Analyzing Open Space Policies in a Locational Equilibrium

Model with Endogenous Landscape Amenities.

Randy Walsh1

University of Colorado

Preliminary Draft

Comments Welcome.

January, 2003

1The author thanks Helen Ladd, Tom Nechyba, Holger Sieg, and especially V. Kerry Smith fortheir help and support. The author also thanks H. Spencer Banzhaf and Mark Coppejans for theirhelpful conversations. Dissertation support from Resources For the Future and the Lincoln Instituteof Land Policy is gratefully acknowledged. The views presented in the paper are those of the authorand not the supporting institutions.

Abstract

Open space protection and the new ‘Smart Growth’ movement have to date been policy

slogans lacking any formal analysis and evaluation. Evaluation of land protection policies

requires a structural model for land markets with spatial delineation so that the impacts of

policy on locational attributes can be described. This paper uses estimates for household

preferences derived from a locational equilibrium model to compute general equilibrium

responses and associated welfare changes in response to spatially delineated open space

protection policies and development restrictions. Moreover, the framework accounts for the

endogeneity of open space amenities. Results from general equilibrium policy experiments

highlight the importance of accounting for general equilibrium effects in analyzing the im-

pacts of open space policies. When the endogeneity of open space amenities is accounted

for, the welfare impacts of land protection policies are reduced as households adjust in

equilibrium in a way that offsets the impacts of the exogenous change. The impacts of de-

velopment restrictions are shown to depend on the characteristics of the sub-regions where

the restrictions are imposed.

1 Introduction

The United States is currently experiencing an explosion of growth control initiatives. These

efforts are part of a larger ‘Smart Growth’ movement that seeks to promote increased density

in urban development and to protect open space. Unfortunately, little is known about the

impacts of land protection policies on the entire landscape and the responses of consumers

to these changes.

Three aspects of land protection policies and growth restrictions complicate structural

modeling of market responses to them. First, it is necessary to account for the spatial

nature of the problem. An acre of land protected at location A is not equal to an acre of

land protected at location B. Second, it is important to account for land market equilibrium

effects from non-marginal land protection policies. Third, landscape amenities associated

with open space include undeveloped private and protected public lands. As a result, at

least some open space amenities must be treated as endogenous. Households’ adjustments

in location and lot size caused by new land protection policies give rise to new patterns of

developed and open land. If households are concerned about the pattern of protected and

unprotected open space, enodgenous changes in development patterns associated with new

land protection must be reflected in the analysis of the net gains from public intervention.

To account for these issues, a general equilibrium (GE) model is developed which in-

cludes both the spatial delineation of land parcels and the endogeneity of open space ameni-

ties. Household preferences are estimated using an extension of the empirical locational

equilibrium model initially implemented by Epple and Sieg (1999). This framework esti-

mates a micro-consistent model of household preferences for location and lot size based

on the different distributions of households observed across areas distinguished by location

specific attributes and land prices. A stylized land supply model is calibrated using the

empirical results from a reduced form disaggregate transition probability model to provide

land supply models for each of 91 discrete zones within Wake County, North Carolina.

1

These two components are then combined in a GE framework.1

Wake County is one of the fastest growing regions of the country, with a population

that expanded from 303,240 in 1980 to 513,901 in 1995. Construction of new single family

homes has expanded from 3,500 per year to 8,000 per year over the last 10 years.2 In the

November, 2000 elections, Wake County passed a $15 million bond referendum for open

space protection.

The policy analysis in this paper considers two types of policies. The first set of poli-

cies takes advantage of this initiative considering three stylized land protection policies for

spending the $15 million. The second set of policies explore the impacts of development

restrictions by implementing two different development freeze policies. These policies freeze

residential development at its 1984 levels in a selected subregion of Wake County.

The paper is organized into seven sections. The next section expands the discussion of

the role of open space in residential behavior and develops a theoretical model of an equi-

librium with endogenous landscape amenities. Section three presents the implementation

strategy for the locational equilibrium model. Section four describes the data used in the

analysis. Section five presents results from the locational equilibrium estimator. Section six

develops the three open space policies and two development freeze policies. Section seven

presents comparative statics for general equilibrium computations under the five policy

experiments and section eight summarizes the conclusions.

1Sieg, Smith, Banzhaf, and Walsh (2002) adapt the Epple-Sieg (1999) model to a G.E. framework basedon constant elasticity housing supply functions. This work extends their framework by endogenizing thelocation specific amenities (open space), allowing for more complex substitution patterns between publicgoods by introducing augmented prices, and developing a more detailed description of the supply side of themodel.

2The analysis of this paper addresses the role of open space in the intra-metropolitan location decisions ofhouseholds. To this end, a static equilibrium is computed for a given snapshot in time with the populationheld fixed. Changes in the aggregate landscape pattern will also have potential implications for inter-metropolitan location decisions. While of interest, these migrations are outside the scope of the locationalequilibrium model and are left to further research.

2

2 Modeling the Link Between household Choices and Open

Space Conversion

The role of open space amenities in preferences has not been evaluated in the literature.

These attributes are assumed to be “good things” with little specific information about

what they are. For this analysis the preferences for open space will be assumed to have a

‘private’ and ‘public’ component. These two components are assumed to impact household

lot demands differently across intensive and extensive margins. The characterization of the

public component of open space recognizes that it arises as an impure or mixed public good,

resulting from a composite of private land development decisions and public protection of

lands. Equilibrium in the system of neighborhood land markets is presented as a Nash

equilibrium characterized by a vector of neighborhood land prices and realizations of the

endogenous component of open space.

2.1 Background

Early efforts to characterize the amenity effects of open space were undertaken using hedo-

nic housing price models. Hedonic models measure only the marginal value of changes in

open space amenities and can not be used to analyze the impacts of non-marginal policies.3

Nevertheless, they can provides insight into how landscape amenities should be measured.4

Weicher and Zerbst (1973) present one of the earliest empirical treatments of open space

3There are two qualifications to this point. First, Palmquist (1992) demonstrates that in the case oflocalized externalities (for example highway noise in a single neighborhood), reduced form hedonic models aresufficient for welfare measurement of non-marginal changes. Second, Bartik (1988) provides a methodologyfor identifying bounds on the WTP of non-marginal changes based on hedonic models.

4Contingent valuation methods have also been used to study consumer preferences over open spaceamenities. For example Halstead (1984) provides estimates of Massachusets’ resident WTP for protectingagricultural land and Ready, Berger, and Blomquist (1997) provide measures of the willingness to pay ofKentucky residents for a program that would provide incentives for horse breeders to locate in the state.These studies recover consumers’ willingness to pay for a movement from one state of the world to another.Successful policy analysis therefore requires a complete understanding of the price and amenity levels thatwill be available after the policy is implemented. Thus, the methodology is of limited use in this application.

3

amenities in their analysis of the externalities associated with neighborhood parks in Colum-

bus, Ohio. They reduce the measurement of these amenities to a set of dummy variables

which describe immediate adjacency to protected open space and find positive price effects

only for houses which directly face the protected open space. In their work on open space

protection in Boulder, Colorado, Correll, Lillydahl, and Singell (1978) suggest that open

space is “a public good which benefits everyone in the Boulder area” and a ‘quasi-public

good’ due to exclusion from specific protected parcels primarily due to distance. This sec-

ond, ‘quasi-public’, aspect of open space is considered in their hedonic housing model. They

find that a one foot increase in walking distance to protected open space leads to a $4.20

reduction in expected housing price.

Li and Brown (1980) consider the impact of a large number of neighborhood quality

variables for a hedonic model in the suburbs of Boston. Their analysis includes the number

of housing units per square mile within each house’s census tract as a measure of “open

or green space” along with distance measures. More recently Geoghegan, Wainger, and

Bockstael (1997) provide the most comprehensive consideration of landscape amenities to

date. They include ecologically based indexes of landscape diversity and fragmentation with

measures of the percent of neighboring land in open space and residential use in a hedonic

model estimated in Maryland’s Patuxent watershed. By using GIS software it is possible

to consider different aggregations for a variety of scales including a .1 km and 1 km radius

of each house. They find prices increasing in percent open space within a .1 km radius of

the house, but decreasing in percent open space within a 1 km radius of the house.5

5In one specification with varying coefficients, the percent open space measure becomes a bad at distancesgreater than 67 km from Washington D.C.

4

2.2 Open Space in Household Preferences

To account for the distinction between the quasi-public and public good roles of open

space, preferences are defined over two distinct components of open space, Op and On. Op

is defined to represent private access to open space and is proxied for using a measure of

the distance from a given lot location to the nearest protected parcel of open space. On

parallels Correll et al’s (1978) public component and measures the ambient level of open

space amenities available in the neighborhood. It is represented by the percentage of a

given lot’s neighborhood which is in open space (both protected and unprotected). For

each lot location, Op is assumed to be determined as a result of exogenous land protection

policies. On on the other hand is endogenous to the model and arises from the aggregation of

household lot consumption decisions along with the exogenously determined land protection

policies. One further distinction is assumed regarding the two open space measures. Op

is assumed to be viewed by households as part of the overall service flow received from

the residential lot bundle while On is assumed to be separable from the lot consumption

decision. On influences household behavior only through the extensive margin or location

decision.

Under this characterization, open space is modeled within a framework which accounts

for both the exogenous (‘private’) and endogenous (‘public’) components of the landscape

amenity. Equation 2.1 presents a general utility function for household i conditional on

choosing lot l.

uil = Ui

[l(Cl, O

pl ), z, On

l

({Ci}L

i=1

)](2.1)

Cl defines the characteristics of the lot itself (including acreage) and Opl captures the ex-

ogenous amenities associated with the lot. l(.) is a sub-function which maps Cl and Opl

pairs to lot service flows. The endogenous or neighborhood component of the landscape is

captured by Onl

({Ci}L

i=1

). This function aggregates all household residential lot decisions

5

into a measure of the neighborhood amenities provided by the landscape. The mechanism

by which household lot decisions impact the endogenous landscape amenity is through the

conversion of open space to residential use.6 Finally, z is a Hicksian composite good which

includes housing structures.

Under this specification, Cl is analagous to what Cornes and Sandler7 term an ‘im-

pure public good’ and Andreoni’s (1989) model of a ‘warm glow’. Each household’s lot

consumption enters preferences directly through the lot bundle and indirectly through the

aggregation of lot consumption to determine the level of On. 8

To facilitate implementation of this general model several simplifying assumptions are

made. First, to allow the application of empirical techniques which account for heteroge-

neous tastes over differentiated products or communities, the landscape is divided into a

set of J spatially discrete zones.9 All residential lots within a given zone are assumed to

provide identical landscape amenities (exogenous and endogenous) and sell for the same per

unit price. The general characteristics of each residential lot Cl are collapsed to a single

measure of the lot’s size and all land is assumed to be leased from absentee landlords. It is

also useful to switch to a dual representation of preferences to describe the restrictions to

preferences and how they affect prices. Under these assumptions, conditional on choosing

zone j household i’s indirect utility function is presented in equation 2.2.

Vi(Pj , Opj , O

nj , yi) = vi

[h

(Pj , O

pj

), yi, On

j (.)]

(2.2)

Pj is the price of land in zone j and yi is household i’s income. There are assumed to be N

households consuming residential land in the metropolitan area. Their zone choice and land

6To simplify estimation, non-residential development is excluded from the model.7Cornes and Sandler (1996) page 255.8This specification only differs from that of Cornes and Sandler (1996) and Andreoni (1989) in the

complexity of the aggregation function. Cornes (1993) provides a discussion of different aggregation schemesfor public goods.

9Berry, Levinsohn, and Pakes (1995) develop an approach for use in differentiated product markets. Eppleand Sieg (1999) pioneer a new approach for use in hierarchical community sorting models.

6

demand are given by ji and di respectively. Prices and income are normalized by the price

of the numeraire which is constant across the entire metropolitan area. Given a discrete set

of location choices, the consumer’s problem is given in equations 2.3 and 2.4.

j∗i = arg maxj

{v

[h

(Pj , O

pj

), yi, On

j (.)] }

(2.3)

d∗i = −

∂ v

[h

(Pj∗

i,Op

j∗i

), yi, On

j∗i(.)

]∂Pj∗

i

∂ v

[h

(Pj∗

i,Op

j∗i

), yi, On

j∗i(.)

]∂yi

(2.4)

In equilibrium, all households are assumed to satisfy both of these equations.

2.3 Equilibrium in the Land Markets

The landscape mosaic represented by {j∗k , d∗k}Nk=1 arises from the interaction of supply and

demand in the residential land market. Because neither side of the market internalizes

the externalities that arise through the public component of the metropolitan landscape,

Onj

({jk, dk}N

k=1

), the supply of open space suffers from the problem of inefficient levels of

provision associated with local public goods.

This externality complicates characterization of equilibrium in the model. As consumers

respond to exogenous changes in the market, not only will prices adjust, but changes in

location choice and land demand will cause development patterns to change and therefore

lead to new values for the public component of open space. These open space changes then

feed back into consumer’s land demand and location choice. In order to analyze the impact

of exogenous changes, it is therefore necessary to identify a new equilibrium in the system.

Given a finite set of location choices, J and households I, such an equilibrium is char-

acterized by equations 2.5 thru 2.8.

∀ i j∗i = arg maxj∈J

{v

[h

(Pj , O

pj

), yi, On

j

] }(2.5)

7

∀ i d∗i = −

∂ v

[h

(Pj∗

i,Op

j∗i

), yi, On

j∗i(.)

]∂Pj∗

i

∂ v

[h

(Pj∗

i,Op

j∗i

), yi, On

j∗i(.)

]∂yi

(2.6)

∀ j Sj(Pj) =∑i∈I

1j∗i =j · di(.) (2.7)

∀ j Onj = On

j

({j∗i , d∗i }N

i=1

)(2.8)

The interpretation of these conditions is straightforward. Equations 2.5 and 2.6 require

each household to behave optimally at both the extensive and intensive margin. Equation

2.7 requires the residential land supply in zone j equals demand in zone j and 2.8 guar-

antees that the endogenous public good levels realized in each zone are obtained from the

aggregation of each household’s optimal choice as described in 2.5 and 2.6. The conditions

defined by equations 2.5 thru 2.8 represent a Nash equilibrium in which each household’s

location choice and lot consumption is optimal given the decisions of all other households.

2.4 Supply Model

The supply model is constructed based on an empirical model of the conversion of land

from undeveloped to residential use. These estimates were developed by Walsh (2002)

and provide for each parcel a probability distribution of the reservation price at which the

parcel will be converted. Integration of the supply and household choice models require

a land supply function that maps zone specific residential land prices Pj to the supply of

residential land in each zone Sj . Equation 2.9 is used to generate these zone specific land

supply functions.

Sj(Pj) = Llj +

∑i∈j

P [Sij < Pj ] ∗ AREAij (2.9)

where P [.] is the CDF for the reservation price of parcel i in zone j and Llj is the area of land

in residential use in neighborhood j as of 1984. Figure 1 presents a graphical representation

8

Figure 1: Impact of Land Protection on Residential Land Supply Model

Residential Land Supply

Pric

e

Low Reservation PriceProperties Protected

High Reservation PriceProperties Protected

Baseline Supply

Lu’ Lu Ll

A

of equation 2.9 under the assumption of a logistic distribution of reservation prices.

Figure 1 also demonstrates how government purchases of land effect market conditions

under the land supply model. New land protection has two effects on the supply model

in each zone. First, protection reduces the total or aggregate supply of land available for

residential development. This results in a one for one reduction in the upper bound, Lu. In

addition, depending on where in the distribution of reservation prices the protected parcels

fall, removal of parcels from the land market will cause a displacement of the supply curve.

The distribution of the reservation prices of parcels identified for protection under each of

the different policies will depend on attributes (some of which are unobserved) of the parcels

selected for protection under each of the policy scenarios. Figure 1 demonstrates how two

policies for protecting an identical acreage of land can have a different effect on supply under

9

this approach. The first policy results in purchases of parcels with low reservation prices

while the second policy purchases parcels with high reservation prices. The key difference is

that the second policy will have little effect on land market outcomes until demand reaches

point A in the graph while the first policy has an impact as soon as demand increases above

Ll.

3 Implementing the Locational Equilibrium Estimator

To estimate a structural model of preferences consistent with equation 2.3, the indirect

utility specification presented in equation 3.10 is adopted.

Vi(Pj , yi, Opj , O

nj , Lj) =

11 − ν

y1−νi − 1

1 + ηB

(Pj

1 + (Opj )λ

)η+1 G(On

j , Lj)αi (3.10)

This specification incorporates Willig’s (1978) pure re-packaging model using a functional

form suggested by Hanemann (1984).10 The model treats the private component of open

space as a quality adjustment to lot price. This approach is consistent with the characteri-

zation of a service flow derived from a lot bundle as discussed above in section 2.111 G is a

function that indexes spatial amenities as well as other spatially differentiated attributes of

location such as distance to the central business district. It includes the public component

of open space as well as a measure of other land uses in each zone. αi is assumed to cap-

ture the unobserved heterogeneity in household tastes for the index of locational attributes,

including the public good component of open space amenities.

The price elasticity of land is generally less than one in most applications. As a result,

this specification restricts Op to be a substitute for private land. With a price augmentation

10Hanemann’s (1984) equation 3.21a is adjusted to control for an index of location specific amenities,g(On

j , Lj). The augmentation factor is given by 1 + (Opj )λ.

11To see that this specification is consistent with equation 2.3 set h(.) = 11+η

B(

Pj

1+(Opj)λ

)η+1

.

10

framework, increases in Op will reduce the demand for private land.12

The treatment of private (exogenous) and public (endogenous) features of open space

in the indirect utility function yields a model satisfying a conditional form of the single

crossing property in permanent income and tastes for the location specific amenity index.

That is, the specification implies a sorting of households with the augmented price and level

of G as the basis for stratification.13 This property is more easily verified by considering

the form of the indirect utility function in equation 3.11.

Vi(P̃ , y, G) =[

11 − ν

y1−νi − 1

1 + ηB P̃ η+1

]Gαi (3.11)

P̃ is the augmented price. The slope of indifference curves in the {G, P̃} plane are given

by:

M(α, y, B, G, P̃ ) =dP̃

dG

∣∣∣∣∣V =V̄

=α

(1

1−ν y1−ν − 11+η B P̃ η+1

)G B P̃ ν

(3.12)

Over the plausible range of parameter estimates M(.) is strictly increasing in α and y.

Given α, this condition assures that households stratify by income. That is, higher income

households sort to higher G and P̃ communities. Similarly, holding income fixed, households

sort with α (e.g. households with higher values of α select higher G and P̃ communities).14

The parameters of the household utility model are estimated by taking advantage of

conditions for a locational equilibrium. This analysis extends the Epple-Sieg framework

by allowing open space to have two effects on people’s preferences. The protected public

land, Op, influences demand for lot size directly. The neighborhood quality measure On

acts at the extensive margin, affecting where people decide to live. As a result it influences

demand for lot size only indirectly. On aggregates each household’s lot demand choices

12The impact of this maintained assumption will be evaluated in future work.13In typical application single crossing implies sorting across products/zones by quality and price. Here

the sorting occurs in quality and augmented price, P̃ =Pj

1+(Opj)λ .

14For a further discussion of single-crossing in this context see Epple and Sieg (1999).

11

along with pre-defined land protection to measure the relative amount of open space. It is

possible compute the new land market equilibrium resulting from exogenous policy changes

in a manner consistent with the endogeneity of On. Finally, this specification allows for

heterogeneous tastes thru random effects for location specific amenities. The estimation

strategy recovers four sets of parameters: the parameters of the joint distribution of income

and tastes for location specific amenities; the non-stochastic parameters of the indirect

utility function; the parameter of the function mapping open space to the augmentation

parameter; and, the parameters of the public good index.

A two-stage simulation-based process is used to estimate the model’s parameters. The

first stage recovers the heterogeneity parameters, indirect utility parameters, and the pa-

rameters of the augmentation function (first stage parameters). The basic algorithm for the

first stage begins with an initial value for the first stage parameters. A simulation algorithm

maps these parameter values into a unique vector (normalized to a relative scale) of local

amenity levels, Giindex, which implies a sorting across zones that matches the predicted

zone populations to actual zone populations. Each iteration of the first stage parameter

vector together with the implied relative levels of the public good indices leads to a unique

sorting of households (characterized by income and taste for locational amenity levels) across

zones. This sorting is used to recover a predicted distribution of land demands for each

zone. Quartiles of the predicted land demand distribution for each zone are differenced

from those actually observed in each zone. These differences form the basis of a Minimum

Distance Estimator (MDE). A numerical optimization routine is then employed to find the

set of parameters which minimize the value of the MDE’s objective function.

The specifics of the model can be outlined as follows. Each household can choose to

live in one of ninety-one discrete zones within a predefined metropolitan area. Conditional

on choosing zone j, household i’s indirect utility function is given by equation 3.11. Pj

is assumed to equal the average 1992 land assessment per square foot annualized using

Poterba’s (1992) approach for incorporating tax and appreciation effects as discussed below.

12

These estimates are developed from assessments and are assumed to reflect how open space

can result in differential site rents. The model assumes that the privately capitalized open

space component Opj is equal to the average distance from a home in zone j to a protected

parcel of open space. The neighborhood or endogenous component of open space, ONj

equals the percentage of the land area in zone j which is undeveloped. Permanent income

and heterogeneity in the taste for the locational attributes are introduced thru yi and αi

respectively. These variables are not directly observed but are assumed to follow a bivariate

log-normal distribution.

Using Roy’s identity, conditional on choosing community j, household i’s optimal resi-

dential land demand is given by:

LDi,j =

11 + (Op

j )λB P̃ η

j yνi (3.13)

From this derivation it can be seen that η and ν are the price and income elasticity of

demand for residential acreage respectively.

As an illustration of how changes in G effect location decisions, consider the locus of

households that are indifferent between community 1 and community 2, defined implicitly

by the requirement:

[1

1 − νy1−ν − 1

1 + ηBP̃ η+1

1

]Gα

1 =[

11 − ν

y1−ν − 11 + η

BP̃ η+12

]Gα

2 (3.14)

This expression can be solved for α:

α =ln

[1

1−νy1−ν− 1

1+ηBP̃ η+1

1

11−ν

y1−ν− 11+η

BP̃ η+12

]ln

[G2G1

] (3.15)

households whose endowments place them above the locus will choose to live in commu-

nity 2 while those with endowments below the locus choose community 1. Equation 3.15

establishes that as[

G2G1

]increases the indifference surface will shift down with those house-

13

holds located near the indifference locus defined by (3.14) moving from community 1 to

community 2.

There is no closed form solution for the land demand quartiles that form the basis of

the MDE estimator. Instead, simulation methods are used to identify the residual vector

associated with each selection for a vector of parameters. The basic algorithm can be

outlined as follows. Let X be a vector of N = 250 equally spaced numbers between 0 and

1. Define X̂ = F−1(X), where F−1(.) is the inverse of the Normal CDF. After generating

a vector of N income draws consistent with the log normal distribution, given µln y and

σln y,15 one can define equation (3.16) for each potential vector of parameter values.

Ki12 = ln

11−ν y1−ν

i − 11+ηBP̃ η+1

1

11−ν y1−ν

i − 11+ηBP̃ η+1

2

(3.16)

Conditional on yi, the set of households preferring community 1 over community 2 (and

hence the set of households who choose community 1) is given by:

C1�2|yi=

α

∣∣∣∣∣∣ α <Ki

12

ln(

G2G1

) (3.17)

Given G1, we can solve for the measure of the population choosing community 1 as a

function of G2:

M1|G1(G2) =

1N

N∑i=1

Fαi

Ki12

ln(

G2G1

) (3.18)

Where Fαi is the Normal CDF with:

Mean = µln α +σln α

σln yρ (ln y − µln y) (3.19)

15Specifically, yi = exp(µln y+X̂i σln y). The actual process is slightly more complicated. First, because theutility specification is inconsistent for extremely low values of permanent income it is necessary to truncatethe left edge of the distribution. This is done at $6800, the 1990 poverty threshold for a one person familyunder the age of 65. Second, the mean of the income distribution is not identified separate of the demandparameter B and is therefore set at the mean income for Wake County. The value for the mean of the logof income which yields this level of mean income is therefore a function of mean income and the variance ofthe log of income.

14

Variance = σ2ln α (1 − ρ2). (3.20)

In the first stage, it is not possible to identify the absolute levels of the G-index vector

or the mean of the log of α. A specific form of relative identification defined in 3.21 is

possible .

G̃j =G

exp(µln α)j

Gexp(µln α)1

(3.21)

This indeterminacy requires a normalization rule. This is accomplished by assuming G1 = 1

and µln α = 0 for the purpose of first stage estimation.16 The value of G2 is then defined

implicitly in equation 3.18. This relationship can be solved using a line search algorithim.

The solution algorithm iterates through the communities to solve for the entire G vector.

Once this vector has been identified, the income quartiles in each zone can be identified.

These income quartiles are then substituted into the land demand function implied by

Roy’s identity in equation 3.13 to derive the land demand quartiles that form the basis of

the MDE.

To decompose the G-index, in the second stage of the estimation procedure the locational

attributes are assumed to follow a semi-log function, Gj = exp(X ′jγ + εj). G1 is treated as

a nuisance parameter to be estimated as part of the second stage of the model. This yields

the following linear model:

ln(G̃j)exp(µln α)

= − lnG1 + X ′jγ + εj (3.22)

Two normalizations identify this model. First, the intercept of the semi-log model for

G̃j is assumed equal to the lnG1. Second the coefficient on the first element of the local

public good index is set equal to 1. Under this normalization, the coefficients on locational

16These normalizations serve to identify the first stage parameters, which are invariant to this normaliza-tion, and are not utilized for identification of the second stage parameters.

15

attributes can be interpreted relative to open space percentage and the value of µln α reflects,

on average, the relative importance of the locational attribute index in preferences.

Because B and the mean of permanent income are not separately identified, the estima-

tion procedure requires an estimate of the mean permanent income in Wake County. This

number should be inclusive, accounting for wages, interest income, dividends, capital gains,

transfer payments, payments in kind and the rental value of owner occupied housing. There

are two potential sources of income data, the Census Bureau’s Annual report on household

income17 and The Bureau of Economic Analysis’ Personal Income Series (BEA). The cen-

sus report is based on responses to the March Consumer Population Survey (CPS) while

the BEA numbers are developed using various government and business sources including

industrial and population censuses and employer’s wage reports under the Social Security

Program. According to the Census Bureau, the CPS’ survey based money income aggre-

gates for 1990 were 12% lower than those derived by the BEA. This is due in large part to

under-reporting of non-wage income on the CPS’ survey instruments.18 Additionally, the

BEA numbers account for the rental value of owner occupied homes. For these reasons,

the figure $56,123 per household which is derived from the BEA’s Personal Income Series

is used for mean permanent income in Wake County.19

4 Data

The study area for this project is Wake County, North Carolina. The county has experi-

enced rapid development. It includes both protected open space and a significant quantity

of unprotected open space at the edges of its developed areas. The empirical model requires

17Money Income of Households, Families, and Persons in the United States:1992, U.S. Department ofCommerce, Economics and Statistics Administration, Bureau of the Census.

18See US-Census-Bureau (1992), Appendix C for a more complete discussion of the issues associated withincome data.

19The source of the imputation for Wake County is Woods-Poole (1995).

16

dividing the county into a set of spatially distinct choice alternatives. This task was im-

plemented by aggregating up approximately 700 small spatial units labeled as nodes into

91 discrete zones. The nodes that form the building blocks for these zones were defined by

the Wake County Public School System (WCPSS). WPCSS constructed the nodes to take

account of neighborhood and subdivision boundaries in establishing the primary and sec-

ondary school assignments for the consolidated county-wide school system. The nodes were

aggregated to produce zones whose boundaries reflect the intersection of local jurisdictional

boundaries, major roadways and school attendance boundaries. The goal of this approach is

to create zones which are as homogeneous as possible in location specific attributes. Figure

2 shows the boundaries of the 91 zones.

Information on lot size, 1992 tax assessments (distinguished into separate land and

structure assessments) and current land use were assembled from GIS parcel data and tax

records supplied by the Wake County Assessor’s Office. This data set contains information

on approximately 230,000 parcels of land in Wake County. Collectively the parcels cover

510,677 acres of land and account for 95% of the area of Wake County, with the remaining

5% comprised mainly of roads and road right of ways. Each parcel is identified as having

one of 24 land use codes. Based on these codes and protected open space data discussed

below, each parcel is placed into one of the 5 categories presented in table 1.20

Table 1: Land Use Summary from Parcel Maps

Land Use Acres Percentage of TotalBusiness/Commercial 16,694 3.27%Residential 102,897 20.15 %Protected Open Space 81,084 15.88%Privately Held Open Space 295,566 57.88%Other 14,436 2.83%Total 510,677 100%

20Privately held open space is comprised of the following land uses: agricultural uses, vacant, cemetery,golf course, single family residential greater than 10 acres, and all parcels that were developed after 1992.

17

Figure 2: Map of 91 Zones and Protected Open Space

��

�

�

��

�

�

���

��

���

�

�

�

�

�

�

�

�

�

Shaded areas represent parcels of protected open space.

18

Two open space measures are developed for use in the locational equilibrium model.

The first is the endogenous or neighborhood component of open space, Onj which is proxied

for by using the percentage of each zone’s total land area which is in open space. This

measure is comprised of a mixture of publicly protected land and privately held land in

open space uses such as agriculture. Onj enters directly into the index of local amenities,

Gj . The second measure is the exogenous component of open space, Opj . This measure

captures the average distance to protected open space for each home in a given zone. In

order to construct this measure for each zone, data were assembled from the Army Corps

of Engineers, North Carolina Department of Environment and Natural Resources and local

planning agencies. The resulting data set provides a unified GIS description of more than

450 individual parcels of protected open space in Wake County. The shaded areas in Figure

2 represent these protected parcels. ARCVIEW was used to calculate the distance from

each land parcel to the nearest one of these 400+ protected areas. Finally, these averages are

linearly transformed so that the OP ∈ {0, 1} with the zone with the largest average distance

having a measure of 0 and the zone with the shortest average distance have a measure close

to 1.21 This scheme creates a measure that is increasing in the level of amenity conveyed.

Additional data were collected to control for other location specific amenities. To control

for commuting distances, the minimum of the average distance to the center of Raleigh

and the average distance to Research Triangle Park (RTP) were calculated for each zone.

Additionally, indicator variables for each of the 13 local jurisdictions are used to control for

other unobservable attributes. Summary statistics for the 91 zones are contained in table

2.

Finally, the model requires that land prices be converted to annual rental values. Using

21Specifically, On = − average distancej − max average distance

max average distance.

19

Table 2: Summary Statistics for 91 Residential Zones

Mean Std. Dev. Min. Max.

Average Assessed Lot Price ($ per ft2) 0.165 0.128 0.013 0.553

Lot Expenditure 25th Quartile 15741.44 15630.43 1742.4 88862.4

Lot Expenditure 50th Quartile 23450.6 23254.7 3920.4 131551.2

Lot Expenditure 75th Quartile 43703.6 78702.25 5662.8 652528.8

Residential Lot Count 1005.978 757.86 3 3026

Population Share 0.011 0.008 0 0.033

Ratio of Commercial to Residential Acres 0.2428 0.3225 0 1.9812

Percent of Zone in Open Space (On) 0.61 0.215 0.17 0.965

Average Distance to Protected Open Space (feet) 3004.69 3065.06 320.31 20326.39

Private Open Space Measure (Op) 0.856 0.15 0 0.983

Average Distance to CBD (feet) 40298.07 25625.36 2018.619 96833.3

Table 3: Values for Poterba Calculation

τ owner’s marginal tax rate 15%τp property tax rate (varies) 0.66% - 1.30%i interest rate 8.692%β risk premium 4%m maintenance 2%π home appreciation rate 2.886

the calculation suggested by Poterba (1992), annualized rents are given by equation 4.23.

R = [(1 − τ)(i + τp) + β + m + δ − π] PH (4.23)

The specific variables and their values are given in table 3.

5 Results From the First Stage of the Household Model

The estimated first stage parameters for the household location model are reported in

table 4. All of these estimated parameters are plausible and where it is possible to make

20

Table 4: Household Location Model’s First Stage Parameter Estimates

Parameter Estimate Estimated Asymptotic S.E.

Variance of Ln (α) 0.2981 (0.0033)

Variance of Ln (y) 0.2823 (0.0061)

Price Elasticity (η) -0.6174 (0.0166)

Income Elasticity (ν) 0.7474 (0.0844)

Demand Parameter (B) 1.5545 (0.0051)

α-y Correlation (ρ) -0.0196 (0.004)

Augmentation Parameter (λ) 21.8257 (0.0001)

comparisons with the existing literature they fall within the range of past estimates. As

expected, the estimated variance of the log of permanent income, ln(y), is below estimates of

the variance of current log-income derived from fitting log-normal distributions to current

income.22 The estimated price elasticity of -.62 is consistent with earlier literature. For

example Sirmans and Redman (1979) estimate price elasticities of land consumption for

52 different urban areas for the years 1967, 1971 and 1975. Their estimates for the price

elasticity in the Raleigh Metropolitan area range from -.70 in 1975 to -.76 in 1967. Across

the 52 urban areas in their sample, the majority of their estimates fall between -.45 and -.75.

The literature has not explored income elasticities for residential land demand, however the

estimate of .75 is similar to its counterpart in housing demand studies.23 While significantly

different from 0, the estimate of the correlation parameter ρ suggests little correlation

between tastes for location specific amenities and permanent income.

Finally, the estimated value of 21.83 for the augmentation parameter λ is consistent with

the a priori expectation that private lot consumption and proximity to protected open space

22For example, Epple-Sieg (99) estimate .755 as the variance of ln current income in the Boston Metroarea.

23For instance, Polinsky (1977) provides estimates of housing demand income elasticities of .75.

21

Figure 3: Effective Price Function - Household Location Model∗

0 0.5 1 1.5 20.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Average Distance (Miles) to Protected Openspace

Val

ue o

f Aug

men

tatio

n P

aram

eter

(lam

bda

= 21

.83)

∗ For better scaling, one observation corresponding to an average distance of 3.8 miles has been omitted.

are substitutes. The implications of the parameter estimate are illustrated in figure 5. The

figure shows how the average distances to protected open space (on the x-axis) translate

into values for the price augmentation factor 1 + (Opj )

λ (on the y-axis). The results suggest

that proximity to protected open space is relevant as a source of differential land values

only when the average distance is less than half a mile. As the average distance moves from

half a mile to one quarter of a mile, the augmentation factor increases by 17.5%. Evaluated

at the mean (across zones) of the 50th percentile of lot expenditure ($23,451) this change

in augmentation factor roughly corresponds to a one time incremental willingness to pay

for the change in average distance of $4,104. For comparison, using the MWTP measure

of $4.20 per foot of walking distance to protected open space developed by Correll et al.

(1978) leads to an estimate of $12,250 as the value of decreasing the distance to protected

open space for a given house by a quarter mile.24

24The consumer price index was used to convert this figure 1992 dollars.

22

In addition to the first stage parameters discussed in the previous section, the first

stage estimation recovers the index of local amenities, Gj , for each zone. The percent

open space measure enters the model through this index. To recover the specific role of

open space in the indirect utility function it is necessary to decompose the G-index into its

component parts. To facilitate this decomposition, the relationship between the G-index

and the locational attributes is assumed to follow a semi-log function, lnGj = X ′jγ + εj .

Under this assumption, the equality presented in equation 5.24 holds.25

ln(G̃j)exp(µln α)

= − lnG1 + X ′jγ + εj (5.24)

Where G̃j is the value recovered for each zone from the initial estimation step. Two further

normalizations are required to identify the model. First, I assume that the matrix of

locational attributes X does not include a vector of ones. Second, the coefficient on the first

element of the local public good index, in application the percentage open space measure,

is set equal to 1. Under this normalization, the coefficients on locational attributes can be

interpreted relative to open space percentage and the value of exp(µln α) reflects, on average,

the relative importance of the locational attribute index in preferences.

A GMM procedure is then utilized to estimate the parameters of the model. The

parameter vector is comprised of the parameters of the index γ,26 lnG1 and exp(µln α). The

moments used in estimation are then of the form in equation 5.25.

1J

J∑j=1

(εj) X ′j (5.25)

where εj is derived from equation 5.24 and is given in equation 5.26.

εj =ln(G̃j)

exp(µln α)+ lnG1 − X ′

jγ. (5.26)

25To derive this expression, note that ln G̃j = exp(µln α)(ln Gj − ln G1).26with the parameter on open space percentage fixed at one.

23

This structure assumes that E[εjX′j ] = 0. The set of explanatory variables X includes the

percentage of the zone in open space (the square of this measure is also included to allow

for non-linear open space effects). It is to be expected that this measure is correlated with

the the error term ε thus violating this assumption underlying the moment conditions of

equation 5.25. Fortunately, the structure of equation5.25 allows for the use of instruments to

overcome this problem. Instrumenting is accomplished by using a vector of instruments Z ′j

which includes all of X except the open space percentage measures and additional variables

assumed to be correlated with open space percentage, but not correlated with ε. The

Instrumental Variables specification is given in equation 5.27.

1J

J∑j=1

(εj) Z ′j (5.27)

The estimation results for eleven different specifications of the models of equations 5.25

and 5.27 are presented in the rows of Table 5. Models I thru V do not instrument for the

open space percentage measures while Models VI thru XI use a set of soil-based predictors

of the suitability for residential construction and value in non-developed use as instruments

for the open space percentage measures. In addition to the coefficients on the explanatory

variables, the table reports the estimate of lnG1 which is one of two additional parameters

estimated in this stage. The second parameter is the exponent of the mean of the log of α

which is labelled K in the table.

Model I only includes the open space measure. Because the role of open space percentage

is of most concern, the square of open space percentage is also included in the model to

allow for the presence of a non-linear relationship. As discussed above, the coefficient on

open space percentage is normalized to one. The negative coefficient on the quadratic term

implies that G is increasing in open space percentage over an initial range of values and

then beyond some critical point a negative relationship holds.27 The values for this critical

27Several additional models, including cubic, quartic and spline models, were run to test the sensitivity of

24

Tab

le5:

Dec

ompo

siti

onof

Aug

men

tati

onM

odel

’sG

-ind

ex

Open

Pct

.M

inM

ean

S&

SLn

Jur.

I.V

.C

riti

cal

Model

Space

2B

us/

Com

Em

p.

Dis

t.E

mp.

Dis

t.E

mp.

Dis

t.G

1K

Ind.

Poin

t

I-1

.5221

-0.5

839

0.0

4733

0.3

285

(0.2

638)

(0.3

289)

(0.0

187)

II-1

.6472

0.6

986

-0.7

311

0.0

388

0.3

035

(0.3

607)

(0.4

124)

(0.4

460)

(0.0

177)

III

-1.5

990

0.6

837

-0.0

492

-1.3

638

0.0

243

0.3

127

(0.4

890)

(0.5

349)

(0.0

364)

(1.0

726)

(0.0

160)

IV-1

.4892

0.6

032

-0.0

439

-1.3

758

0.0

274

0.3

357

(0.2

461)

(0.3

735)

(0.0

151)

(0.5

210)

(0.0

090)

V-1

.3514

0.4

428

0.1

469

-0.0

938

0.0

328

0.3

700

(0.2

033)

(0.2

604)

(0.0

719)

(0.1

819)

(0.0

133)

VI

-1.2

340

0.0

957

-0.0

997

0.1

305

X0.4

052

(0.4

759)

(0.2

760)

(0.4

457)

(0.1

702)

VII

-1.4

873

0.2

387

-0.0

014

-0.3

691

0.0

722

X0.3

362

(0.7

578)

(0.4

214)

(0.0

079)

(0.7

421)

(0.0

872)

VII

I-1

.5255

0.2

628

-0.0

014

-0.4

159

0.0

675

X0.3

277

(1.0

205)

(0.5

698)

(0.0

082)

(1.0

058)

(0.1

021)

IX-0

.9416

-0.0

585

0.2

122

2.0

432

XX

0.5

310

(0.2

309)

(0.1

326)

(0.2

129)

(16.4

103)

X-1

.5621

0.2

433

0.0

001

-0.4

136

0.0

808

XX

0.3

201

(0.7

186)

(0.3

866)

(0.0

066)

(0.7

231)

(0.0

897)

XI

-1.5

687

0.2

447

-0.0

001

-0.4

242

0.0

792

XX

0.3

187

(0.9

456)

(0.4

785)

(0.0

069)

(0.9

500)

(0.1

089)

25

point are included in the table. For the simple specification of Model I, the value of this

critical point is 33%. To control for additional constructed attributes of the landscape,

Model II adds as an explanatory variable the percentage of each zone that is in a business

or commercial usage. This measure is treated as exogenous. The coefficient on this variable

is positive in nine of ten specifications, but is statistically insignificant, even at the 20%

level, in all but models IV and V which control for distance to employment centers but do

not instrument for the endogeneity of open space percentage.

Since the early work of Muth (1969) and Mills (1972) urban economists have focused

on the role that proximity to employment centers plays in the value of different locations

within a metropolitan area. Eight different employment centers within Wake County were

identified 28. The distance to each of these employment centers from all houses within

each zone was calculated. Three different strategies are considered for including these eight

employment centers in the model. The first two approaches average across all houses in each

zone to include the average mean distance and the average minimum distance to employment

centers. Results including these measures are reported in rows III and IV of table 5. The

third approach is labeled ‘S. and S. Employment Distance’. It is based on the approach

advocated by Small and Song (1994) for aggregating a set of multiple employment centers

whose distances to a specific parcel are given by {dn} - measured in miles. The Small and

Song measure, D, is given by:

D =N∑

n=1

Ane−bndn (5.28)

To implement this measure, it is assumed that An and bn are constant across employment

centers. A is the coefficient estimate from the second stage. b is set equal .0686, the value

that maximizes the fit of model V. Because of its construction, the expected sign on the

the shape of this relationship to this functional form. The results of this analysis suggested no qualitativedifference between the simple quadratic form and the more complicated models.

28See Walsh (2002).

26

Small and Song measure will be positive.29 All three of the employment center measures

result in the expected sign.

As previously discussed, the endogeneity of each zone’s open space percentage is a

potential concern. To address this issue, columns VI thorugh XI instrument for open

space percentage using soil based measures that are discussed below in the supply model -

aggregated to the zone level. Unfortunately, the move to an instrumental variables strategy

lead to instability in the Small and Song version of the model. Rows VI through VIII

of the table report instrumental variable results for the models of rows II-IV. Finally, to

further control for unobserved components of local goods, Columns IX through XI include

indicator variables for location within Raleigh and Location outside of incorporated areas.

As previously discussed, the sign on Business and Commercial development is consistently

positive but insignificant across the models. The coefficient on the employment center

variables has the expected sign in all models except model X, but goes from significant to

insignificant once instruments for open space percentage are included.

From the perspective of the policy simulations, the most important parameter in the sec-

ond stage decomposition is the coefficient on the quadratic open space term. This coefficient

is stable and significant across all specifications – in all models except specification VIII the

coefficient passes a two-tailed significance test at the 10% level. The coefficient values range

from a high value of -1.65 to a low value of -0.94. These values correspond to critical points

in the range of 0.30 to 0.53, with 10 of the 11 models yielding critical points between .30 and

0.41. These empirical estimates suggest that local amenities are maximized when the level

of open space provision lies somewhere between 30 and 40 percent of a given neighborhoods

land area. Because they include instruments for the open space measures and indicator

29Several other approaches were attempted for aggregating employment centers and discarded for differentreasons: Including all 8 employment distances resulted in a mix of positive and negative coefficients whichis intuitively unpleasing; log specifications did not improve fit, neither did the geometric mean; finally, Iattempted to estimate the parameter b of the Small and Song model as part of the second stage. This workedwell for simple specifications, but failed to converge or converged to −∞ when jurisdiction fixed effects orI.V. estimates were attempted.

27

variables for the local jurisdictions, models X and XI are deemed most appropriate for use

in the general equilibrium policy simulations. The parameter estimates that are important

for the policy simulation are K, ln G1, and the coefficient on the quadratic open space term.

Because the estimates of these parameters vary so little between models X and XI vary so

little the impact of choosing one over the other is negligible. For implementation of the

policy simulations, the estimates of model XI will be utilized.

6 Policy Simulations

In this section, two distinct types of policies are analyzed using the model –

land/development rights acquisition and development restrictions. The simulation results

show the significance of spatial heterogeneity between different policies and highlights the

diversity of outcomes across both space and household type.

The section begins with a discussion of land protection policies in the U.S., identifying

two distinct types of policies to be analyzed using the model – land acquisition and develop-

ment restrictions. Consistent with these two categories of protection policy, the paper next

develops five distinct policy simulations. The first 3 policies are land acquisition policies

designed to mimic different policy goals - ecological concerns, open space protection, and ur-

ban parks. The last two policies freeze development in two different geographically defined

regions at their 1984 levels. The first region roughly corresponds to Wake County’s largest

and fastest growing suburb Cary, N.C. and the second region is comprised of a narrow ring

of low density zones that abut the urban core of Wake County.

The next the section analyzes the results of the policy simulations. This discussion

begins with the actual implementation of the different policies. Next welfare measurement

in the G.E. framework is considered. Analysis of the policy simulations themselves begins

with the 3 land acquisition policies followed by the two development restriction policies.

Within these two sets of discussions, several levels of analysis are undertaken. First, at

28

the very micro level, the impacts on several specific individual zones are considered. This

discussion is used to dissemble the complicated set of interactions that take place in the

model. This is followed by analysis of the aggregate policy outcomes and decomposition of

the welfare analysis along income categories. The paper concludes with a discussion of the

policy implications of the simulations.

6.1 Policy Context

The objective of the analysis is to design policy experiments which reflect the actual actions

being taken and considered by government agencies. The development of these experiments

begins with a review of existing and proposed policies.

Current open space programs stem from efforts aimed at slowing the rate of farmland

conversion.30 For example, the 1981 Farmland Protection Policy Act instructed federal

agencies to reduce or eliminate the contribution of federal programs to the conversion of

agricultural lands. These efforts were complemented by state-wide efforts to provide tax

incentives to retain land in agricultural open space. By the mid 90’s, all 50 states had

adopted use-value taxation policies which provided preferential tax treatment for land in

agricultural use.31 In a second wave of policy activity these programs have been augmented

by land acquisitions and purchases of development rights (PDRs). As of 1997, 14 statewide

PDR programs had permanently protected 407,000 acres of farmland at a cost of $738

million.32 These efforts focused primarily on protecting productive agricultural resources

at the urban fringe and had environmental and aesthetic concerns as secondary objectives.

Kline and Wichelns (1996) provide evidence that public support for these programs arose

largely from environmental and aesthetic concerns.

30For a more complete discussion of farmland preservation efforts, see Adelaja and Schilling (1999).31Buist, Fischer, Michos, and Tegene (1995)32Derr and Dhillon (1999)

29

More recent open space protection programs reflect this public sentiment. At the federal

level, recent proposals include $9.5 Billion in bonding authority that would be used to

support state, local and tribal efforts to preserve and enhance green space, protect water

quality (largely through acquisition of land buffers) and clean up brownfields33. State

programs also are moving in this direction. For instance, the state of Maryland recently

launched the “Rural Legacy” Program which provides $71.3 million over 5 years for the

purchase of conservation easements and fee simple transfers involving large continuous tracts

of agricultural, forested, and natural areas.34 The state of North Carolina recently passed

legislation which sets a goal of protecting an additional 1 million acres of farmland, open

space and conservation land by December 31, 2009.35 Pro-rated by land area, this translates

to the protection of an additional 15,496 acres in the dissertation’s study area – Wake

County, NC.

In addition to protecting individual parcels of land, recent efforts have also focused on

reducing or freezing development across larger regions using urban growth boundaries, re-

strictive zoning and in some cases large scale purchases. Urban growth boundaries were

pioneered by the state of Oregon. The Oregon Legislature voted in 1973 to adopt the na-

tion’s first state-wide set of land-use planning laws. As a result, each of Oregon’s 241 cities

is surrounded by an urban growth boundary. Urban services such as sewers aren’t extended

beyond their boundaries and the zoning prohibits urban development or the creation of

small new lots. Restrictive zoning is also being used to freeze or greatly reduce urban devel-

opment in large areas. For instance, in 1980 Montgomery County, Maryland established the

“Agricultural Reserve” zone. an area of approximately 93,000 acres encompassing a large

portion of the county’s remaining contiguous farmland and rural open spaces. Development

in the zone is restricted to one dwelling per 25 acres. In some cases, cities have used outright

33Clinton-Gore Livability Program34Source: The Trust for Public Lands.35North Carolina H.B. 1633, year 2000 legislative session.

30

purchases of land which is then kept in agriculture in order to maintain large rural zones.

For example, Boulder, Colorado has used revenues from a sales tax established in 1967 to

protected 41,000 acres of land. The protected land provides an agricultural and open space

buffer zone completely surrounding the City of Boulder.

6.2 Open Space Protection Policies

The land protection policies simulated in this section attempt to mimic these two types of

open space protection policies. This section describes the motivation and mechanics for the

five different policy scenarios to be evaluated in the paper. These simulations attempt to

“reconstruct history” by evaluating what would the character of the county been in 1992

had it been possible to change either the set of protected land parcels or land policies as of

1984. The discussion begins with the three land acquisition policies and follows with the

two land control policies.

6.3 Three Land Acquisition Policy Scenarios

In November of 2001, Wake County passed a bond initiative designed to raise $15 million

for land protection through direct acquisition and the purchase of development rights. The

three land acquisition policies are based on different strategies for spending this $15 million.

Each of the three different policies prioritizes parcels for protection in a different way. Policy

I is designed to describe land protection policies that focus on ecological values and water

quality. Policy II represents a policy directed at preserving agricultural land and open space

at the urban fringe. Policy III focuses on urban/suburban parks, protecting open space in

the more densely populated portions of Wake county.

To implement the policies, it is necessary to determine how much land can be protected

for the total dollar amount assumed available for protection, $15 million. To assure compa-

rability on the cost side of the analysis each policy is assumed to be supported through the

31

Wake County Bond issue. This implies land can be protected by both fee simple transfers

and PDRs. Thus using land prices to calculate the quantity of land that can be protected

would lead to an understatement of the amount of land that can be effectively protected

with PDR’s because land can be protected through PDRs at a lower cost than through

direct acquisition. The seller of the development rights retains the right to agricultural and

open space amenities associated with the property. Conservation easements also provide

numerous tax advantages.36 Derr and Dhillon (1999) suggest that 2/3 to 3/4 of market

value is accounted for by a property’s development potential. Based on their estimates,

the analysis assumes $15 million available for protection will protect approximately $22.5

million (i.e. 3/2 of $15 million) worth of residential land. The parcels protected under

each of the three policies are shown in Figure 4. The first four rows of Figure 6 summarize

the implementation of the three policies. Total acreage protected is 88689, 98759 and 4176

acres under policies I thru III respectively. Average parcel size varies significantly across the

policies: policy I protects 54 parcels with an average size of 161 acres; policy II protects 27

parcels with an average size of 365 acres; and policy III protects 82 parcels with an average

parcel size of 51 acres.

The land protection policies are realized in the model by adjusting the land supply func-

tions for the impacted zones and recalculating the open space access measures to reflect the

additional parcels of protected open space. The land supply adjustments are implemented

by removing the newly protected parcels from the set of potentially developed parcels.

6.3.1 Policy I (Forested Wetlands)

Protection of ecosystem functions thru open space policy recognizes the interconnections

between intensity of land use and the quality of related environmental resources. Policy I ap-

36An overview of easement valuation issues is contained in Wiebe and Tegene (1996). For specific discussionof the issues associated with the value of the option to develop see Tegene, Wiebe, and Kuhn (1999).

32

proximates these concerns by identifying contiguous forested wetlands for protection. These

parcels are identified by establishing a concordance between Wake County land parcels data

and GIS soil maps provided by the Wake County Conservation Service. The process identi-

fies the total acreage of wetland (hydric) soils contained within each parcel. Using the land

classification information included in the parcel data set it is possible to isolate the forested

parcels with the largest total wetland soil acreage. These forested parcels with wetland soils

are sorted from those containing the highest total wetland soil acreage to those containing

the lowest total wetland soil acreage. Land protection starts with the largest in this order-

ing and continues through the list until $25 million worth of property is identified. Under

this policy, 54 parcels totaling 8,689 acres are protected in 27 different zones. The price of

the land protected under this policy ranges from a low of $548 per acre to a high of $7,597

per acre. The average price of the land protected is $2,534 per acre.

6.3.2 Policy II (Ag/Forests)

Agricultural preservation programs typically target land within previously delineated agri-

cultural zones. Policy II Approximates this land protection strategy by identifying the

largest parcels in forested or agricultural use for protection. The mechanics are similar

to the approach taken in policy I. Agricultural and forested parcels, as identified by the

Wake County Land Parcels Data Set, are ordered from largest to smallest. Land protection

begins with the largest parcel and continues until $25 million worth of parcels is protected.

Twenty seven parcels are protected in 16 zones. A total of 9,859 acres are protected at

prices ranging from $681 per acre to $5,165 per acre. The average land price under this

policy is $2,208 per acre.

33

6.3.3 Policy III (Urban Ag/Forests)

Policy III targets protection activities to the most densely populated zones of Wake County.

This policy is consistent with ‘Smart Growth’ policies which focus on the establishment

of urban parks and suburban green spaces. The implementation strategy for this policy

scenario is identical to policy II except that parcels located within the 45 most densely

developed zones are the only ones eligible for protection. Under this policy, 82 parcels are

protected in 15 different zones for a total of 4,176 acres. The average land price for protected

parcels is $5,340 per acre. The minimum price under this policy is $4,321 per acre and the

maximum is $11,913 per acre.

6.4 Two Development Freeze Policies

Policies IV and V Identify a set of zones in Wake County and freeze residential development

in these zones at their 1984 level. This is accomplished by fixing the model’s land supply

function for these zones at their 1984 level of residential development. Because these policies

are designed to replicate zoning or growth restrictions, under the development freeze policies

there is no increase in the access to publicly owned open space, OP . Two different policy

experiments are undertaken. Policy IV attempts to mimic a growth ring policy by freezing

development in a set of relatively low density zones in a ring around Raleigh. Policy V takes

a different approach, freezing residential development in a set of zones roughly concurrent

with the town of Cary. One key difference between these two policies is that the ring policy

freezes development in a relatively low price level set of zones while the Cary policy freezes

development in high price zones.

Implementation of these policies differs from that of the land protection policies. First,

no new protected open space is created under these policies so no adjustments are made to

the open space access measures for the different zones. Second, the land supply adjustments

for these policies are an order of magnitude greater than those for the land protection

34

policies. The policies are implemented in the model by fixing the land supply in the impacted

zones at their 1984 level.

6.4.1 Policy IV (Growth Ring Policy)

As the name suggests, the Growth Ring Policy (Policy IV) replicates a policy which attempts

to control sprawl by freezing development in a ring of low-density development immediately

adjacent to the urban core. The zones chosen for inclusion in this policy are the zones

closest to the center of the county with a 1984 density of development less than .1 residential

household per acre. Summary statistics for these zones are presented in the bottom of figure

17.

6.4.2 Policy V (Cary Policy)

The Cary Policy (Policy V) explores the impact of freezing development at its 1984 levels

in a set of zones roughly consistent with Wake County’s fastest growing suburb, Cary. In

many ways, this policy scenario mimics Montgomery County, Maryland’s establishment of

an “Agricultural Reserve”. Summary statistics for these zones are also presented in the

bottom rows of figure 17.

6.5 Policy Simulations

This section presents the simulation results for the five policy scenarios. The discussion

begins by considering the issues associated with welfare measurement in the General Equi-

librium framework. Next, in order to better understand how the general equilibrium cal-

culation leads to aggregate outcomes, the impacts of the three land acquisition policies on

specific zones that were affected in different ways by each policy are analyzed. Finally, the

aggregate results from all five policy scenarios are presented.

35

6.6 Welfare Measurement

Allowing for the relocation of households and endogenous adjustment of public good levels

within the G.E. framework complicates the problem of assessing welfare impacts. The G.E.

benefit measure must account for four simultaneously determined endogenous adjustments

(relative to the baseline equilibrium) that are associated with the counterfactual equilibria.

First, household i’s G.E. location choice j′ may differ from its original location choice j.

Second, as households relocate and adjust their optimal lot-size the open space percentages

in each zone adjust, leading to new levels of the public good index. These new levels are

denoted by G∗. Because On enters the G-index in a quadratic form, the direction of the

change in G depends on the change in On and the initial level of On. Above the critical point

of 32% increases (decreases) in On reduce (increase) the level of G. Below the critical point,

the relationship is reversed. Third, household location adjustments and the supply effects

associated with the additional land protection cause prices (augmented prices) to adjust

from P 0 to P ∗ (P̃ 0 to P̃ ∗). Finally, because of the model’s implicit treatment of households

as renters, price increases (decreases) translate to transfers away from (to) households to

(away from) absentee landlords. To account for this transfer, the property value change per

household is included in the general equilibrium benefit measure.

To consider the respective impacts of these effects on the measured general equilibrium

benefit, it is helpful to begin by defining the G.E. benefit measure in general terms using

equation 6.29.37

Benefiti =[y0

i − ei

(P̃ ∗

j′ , G∗j′ , U

0i

)]+ Change in Capitalizationi

(6.29)

The first term in equation 6.29 is the Hicksian Willingness to Pay for the General Equilib-

rium outcome.38 The second term accounts for transfers to (from) absentee landlords as

37Where i indexes both an individual household and the parcel upon which it is located.38The analytical expression for the G.E. WTP is given by:

36

a result of price changes. It is the change in land rent for individual i′s initial lot and is

defined as (P ∗j − P 0

j )*Lot Size0i . Further decomposing the G.E. benefit measure by adding

and subtracting the term ei

(P̃ (Op∗

j , P 0j ), G0

j , U0i

)identifies the partial equilibrium WTP

and an adjustment term. This decomposition is shown in equation 6.30.

Benefiti =[y0

i − ei

(P̃ (Op∗

j , P 0j ), G0

j , U0i

)]+

[ei

(P̃ (Op∗

j , P 0j ), G0

j , U0i

)− ei

(P̃ (Opj∗

j′ , P ∗j′), G

∗j′ , U

0i

)]+ Change in Capitalizationi

(6.30)

The first term in equation 6.30 is household i’s Hicksian willingness to pay for the change

in protected open space assuming no equilibrium adjustments. y0i is household i’s income,

ei(.) is the expenditure function for household i, G0j is the pre-adjustment level of the

amenity index in household i′s initial zone, and U0i is the initial level of utility for the

household. P̃ (Op∗j , P 0

j ) is the augmented price in household i’s initial zone, evaluated at

pre-adjustment prices accounting for the zone’s change in Opj which results from the new

land protection policy. This component of the benefit measure is labelled “ Partial CV (No

Adjustment)” in the tables. The second term in equation 6.30 is the difference between

household i’s willingness to pay for the general equilibrium outcome and the partial WTP

measure captured by the first term.

An additional welfare measure is constructed to explore the relative importance of the

endogenous change in public good levels for explaining the difference between the partial

and general equilibrium CV estimates. It adjusts the general equilibrium CV measure

by subtracting the average change in experienced public good level from each household’s

experienced public good level under the new equilibrium (holding all other endogenous

variables fixed at the new equilibrium levels) and then calculating the CV. The difference

between these results and the general equilibrium CV estimates yield a rough estimate of

CV = y0i − (1 − ν)

11−ν

{B P̃∗η+1

j′1+η

+

(Gj

G∗j′

)αi[

11−ν

(y0i )1−ν − B P̃

η+1j

1+η

]} 11−ν

.

37

the importance of the endogenous public good adjustments for the overall welfare impact of

the policies. This welfare measure is labelled “Partial CV (No Public Good Adjustment)”.

In defining the change in capitalization to equal (P ∗j −P 0

j )*Lot Size0i , the above discussion

implicitly assumes that the quantity of developed land in each zone is identical under

both the baseline equilibrium and the proposed policy. Treatment of parcels that change

development state between the baseline and proposed policy is more complicated.39 For

parcels that are driven by market forces from an undeveloped state under the baseline

scenario to a developed state under the proposed policy, the appropriate measure is (P ∗j −

ri)*Lot Size0i , where ri is the value of the land in undeveloped use. The value of ri is

unknown, but because the parcel was undeveloped in the baseline case and developed under

the proposed policy, abstracting from conversion costs, we know that P ∗j > ri > P 0

j . The

capitalization in this case is positive and substituting the two price levels for ri provides

upper and lower bounds for the capitalization effect. A symmetric argument holds for

parcels which move from a developed state to an undeveloped state. Here the capitalization

is equal to (ri − P 0j )*Lot Size0

i and P 0j > ri > P ∗

j . As in the previous case, it is possible to

construct upper and lower bounds for the capitalization.

These bounds will hold with certainty for parcels for which the conversion decision is

market based. Unfortunately, these bounds do not apply to policy imposed conversion

decisions. Specifically, for parcels that are developed under the baseline equilibrium and

are forced into an undeveloped state under the proposed policy, because 1984 price data is

not available for the analysis, there is no lower bound on the reservation price. Therefore,

a price of $0.00 must be assumed. For the three land protection policy scenarios, the

number of parcels forced to an undeveloped state by policy is small relative to the entire

39Because of the probabilistic construction of the land supply functions, it is the probability of developmentand not actually the development state that changes between the two scenarios. For ease of exposition,the discussion will treat the development decision as deterministic. The actual implementation of thecapitalization measures accounts for the probabalistic nature of the problem and is perfectly analogous tothe deterministic case.

38

sample. Therefore using this approach to identify capitalization for parcels which change

development status leads to tight upper and lower bounds. However, under the development

freeze policies, development is “reversed” in large sections of the County. Therefore, the

impact of assuming a $0.00 reservation price for these parcels is restrictive leading to an

“extreme lower bound” which varies markedly from the upper bound. Under these two

policy simulations, the upper bound is likely to be closer to the actual capitalization change

than is the lower bound.

6.7 Zone-Specific Decomposition

Each of the three Land Protection Policies have both direct and indirect impacts that

lead to a new equilibrium. The direct impacts are complicated.40 First, the protection of

additional parcels in a given zone increases OP , the measure of access to protected open

space.41 This increase makes the given zone more attractive relative to other zones that do

not experience an increase in protected open space. Also, because OP is a substitute for

land in household preferences, ceteris paribus, this increase in Op decreases per household

land demand. The immediate impact of the increase in protected open space is therefore

to increase the number of households choosing to live in the zone and to decrease the per

household demand for land. The impact on price and development levels is indeterminant.

Secondly the increase in protected open space is associated with a decrease in the supply

of residential land. In isolation, this supply decrease would be associated with increased

prices, a reduction in the number of households choosing the zone and a reduction in per

household lot sizes.

40In the discussion, I include the out-migration of households in response to the price effect from reductionsin land supply as a direct effect in order to distinguish the more traditionally modelled component of theproblem from the impacts associated with endogenous open space levels and endogenous zone-wide householdincome distributions.

41Note: this impact will not necessarily be limited to the zone in which the parcel is protected, but canhave a spillover effect to neighboring zones.

39

The indirect impacts of the land protection policies are also complicated. These indirect

impacts result from the endogeneity of prices, open space percentages, and the incomes of

households located within each zone. As prices adjust to restore equilibrium, increases (de-

creases) in a given zones price will lead to out- (in-) migration42 and decreases (increases)

in per household land demand. The second key endogenous element of the model is ON ,

the percentage of land in each zone which is in open space use. This endogenous zone char-

acteristic is a component of the zone’s public good index. It enters the index as a quadratic

and, based on the empirical results, reaches a maximum or ‘bliss point’ at approximately

32%. If under the new equilibrium, a zone’s open space percentage moves closer to (further

from) this bliss point, the public good level, G, will increase (decrease). All else constant,

increases (decreases) in this amenity level will increase (decrease) the number of households

choosing to locate in the zone. Changes in G have no direct impact on per household

lot demand, but do affect aggregate lot demand at the extensive margin and can lead to

changes in both price and the average income of residents living in the zone. The final

important endogenous adjustment is the income mix of each zone. As a new equilibrium

is established, the income distribution in each zone will change. These changes impact the

amount of residential land demanded per household - with increases in a zone’s average

income leading to increased residential development and prices.

The mechanics of the model under the two Development Freeze Policies are identical

to those of the Land Protection Policies, with one key distinction. Under the development

freeze, there is a more significant land supply effect in the impacted zones, but no additional

public access open space is protected. As a result, OP is assumed to remain unchanged in

all zones. Direct impacts are therefore limited to those associated with the change in the

42The use of the terms in-migration and out-migration facilitate the comparisons between the baselineequilibrium and the equilibrium under the five different policy scenarios. However, it is important to notethat these terms should not be taken literally. Instead, they are used to compare the location choices andzone populations under different simulated equilibria which are predicted to developed between 1984 and1992.

40

land supply function in zones experiencing a development freeze.

To further appreciate how the different components of the equilibrium calculation lead

to different aggregate outcomes, it is helpful to consider some specific examples. To meet

this goal, two different zones are analyzed for each of the three land acquisition policies.

Sample zone ‘Aj’ is a zone within which additional land is protected under policy j and

sample zone ‘Bj’ is a zone which does not experience any additional open space protection

under policy j.43 Figure 8 identifies the location of each of the six distinct sample zones.

Results for the six policy/zone pairs are analyzed in figure 7. The top portion of the

table reports changes associated with each of the six sample zones. The bottom portion

of the table reports results associated with households that were located in each sample

zone prior to policy enactment. This distinction is necessary because one of the ways that

households respond to a new land protection policy is to relocate to a new zone. The first

five rows of the table report data associated with the attributes of the partial equilibrium

analysis. Rows six thru nine report equilibrium outcomes associated with each of the six

policy/zone pairs. The bottom portion of the table reports data on the equilibrium location

choices of households that were initially located in each of the six zones. The final row of

table 7 adds the property value change per household in the originating zone to the average

G.E. WTP of households originating in that zone to yield a per household benefit measure.

Under Policy I, in sample zone ‘A1’ the protection of additional open space in and around

the zone leads to a 3.3% increase in the price augmentation factor from 1.086 to 1.122. As

expected, if no adjustments were to occur, this increase in the augmentation factor would

result in the zone’s residents having a significantly positive WTP for the policy ($67.47 per

household). The general equilibrium calculation identifies additional changes. First, new

location and lot size changes result in an increase in the open space percentage in the zone.

43The location of the sample zones is different under the different policies because each policy’s criterialeads to different areas being protected. For example, sample zone ‘A1’ is different from sample zone ‘A2’.

41

Because the initial open space percentage was above the critical point of 32%, this change

is not desirable and implies a drop in the level of the G-index for the zone. The increase

in protected land also reduces the land supply for the zone. This upward influence on the

zone’s price is more than offset by equilibrium adjustments in demand, resulting in a 1.98%

drop in land prices. This price decrease is associated with a decrease in capitalization in the

zone equal to $41.22 per household.44 To evaluate the WTP of the zone’s households for

the equilibrium outcome it is necessary to compare the augmented price and G-index level

experienced by households under the new equilibrium to the corresponding levels prior to

the protection of additional land. Under this policy’s new equilibrium, the zone’s households

experience offsetting decreases in both the G-index level and augmented price level. The

change in G-index level dominates the augmented price change leading to a G.E. WTP of

-$62.01 per household. Adding this WTP measure to the zone’s change in property value

yields a benefit estimate for zone ‘A1’ under policy I of -$103.23 per household. G.E. effects

completely reverse the positive benefits predicted by the partial equilibrium analysis.

Because, under policy I, no new open space is protected in or near Zone ‘B1’ it expe-

riences no change in its augmentation factor and there are no partial equilibrium effects.

In equilibrium, demand for land in the zone increases, driving the price of land up and the

percent open space down. Because the original open space percentage was below the criti-

cal point, this decrease in open space reduces the level of the G-index for the zone. Under

the new equilibrium, on average the zone’s initial residents locate in zones which provide

increases in both the G-index and augmented price. The augmented price effect dominates

yielding an average G.E. WTP measure for the zone’s households of -$56.15. In contrast

to zone ‘A1’, accounting for the change in property values has a positive effect, yielding a

benefit measure of -$2.94 per household.

Additional facets of the model are demonstrated by the impact of policy III on zone

44This is the lower bound estimate. The upper bound estimate is less than 1% higher.

42

‘B3’. First, even though no land is protected within the zone under this policy, additional

protected land near the zone’s border yields a direct spill-over effect causing an increase

in the augmentation factor and leading to a positive partial equilibrium willingness to pay

measure. Under the new equilibrium, demand for land in the zone increases. This increase

in demand leads to decreases in the open space percentage. Because the initial open space

percentages are greater than the critical point, these open space decreases are associated

with increases in the zone’s G-index level. This effect is self reinforcing and results in an

11.4% increase in prices in the zone – yielding a a positive capitalization change of $240.76

per household.45 This large change dominates the G.E. WTP for the zone’s households,

resulting in an annual benefit per household of $172.32.

Considered as a whole, these results highlight three key characteristics of the policy

computations. First, partial equilibrium analysis yields distinctly different results from the

general equilibrium analysis. Second, under all three policies there is significant heterogene-

ity in outcomes across zones. Under each of the policies there are zones with positive and

negative average benefits. Third, even in zones which experience no change in protected

open space, direct and pecuniary spill-overs can lead to significant impacts.

6.8 Average Policy Results

Having considered the specific components of the adjustments, the analysis now turns to

the aggregate results of the policy simulations. Figure 6 presents summary statistics for the

changes, relative to the base-line no-policy model run, for the five different policy scenarios.

Additional spatial data regarding the impacts of the five policies on the model’s equilibrium

is contained in the maps of Figures 10 through 14 and figures 16 and 17. The following

provides a discussion of the aggregated simulation results.

45This is the lower bound estimate. The upper bound estimate is $256.89.

43

Figure 6 summarizes the outcomes under the 5 policy scenarios. The first four rows

of the table describe the specifics of the three land protection policies. In the household

preference model, access to open space is modelled as augmenting prices. The change in the

price augmentation factor measures how much the new land protection increased access to

protected open space. Row four reports the average change in the price augmentation factor

under the three land protection policies.46 The heterogeneity in this measure across the

three land protection policies demonstrates that the spatial distribution of land protection

is important for determinning the direct benefit of land protection. Policy III which focuses

protection in more densely populated areas and protects many small parcels leads to the

greatest increase in access to protected open space and Policy I to the smallest increase

(when averaged across zones).

The table’s fifth row reports the change in residential development, relative to the base-

line, across the five policy simulations. All three of the land protection policies reduce total

residential development. However, the reduction in development from land acquisition is

much less than one for one. Policy III has the largest reduction in development of all of

the land protection policies, but only results in a .12 reduction in acres developed per acre

protected.

The development freeze policies lead to much larger changes in development. The

Growth Ring Policy leads to the largest reduction in development. This is because the

policy forces households out of low G, low price zones where lot sizes are large into rela-

tively higher priced, higher G areas. The net reduction in development under this policy is

2668 acres. The Cary Policy actually increases residential development by 932 acres. This

is because, unlike the growth ring policy, the Cary policy reduces populations in high G,

high priced zones. On average, these households relocate to lower priced zones where per

household lot size is larger. Row six reports the relationship between the number of acres

46Recall that the two development freeze polices leave this factor unchanged.

44

protected and the reduction in development for the Land Protection Policies. Row seven

reports the change in average lot size and provides another measure of the overall impact

on developed land. The growth ring policy has the largest impact, reducing average lot size

by 4.2%.

Row eight of the table reports the average (across zones) change in endogenous public

good level. For some summary statistics such as this change in public good level, it unclear

what is the appropriate unit of observation over which to calculate averages. Averaging

across zones holds the zone constant, but due to sorting doesn’t necessarily reflect the

change actually experienced by the population. Averaging across the change experienced by

households corrects for this problem, but no longer holds the zone constant. This distinction

is most important for the change in public good levels. Row eight of the table reports the

average across zones, which is negative for all five policies. Row nine reports the change

actually experienced by households which is positive for all policies except Land Protection

Policy I. Row nine of Figure 6 reports the average change in endogenous public goods

level experienced by households under the five policies. The difference between the results

reported in rows eight and nine demonstrates that except for the case of Land Protection

Policy I on average, households end up in zones with higher levels of the endogenous public

good level than they experienced under the baseline. Rows eleven and twelve report the

low and high estimates of capitalization changes.47 These figures reflect a combination of

general equilibrium effects and the capitalization of changes in relative public good levels

into residential land prices.

The capitalization changes are tightly bounded for the land protection policies. This

is not the case for the development freeze policies. The large difference stems from the

problem that no lower bound (above $0.00) on the reservation price is available for those

parcels that were developed under the baseline scenario, but are blocked from development

47For each household, these are calculated as discussed above.

45

by the proposed policy. For the two development freeze policies, under which development is

blocked in large sections of the county, the lower bound reservation price of $0.00 leads to an

“extreme lower bound”. For these policies, the upper bound is likely to be the more closely

reflect the actual measure. Unfortunately, without data on 1984 prices, it is impossible to

provide definite evidence of this relationship.

The results demonstrate that their is heterogeneity in the effects of the different policies

on land capitalization. Land Protection Policy I and the Growth Ring Policy lead to positive

capitalization effects, Land Protection Policies II and III lead to negative capitalization and

the direction of average capitalization is uncertain under the Cary Policy.

Row thirteen reports the average compensating variation(CV) for each of the policies

and rows fourteen and fifteen report the sum of average land appreciation and average CV

for the policies.48 In general these two components of the total welfare effect appear to be

of equal importance for calculating the total welfare impacts of the policies. They capture

the difference in welfare between owners and renters.

The final two rows of Figure 6 evaluate the importance of general equilibrium adjust-

ments and endogenous public goods adjustments in determining the average CV for the

policies. The first of these two rows reports the CV for additional open space protection

(Land Protection Policies) under the assumption of no adjustments: households remain in

their initial locations, prices are fixed, and endogenous public goods levels do not adjust.

This measure is similar to what would be produced based on the use of marginal willingness

to pay estimates derived from an hedonic regression. These estimates vary markedly from

the total willingness to pay figures reported in row 13, even differing in sign for one of the

three land protection policies. The final row of the figure explores the relative importance of

the endogenous change in public good levels for explaining the difference between the par-

48These totals can be interpreted two ways: 1) This total represents the sum of renter CV for the policyplus the profit/loss of risk neutral landlords; or 2) Assuming that all households own their initial lot, this is ameasure of the average total CV that ignores income effects associated with land appreciation/depreciation.

46

tial and general equilibrium CV estimates. It adjusts the general equilibrium CV measure

by subtracting the average change in experienced public good level from each household’s

experienced public good level under the new equilibrium (holding all other endogenous

variables fixed at the new equilibrium levels) and then calculating the CV. The difference

between these results and the general equilibrium CV estimates yield a rough estimate of

the importance of the endogenous public good adjustments for the overall welfare impact

of the policies. The results suggest that the endogenous public goods adjustments play an

important role in the overall welfare measurements.

6.9 Policy Implications

The five policy scenarios highlight the different ways in which the various exogenous and

endogenous forces act to shape the land market equilibrium within the model. In all cases,

accounting for the adjustments that households make in response to land protection policies

is shown to be a critical component of the analysis. Seen through the lens of the locational

equilibrium model, these household adjustments become the most important factor in the

analysis.

The three land protection policies highlight the fact that simply buying X acres of land

for protection as open space will not lead to an X-acre reduction in residential develop-

ment. The results for the land protection policy scenarios yield reductions in residential

development equal to only 2.16 % and and 3.03% of the total acreage protected when the

County’s largest contiguous parcels are targeted (Policies I and II). When, under Policy III,

a larger number of much smaller parcels are protected this figure rises to 12.13%. Policy

III also suggests that protecting parcels that are more likely to be developed in the near

future can increase the impact of the protection policy on residential development.

All five of the policy simulations demonstrate the importance of accounting for equilib-

rium effects both related to price adjustments and endogenous privately owned open space.

47

When CV measures are calculated with no adjustments, the estimates differ significantly

from the G.E. estimates, differing not only in magnitude but in sign under three scenarios.

Additionally, the second set of partial CV calculations demonstrates that the endogenous

adjustments in privately provided open space are a significant component of the difference

between G.E. and P.E. measures. Further, the results suggest that while households will

adjust to offset the intended impacts of the policies, in all but one of the policy simulations,

the net welfare impact of these policies is positive.

The development freeze policies (Growth Ring and Cary) explore the impact of policy

actions with much greater land supply implications, freezing development in large regions

of Wake County at 1984 levels. Both policies lead to large scale reshuffling of the County’s

population. One insight from these two policies is the role of the relative differences in the

land supply functions between the freeze and non-freeze zones in determining the net change

in residential development. The Growth Ring Policy freezes development in relatively low

price/high supply zones moving households to higher price/low supply zones. Thus the

average household experiences higher land prices under the policy and county-wide residen-

tial development is reduced significantly. The Cary Policy works in exactly the opposite

direction, leading households to, on average, experience lower land prices. The net effect is

an increase in county-wide residential development. These simulations suggest that policies

such as the Growth Ring Policy that restrict development in low price areas will in general

lead to reductions in County-wide development levels. Conversely policies such as the Cary

Policy which restrict development in relatively high price areas may be expected to lead to

increases in county-wide residential development.

The analysis also highlights the fact that for each policy their are winners and losers.

For instance, under the Growth Ring Policy, land owners benefit at the expense of renters,

while under the Cary Policy, renters benefit and the effect on landowners is unclear. Figures

10 through 14 map the spatial delineation of the effects of the different policies. The tables

of figures 16 and 17 decompose the effects of the policies between those zones directly

48

effected by the policies and those that are not. Under two of the three Land Protection

Policies positive capitalization occurs in the zones where land is protected and in one of

the three Land Protection Policies positive capitalization spills over into the zones that are

not directly impacted. The CV measures are also mixed between regions under the land

protection policies. Under the development freeze polices, the direction of CV measures

and capitalization are the same across both sets of zones, but the relative magnitudes are

different yielding differences in the net welfare effect.

Finally, while it may be a mistake to draw general conclusions from a single policy simu-

lation, the results of the Cary Policy are intriguing. The policy freezes development levels in

14 zones at their 1984 levels. By 1992, under the baseline scenario, three neighboring zones

from within this set if 14 had become densely developed. When under the Cary Policy this

concentration of residential development is prevented from occurring, a new zone of dense

development appears in another portion of the county looking very much like the original

(see figure 15). The result brings to mind the task of holding two balloons under water

using only one hand.

7 conclusion

The analysis by individual zones under land acquisition policies identified three key charac-

teristics of land markets with endogenous open space amenities. First, partial equilibrium

analysis yields distinctly different results from the general equilibrium analysis. Second,

under all three policies there is significant heterogeneity in outcomes across zones. Under

each of the policies there are zones with positive and negative average benefits. Third,

even in zones which experience no change in protected open space, direct and pecuniary

spill-overs can lead to significant impacts.

The key result from the aggregate analysis of the five polices is that household adjust-

ments will offset the intended effects of the land protection policies. Protecting a given

49

subset of parcels does not lead to a one for one reduction in developed acres because house-

holds adjust to the land protection policy by moving into previously undeveloped parcels.

This adjustment is also apparent in the response of households to the Cary Policy under

which households relocate and form what is essentially another Cary in land that otherwise

would have remained low density.

The characteristics of the areas where land protection or development restrictions are

undertaken is also important. Urban parks are predicted to have a much larger positive

welfare impact than protecting land at the urban fringe – even when the differential cost

of protecting the land is accounted for. The two development freeze policies suggest that

residential development can be reduced by blocking development in low price regions, but

that reducing development in high priced high public good regions will lead to an increase

in development levels.

The simulations also demonstrate that there are winners and losers under all of the

policies. Heterogeneity in benefits can be considered along spatial dimensions, income, and

the differences between owners and renters.

Finally, it is important to note that the model only captures those benefits associated

with differential proximity to open space amenities. Benefits such as ecological concerns

and ground water protection which are likely to be shared equally regardless of location

within the County can not be captured in the model.

50

References

Adelaja, A. and Schilling, B. (1999). Innovative Approaches to Farmland Preservation, pp. 113–137. AshgatePublishing.

Andreoni, J. (1989). Giving with Impure Altruism: Applications to Charity and Ricardian Equivalence.Journal of Political Economy, 97 (6), 1447–1458.

Bartik, T. (1988). Measuring the Benefits of Amenity Improvements in Hedonic Price Models. Land Eco-nomics, 64, 172–183.

Berry, S., Levinsohn, J., and Pakes, A. (1995). Automobile Prices in Market Equilibrium. Econometrica, 63(4), 841–890.

Buist, H., Fischer, C., Michos, J., and Tegene, A. (1995). Purchase of Development Rights and the Economicsof Easements. . USDA-Economic-Research-Service.

Cornes, R. and Sandler, T. (1996). The Theory of Externalities, Public Goods and Club Goods, 2nd. Edition.Cambridge University Press, Cambridge.

Cornes, R. (1993). Dyke Maintenance and Other Stories: Some Neglected Types of Public Goods. QuarterlyJournal of Economics, 108, 259–71.

Correll, M., Lillydahl, J., and Singell, L. (1978). The Effects of Greenbelts on REsidential Property Values:Some Findings on the Political Economy of Open Space. Land Economics, 54 (2), 207–217.

Derr, D. and Dhillon, P. (1999). Purchase of Development Rights Program, the Northeast Experience, pp.93–112. Ashgate Publishing.

Epple, D. and Sieg, H. (1999). Estimating Equilibrium Models of Local Jurisdictions. Journal of PoliticalEconomy, 107(4), 645–681.

Geoghegan, J., Wainger, L., and Bockstael, N. (1997). Spatial Landscape Indices in a Hedonic Framework:an Ecological Economics Analysis Using GIS. Ecological Economics, 23, 251–264.

Halstead, J. (1984). Measuring the Non-Market Value of Massachussets Agricultural Land: a Case Study.Journal of Northeastern Agricultrual Economic Council, 13 (1), 226–247.

Hanemann, W. (1984). Discrete/Continuous Models of Consumer Demand. Econometrica, 52, 541–561.

Kline, J. and Wichelns, D. (1996). Public Preferences Regarding the Role of Farmland Preservation Pro-grams. Land Economics, 72 (4), 538–549.

Li, M. and Brown, H. (1980). Micro-Neighborhood Externalities and Hedonic Housing Prices. Land Eco-nomics, 56 (2), 125–141.

Mills, E. (1972). Urban Economics. Scott Forestman. Glenview, IL.

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

Palmquist, R. B. (1992). Valuing Localized Externalities. Journal of Urban Economics, 31, 59–68.

Polinsky, A. (1977). The Demand for Housing: A Study in Specification and Grouping. Econometrica,45 (2), 447–461.

Poterba, J. (1992). Taxation and Housing: Old Questions, New Answers. American Economic Review, 82(2), 237–242.

Ready, R., Berger, M., and Blomquist, G. (1997). Measuring Amenity Benefits from Farmland: HedonicPricing vs. Contingent Valuation. Growth and Change, 28, 438–458.

Sieg, H., Smith, V., Banzhaf, H., and Walsh, R. (2002). Measuring the Impact of Air Quality on HousingMarkets and Residential Choices in Southern California. Discussion Paper.

Sirmans, C. and Redman, A. (1979). Capital-Land Substiturion and the Price Elasticity of Demand forUrban Residential Land. Land Economics, 55 (2).

Small, K. and Song, A. (1994). Population and Employment Densities: Structure and Change. Journal ofUrban Economics, 36 (3), 292–313.

51

Fig

ure

4:Lan

dP

rote

ctio

nPol

icie

s

Pol

icy

I(F

ores

ted

Wet

land

s)Pol

icy

II(A

g/Fo

rest

s)Pol

icy

III

(Urb

anA

g/Fo

rest

s)

Shaded

are

as

repre

sent

the

addit

ionalpro

tect

edla

nd

under

each

policy

.

52

Fig

ure

5:D

evel

opm

ent

Free

zePol

icie

s

Pol

icy

IV(G

row

thR

ing

Pol

icy)

Pol

icy

V(C

ary

Pol

icy)

Shaded

are

as

repre

sent

zones

wher

edev

elopm

ent

isfr

oze

nat

1984

level

s.

53

Fig

ure

6:A

ggre

gate

Sum

mar

yof

allPol

icie

s

Land

Pro

tect

ion

Land

Pro

tect

ion

Land

Pro

tect

ion

Gro

wth

Rin

gC

ary

Policy

IPolicy

IIPolicy

III

Policy

Policy

Acr

esP

rote

cted

8689

9859

4176

..

Num

ber

ofParc

els

Pro

tect

ed54

27

82

..

Aver

age

Parc

elSiz

e(a

cres

)160.9

1365.1

550.9

3.

.

Change

inA

ver

age

Zone

Augm

enta

tion

Para

met

er+

0.0

080

+0.0

041

+0.0

145

..

Change

inR

esid

enti

alA

cres

-187.6

2-2

98.4

62

-506.6

31

-2667.7

1932.0

4

Change

inD

evel

oped

Acr

es/

Acr

esP

rote

cted

0.0

22

0.0

30.1

21

..

Per

cent

Change

inA

ver

age

Lot

Siz

e-0

.338%

-0.4

59%

-0.8

36%

-4.1

71%

+1.5

9%

Change

inA

ver

age

Zone

Public

Good

Lev

el-0

.00023

-0.0

0037

-0.0

0096

-0.0

039

-0.0

043

Change

inA

ver

age

House

hold

’sP

ublic

Good

Lev

el-0

.00041

+0.0

0049

+0.0

039

+0.0

0104

+0.0

0731

Per

cent

Change

inA

ver

age

Zone

Land

Pri

ce+

0.0

65%

-0.2

30%

-0.2

92%

+5.7

4%

-13.5

4%

Aver

age

Capit

aliza

tion

Change

(lo)

+$3.1

6-$

7.8

6-$

2.5

0-$

0.1

6-$

323.5

7

Aver

age

Capit

aliza

tion

Change

(hi)

+$3.1

9-$

7.7

8-$

0.8

4+

$117.3

0+

$70.6

2

Aver

age

CV

for

Policy

-$0.3

0$5.6

9$26.5

9-$

150.0

7+

$208.3

3

Avg.

CV

+A

ver

age

Capit

aliza

tion

Change

(lo)

+$2.8

6-$

2.1

7+

$24.0

9-$

150.2

3-$

115.2

4

Avg.

CV

+A

ver

age

Capit

aliza

tion

Change

(hi)

+$2.8

9-$

2.0

9+

$25.7

5-$

32.7

7+

$278.9

5

Aver

age

Part

ialC

V(N

oA

dju

stm

ents

)+

$4.9

0+

$2.6

1+

$47.3

5.

.

Aver

age

Part

ialC

V(N

oP

ublic

Good

Adju

stm

ent)

+$8.0

9-$

4.3

2+

$18.6

2-$

171.3

6+

$59.3

4

54

Figure 7: Decomposing the Policy Impacts

Policy Evaluated Policy I Policy II Policy III

Sample Zone A1 B1 A2 B2 A3 B3

Initial Open Space Percentage 86.4% 21.1% 86.9% 22.4% 63.4% 75.2%

Acres Protected 170.3 0 342.7 0 931.3 0

Initial Augmentation Factor 1.086 1.141 1.026 1.301 1.079 1.096

Change in Augmentation Factor 0.036 0 0.063 0 0.262 0.015

Avg. Partial Equilibrium WTP $67.47 0 $66.37 $0.00 $315.10 $29.02

G.E. Open Space Percentage 88.2% 21.0% 86.9% 22.3% 71.4% 73.5%

Change in G - index -0.025 -0.00034 0 -0.00013 -0.0679 0.0182

Pct. Price Change -1.98% 2.16% 8.14% 0.42% 4.88% 11.4%

Avg. Cap. Chg. per Household (lo) -$41.22 $53.21 $91.89 $13.6 $73.99 $240.76

Effects Experienced by Initial

Residents of Sample Zone:

Avg. Change in G-index -0.01128 0.00432 -0.004 -0.0001 -0.02867 -0.00257

Avg. Chng. in Aug. Price ($/sqft.) -$0.051 $0.022 $0.019 $0.0042 -$0.156 $0.099

Avg. G.E. WTP -$62.01 -$56.15 -$20.67 -$15.39 -$48.3 -$68.44

G.E. Benefit per hshld. -$103.23 -$2.94 $71.22 -$1.79 $25.69 $172.32

55

Fig

ure

8:Sp

atia

lD

istr

ibut

ion

ofN

etB

enefi

ts

��

�

�

�

�

Pol

icy

1(W

etla

nds/

Fore

st)

Pol

icy

2(A

g/Fo

rest

s)Pol

icy

3(U

rban

Ag/

Fore

sts)

Lig

htl

ysh

aded

regio

ns

corr

espond

wit

hzo

nes

whic

hex

per

ience

posi

tive

net

ben

efits

.D

ark

lysh

aded

regio

ns

repre

sent

addit

ions

topro

tect

edla

nd.

Zones

mark

ed

‘A’and

‘B’co

rres

pond

toth

edec

om

posi

tions

inta

ble

7.

56

Figure 9: Summary of CV for all Policies by Income Quartile

Quartile Average CV Average Lot Appreciation Total WTP

Policy I

1 0.7242139 0.0087559 0.73296982 0.4850277 -0.037467 0.44756073 0.0491235 0.308687 0.35781054 -0.434225 -1.684508 -2.1187335 -2.33483 -1.256525 -3.591355

Policy II

1 1.518048 7.886856 9.4049042 2.89402 13.27109 16.165113 4.486893 17.65625 22.1431434 6.516337 21.2162 27.7325375 13.04507 36.97456 50.01963

Policy III

1 13.07561 20.51944 33.595052 18.91049 30.19866 49.109153 24.02852 41.97718 66.00574 30.40838 48.91644 79.324825 46.54785 74.07454 120.62239

Growth Ring Policy

1 -85.66735 117.8932 32.225852 -116.0976 168.216 52.11843 -140.9126 215.9647 75.05214 -171.7469 263.9082 92.16135 -235.9267 375.5817 139.655

Cary Policy

1 100.1223 -13.29592 86.826382 148.5933 -37.50212 111.091183 191.3769 -60.83693 130.539974 240.7793 -85.5279 155.25145 360.8038 -187.3671 173.4367

57

Figure 10: Policy I: Changes in Residential Development, Public Good Level, Populationand Price

Residential Development Public Good Level

Population Price

Lightly shaded zones experienced increases in each of the four measures. Unshaded zonesexperienced decreases in each of the four measures.

58

Figure 11: Policy II: Changes in Residential Development, Public Good Level, Populationand Price

Residential Development Public Good Level

Population Price

Lightly shaded zones experienced increases in each of the four measures. Unshaded zonesexperienced decreases in each of the four measures.

59

Figure 12: Policy III: Changes in Residential Development, Public Good Level, Populationand Price

Residential Development Public Good Level

Population Price

Lightly shaded zones experienced increases in each of the four measures. Unshaded zonesexperienced decreases in each of the four measures.

60

Figure 13: Growth Ring Policy: Changes in Residential Development, Public Good Level,Population and Price

Residential Development Public Good Level

Population Price

Lightly shaded zones experienced increases in each of the four measures. Unshaded zonesexperienced decreases in each of the four measures.

61

Figure 14: Cary Policy: Changes in Residential Development, Public Good Level, Popula-tion and Price

Residential Development Public Good Level

Population Price

Lightly shaded zones experienced increases in each of the four measures. Unshaded zonesexperienced decreases in each of the four measures.

62

Figure 15: Cary Policy: Relocation from Three Dense Zones (relative to baseline equilib-rium)

Three shaded zones are the dense population core of the development freeze region underthe Cary Policy (Policy V). Under Policy V, more than 5,000 households relocate from these3 zones to the striped zone.

63

Fig

ure

16:

Sum

mar

yof

Lan

dP

rote

ctio

nPol

icie

s

Policy

IPolicy

IIPolicy

III

Zones

Zones

Not

Zones

Zones

Not

Zones

Zones

Not

Effec

ted

Effec

ted

County

Effec

ted

Effec

ted

County

Effec

ted

Effec

ted

County

by

Policy

by

Policy

Wid

eby

Policy

by

Policy

Wid

eby

Policy

by

Policy

Wid

e

Acr

esP

rote

cted

8689

08689

9859

09859

4176

04176

Num

ber

ofParc

els

Pro

tect

ed54

054

27

027

82

082

Aver

age

Parc

elSiz

e(a

cres

)161

0161

365

0365

51

051

#ofZones

27

64

91

16

75

91

15

76

91

Change

in#

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ouse

hold

s+

82

-82

0-2

38

+238

0+

578

-578

0

Change

inR

esid

enti

alA

cres

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3+

1.9

1-1

87.6

2-2

96.7

76

-1.6

86

-298.4

62

-457.2

66

-49.3

65

-506.6

31

Pct

.C

hange

inA

ver

age

Lot

Siz

e-1

.034%

+0.0

83%

-0.3

38%

-0.0

18%

-0.2

03%

-0.4

59%

-5.2

66%

+0.6

69%

-0.8

36%

Pct

.C

hange

inA

vg.

Zone

Pri

ce+

0.4

53%

+0.0

428%

+0.0

65%

-1.1

8%

-0.2

05%

-0.2

304%

+2.0

02%

-0.8

24%

-0.2

916%

Pct

.C

hange

inA

vg.

Aug.

Pri

ce-1

.168%

+0.0

34%

-0.0

41%

-2.9

75%

-0.2

15%

-0.3

03%

-2.5

69%

-1.0

80%

-1.3

90%

Change

inP

ublic

Good

Lev

el(G

)-0

.00076

-2.1

26E

-06

-0.0

0023

-.00213

+5.9

6E

-07

-0.0

0037

-.00528

-.0001

-0.0

0096

Chg

inO

pen

Pct

+0.0

63%

-0.0

0354%

+0.0

16%

+0.1

778%

+0.0

0865%

+0.0

38%

+0.4

458%

+0.0

181%

+0.0

89%

Chg

inA

ugm

ent

+.0

2643

+.0

00194

+.0

0798

+.0

2140

+.0

00447

+.0

0413

+.0

7728

0.0

02167

+.0

145

Chg

inA

vg.

Inco

me

-$36.1

2+

$20.7

40

-$156.1

6+

$0.6

80

-$730.1

1+

$294.1

70

House

hold

Change

Augm

ente

dP

rice

-1.2

05%

-0.2

01%

-0.4

38%

-1.7

88%

+0.6

26%

+0.2

98%

-0.9

32%

-0.8

59%

-0.8

80%

House

hold

Chg.

inP

ublic

Goods

-0.0

0084

-0.0

0028

-0.0

0041

-0.0

0192

0.0

0086

0.0

0049

-0.0

0021

0.0

0063

0.0

0039

Aver

age

P.E

.C

Vfo

rPolicy

$18.9

2$0.5

6$4.9

0$16.6

3$0.4

1$2.6

1$9.5

5$141.8

5$47.3

5

Aver

age

CV

for

Policy

$3.5

5-$

1.4

9-$

0.3

0-$

0.2

7$6.6

3$5.6

9$20.9

4$28.8

5$26.5

9

Avg.

Chg.

Capit

aliza

tion

(lo)

$6.1

3$2.2

5$3.1

6-$

16.9

7-$

6.4

3-$

7.8

6$37.5

4-$

18.5

1-$

2.5

0

Sum

CV

&Land

App.

(lo)

$9.6

8$0.7

6$2.8

6-$

17.2

4$0.2

0-$

2.1

7$58.4

8$10.3

4$24.0

9

Base

line

#ofH

ouse

hold

s24,3

09

78,6

27

102,9

36

13,9

71

88,9

65

102,9

36

29,4

11

73,5

25

102,9

36

Base

line

Avg.

Zone

Pri

ce$/acr

e/yr

902

6755

5018

755

5928

5018

5744

4875

5018

Base

line

Public

Good

Lev

el0.6

667

0.8

498

0.7

954

0.6

61

0.8

24294

0.7

954

0.8

6432

0.7

8185

0.7

954

Base

line

Open

Pct

77.4

7%

53.1

3%

60.3

5%

56.5

7%

78.0

6%

60.3

5%

51.1

1%

62.1

7%

60.3

5%

Base

line

Augm

ent

1.0

646

1.2

31.1

81

1.0

309

1.2

129

1.1

81

1.1

369

1.1

896

1.1

81

64

Fig

ure

17:

Sum

mar

yof

Dev

elop

men

tFr

eeze

Pol

icie

s

Gro

wth

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gPol

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hang

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rage

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Size

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$258

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aliz

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52.7

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57

Avg

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Avg

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Sum

CV

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3.42

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Bas

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65

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