405 observed urban development conversions 

and 102 observed forest conversions. Of those observations that begin in forest, 

there are 716 observed urban conversions and 170 agricultural conversions.

3 Kline et al. (2003) used another approach that weights the distance from cities with population, creating a gravity index. Our approach has the advantage of explicitly weighting 

distance by the economic determinant of urban development (net returns), though a fruitful 

future research approach could explore combining our approach with a gravity index. 
19

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

Table 6—Parameter estimates for model 1

Starting in agriculture Starting in forest

B SE t B SE t

Agriculture choice: Agriculture choice:

 Ag returns 3.59 2.53 1.42 Constant -5.15 0.27 -19.18

 Ag returns * LCC 3,4 1.00 1.40 0.72 Ag returns 2.82 1.58 1.79

 Ag returns * LCC 5-8 5.18 2.31 2.24 Ag returns * LCC 3,4 -1.02 2.04 -0.50

Forest choice: Forest choice:

 Constant -4.51 0.32 -14.31 Forest returns 22.87 3.66 6.25

 Forest returns 8.31 6.25 1.33 Forest Ret*LCC 3,4 -17.01 3.06 -5.56

 Forest ret * LCC 1-4 -15.28 5.92 -2.58 Forest Ret*LCC 1,1 -20.79 4.10 -5.06

Urban choice: Urban choice:

 Constant -3.01 0.34 -8.85 Constant -3.98 0.20 -20.40

 Urban returns 0.15 0.03 4.47 Urban returns 0.26 0.02 12.84

 Urb ret*city dist -21.76 2.72 -7.99 Urb Ret*City Dist -9.37 1.24 -7.55

 Urb ret*road dist -0.24 0.64 -3.75 Urb Ret*Road Dist -0.06 0.03 -2.15

Random effects Random effects 

 standard deviations: standard deviations:

 Ag parcel 0.41 0.10 4.28 Ag parcel 0.33 0.13 2.52

 Forest parcel 0.01 0.23 0.03 Forest parcel 0.15 0.09 1.62

 Urban parcel 0.44 0.09 4.71 Urban parcel 0.39 0.07 5.39

 Ag block 2.30 0.29 7.94 Ag block 2.22 0.20 10.97

 For block 1.57 0.29 5.40 For block 0.68 0.12 5.52

 Urban block 1.57 0.23 6.81 Urban block 0.72 0.12 5.84

 Ag block * d8692 1.05 0.37 2.88 Ag block * d8692 0.48 0.19 2.58

 For block * d8692 1.15 0.32 3.62 For block * d8692 0.38 0.13 2.89

 Urb block * d8692 0.89 0.31 2.86 Urb block * d8692 0.60 0.16 3.87

 Ag block * d9200 0.70 0.31 2.27 Ag block * d9200 0.91 0.44 2.07

 For block * d9200 0.55 0.50 1.10 For block * d9200 1.05 0.16 6.68

 Urb block * d9200 0.31 0.34 0.92 Urb block * d9200 0.88 0.16 5.44

 Log likelihood -1293.38 Log likelihood -2391.4

 N 3,789 N 7,489

Notes: All returns are measured in thousands of dollars. All parameters with t-stats above 1.96 are significantly different from 

zero at the 5 percent level.

All parameter estimates are presented in table 6. The parameters generally 

conform to expectations, with positive signs on most of the parameters on land-use 

returns. Further, the marginal effect on forest returns generally falls for land that is 

of different quality than LCC 5 through 8 while the marginal effect on agricultural 

returns falls for agricultural parcels of lower land quality. We see the effects of 

location on urban development probabilities as urban returns will have smaller 

marginal effects for plots farther from cities and roads. Conclusions about statistical 

significance for individual variables should not be drawn by parameter estimates 

in highly nonlinear models such as this one. A more complete analysis of statistical significance will be accomplished in the “Marginal Effects” section where we 
20

RESEARCH PAPER PNW-RP-600

account for the nonlinear structure of the model and evaluate marginal effects at 

each plot. The parameters also reveal substantial unobserved heterogeneity in that 

most of the standard deviations for the various random effects are significantly different from zero at the 5 percent level. There is also evidence that the block random 

effects change over the various transition periods.

The model includes an estimated urban development gradient by interacting distance to nearest city with county urban returns. However, there are two 

major regulatory policy changes during the time period of this study that might be 

expected to influence the urban development gradient. First, Oregon’s well-known 

urban growth boundaries were first instituted by about 1980, with an explicit goal of 

concentrating development in nearby cities. Second, Washington’s Growth Management Act of 1990 also specified the use of urban growth boundaries, and was implemented in most cities during the mid-1990s. As such, one might expect the urban 

development gradient to differ across the two states, at least prior to the 1992–2000 

transition period. This possibility is explored by including an interaction between 

the urban development gradient and a dummy representing whether the parcel is in 

Oregon. We then introduce interactions between the urban development gradient 

and two separate dummies representing the 1986–1992 and 1992–2000 transition 

periods. We also introduce three-way interactions between the Oregon dummy, the 

urban development gradient, and the same two separate dummies representing the 

1986–1992 and 1992–2000 transition periods. As such, this flexible specification 

allows the urban development gradient to vary across states and across transition 

periods. Likelihood ratio tests of these five additional parameters fail to reject the 

null hypothesis that they are jointly zero (5 percent level) for both the agriculture 

and forest models. As such, there is no evidence that Oregon and Washington had 

significantly different development gradients over the various transition periods in 

the data.

Model 2: RPL With Agglomeration Economies

The second model we estimate adds variables representing an explicit spatial 

dependency:

RC(i)Bkt–rCijkt=αjk+β0jk RC(i)kt+β1jk LQik RC(i)kt+β2jk LUB(i)kt+[ωik+φB(i)k+εijkt] (15)

where LUB(i)kt represents the share of landscape block B in use k at time t – a 

measure of neighboring land use. The idea behind adding LUB(i)kt as an explanatory 

variable in equation (15) is to capture potential agglomeration economies induced 

by spatial externalities across land uses. The net revenue of converting to parcel i to 

use k in time t (RC(i)Bkt – rCijkt) is hypothesized to be higher if there are more neighbors also in use k. Conversion of land to an alternative use is similar to the decision 
21

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

to adopt a new technology in that there is likely a fixed cost of learning the new 

technique (Lewis et al. 2011). The fixed costs of converting to agriculture or forest 

will be lower if there are more close neighbors who have demonstrated what crops, 

tree species, or management techniques work in the many microclimates around the 

Pacific Northwest. For example, wine and hop production work best with certain 

microclimates and the prevailing direction of slope, and the presence of neighboring 

wine and hop production provides an avenue for learning how to manage the new 

land use. Inclusion of LUB(i)kt in (15) for k = agriculture or forest can thus be thought 

of as capturing the fixed costs of learning the new use.

Measures of neighboring urban land used as explanatory variables in parcelscale econometric models dates back to Irwin and Bockstael (2002). In their 

model of development, Irwin and Bockstael (2002) postulated that urban development creates a negative externality that lowers the likelihood of development on 

neighboring parcels, and they found supporting evidence in an exurban region of 

Maryland. However, it is also possible that having more neighboring developed 

parcels induces positive externalities that increase the likelihood of development on 

a particular parcel. For example, some may be reluctant to live “in the woods” with 

no close neighbors. As another example, the presence of more developed neighbors 

likely lowers the cost of extending public utilities such as sewer to a new housing 

development as construction of such utilities tends to be associated with high fixed 

costs. In any event, inclusion of LUB(i)kt in equation (15) allows for an empirical 

test of the type of spatial externalities associated with agglomeration economies. 

Although the correct neighborhood size for specifying agglomeration economies 

is unclear, and not clearly testable, the LCT blocks themselves provide reasonable 

approximations of the neighborhood in which agglomeration economies operate. 

Alternative sizes (e.g., 1000-m radius, 100-m radius, etc.) are not implementable for 

plots near the edge of LCT windows because land use is not observed outside the 

windows. Below, we discuss a random-parameters specification of the parameter 

β2jk to account for the fact that each plot within block B is in a different location.

Identification Strategy With Agglomeration Economies

Building off Manski’s (1993) analysis of general social interactions, Irwin and 

Bockstael (2002) argue that measures of neighboring land use are necessarily 

endogenous in an econometric land-use model. In our case, endogeneity bias would 

arise because the neighboring land-use variable LUB(i)kt is necessarily correlated 

with the unobservable block-level random effect φB(i)k. For example, when k = 

urban, φB(i)k captures unobserved urban amenities and disamenities such as protected open-space, school quality, scenery, and other local public goods. However, 

when φB(i)k is high, signaling a landscape block with many local public goods, there 
22

RESEARCH PAPER PNW-RP-600

will likely be more development, and so LUB(i)kt is necessarily correlated with φB(i)k

when k = urban. Likewise, when k = forest or agriculture, φB(i)k picks up the microclimate effects of the Pacific Northwest that influence crop and timber types, and 

crop and timber yields. When φB(i)k is high, signaling an attractive microclimate for 

use k, there will be more neighboring land in that use, and so LUB(i)kt is necessarily 

correlated with φB(i)k when k = agriculture or forest. The urban economics literature 

on identifying agglomeration economies makes essentially this same argument: 

geographic concentration of an industry does not necessarily signal the presence of 

agglomeration economies because certain geographic regions have inherent natural 

advantages for that industry (Ellison and Glaeser 1997).

We adopt the recently developed control function strategy for identifying the 

effects of neighboring land-use (LUB(i)kt) on land-use change. We follow Train 

(2009: chap. 13) in outlining the control function approach for our model. The 

control function works by specifying the endogenous land-use share variable 

LUB(i)kt as a function of observed instruments and unobserved factors, where the 

notation with parcel i is suppressed for simplicity:

LUBkt = W(zBk,γ) + θBkt (16)

where the block random effect φBk and θBkt are assumed to be uncorrelated with the 

vector of instruments zBk, while there is assumed to be correlation between φBk and 

θBkt. It is this correlation between φBk and θBkt that induces the concern that blocklevel land-use shares LUBkt are endogenous in (15). The control function approach 

works when the distribution of φBk conditional on θBkt takes a convenient form. 

Following Train (2009: chap. 13), we decompose φBk into its mean conditional on 

θBkt and deviations around this mean:

	 φBk = E(φBk│θBkt ) + φ~

Bk = λθBkt + φ~Bk (17)

Deviations φ~

Bk are not correlated with θBkt by construction, and so therefore 

not correlated with the block-level land-use share variable LUBkt. The term 

E(φBk│θBkt ) is known as the control function, and we follow Train in setting up 

the simplest specification of the control function E(φBk│θBkt ) = λθBkt. Substituting 

(17) into (15) yields:

	 αjk+β0jk RC(i)kt+β1jk LQik RC(i)kt+β2jk LUB(i)kt+[ωik+λθB(i)kt+φ~

B(i)k+εijkt] (18)

where the control function is simply an additional independent variable, and 

φ~

B(i)k is the new block-level random effect, which is uncorrelated with the block 

level land-use share LUB(i)kt by construction. It is this transformation of the original 

block-level random effect (φBk) into an observable λθB(i)kt and an unobservable φ~

B(i)k

that corrects for the endogeneity of block-level land-use shares.
23

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

Implementation of this model requires two steps. First, equation (16) is estimated by ordinary least-squares with the following block-level instruments: the 

shares of the block in the various soil quality classes (LCC), the distance of the 

centroid of block B to the nearest city greater than 10,000+ people, and the distance 

of the centroid of block B to the nearest major road. These variables are arguably 

exogenous in that they should only influence land-use decisions on parcel i through 

their effects on block-level land-use shares. Second, residuals from the first stage 

are calculated as estimates of θB(i)kt and included as separate regressors into maximum simulated likelihood estimation of (18). The remaining block-level random 

effect φ~

B(i)k is then uncorrelated with LUB(i)kt, and the endogeneity problem is 

solved. As one final specification note, we specify the parameter β2jk on the land-use 

share variables LUB(i)kt as random parameters at the parcel level—formally denoted 

βi2jk—to account for the fact that different plots are at different geographical locations within each block.

Evaluating the Instruments in the Control Function Approach

Similar to standard instrumental variables estimation in linear models, two features 

make a good instrument in the control function approach to nonlinear models. 

First, the instruments must be correlated with the endogenous variables representing block-level land-use shares. The first stage of the control function approach is 

to regress observed land-use shares at the block level at four points in time (1973, 

1980, 1986, 1992) on the set of instruments representing exogenous land quality at 

the block level. Table 7 presents ordinary least squares (OLS) parameter estimates 

for three different models, one for each land-use category. Results generally conform to expectation, as landscape blocks farther from cities and roads have smaller 

shares in urban. Likewise, soil quality is particularly important for forest and 

agriculture shares, as blocks with higher shares of low-quality soil have more forest 

and less agriculture. The respective R2

 statistics indicate that the block-level land 

quality measures explain more variation in block-level forest and agricultural lands 

than they do block-level urban. In total, we would reject the null that all parameters 

are jointly zero in each model (5 percent level), indicating that these instruments are 

correlated with observed block-level land-use shares.

The second characteristic of good instruments in this model is that they must 

be uncorrelated with the main block-level random-effect from the base model in 

equation (15) – φBk. This characteristic is more difficult to evaluate with data as 

the random effect is an unobservable. Therefore, we state clearly what our primary identifying assumptions are for the control function to generate consistent 

parameter estimates. The maintained identifying assumption is that it is parcel i’s 
24

RESEARCH PAPER PNW-RP-600

LCC rating that affects the land-use decision on parcel i, and not the LCC ratings 

of other parcels in the landscape block in which i resides. Likewise, it is parcel i’s 

distance from cities and roads that affects the decision to develop parcel i, and not 

the distance from roads and cities of the centroid of the landscape block in which 

parcel i resides. In general, a good (excluded) instrument affects the dependent 

variable indirectly through the endogenous variable, and should not itself be a direct 

independent variable in the primary estimation equation. This description fits our 

particular application, as neighboring land quality should influence a parcel’s landuse decision (the dependent variable) only indirectly through its effect on neighboring land-use shares (the endogenous variable).

Table 7—Parameter estimates from 

regressing block-level land-use shares 

on instruments 

B Se t

Dependent variable = block urban share:

 Constant 0.13 0.05 2.66

 LCC 3 or 4 share 0.08 0.07 1.15

 LCC 5 or 6 share -0.07 0.05 -1.37

 LCC 7 or 8 share -0.09 0.04 -2.10

 City dist centroid -0.74 0.20 -3.73

 Road dist centroid -4.26 0.79 -5.39

 R2 0.28

Dependent variable = block forest share:

 Constant -0.01 0.04 -0.38

 LCC 3 or 4 share 0.59 0.05 11.61

 LCC 5 or 6 share 0.98 0.06 16.75

 LCC 7 or 8 share 0.95 0.07 13.99

 City dist centroid -2.17 0.89 -2.45

 Road dist centroid 2.44 2.06 1.19

 R2 0.50 

Dependent variable = block Ag share:

 Constant 0.81 0.06 13.92

 LCC 3 or 4 share -0.62 0.07 -8.66

 LCC 5 or 6 share -0.75 0.06 -11.79

 LCC 7 or 8 share -0.85 0.06 -14.14

 City dist centroid -0.85 0.39 -2.15

 Road dist centroid 0.20 1.29 0.15

 R2 0.50 

 N 508
25

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

Model 2 Results

All parameter estimates for model 2 with agglomeration economies are presented 

in table 8. Given that we include independent variables that are estimated residuals from the first-stage model, standard errors must be adjusted to account for this 

extra source of variation. We use the bootstrap approach developed by Petrin and 

Train (2002) for use with control function estimation. In particular, we repeatedly 

estimate the primary discrete-choice land-use model with bootstrapped samples of 

the first-stage residuals. The variance in parameter estimates over the bootstrapped 

samples is added to the traditional variances, and the total adjusted standard errors 

are presented in table 8. This approach of repeatedly estimating a maximum simulated likelihood model is extremely computationally intensive.

The parameters generally conform to expectations, with positive signs on most 

of the parameters on land-use returns. Further, the probability of converting to 

forest generally falls for land that is of different quality than LCC 5 through 8 while 

the probability of converting to agriculture is slightly higher for agricultural parcels 

of lower land quality. We again see the effects of location on urban development 

probabilities as urban returns will have smaller marginal effects for plots farther 

from cities and roads. A likelihood ratio test rejects the null hypothesis that the 

additional variables added from model 1 to model 2 are jointly zero at the 5 percent 

level, providing some evidence that neighboring land-use shares affect land-use 

transition probabilities. Again, conclusions about statistical significance for individual variables should not be drawn by parameter estimates in highly nonlinear 

models such as this one. A more complete analysis of statistical significance will be 

accomplished in the “Marginal Effects” section where we account for the nonlinear 

structure of the model and evaluate marginal effects at each plot. The parameters 

also reveal substantial unobserved heterogeneity in that most of the estimated standard deviations for the various random effects are significantly different from zero 

at the 5 percent level. There is also evidence that the block random effects change 

over the various transition periods, and that the parameters on the land-use share 

variables are random and not fixed.

Marginal Effects

In this section, we examine the statistical significance of some of the individual 

variables by calculating marginal effects, along with their standard errors. All 

marginal effects are calculated for a discrete change in variable x by calculating the 

probability of a land-use transition with the change, x + c, less the probability of 

the land-use transition without the change, where c is the change. The probability 

of the land-use transition—equation (10)—is calculated by simulation. Standard 

errors for the marginal effects are calculated using the Krinsky and Robb (1986) 
26

RESEARCH PAPER PNW-RP-600

Table 8–Parameter estimates for model 2 (with agglomeration economies)

Starting in agriculture Starting in forest

B	 Adj SE	 Adj t	 	 B	 Adj SE	 Adj t

Agriculture choice: Agriculture choice:

 Ag returns 4.98 2.63 1.89 Constant -6.43 0.92 -7.02

 Ag returns * LCC 3,4 0.97 1.54 0.63 Ag returns 0.69 1.71 0.41

 Ag returns * LCC 5-8 4.36 2.40 1.81 Ag returns * LCC 3,4 0.38 2.21 0.17

Forest choice: Forest choice:

 Constant

 Forest returns

 Forest ret*LCC 1-4 -6.10 1.19 -5.13 Forest returns 16.12 4.58 3.52

6.32 7.33 0.86 Forest ret*LCC 3,4 -15.81 3.39 -4.67

-13.08 6.38 -2.05 Forest ret*LCC 1,1 -18.54 4.80 -3.86

 Urban choice Urban choice

 Urban returns -4.99 1.01 -4.94 Constant -5.89 0.89 -6.65

 Urb ret*cty dist 0.12 0.04 2.85 Urban returns 0.28 0.03 10.28

 Urb ret*road dist -9.75 3.41 -2.86 Urb ret*city dist -9.95 1.86 -5.36

 Urban returns -0.26 0.07 -3.87 Urb ret*road dist -0.07 0.04 -1.82

Land use shares: Land use shares:

 Ag share 0.25 1.08 0.23 Ag share 5.32 1.55 3.43

 Forest share 3.38 1.87 1.81 Forest share 0.84 1.17 0.72

 Urban share 13.87 6.36 2.18 Urban share 5.31 4.33 1.23

 Ag residuals 2.11 1.17 1.80 Ag residuals 1.29 1.43 0.91

 Forest residuals -5.66 2.03 -2.78 Forest residuals 0.90 0.98 0.92

 Urban residuals -13.14 6.78 -1.94 Urban residuals -1.43 5.03 -0.29

Random effects standard deviations: Random effects standard deviations:

 AgP arcel 0.08 0.09 0.83 Ag parcel 0.37 0.13 2.83

 Forest parcel

 Urban parcel

 Ag block 0.31 0.20 1.58 Forest parcel 0.11 0.07 1.58

0.08 0.10 0.78 Urban parcel 0.01 0.08 0.07

2.75 0.33 8.42 Ag block 1.85 0.30 6.24

 For block 1.45 0.33 4.35 For block 1.57 0.16 9.56

 Urban block 0.69 0.29 2.36 Urban block 0.96 0.27 3.53

 Ag block * d8692 0.97 0.36 2.69 Ag block * d8692 0.85 0.26 3.28

 For block * d8692 0.71 0.29 2.41 For block * d8692 0.55 0.19 2.93

 Urb block * d8692 1.30 0.34 3.86 Urb block * d8692 0.55 0.19 2.94

 Ag block * d9200 0.32 0.33 0.97 Ag block * d9200 0.12 0.47 0.26

 For block * d9200 1.40 0.54 2.62 For block * d9200 0.58 0.17 3.40

 Urb block * d9200 0.72 0.43 1.68 Urb block * d9200 1.57 0.31 5.08

 Ag share 1.45 0.40 3.65 Ag share 1.44 0.56 2.60

 Forrest share 0.06 0.57 0.11 Forrest share 3.79 0.19 19.65

 Urban share 1.22 0.54 2.27 Urban share 2.31 0.56 4.11

 Log likelihood -1253.7 Log likelihood -2034.23

 N 3,789 N 7,489

Notes: All returns are measured in thousands of dollars. All parameters with t-stats above 1.96 are significantly different 

from zero at the 5 percent level. Standard errors are bootstrapped.
27

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

simulation method. In particular, a parameter vector is drawn from the estimated 

distribution to calculate the estimated land-use transition probabilities in equation (10). The simulated parameter vector is equal to βs = β^

 + C′xk, where β

^ is the 

estimated parameter vector for all parameters (including random effects), C is the

k × k Cholesky decomposition of the estimated variance-covariance matrix, and xk 

is a K-dimensional vector of draws from a standard normal distribution. Performing this simulation 1,000 times allows computation of the standard deviation of the 

1,000 simulated marginal-effect estimates to generate a standard error for marginal 

effects.

Figures 3 through 5 present marginal effects for a $100 increase in each of 

the land-use returns for model 1 (no agglomeration economies), calculated at the 

value of independent variables of each sample point. The figures are scatter 

plots, where each point on the graph indicates an estimated marginal effect (and 

corresponding z-statistic) for a sample point. The effect of the model’s nonlinearity 

comes through when examining the various patterns of these marginal effects. In 

general, higher forest returns increase the probability of remaining in forest while 

Figure 3—Marginal effects of a $100 increase in forest returns for model 1 on choosing forest. Land 

Classification Categories (LCC) are as follows: 1 = LCC 1 or 2; 2 = LCC 3 or 4; and 3 = LCC 5+.
28

RESEARCH PAPER PNW-RP-600

Figure 4—Marginal effects of a $100 increase in agricultural returns for model 1 on choosing agriculture. Categories (LCC) are as follows: 1 = LCC 1 or 2; 2 = LCC 3 or 4; and 3 = LCC 5+.

Figure 5—Marginal effects of a $100 increase in urban returns for model 1 on choosing urban.
29

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

higher agricultural returns increase the probability of remaining in agriculture in 

statistically significant manners. The magnitude of the marginal effects is generally 

higher for lower quality LCC classes, although there is significant heterogeneity in 

these results. Higher forest returns have no significant effect on converting from 

agriculture to forest, whereas higher agricultural returns generally have no significant effect on converting from forest to agriculture. This lack of significance likely 

comes from the fact that very few parcels are observed to transition between forest 

and agriculture in the Pacific Northwest, so there is likely not enough variation to 

estimate these effects with precision. A clear urban development gradient emerges 

from this model as higher urban returns typically have a statistically significant 

positive effect on the probability of urban development for those plots near cities, 

with no significant effect or even negative effects for those plots far from cities.

Figures 6 through 8 present the same marginal effects for a $100 increase in 

each of the land-use returns for model 2 (with agglomeration economies), again calculated at the value of independent variables of each sample point. The pattern 

that emerges is very similar to model 1 without agglomeration economies, suggesting that inclusion of agglomeration economies has minimal implications for the 

Figure 6—Marginal effects of a $100 increase in forest returns for model 2 on choosing forest. 

Categories (LCC) are as follows: 1 = LCC 1 or 2; 2 = LCC 3 or 4; and 3 = LCC5+.
30

RESEARCH PAPER PNW-RP-600

Figure 7—Marginal effects of a $100 increase in agriculture returns for model 2 on choosing agriculture.

Figure 8—Marginal effects of a $100 increase in urban returns for model 2 on choosing urban.
31

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

marginal effects of the net returns variables. One must be cautious with this interpretation; however, as the generally positive signs on the land-use shares parameters 

implies a degree of path-dependence in land-use change that could cause long-term 

divergence in land-use patterns generated across the two models. We explore this 

in the “Landscape Projections and Out-of-Sample Forecast Test” section with full 

landscape forecasts over a 40-year time horizon.

Figure 9 examines the marginal effects of a 10 percentage point increase in the 

landscape block’s land-use share in specific uses for lands starting in agriculture. 

Figure 9A examines the effects of more agricultural neighbors on the probability of 

agricultural land remaining in agriculture. No statistically significant effect is found 

for any observation. Figure 9C examines the effects of more forest neighbors on 

the probability of agricultural land converting to forest. There is some evidence for 

statistically significant agglomeration economies here, though it is weak. Figure 9E 

examines the effects of more urban neighbors on the probability of agricultural land 

converting to urban. Here there are generally consistent positive and statistically 

significant effects, which tend to increase in magnitude as the initial share of the 

block in urban development increases. Therefore, there appears to be strong evidence of urban agglomeration economies in the development of agricultural land, 

even when controlling for the average level of urban rents.

Figure 10 examines the marginal effects of a 10 percentage point increase in the 

landscape block’s land-use share in specific uses for lands starting in forest. Figure 

10A examines the effects of more agricultural neighbors on the probability of forest 

land converting to agriculture. We see strong evidence of positive agglomeration 

economies when converting forest land to agriculture. Figure 10C examines the 

effects of more forest neighbors on the probability of forest land remaining in 

forest. There is some evidence for statistically significant disagglomeration economies here, particularly for blocks that have sizable amounts of initial forest. These 

significant effects appear to be driven by the large estimated standard deviation of 

the random parameter on the forest share variable. Figure 10E examines the effects 

of more urban neighbors on the probability of forest land converting to urban. 

Here there are generally positive but statistically insignificant effects, which tend 

to increase in magnitude as the initial share of the block in urban development 

increases. One could use a one-tailed test to interpret some weak positive agglomeration economies for urban development on existing forest land.
32

RESEARCH PAPER PNW-RP-600

Figure 9—Marginal effects of a 10 percentage point increase in landscape block land-use share of the 

own use for model 2, lands starting in agriculture. Note: Figure 9A calculates the effect of an additional 10 percentage points in the block’s share of agricultural land on the probability of remaining in 

agriculture, plotted against the initial block share of agriculture. Figure 9C calculates the effect of an 

additional 10 percentage points in the block’s share of forest land on the probability of converting to forest, plotted against the initial block share of forest land. Figure 9E calculates the effect of an additional 

10 percentage points in the block’s share of urban land on the probability of converting to urban, plotted 

against the initial block share of urban.
33

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

Figure 10—Marginal effects of a 10 percentage point increase in landscape block land-use share for 

model 2, lands starting in forest. Note: Figure 10A calculates the effect of an additional 10 percentage 

points in the block’s share of agricultural land on the probability of converting agriculture, plotted 

against the initial block share of agriculture. Figure 10C calculates the effect of an additional 10 

percentage points in the block’s share of forest land on the probability of remaining in forest, plotted 

against the initial block share of forest land. Figure 10E calculates the effect of an additional 10 percentage points in the block’s share of urban land on the probability of converting to urban, plotted against 

the initial block share of urban.
34

RESEARCH PAPER PNW-RP-600

Landscape Projections and Out-of-Sample 

Forecast Test

With the estimated parameters for both models 1 and 2 in hand, we can project 

landscape-scale land-use change for the western halves of Oregon and Washington. 

Before doing so, we must adjust the estimated alternative-specific constants to correct for our oversampling of “change” pixels in the estimation sample. For standard 

logit estimation (rather than random parameters logit), each alternative-specific 

constant is adjusted by adding the log of the ratio of Aj

 to Sj, where Aj is the share 

of observations in the population who choose land-use j, and Sj

 is the share of the 

sample who choose land-use j (Train 2009: chap. 3). It is unclear if this method 

works for random parameters logit models with simulated probabilities, so we 

instead use the more general recalibration method for adjusting alternative-specific 

constants (see Train 2009: chap. 2.8 for this method). This method is used to adjust 

alternative-specific constants to match a specific forecast area or time period by 

using observed changes to recalibrate the constants.4

 This approach captures average unobserved effects for that time period or area into the alternative-specific constants by iterating the constants until the predicted land-use shares equal the actual 

land-use shares. We calibrate our forecasts to the 1992–2000 transition period in 

the LCT—the final observed period. The process works as follows. First, let Sjk

denote the share of plots that transition from j to k during this period, and let αj

0

k

be the original alternative-specific constant. Second, using the estimated discretechoice model, predict the share of plots that transition from j to k and label them S

^

j

0

k. 

Third, compare the predicted and actual shares and adjust the alternative-specific 

constant if needed. The adjustment αj

1

k = αj

0

k + ln(Sjk/S

^

j

0

k

) guarantees that adjustment 

will always move the actual and predicted shares closer. All adjustment factors and 

corresponding predicted and actual shares are presented in table 9.

To examine model validity in forecasting, we perform an out-of-sample 

forecast test by comparing forecasted transition probabilities to actual transition 

probabilities on a separate sample of 16,000 LCT plots that began the 1992–2000 

period in either agriculture or forest. The econometric model was used to forecast 

transition probabilities between 1992 and 2000. This approach follows Kline et 

al. (2003) in reserving data not used in estimation as a validation dataset. Table 10 

presents average actual and estimated transition probabilities grouped by various 

land quality classes—soil quality and distance to the nearest city. Results show that 

the estimated and actual transition probabilities are reasonably close in values, thus 

providing some confidence as to the general validity of the estimated econometric 

models for projections.

4 Alternatively, one can also adjust for such oversampling by weighting the likelihood 

function (see Lewis and Plantinga 2007).
35

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

Table 9—Adjustments of alternative specific constants to correct for 

oversampling “change” pixels—calibrated to 1992–2000 Land Cover 

Trend transition period

	 Actual share	 Predicted share

Adjustment	 (1992–2000)	 (1992–2000)

Model 1:

 Forest to agriculture -2.9753 0.0015 0.0016

 Forest to urban -4.1146 0.0168 0.0173

 Agriculture to forest -4.4665 0.0039 0.0039

 Agriculture to urban -5.7132 0.0154 0.0154

Model 2:

 Forest to agriculture -6.8140 0.0015 0.0016

 Forest to urban -4.4286 0.0168 0.0173

 Agriculture to forest -4.2617 0.0039 0.0039

 Agriculture to urban -5.4088 0.0154 0.0154

Table 10—Out-of-sample forecast test for 1992–2000 period

Sample transition Model 1 transition Model 2 transition 

probabilities probabilities probabilities

Ag Forest Urban Ag Forest Urban Ag Forest Urban

Land starting in agriculture:

 Plots with 0.9823 0.0024 0.0153 0.9824 0.0032 0.0144 0.9842 0.0023 0.0135

 LCC 1 or 2

 Plots with 0.9803 0.0046 0.0151 0.9819 0.0041 0.0140 0.9823 0.0036 0.0141

 LCC 3 or 4

 Plots with 0.9722 0.0040 0.0238 0.9788 0.0093 0.0119 0.9803 0.0088 0.0110

 LCC 5 to 8

 Plots ≤ 5 km 0.9583 0.0053 0.0364 0.9724 0.0029 0.0247 0.9733 0.0037 0.0231

 from a city

 Plots > 5 km 0.9931 0.0028 0.0041 0.9872 0.0052 0.0076 0.9884 0.0037 0.0079

 from a city

Land starting in forest:

 Plots with 0.0000 0.9708 0.0292 0.0023 0.9804 0.0172 0.0030 0.9775 0.0194

 LCC 1 or 2

 Plots with 0.0043 0.9622 0.0335 0.0030 0.9756 0.0215 0.0019 0.9761 0.0220

 LCC 3 or 4

 Plots with 0.0002 0.9955 0.0044 0.0013 0.9932 0.0055 0.0010 0.9927 0.0063

 LCC 5 to 8

 Plots ≤ 5 km 0.0031 0.9373 0.0596 0.0026 0.9580 0.0394 0.0014 0.9537 0.0449

 from a city

 Plots > 5 km 0.0016 0.9897 0.0088 0.0019 0.9909 0.0071 0.0015 0.9916 0.0069

 from a city

LCC = Land Classification Class.
36

RESEARCH PAPER PNW-RP-600

For future landscape projections, we now draw a random sample of 20,000 pixels from the population of private pixels in this region that begin in the year 2000 

in either agriculture or forest to project future land-use change by ecoregion. This 

larger draw is desirable because we do not have the computational restrictions that 

we do under the estimation process, which takes days to run with the bootstrapping 

procedure. The larger draw also ensures we have good coverage of the distribution 

of land quality within each LCT landscape block. For each plot, the transition probabilities between forest, agriculture, and urban development are calculated. Next, 

average block-level transition probabilities are computed and multiplied with the 

relevant land-use shares for each LCT block to generate block-level land-use projections for an 8-year period. Transition probabilities are then updated to reflect the 

changed landscape and another 8-year period is projected. This process continues 

for a 40-year time horizon up to 2040.

A primary benefit of the econometric modeling framework is the ability to 

simulate changes in the net returns to land, where these changes could be driven 

by policy or other factors. We use the recent housing market boom and bust to 

project three different levels of urban returns. First, we project land use to 2040 and 

keep the real levels of all net returns at 1990s levels—specifically the average of 

1990–1992. The second scenario uses the peak urban returns from the recent housing market boom, but does not alter agriculture or forest returns from 1990s levels. 

Because the Lubowski dataset does not include any returns estimates past the 

1990s, we consult the widely used Case-Schiller housing market index, which had 

a peak value in 2006 at 184 percent of the 1992 level in real terms. Therefore, we 

multiply all urban returns by 1.84 in the second scenario. The third scenario uses a 

more modest urban return estimate by considering the 2012 Case-Schiller housing 

market index, which is 114 percent of the 1992 level in real terms. Therefore, we 

multiply all urban returns by 1.14 in the third scenario. This exercise allows us to 

explore land-use change scenarios within the full range of observed urban returns 

over the past 20 years.

Ecoregion urban land-use projections are presented in table 11. The ecoregion 

is a convenient reporting scale given that LCT blocks are random samples 

within ecoregions. Our projection is that there are very modest increases under 

all scenarios in urban land expected for the Coast Range, Cascades, and North 

Cascades regions. Little urban development exists in these mountainous regions, 

which are generally far from roads and cities. The Puget Lowland and Willamette 

Valley ecoregions are projected to see much more substantial increases in urban 

development, with much more variation across the scenarios. Projections for the 

Puget Lowland range from a 37 percent increase in urban development up to a 
37

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

122 percent increase under the peak 2006 urban return level. Likewise, projections 

for the Willamette Valley range from a 33 percent increase up to a 79 percent 

increase. Clearly, the real urban return level going forward has major implications 

for urban development in the Puget Lowland and Willamette Valley. Likewise, there 

is some variation across model 1 and model 2, with the path dependence feature 

of agglomeration economies in model 2 inducing slightly higher levels of urban 

development. However, the assumed urban return level has a much larger effect on 

urban projections than does the assumption about agglomeration economies.

Ecoregion forest and agricultural land-use projections are presented in tables 

12 and 13. Similar to urban land use, very modest changes in forest and agricultural 

lands are expected for privately owned portions of the Coast Range, Cascades, and 

North Cascades. The Puget Lowland is expected to lose the most forest, and these 

projections are sensitive to the assumed urban return level. The most extreme loss 

would occur if urban returns jump back to peak 2006 levels. Projected forest losses 

Table 11—Ecoregion urban land-use projections for 2040 under alternative urban returns 

scenarios (private land)

 Model 2 (with 

Model 1	 	 agglomeration economies)

Urban share Urban share Urban share

(2000)	 (2040)	 Change	 (2040)	 Change

Coast Range: 4.24 Percent Percent

 1992 urban return level 4.95 16.78 5.25 23.95

 2012 urban return level 4.97 17.44 5.30 25.14

 Peak (2006) urban return level 5.25 23.98 5.68 34.20

Puget Lowland: 22.27

 1992 urban return level 30.59 37.36 32.88 47.62

 2012 urban return level 32.75 47.06 35.83 60.88

 Peak (2006) urban return level 44.31 98.97 49.49 122.22

Willamette Valley: 13.18 

 1992 urban return level 17.55 33.13 18.56 40.80

 2012 urban return level 17.95 36.12 19.23 45.89

 Peak (2006) urban return level 21.00 59.28 23.67 79.51

Cascades: 2.81

 1992 urban return level 3.45 22.66 4.09 45.48

 2012 urban return level 3.48 23.75 4.12 46.58

 Peak (2006) urban return level 3.77 34.10 4.40 56.72

North Cascades: 2.68

 1992 urban return level 4.24 58.53 4.50 68.16

 2012 urban return level 4.43 65.39 4.66 73.94

 Peak (2006) urban return level 6.01 124.57 5.90 120.19
38

RESEARCH PAPER PNW-RP-600

for the Willamette Valley are much more modest. Agricultural losses as percentage 

points are highest for the more agricultural Willamette Valley, and are somewhat 

sensitive to the assumed urban return level. Because models 1 and 2 generate 

similar projections within an assumed level of urban returns, the assumption of 

urban return level has a larger effect on forest and agricultural projections than any 

assumptions about the presence of agglomeration economies.

Conclusion and Suggestions for Future Research

This paper develops a plot-level spatial econometric land-use model and estimates 

it with USGS LCT GIS panel-data from 1980 to 2000 for the western halves of the 

states of Oregon and Washington. The discrete-choice framework we use models 

plot-scale choices of the three dominant land uses in this region: forest, agriculture, 

and urban development. The land-use choice is a function of county average net 

returns to alternative land uses, and plot level measures of land quality, including 

Table 12—Ecoregion forest land-use projections for 2040 under alternative urban returns scenarios 

(private land)

Model 2 (with 

Model 1	 	 agglomeration economies)

Forest share Forest share Forest share

(2000)	 (2040)	 Change	 (2040)	 Change

Coast Range: 75.36 Percent Percent

 1992 urban return level 74.78 -0.77 74.54 -1.09

 2012 urban return level 74.75 -0.82 74.49 -1.16

 Peak (2006) urban return level 74.44 -1.22 74.12 -1.66

Puget Lowland: 52.52

 1992 urban return level 45.05 -14.22 44.53 -15.21

 2012 urban return level 43.02 -18.08 42.12 -19.80

 Peak (2006) urban return level 32.28 -38.53 31.26 -40.47

Willamette Valley: 35.49

 1992 urban return level 34.75 -2.08 33.96 -4.30

 2012 urban return level 34.44 -2.96 33.58 -5.38

 Peak (2006) urban return level 32.02 -9.76 31.22 -12.02

Cascades: 85.12

 1992 urban return level 84.29 -0.97 83.56 -1.82

 2012 urban return level 84.25 -1.01 83.53 -1.87

 Peak (2006) urban return level 83.95 -1.37 83.23 -2.22

North Cascades: 63.70

 1992 urban return level 61.61 -3.28 61.75 -3.07

 2012 urban return level 61.42 -3.58 61.59 -3.32

 Peak (2006) urban return level 59.82 -6.09 60.34 -5.29
39

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

soil classes and Euclidian distances to cities and roads. The estimation includes 

measures of spatial land-use agglomeration economies in a framework that allows 

for both spatial and temporal correlation in the unobservables. We specify a random 

parameters logit RPL model, which is estimated by maximum simulated likelihood. 

The estimation uses discrete-choice panel data techniques and instruments for the 

spatial agglomeration variables with landscape-level land quality variables in an 

application of the recently developed control function. The combination of panel 

data RPL with the control function is a novel approach to estimating a fully spatial 

multinomial discrete-choice land-use model with GIS landscape data.

The estimated econometric model is used to project landscape change in the 

presence of alternative assumptions regarding future urban returns. The level 

of future returns to urban uses is uncertain, especially given the recent housing 

boom and bust, which has seen wide swings in urban returns. The landscape 

projections indicate substantial urban growth and loss of forest and farmlands in 

the Puget Lowland and Willamette Valley ecoregions, with minimal changes in 

the Coast Range, Cascades, and North Cascades regions. Although these results 

are not surprising, our analysis of the sensitivity of projections to alternative real 

Table 13—Ecoregion agricultural land-use projections for 2040 under alternative urban returns scenarios 

(private land)

 Model 2 (with 

Model 1	 	 agglomeration economies)

Ag share Ag share Ag share

(2000)	 (2040)	 Change	 (2040)	 Change

Coast Range: 9.89 Percent Percent

 1992 urban return level 9.74 -1.50 9.67 -2.24

 2012 urban return level 9.75 -1.40 9.67 -2.24

 Peak (2006) urban return level 9.78 -1.13 9.66 -2.35

Puget Lowland: 12.53

 1992 urban return level 11.58 -7.54 9.88 -21.12

 2012 urban return level 11.45 -8.58 9.34 -25.43

 Peak (2006) urban return level 10.63 -15.11 6.54 -47.77

Willamette Valley: 47.26

 1992 urban return level 43.63 -7.68 43.41 -8.16

 2012 urban return level 43.55 -7.86 43.12 -8.77

 Peak (2006) urban return level 42.91 -9.21 41.05 -13.15

Cascades: 5.35 

 1992 urban return level 5.38 0.55 5.36 0.21

 2012 urban return level 5.38 0.66 5.36 0.32

 Peak (2006) urban return level 5.39 0.85 5.38 0.65

North Cascades: 6.07

 1992 urban return level 6.26 3.19 6.02 -0.74

 2012 urban return level 6.27 3.38 6.03 -0.58

 Peak (2006) urban return level 6.30 3.79 6.07 -0.02
40

RESEARCH PAPER PNW-RP-600

urban returns levels is perhaps less well understood, and yet extremely relevant for 

environmental planning. The Puget Lowland ecoregion is the most sensitive portion of the Northwest to swings in the returns to urban uses of land. In particular, 

the share of the Puget Lowland ecoregion projected to be developed is between 

12 and 14 percentage points higher if the level of real urban returns remains at the 

levels observed in 2006 as compared to whether real urban returns were at the more 

modest levels observed in 2012. Variation in the projected development share of 

the Puget Lowland ecoregion between 12 and 14 percentage points presents major 

challenges for environmental management, as 12 percent of a 1.8 million ha region 

is approximately 0.2 million ha. The four other Northwest ecoregions have much 

less variation in response to alternative levels of future urban returns.

The analysis presented here provides a technical foundation for developing 

larger scale models from the LCT database, which includes a random sample of 

10- by 10-km landscape blocks within each ecoregion in the contiguous United 

States for 1973, 1980, 1986, 1992, and 2000. Additional data for 2006 are currently being processed by USGS, and the LCT data are expected to be updated in 

the future. The combination of a repeated spatial-panel database and continued 

updating makes the LCT a candidate database for future large-scale econometric 

land-use models. Many past national and regional-scale models have been estimated 

from the NRI (e.g., Langpap and Wu 2011, Lewis and Plantinga 2007, Lubowski 

et al. 2006). For example, the Forest Service has extensively used the NRI-based 

Lubowski et al. (2006) model for RPA and climate change assessments. However, 

because the NRI has no plans to release post-1997 plot-level data with a similar 

sampling methodology to 1982–1997 NRI data, a new data source and new model 

will need to be developed to account for post-1997 land-use decisions. Our analysis 

shows that the LCT provides a plausible alternative database to the NRI for future 

national-scale land-use models. We provide evidence in the “Basic Econometric 

Framework and Database Consruction” section that the LCT does not systematically underrepresent urban development as compared to the NRI. This contrasts 

with what others have found with different land-cover data sources derived solely 

from automated interpretation of satellite imagery (Irwin and Bockstael 2007, Kline 

et al. 2009). Although the LCT uses satellite imagery as a primary data source, 

the USGS manually edits and combines the satellite imagery with aerial photos, 

topographic maps, and Google Earth to improve classification accuracy.

There are many potential avenues for future econometric modeling from 

LCT data. First, scaling the regional analysis here up to the national level would 

serve multiple purposes of interest for the Forest Service, including national-scale 

resource assessments, analysis of national climate change policies such as carbon 
41

A Spatial Econometric Analysis of Land-Use Change With Land Cover Trends Data

sequestration payments, and analysis of large-scale open-space conservation 

programs and ecosystem services. An open question is whether a single national 

model would be preferable to a set of multiple regional-scale models such as we 

have here. A single national-scale model would have an advantage of simplicity (one 

set of parameters), and would be particularly applicable for simulations of nationalscale land-use programs (e.g., carbon sequestration payments) that require some 

approach to endogenizing net returns measures as a function of land-use changes 

(e.g., Lubowski et al. 2006). On the other hand, estimating multiple regional-scale 

models would surely provide more accurate local- and regional-scale projections 

by estimating regional parameters. One useful research project that would yield 

insights here would involve testing whether estimated parameters are structurally 

different across regions.

Second, unlike land-use survey-based datasets such as the NRI, the LCT allows 

researchers to observe the spatial pattern of land-use change, opening up the possibilities for more complete spatial econometric modeling. Our analysis with LCT 

block-level unobservables and block-level land-use patterns provides one possibility 

for specifying spatial econometric land-use models, but the availability of LCT data 

enables researchers to explore alternative spatial specifications of land-use models. 

We view this as a fruitful future path for improving the spatial properties of empirical models and corresponding landscape simulations. Another useful improvement 

over the present analysis would be to include finer scale data on independent variables that drive land-use decisions, such as parcel-level land-use regulations. Alternatively, a fruitful approach to improving spatial specificity could adapt Bockstael’s 

(1996) two-step approach of including estimated parcel-level land-use returns 

directly into the econometric land-use model, where the returns are estimated in a 

first-step hedonic price model that explains property sales or rental prices. However, 

adding such spatial detail is extremely labor intensive, and so there will certainly 

be tradeoffs between increasing spatial specificity and the scale with which a model 

can be estimated and applied in a simulation or projection.

Finally, on a more regional note, the most common land cover change in the 

Pacific Northwest LCT data arises from timber harvesting, which can be tracked 

with the LCT methodology by following transitions between covers classified as 

forest, mechanically disturbed, and grass/shrub. Timber harvesting is not a change 

in land use as modeled in this paper, but the LCT data provide a source for econometrically modeling the spatial properties of the timber harvest decision and its 

relevant impacts on environmental resources.
42

RESEARCH PAPER PNW-RP-600

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