Environment and Planning B: Planning and Design 2014, volume 41, pages 000 – 000

doi:10.1068/b130118p

Effects of alternative developer decision-making models on the production of ecological subdivision designs: experimental results from an agent-based model

Nicholas R MaglioccaDepartment of Geography and Environmental Systems, University of Maryland, Baltimore County, Baltimore, MD 21250, USA; e‑mail: nmag1@umbc.eduDaniel G BrownSchool of Natural Resources and Environment, University of Michigan, Ann Arbor, MI 48109‑1041, USA; e‑mail: danbrown@umich.eduVirginia D McConnell¶Department of Economics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA; e‑mail: mcconnell@rff.orgJoan I NassauerSchool of Natural Resources and Environment, University of Michigan, Ann Arbor, MI 48109‑1041, USA; e‑mail: nassauer@umich.eduS Elizabeth WestbrookSchool of Natural Resources and Environment, University of Michigan, Ann Arbor, MI 48109‑1041, USA; e‑mail: tsuga.agua@gmail.com Received 26 June 2013; in revised form 29 August 2013; published online 24 June 2014

Abstract. Approaches to residential development have clear effects on the surrounding environments, including those on habitat protection, water quality, transportation and congestion costs, and loss of public open space. Ecological subdivision designs (ESDs) are a means to mitigate some of the most negative effects of low-density dispersed land-use patterns, yet there is not widespread adoption of these alternative approaches to subdivision development. In this paper we attempt to improve understanding of how developers make decisions over development designs and what influences those decisions. Using an agent-based model of residential-housing and land markets, the effects of different developer-decision frameworks on development designs and land use are assessed. The importance of uncertainty in the outcome of new designs, such as ESDs, and the effect of that uncertainty on the cost of credit are possible explanations for the prevalence of conventional, low-density development types, and may be impeding adoption of ESDs.

Keywords: agent-based modelling (ABM), development process, environmental design, housing, land use

1 IntroductionLow‑density and land‑intensive development patterns, referred to as ‘urban sprawl’ or ‘exurban growth’, are increasingly prevalent in US landscapes (An et al, 2011; Irwin and Bockstael, 2002). In 2000 approximately 25% of the area of the contiguous US was settled at densities greater than one acre per housing unit (Brown et al, 2005). Reduced wildlife habitat and species diversity, increased water pollution from stormwater runoff, higher transportation and congestion costs, and loss of public open space are just some of the negative externalities associated with urban sprawl (Carter, 2009; Johnson, 2001).

¶ Also at Resources for the Future, Washington, DC, USA.

2 N R Magliocca, D G Brown, V D McConnell, and coauthors

The need to understand the mechanisms and impacts of the exurban development process is shared by policy makers and researchers alike (An et al, 2011; Atkinson and Oleson, 1996; Brown and Robinson, 2006; Magliocca et al, 2011). To date, most research on exurban development has focused on residential household decision making and location choices (eg, Irwin and Bockstael, 2002; 2004; Wu and Plantinga, 2013). Comparatively little work has addressed the effects of residential developer decision making on development patterns (An et al, 2011). In particular, the effects of how developers make decisions about the types and diversity of exurban developments are poorly understood. This is a considerable gap in the literature given that developers are intermediaries between housing and land markets (Coiacetto, 2001; Drewett, 1973; Gillen and Fisher, 2001; Leishman et al, 2000). This paper explores how developer decision making under uncertainty affects developer profit levels, consumer utility, and the composition of the housing supply, which has direct implications for the environmental impacts of development.

Developers face a range of uncertainties in the development process including variable zoning regulations and fees, lengthy approval processes, difficulties accessing credit, and variable consumer demand (Mohamed, 2006a; 2006b). As a consequence, ‘satisficing’ has been offered as an explanation for developer behavior resulting in the limited supply of environmentally friendly housing types available on the market (Baerwald, 1981; Hepner, 1983; Leung, 1987; Mohamed, 2006a). Satisficing behavior is characterized by aspiration to the first satisfactory solution that can be found, because the search for optimal solutions in situations of high uncertainty or limited information incurs high transaction costs. This is a form of ‘bounded rationality’ in human decision making (Simon, 1957). Simon (1957, page 198) articulated the concept of bounded rationality arguing “bounds on people’s knowledge and limits on the cognitive abilities prevent them from finding optimal solutions.” A consequence of bounded rationality is the use of simple decision rules which the decision maker is reluctant to change (Mohamed, 2006a). This is consistent with empirical work that finds developers tend to choose development locations and types from a small subset of potential options defined and evaluated against their own recent choices (Carter, 2009; Kenney, 1972; Nicol and Hooper, 1999). Consequences of developer satisficing include foregoing profit opportunities (Mohamed, 2006a) and preferences for housing types with short build and sell times that limit choices available to consumers (Leung, 1987; Nicol and Hooper, 1999); both of which can produce development patterns with negative economic and environmental externalities.

Ecological subdivision designs (ESDs) are a means to mitigate the negative effects of urban sprawl (Carter, 2009). Ecological design alternatives are defined as “residential or mixed use subdivisions typically designed to minimize site disturbance and protect ecologically sensitive areas of a site” (Carter, 2009, page 117). Following Nassauer et al (2009), Westbrook (2010) defines ecological design as a means of achieving ecosystem services by intentional landscape changes, such as decreasing lot size to increase public open space and the use of native vegetation for landscaping (Nassauer and Opdam, 2008). In addition to their ecological benefits, evidence from a survey of 494 homeowners in Southeastern Michigan performed by Nassauer et al (2009), eliciting preference ratings for images displaying properties typical of conventional and ESDs across price ranges, demonstrated that consumers preferred properties typical of ESDs over conventional designs. A follow‑up study by Westbrook (2010) compared results of the 2009 Nassauer et al survey with responses from twenty developers of single‑family homes in semistructured interviews to understand developers’ perceptions of profitability and preferences for (ie, likelihood to develop) each housing type. Developers generally perceived homebuyer preferences for ecological over conventional designs correctly, but their profitability perceptions and development preferences were not strongly related to perceived homebuyer preferences. These results indicated that developers

Effects of alternative developer decision‑making models 3

correctly perceive consumer demands for ESDs, and therefore inaccurate perception of demand is insufficient to explain the prevalence of conventional housing offerings.

Conceptually, ESDs offer a viable means to mitigate some of the negative effects of urban sprawl, but the supply of ESDs and other similar innovative development designs is limited in growing exurban areas (Bowman and Thompson, 2009; Carter, 2009; Mohamed, 2006a; Nicol and Hooper, 1999; Ryan, 2006). Many possible explanations for this observation exist, ranging from prohibitive construction costs associated with ESDs, developer and builder inexperience, and/or insufficient consumer demand, but this study will focus on two possible and nonmutually exclusive explanations: (1) cost differentials between conventional designs and ESDs present limited profit opportunities for ESDs; and/or (2) subjectivity in developer decision making favors conventional housing types. The first possibility suggests that, if costs associated with producing ESDs are significantly higher than those for conventional housing types, then developers are making the economically rational choice to produce conventional housing types. Because construction costs for ESDs were not available from the developers surveyed by Westbrook (2010), the effects of construction cost differentials cannot be tested directly without additional data collection.(1) However, risk‑based lending rates also contribute to cost differentials, and can be tested here to explore the influence of cost differences on housing offerings. The second possibility implies that, even if development costs were equal, subjectivity in developer decision making associated with familiarity and expertise may lead to development decisions that favor conventional housing types.

Experiments with an agent‑based model explore these potential barriers to introducing ESDs into the housing market. A set of alternative decision‑making models are assumed, and their effects on housing offerings in the presence and absence of risk‑based lending rates to developers for housing construction are investigated. After describing how prospect theory provides a useful lens for understanding development decisions under uncertainty, section 3 will briefly summarize an existing model of the residential housing and land markets, called CHALMS (Magliocca et al, 2011), and then describe the modifications made to model ESDs, risk‑based lending rates, and alternative developer decision‑making frameworks in the CHALMS–ESD model. Section 4 presents the results from a series of model experiments testing the effects of alternative developer decision‑making frameworks on housing offerings. In section 5 we discuss the potential of prospect theory to explain the under‑provisioning of ESDs as a result of satisficing behavior. Finally, in section 6 we conclude with remarks about the importance of modeling satisficing behavior in housing and land markets, and the utility of agent‑based virtual laboratories as a means to do so.

2 Insights from prospect theoryProspect theory (Kahneman and Tversky, 1979; Tversky and Kahneman, 1981) provides a plausible explanation for why developers may build conventional subdivision designs even if others might be more profitable. Emerging from the field of behavioral economics, prospect theory posits that absolute levels of wealth do not influence decisions as much as relative changes in wealth. Following this reasoning, a value function is used (figure 1) to translate changes in wealth to a corresponding value for the wealthholder, and gains and losses can be mapped from a reference point (Mohamed, 2006b, page 30). A characteristic

(1) Although additional costs from secondary investments associated with ESDs, such as landscaping, are likely incurred, different construction costs for ESDs were not specified for the housing types represented in Westbrook’s (2010) survey, and are thus not considered here. Other sources suggest, however, that conversion costs from greenfield lots to each of the possible housing types are not expected to be different enough to influence developer decision making (Joan Nassauer, personal communication), and ‘implicit costs’ stemming from uncertainty in the development process may play a larger role in development decisions than direct costs (Wrenn, 2012).

4 N R Magliocca, D G Brown, V D McConnell, and coauthors

of this theory, with particular relevance to developers, is known as the ‘endowment effect’ (Kahneman et al, 1991). The endowment effect predicts that once a certain level of wealth is obtained a person will place more value on retaining that wealth than they did on acquiring it in the first place. The endowment effect provides several potential explanations for why Westbrook’s (2010) survey found developers do not prefer and perceive a low profitability for ESDs despite consumers’ stated preferences.

Developers might perceive low profitability for ESDs because the endowment effect conditions consumers’ willingness to pay (WTP) for environmental amenities associated with ESDs. Housing consumers may be willing to pay more to protect environmental amenities associated with their residence than they would have been willing to pay to acquire them as part of the initial housing price (Mohamed, 2006a). Thus, stated consumer preferences might reflect the value of housing to consumers after purchase, which may not translate into a higher initial WTP for ESDs. This may account for the discrepancy in Westbrook’s (2010) findings between consumers’ stated preferences and developers’ low perceived profitability for ESDs.

Developers might also be unlikely to build ESDs because they perceive a low likelihood of such housing types meeting short‑term profit targets (ie, a normal rate of return on investment). Profit targets represent a subjective point at which inputs are reduced upon reaching a certain revenue level. Setting short‑term profit targets has been observed across a wide range of professions including taxi drivers (Camerer et al, 1997), physicians (Rizzo and Zeckhauser, 2003), solo proprietors (Wales, 1973), and farmers (Berg, 1961). Mohamed (2006a) proposes that developer satisficing stems from developers choosing housing types perceived most likely to meet short‑term profit targets and avoid short‑term losses, rather than maximizing profits from all potential options. Furthermore, developers might then treat the attainment of profit targets as endowments, such that greater value is placed on avoiding losses from additional variable costs associated with ESDs (eg, landscaping, maintaining environmental amenities, altered site preparation) than on potential profits that might result from those investments (Mohamed, 2006a). In other words, the forgone gains are less painful than perceived losses (Kahneman et al, 1991). This behavior is what Samuelson and Zechauser (1988) refer to as the ‘status quo bias’. The resulting satisficing and loss‑aversion behavior may lead developers to favor conventional projects over ESDs.

In addition, profit targets are subject to a number of land, credit, and policy uncertainties that constrain the types and locations of development [see Carter (2009) and Adams and Watkins (2008) for detailed discussions]. Risk‑based lending rates, in particular, influence the types of houses developers build (Bookout, 1990). Due to lenders and homebuyers’ preferences for housing types with proven resale value, credit is often easiest to secure for ‘tried and tested’ housing types (Ball, 1999), thus reinforcing the status quo bias. However,

Figure 1. A value function mapping gains and losses from a reference point (origin) according to prospect theory (source: Kahneman and Tversky, 1979).

Value

Losses Gains

Effects of alternative developer decision‑making models 5

the effects of risk‑based lending rates on developer decision making and profit targets likely depend on who bears the risk of potential losses. Since lenders bear substantial risk from failed development projects, the profit targets of smaller developers are likely subject to risk‑based lending rates, whereas larger developers with sufficient capital available may set their profit targets independent of such limitations (Chan, 1999; Dowall, 1984). Risk‑based lending rates may interact with developer‑satisficing behavior to further reinforce negative perceptions of and preferences for ESDs.

3 MethodsDevelopers could be using a range of different decision frameworks and may differ in how they consider alternative projects. Standard theory from business and economics assumes underlying profit maximizing motives, but actual decisions are often complex and subject to many uncertainties. Prospect theory provides a theoretical explanation for why development decisions might favor traditional rather than alternative development designs such as ESDs that may be more or equally profitable. The CHALMS model is modified to implement insights from prospect theory and parameterized with survey data to test the effects of profit maximization versus satisficing (ie, loss aversion) decision‑making frameworks on housing offerings. In particular, the model is used as an agent‑based virtual laboratory to test for mechanistic explanations of changes in the timing and number of houses built stemming from differences in the developer’s decision‑making processes. However, the model is not intended to make any substantive contribution to our understanding of the effects of satisficing behavior on spatial patterns of development, as it is not calibrated to reproduce spatial patterns from any particular location. More detailed empirical data would be needed for such a task.

3.1 Experimental setupThe analysis will explore three alternative developer decision‑making frameworks:1. Profit maximization. Developers choose to build housing types that maximize potential revenue net of costs.2. Loss aversion. Consistent with the valuation rationale posited by prospect theory, developers place more value on potential losses than potential gains for any given housing type.3. Developer preference. The developer preference decision‑making framework is implemented as a ‘pure preference’ for each housing type—reported as ‘likelihood to develop’ in the Westbrook (2010) developer survey, which alters the developer’s calculation of expected returns independent of economic or other psychological influences.

The effects of each of these decision models on developer profits, consumer utility levels, and housing‑market outcomes are investigated. Costs to the developer associated with uncertainty in the development process (ie, during both construction and sale) are implemented through variable borrowing costs. Each decision model will be tested in the context of fixed and variable (ie, based on perceived profit risk) lending rates. The profit‑maximization decision‑making framework with fixed lending rates is taken as the baseline case against which alternative decision‑making frameworks and lending rates are compared.

Each model version is run thirty times with twenty annual time steps (with ten previous time steps as model spin‑up), and average outcomes across runs are reported. Construction costs for conventional and ESD housing types are assumed to be equal so that we can isolate the effects of alternative decision‑making frameworks and risk‑based lending rates. In addition, Shannon’s evenness index is calculated for each model version to detect uneven distributions of housing types in overall housing offerings.

6 N R Magliocca, D G Brown, V D McConnell, and coauthors

3.2 CHALMS model description CHALMS simulates a growing exurban area in which land is converted from farming to residential housing of varying densities over time (figure 2). The landscape is an 80 × 80 cellular grid with each cell representing an acre for a total region of 6400 acres, or 10 square miles. The model is initialized with a small established development area representing a fringe suburban business district (SBD), which is surrounded by undeveloped farmland divided into fifty farms. Farms are distinguished by their distance from the SBD and differ randomly in size and productive capacity. A complete description of model parameters is provided in Magliocca et al (2011). Farmers also differ in how they form expectations about future prices for their land. Farmers compare the returns from farming with expected profits from selling their land to a single representative developer and make a decision each period whether to continue farming or enter the land market. Inequality between the developer’s demand for land and the total supply of land from farmers establishes the bargaining power of farmers, which influences land transaction prices.

A single developer determines housing profitability among different types, which vary by both structure and lot size. The single‑developer simplification was made to facilitate the interpretation of the mechanisms shaping housing outcomes without the complicating effects of competition among developers. The results are discussed in light of this simplification, and the implementation of multiple developers remains a priority for future model development. The developer sells a housing good (ie, a combination of a given house type and lot size) to a consumer who (a) prefers to be close to the SBD to minimize transport costs, and (b) is differentiated by both income and preferences over different housing types. CHALMS tracks development over time, incorporating elements of path dependence and stochastic uncertainty into development decisions. Price‑prediction models for the developer and farmers are used to form expectations of future land and housing prices, respectively, and are described by Magliocca et al (2011).

3.3 CHALMS–ESD model description3.3.1 Housing typesCHALMS was modified to accommodate seven housing types based on subdivision characteristics and designs from the Nassauer et al (2009) homeowner survey that were employed in Westbrooks’s subsequent developer survey (Westbrook, 2010). These include

Figure 2. Conceptual map of agent and market interactions in CHALMS. The numbers indicate the (counter‑clockwise) sequence of events within one simulated time period (t). Agents (shown in italics) are labeled with the underlying conceptual model that governs their behavior. Intertemporal processes (t +1) shown include updating developer’s rent prediction models, updating the farmers’ land price prediction models, and exogenous growth of the consumer population.

Housing supply

Housing demand

Update prediction

models (t +1)

Update prediction

models (t +1)

Population growth (t +1)

Land supply

Land demand

Bid Ask

AskBid

2. Spatial rents

Consumers: utility

maximization

1. Housing‑ market

interactions

3. Land‑ market

interactions

Developer: rent

expectations

Developer: profit

maximization

Farmers: land‑price

expectations

4. Spatial land prices

Effects of alternative developer decision‑making models 7

three prototype conservation subdivision design options as alternatives to conventional designs within each of high (H)‑priced and medium‑to‑low (ML)‑priced housing categories (table 1). ‘Ecoconservation’ subdivisions feature a higher overall proportion of public forested and nonforested open space than the conventional design, and consequently private lot sizes are reduced for the ML‑priced and H‑priced housing types, respectively (Westbrook, 2010, page 15). Ecoinnovation subdivision designs emphasize the replacement of half of lawn turf grass with native herbaceous vegetation (Westbrook, 2010, page 15). A third established design was also included: ‘Ecoremnant (H‑priced market only), which consists of lots larger than one acre and remnant forest or wetland covering at least 10 acres of the subdivision (Westbrook, 2010, page 16). Each housing type has a natural amenity level according to its respective subdivision design, which is specified arbitrarily as a dimensionless number representing relative utility to consumers. House sizes for all designs are kept constant, but higher priced houses are associated with larger lots.

3.3.2 Agents’ price expectation modelsDevelopers and farmers make pricing decisions informed by expectations of future housing and land prices, respectively. Adapted from price expectation models used in agent‑based financial literature (eg, Arthur, 1994; Arthur et al, 1997) to consider spatially explicit information, agents form expectations of next period’s land or housing prices using a set of ‘backward‑looking’ prediction models. Each agent is randomly given one of twenty prediction models that vary in the prediction method and time span over which past observations are considered. Each prediction model may use one of six different prediction methods, which include averaging over time and space, cycle detection, and linear extrapolation. The performance (ie, error) of each model is tracked every period, and the agent acts on the prediction of the currently most‑successful model (ie, the ‘active’ model). In the next period, actual prices are realized and model performances are updated. Agents are, therefore, able to learn which models best predict price trends, and can adaptively switch to following the predictions of a previously ‘dormant’ model if it out‑performs the current ‘active’ model when conditions change. A detailed description of the prediction models is provided in the appendix of Magliocca et al (2011).

Table 1. Parameters for each housing type. Housing types 2, 3, 5, and 6 are considered ecological subdivision designs, as housing type 7 (Ecoremnant) is an established housing type. The developer’s preference is reported in the Westbrook (2010) developer survey, and corresponds with the third decision‑making framework described in subsection 3.1.

Housing type (price range) House size (ft2 )

Lot size (acres)

Amenity level

Construction costs ($)

Developer’s preference

1 Conventional (ML) 2000 0.5 100 270 775 0.852 Ecoconservation (ML) 2000 0.4 400 270 775 0.653 Ecoinnovation (ML) 2000 0.5 300 270 775 0.834 Conventional (H) 2000 2.0 100 295 375 0.625 Ecoconservation (H) 2000 1.9 400 295 375 0.606 Ecoinnovation (H) 2000 2.0 300 295 375 0.607 Ecoremnant (H) 2000 3.0 400 300 620 0.64

Note: ML = medium‑to‑low; H = high.

8 N R Magliocca, D G Brown, V D McConnell, and coauthors

3.3.3 Consumer utility, WTP, and willingness to bid (WTB)A consumer c calculates a standard Cobb–Douglas utility derived from the consumption of a general consumption and housing good. Each housing good is the house and lot size and the natural amenity ‘bundle’ of one of the seven different housing types described above. We assume that consumer c’s utility function has a Cobb–Douglas form:

( , ) ( ) ,U c n I P s l ac n na

n n naskc c c c}= - -;b c f (1)

where Ic is income, n} is the travel cost from the location of house n to the SBD, and ,cb ,cc cf are the consumer’s idiosyncratic preferences for house size (s), lot size (l ),

and environmental amenities (a), respectively. P nask ; is the developer’s asking price for house n, which is determined by the developer’s expected rent, which is formed using the price expectation models described in subsection 3.3.2. The maximum bid of a given consumer (ie, WTP) for any given house is equal to the portion of the consumer’s income allocated to housing [ie, ( )1 ca- in equation (1)].

( , ) ( )( ) .c n IWTP c n c c c} b c f= - + + (2)

With a limited number of houses available at any given point in time, consumers may not always be able to locate in the house that provides the highest utility. Thus, we compute a bid,

( , ),R c n* for each housing option available for each consumer that reflects the relative utility difference between that option and the one that produces the maximum utility, :U *

( , )( , )

.R c n P UU c n*

*nask= ; (3)

The consumer’s bid for any particular house is then the minimum of their constant share of income for housing as shown in equation (2) or the bid given in equation (3). The degree to which the bid differs from WTP(c, n) depends on the relative utility of each housing option, the consumer’s income, and idiosyncratic preferences, as well as the developer’s asking prices [see equation (A1) in the online appendix, http://www.dx.doi.org/10.1068/b130118p].

3.3.4 Developers3.3.4.1 Rent expectations and spatial rent projections. The developer uses housing information, which would be available from a listing service or similar source, to form expectations of annual rental payments for different housing types in the next period. This information includes the average past and current rent, lot size, house size, number of bidders before sale, percentage that sale price was above (or below) the original asking price, the number of houses of each type, and an approximation of residents’ income levels. For any given house, the developer uses financial prediction models (subsection 3.3.2) to form a rent expectation for that house in t 1+ given past rental information. Rent expectations are then used to make spatially explicit rent projections for all housing types in all undeveloped cells.

Rent projections are calculated as the weighted combination of local and regional (suburb‑wide) expected rents for existing houses (Magliocca et al, 2011). The method of rent projection depends on the level of uncertainty in rent expectations. If a given housing type has been built, a spatially weighted extrapolation is made based on distance and price trends. If the given housing type has not yet been built within the region, the developer relies on a hedonic regression model based on existing housing characteristics. The hedonic regression uses median consumer income (xi) from similar housing types, lot size of the given housing type, h (x2), and travel costs to the given location, i (x3), to project an expected rent:

( , ) .R i h x x x0 1 1 2 2 3 3proj b b b b= + + + (4)

Effects of alternative developer decision‑making models 9

For each undeveloped cell, the expected rent for each housing type is projected taking into account the distance of the given cell from the SBD and associated travel costs. Projected rent expectations become the developer’s asking price, ,P nask ; for each existing or newly built house n (subsection 3.3.1).

3.3.4.2 Carrying costs. If newly bought land parcels or newly constructed houses remain vacant, carrying costs are incurred by the developer annually and do not compound over time. Carrying costs represent costs to the developer associated with holding vacant property; for example, interest accrued on loans financing the development project or foregone interest on an alternative safe investment. Carrying costs for vacant land equal 5% interest on the price paid for land. Carrying costs for vacant houses equal 5% interest on the combined price paid for land and annualized construction costs of the particular housing type. Thus, available capital in a given period is constrained by the amount of vacant land or houses the developer owns, which influences how much land the developer can acquire each period.

3.3.4.3 Risk-based lending rates. Due to uncertainty of the profitability of ESDs, it is possible that interest rates for the developer could be higher for ESD construction. To capture this, we assume the lending rate is risk based and applied to construction costs. Risk‑based lending rates, where risk is related to variation in housing rents, are specific to each housing type. Rent uncertainty is calculated as the average coefficient of variation between rents for the current and the last period for all instances of the given housing type across the region (ie, not spatially explicit). Lending rates, rloan, are set initially to 5% for all housing types, and then updated each period as a weighted average between the current lending rate and the normalized rent volatility specific to each housing type according to:

( , ) ( ) ( , )[ ( , )]( , )

,min

r h t r h t v h tv h t1 1loan loanV V= - - + (5)

where Δ is a weight equal to 0.05 and v is the rent volatility. Rent volatility is normalized by its minimum value so that lending rates are adjusted relative to the best performing (ie, most stable rent over time) housing type. We assume that the developer borrows to build houses, so the risk‑based lending rates are applied to the construction costs listed in table 1 such that securing finance to build housing types with high volatility is relatively more expensive than to build those with more stable rents over time.

3.3.4.4 Alternative models for calculations of the developer’s return. The developer forms expectations of rents ,E R h i;G H^ h for each housing type (h) in each cell i in time t based on past rent information through the process described above in subsection 3.3.4.1. Three different models are used to calculate returns: profit maximizing, loss averting, and developer preference.

Profit-maximizing decision framework. Expected returns ,E h iRet ;G H^ h before land purchase are calculated for each housing type net of construction and infrastructure costs (ccost) subject to a risk‑based lending rate (rloan), last period’s carrying costs (Ccarry), which are applied equally over all acres demanded (Ad) in time t, and a profit target (1− r) equal to a normal rate of return (r) of 5%:

, , (1 ), ,

,ccostE h i t r z

E R h i t rA

c t 1Ret

,d t

loan carry;

; ;= -

--

-^ h (6)

where z converts expected returns per lot to expected returns per acre. Depending on the model experiment, rloan is equal to one or one plus some risk‑based rate.

10 N R Magliocca, D G Brown, V D McConnell, and coauthors

The expected return of the housing type that generates the highest expected utility, ,h* for a given cell , ,E h i tRet* *;^ h is the basis for the developer’s WTP for that acre.

The developer forms a WTP for each farm (Fn) as the average return across all cells contained within the farm ( ) .i Fn!

( , ), ,

.F t A rE h j t1WTPRet*

nF j i F loann n

;=

!=

/ (7)

In each landscape cell within a farm, the housing type with the highest expected return is built first, with others following in the order of descending expected returns.

Loss-aversion decision framework. The loss‑aversion decision framework takes into account the prediction error, σ, associated with the most successful rent prediction model for each housing type. Based on this prediction error, expected returns are bracketed by high and low estimates for housing type h in cell i at time t.

, , (1 ), ,

,ccostE h i t r z

E R h i t rA

chigh Ret

,

t

d t

t1 1loan carry;

;v= -

+ --

;- -^ h (8)

, , (1 ), ,

.ccostE h i t r z

E R h i t rA

clow Ret

,

t

d t

t1 1loan carry;

; v= -

- --

;- -^ h (9)

High and low estimates of expected returns are then considered in a risk‑aversion framework modified from Ligmann‑Zielinska (2009) to conform to prospect theory. Potential gains (potgain) and losses (potloss) are calculated relative to a reference point of zero, which represents meeting the profit target of a normal rate of return applied in equations (8) and (9).

( , , )

, ,,

,

( , ), ,

,

, , ;

, , ;

, , ;

potgain

potgain

h i t

E h i t

h i E h i t

E h i t

E h i t

E h i t

0

0

0

0

high Ret

low Ret

if

if

if

high Ret

high Ret

low Ret

1

1

gain

gain

gain

gain

2;

;

;

; G

; H

~

~

=

+

~

~

e

e

o

o

Z

[

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]]]

]]]

(10)

( , , )

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( , ), ,

,

0,

, , ;

, , ;

, , ;

potloss potlossh i t

E h i t

h i E h i t

E h i t

E h i t

E h i t

0

0

0

high Ret

low Ret

if

if

if

high Ret

low Ret

low Ret

1

1loss

loss

loss

loss

1

;

;

; G

;

; H

~

~= +

~

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e

e

o

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Z

[

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(11)where ωgain (3) and ωloss (2.5) are skewedness factors modified from Ligmann‑Zielinska (2009) to reproduce the value function in figure 1. Expected utility from each housing type is then calculated as:

, ,( , , ) ( , , )

( , , ).potgain potloss

potgainE U h i t h i t h i t

h i t; =

+ (12)

Housing types are ranked from highest to lowest expected utility to the developer excluding those with negative expected returns. This ranking gives the order in which housing types will be built.

Effects of alternative developer decision‑making models 11

In each landscape cell, an average of expected return is calculated, , , ,E h i tRet ; t from the set of housing types with positive expected rents, ht. The developer forms a WTP for each farm (Fn) as the average of , ,E h i tRet ; t across all cells contained within the farm ( ):i Fn!

( , ), ,

, , , ,.

ReF t A E U h i tE U h i t E h i t1WTP t

nF j i Fn n ;

; ;

R

R=

!=t

t t/ (13)

Developer Preference Decision Framework. Developer preferences in table 1 are used to explicitly model the status quo bias implied by prospect theory. The decision‑making framework is identical to the loss‑aversion framework, except that a preference specific to each housing type, δh, is applied as a pure preference (subsection 3.3.1) to the expected utility function.

, ,( , , ) ( , , )

( , , ).potgain potloss

potgainE U h i t h i t h i t

h i th; d=

+ (14)

The developer’s WTP for land is the same as in the loss‑aversion framework [equation (14)].

3.4 Housing-market interactions3.4.1 Housing-market competitionA given consumer will bid on the set of houses for which their WTP (subsection 3.3.3) is greater than or equal to the developer’s asking price [see equation (A2) in the appendix]. The housing‑market competition factor, HMC, describes the competition for housing each consumer faces in the housing market:

,N NN NHMCcC H

C H=+- (15)

where NH is the number of houses the consumer bids on and NC is the number of other consumers bidding on those same houses. Consumer c then sets a bid price [equation (3)] for each house in response to market conditions. Competition is high for a given consumer if there are more bidders for the houses he/she is bidding on than there are houses, and the bid will be increased. Competition is relatively low if there are more houses he/she is bidding on than total bidders for those houses, and the bid is adjusted downward. The adjustment of consumers’ bid prices in response to market conditions allows consumers to attempt to maximize their gains from trade and the likelihood that they will be the highest bidder.

3.4.2 Rules for matching consumers with housesAfter the bidding process is completed, the highest bidder for each house is identified. For each consumer in the set of winning bidders, the set of houses for which the consumer owns the highest bid is identified. The consumer’s utility is recalculated [equation (1)] for each of these houses using the winning bid instead of the initial asking price. Given these new levels of utility, the consumer is matched with the house that produces the highest utility. Once a consumer is matched with a house, both the consumer and house are removed from the market. The matching process is reiterated with the remaining bids, which are kept constant, until all consumers are matched, all houses are occupied, or all positive bids are exhausted. This process ensures consumers are matched to houses that generate their maximum possible utility levels given competitive bids from other consumers and discrete housing options provided by the developer.

12 N R Magliocca, D G Brown, V D McConnell, and coauthors

3.5 Land-market interactions3.5.1 Formation of farmer’s WTAFarmer expectations of land prices are formed using the price prediction models described in subsection 3.3.2. A farmer’s decision to sell to a developer or continue farming is based on the expected return from selling his farm relative to the value of the farm’s agricultural return per acre in perpetuity. The farmer’s WTA is set dynamically to the greater of the two values [see equation (A3) in the appendix]. This enables the farmer to capture speculative gains from sale of his land when development pressure is high, while enforcing a rational threshold below which the farmer would be better‑off farming.

3.5.2 Bargaining powerIf the developer’s WTP for a given farm is greater than the farmer’s WTA for his land, then the two enter into bilateral negotiation to determine the final transaction price for each parcel. Bargaining power in the land market, ,f is adapted from Parker and Filatova (2008) and captures differences in the developer’s demand for, and the farmers’ supply of, land at the initial WTP of the developer.

,d Ad A

F

F

Land

Land*

*

f =+- (16)

where dLand is the acreage demanded by the developer and AF* is the acreage supplied by participating farmers. F * is the subset of all farmers for which the condition WTP > WTA is true. If the developer demands more land than farmers supply, f is positive and farmers ask a price above their WTA [see equation (A4) in the appendix]. If farmers supply more land than is demanded by the developer, f is negative and the developer will bid below the initial WTP [see equation (A5) in the appendix]. The amount of land supplied by farmers in any given period depends on the initial WTP of the developer for each farm, which depends on rent expectations in the housing market. Thus, the housing and land markets are explicitly linked.

4 ResultsOverall housing offerings differed most between model versions with and without risk‑based lending rates. Housing stocks were higher overall in model versions with a fixed 5% lending rate which was attributed mainly to the popularity of ML‑priced conventional housing types (1) and greater supply of ESD housing types (2, 3, 5, and 6) (figure 3). Conventional housing types were supplied in greater numbers across all model versions, although alternative decision‑making models favored conventional types slightly more than the profit‑maximizing‑model versions. With fixed lending rates, the developer preference model version more closely mirrored baseline (ie, profit maximizing) housing offerings than did those produced by the loss‑aversion‑model version. Ecoremnant housing types (7) were generally the most popular, especially in later periods and model versions with risk‑based lending rates.

4.1 Timing of ESD introductionThe introduction of ESDs into the housing market occurred at different times according to the level of profit uncertainty (ie, variability in housing rents). ESDs were generally introduced earlier in model versions with fixed lending rates [figure 3(b)]. The first introduction of ESDs occurred after five time steps in both profit‑maximizing model versions, as well as in the loss‑aversion and developer preference model versions with fixed lending rates. An additional time step was required for ESD introduction in risk‑based lending rate‑loss‑aversion and developer preference model versions [figure 3(b)]. However, at these time steps, ESDs had not appeared in all model runs within a particular model version. More widespread

Effects of alternative developer decision‑making models 13

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14 N R Magliocca, D G Brown, V D McConnell, and coauthors

introduction of ESDs, measured as average time until more than one ESD was built in all model runs, was more varied across experimental settings (figure 4). Higher variability in housing rents was associated with later introduction and slower rates of increase of ESDs. Rent variability was generally lower in model versions with fixed lending rates, which led to earlier introduction in all model runs and faster rates of growth. The opposite was observed in housing offerings generated with risk‑based lending rates. For example, the first ESD to be produced at more than one house in every run was in the model version for loss aversion with fixed lending rates. With the lowest housing rent variability of any ESD in any model version [figure (4b)], the H‑priced ecoinnovation housing type (6) was introduced first [figure 4(a)] and grew the fastest (figure 3). The timing and growth of other ESDs followed in order of increasing rent variability.

Figure 4. [In color online.] Evidence of the effects of alternative decision‑making models and risk‑based lending rates measured as time till more than one ecological subdivision design was built in all model runs of a particular model version (a), which was influenced by uncertainty in the profitability of not yet constructed housing types (b) (measured as the average coefficient of variation in housing rents with 95% confidence intervals).

Fixed, profit‑maximizing

Risk, profit‑maximizing

Fixed, loss aversion

Risk, loss aversion

Fixed, developer preference

Risk, developer preference

Tim

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8

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2 3 5 76Housing type(b)

(a)

Figure 5. Rents for ecological subdivision designs (housing types 2, 3, 5, and 6) over time averaged across runs of model versions with fixed and risk‑based lending rates.

40 000

30 000

10 000

20 000

0

Hou

sing

rent

($)

Time step

Fixed lending rate

15 20 25 30

Risk‑based lending rate

Figure 6. [In color online.] Increasing shares of consumer bids to ecological subdivision designs (housing types 2, 3, 5, and 6) in model versions with fixed lending rates compared with model versions with risk‑based lending rates. (a) Fixed, profit maximizing; (b) risk, profit maximizing; (c) fixed, loss aversion; (d) risk, loss aversion; (e) fixed, developer preference; (f) risk, developer preference.

Housing type

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11 14 17 292320 26 11 14 17 292320 26Housing type Housing type

1 2 543 76

16 N R Magliocca, D G Brown, V D McConnell, and coauthors

4.2 Housing supply dynamicsWhen more than one ESD was produced in all runs of a particular model version, the developer observed consumer demands directly and uncertainty in the profitability of ESDs was reduced. In model versions with fixed lending rates, ESD rents decreased over time as the developer gained experience and was better able to predict consumer demands and future rents (figure 5). Lower housing rents increased the accessibility of ESDs for lower income consumers, which resulted in a greater share of consumer bids over time (figure 6). With more consumer competition for ESDs, rent variability was reduced, which resulted in a greater supply of ESDs that further reinforced declining rents.

Regardless of the model version, rent volatility was high for all ESDs at the time of and shortly following introduction into the market. In the presence of risk‑based lending rates, however, such rent volatility kept lending rates high and reduced the profitability of ESDs. Thus, the supply of ESDs remained low and could be purchased by only the wealthiest consumers. This increased housing rents for ESDs over time (figure 5), which reduced the proportion of the consumer pool that could bid on ESDs (figure 6). Fewer consumer bids reinforced the initial volatility of rents and limited the production of ESDs over time.

4.3 Overall market outcomesDifferences in the overall diversity of housing offerings was also observed with different lending rates. Greater supply of ESDs in model versions with fixed lending rates led to more evenly distributed housing offerings (figure 7), whereas housing offerings produced under risk‑based lending rates favored H‑priced conventional and ecoremnant housing types. Evenness of housing offerings influenced and was influenced by the distribution of consumer bids. The diversity of housing offerings in model versions with fixed lending rates facilitated sorting of consumers by income and housing preferences and resulted in more stability in housing rents over time. Because consumers more often purchased the house that maximized their utility, higher average consumer utility levels resulted despite lower average incomes (table 2). Conversely, unevenly distributed housing offerings produced under risk‑based lending rates limited ESDs to high‑income consumers, which increased rent levels and variability for ESDs and decreased consumer sorting among other housing types. The result was generally lower average utility levels despite higher average household income (table 2).

Figure 7. [In colour online.] The evenness of housing type distributed across all possible housing offerings as measured by Shannon’s evenness index. An index value of one would represent a perfectly even distribution among housing types.

Time step10 15 20 25 30

Shan

non’

s eve

nnes

s ind

ex

Risk, profit maximizing

Fixed, profit maximizing

Risk, developer preference

Fixed, developer preference

Risk, loss aversion

Fixed, loss aversion

0.90.80.70.60.50.40.30.20.10.0

Effects of alternative developer decision‑making models 17

Finally, developer profit was higher in model versions without risk‑based lending rates. Across alternative decision‑making models, loss aversion produced comparable or higher developer profits than profit‑maximizing model versions, while the developer preference decision‑making models had the opposite effect.

5 DiscussionProspect theory, and associated endowment effect and status quo bias, provide possible expla‑nations for variations in residential housing supply decisions resulting in limited offerings of ESDs. The resulting model is an implementation of a mechanistic explanation for developer‑satisficing behavior that allowed for testing the effects of loss aversion, pure preferences, and risk‑based lending rates on housing‑market outcomes and their consequences for the supply of ESDs. Risk‑based lending had the largest effects on housing offerings, developer profits, and consumer utilities. ESDs were generally introduced earlier and at higher rates in model versions with fixed lending rates, and overall housing offerings were more evenly distributed among possible housing types. Conversely, housing offerings under risk‑based lending favored conventional and H‑priced ecoremnant housing types, which resulted in limited production of ESDs.

In model versions with fixed lending rates, ESDs captured comparable, if not higher, proportions of consumer bids than conventional housing types by the end of the simulation periods (figure 6). So, if consumers are willing to pay for relatively higher priced ESDs—and developers correctly perceive this, as Westbrook’s (2010) survey findings suggest—why are ESDs and other innovative housing types in limited supply? The answer may lie in developer perceptions of the profit uncertainty of ESDs and the barrier that the combination of those perceptions and variable lending rates pose for introducing ESDs into the market.

The effects of risk‑based lending rates were clear: housing types with relative high rent volatility, even with higher profit potential, were produced in limited quantities. Risk‑based lending rates favored conventional housing types, which possessed a set of characteristics and were offered at prices that consistently appealed to a wide range of consumers and produced longer term reliability in returns. This was consistent with the findings of Nicol and Hooper (1999) that competitive developers must maintain at least one standardized set of starter, middle, and executive homes to compensate for uncertainty in consumer demands for particular housing types. When ESDs were built, rents were typically subject to some short‑term volatility in consumer demand (Mohamed, 2006a). Thus, risk‑based lending rates for these types were relatively high, resulting in only slightly positive or negative profit margins. This dynamic was consistent with the status quo bias observed by Samuelson and Zeckhauser (1988) and developers’ tendencies to favor tried and tested housing types (Ball, 1999).

Table 2. Average developer profit, consumer utility, and consumer income for all combinations of decision frameworks and risk‑based lending rates. Standard deviations are in parentheses.

Model version Fixed, profit maximizing

Fixed, loss aversion

Fixed, developer preference

Risk, profit maximizing

Risk, loss aversion

Risk, developer preference

Average developer profit ($ thousand)

6.41 (0.59)

6.40 (0.50)

5.27 (0.49)

4.54 (1.07)

4.61 (1.37)

4.27 (1.26)

Average consumer utility (thousand)

26.80 (5.52)

28.10 (7.04)

26.60 (5.29)

27.70 (6.27)

25.10 (5.15)

24.50 (3.98)

Average consumer income ($ thousand)

109.10 (3.86)

109.70 (5.48)

108.10 (2.81)

111.80 (3.92)

112.60 (3.82)

113.60 (4.16)

18 N R Magliocca, D G Brown, V D McConnell, and coauthors

Developer perceptions of the low profitability of ESDs stemming from risk‑based lending rates were reinforced by loss‑aversion decision making. The consistency with which conventional types met profit targets created an endowment effect; potential losses associated with not meeting profit targets were valued more heavily than potential gains from ESDs. As a result, potential profit opportunities were foregone or delayed, particularly those associated with ML‑priced ESDs, in favor of meeting short‑term profit targets through conventional housing types.

Thus, the setting of profit targets can be both a consequence and main cause of developer‑satisficing behavior in the model. Regardless of the model version, rent volatility led to perceived uncertainty in profitability and the ability to meet profit targets, which delayed and/or limited the production of new housing types. This mechanism provides a possible explanation for the limited production of innovative subdivision designs in the real world. More broadly, these model results could explain the limited success of policy interventions aimed at reducing uncertainty in the development process, because they have failed to address developers’ underlying motivations for setting short‑term profit targets. Thus, if real developers’ decision‑making processes are indeed consistent with the features of prospect theory implemented here, then these results suggest that the tendency of developers to set profit targets is a leverage point for policy intervention in the development process. Perceived uncertainty in the profitability of ESDs encouraged the production of conventional housing types, which were more likely to meet profit targets. This further exacerbated rent volatility by producing low‑diversity housing offerings that increased competition among consumers for a few housing types. However, when a greater diversity of housing types was offered, consumer sorting by income and housing preferences was facilitated, which reduced rent volatility and increased average consumer utility. Therefore, if policy interventions could help overcome the uncertainty of meeting profit targets when introducing new housing types—by encouraging the introduction of a diversity of presold housing types at fixed prices, for example—then ESDs might see more widespread production.

Alternatively, the subjective decision‑making process implied by prospect theory may just be theory, and developers’ incomplete information, skill, and experience may be a sufficient explanation for under‑provisioning of ESDs and the foregone profit opportunities. Inexperience with ESDs can lead to relatively high construction costs (Adams and Watkins, 2008; Carter, 2009), and variability in consumer demand creates uncertainty around returns. These two factors may be sufficient for developers to favor tried and tested conventional housing types. However, incomplete information can only be part of the explanation for developer satisficing, because Westbrook’s (2010) survey findings suggested that developers perceive consumer preferences for ESDs correctly. Given that model experiments produced housing offerings consistent with observed patterns of limited ESD production, prospect theory provides a complementary explanation for developer satisficing.

Given the high process and parameter uncertainty associated with the residential development process, the model results can rule‑in possible explanations but cannot adjudicate among competing explanations. There is a lack of detailed empirical data for the value of environmental amenities to consumers and variable and fixed construction costs associated with each of the housing types. If the relative differences in either environmental amenity values or construction costs, for example, were parameterized differently between conventional and ESD housing types, an alternative outcome would be likely. In addition, the representation of risk‑based lending rates was highly simplified. The methods through which lenders set rates and developers acquire financing are often unavailable and/or proprietary knowledge. These limitations suggest some future research directions. Detailed developer and consumer surveys designed to elicit construction and financing costs, profit

Effects of alternative developer decision‑making models 19

targets, and consumers’ WTP for ESDs would improve the representation of housing market interactions. In addition, the model could be extended to implement multiple, heterogeneous developers. The lack of experience with ESDs is a source of subjective decision making in the development process. If a developer type with greater tolerance for potential losses led the introduction of ESDs into the housing market, other more loss‑averse developers might follow after potential profit opportunities were made explicit.

6 ConclusionsSimulation of satisficing behavior on the part of developers stemming from loss‑averse decision making and risk‑based lending rates resulted in the limited production of ESDs. Model experiments demonstrated the critical role of developer decision making in selecting conventional housing types on the basis of profit targets. Policies that aim to mitigate some of the negative externalities of urban sprawl by encouraging ESD development should consider the potential effects of loss aversion in developer decision making, which motivates the setting of short‑term profits targets and leads to a limited diversity of housing offerings. Policy interventions that are more effective might then aim to reduce the uncertainty around the likelihood that ESDs can meet profit targets by stabilizing risk‑based lending rates and consumer demand for or potential losses associated with ESDs.

Implementing prospect theory in an agent‑based virtual laboratory provided a mechanistic explanation for some potential sources of developer‑satisficing behavior, as well as demonstrating prospect theory to be a viable framework for representing developers in housing and land markets. The use of an agent‑based virtual laboratory allowed the testing of alternative decision‑making models for which little empirical data exists. Alternative decision‑making models were turned on or off and the effects of each on housing offering efficiency could be determined experimentally. This approach provided insights into how developer decision making can shape housing‑market dynamics and outcomes. The virtual laboratory approach can build understanding of how, why, and under what conditions housing offerings fail to maximize developer profits, consumer utilities, and the potential of ESDs to mitigate some of the negative effects of urban sprawl.

Acknowledgements. The authors gratefully acknowledge financial support from NSF in the form of an IGERT Traineeship (#0549469) at the University of Maryland, Baltimore County (NRM), and a grant to the SLUCE project from the program on Dynamics of Coupled Natural and Human Systems (# GEO‑0814542).

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