Linking Demand and Supply in a Housing Market Sorting Model

H. Allen Klaiber#

The Pennsylvania State University

Agricultural Economics and Rural Sociology

208A Armsby Building

University Park, PA 16802

Daniel J. Phaneuf

North Carolina State University

Agricultural and Resource Economics

Box 8109

Raleigh, NC 27695

Abstract

In this paper we present one of the first micro-level equilibrium sorting models to include explicit

representations of both the demand and supply for housing. We link the two market sides via a price

equilibrium and the market clearing quantity of undeveloped land. We use the full market and demand-

side only models to estimate partial and general equilibrium willingness to pay measures, in order to

assess the importance of accounting for supply responses when evaluating the welfare effects of land use

policies. We find that supply responses are of first order importance for policies that directly impact

home developer's decisions (such as large-tract open space preservation), and that these responses

propagate primarily through price changes rather than changes in the location of new housing. Failure to

account for supply responses when evaluating land use policies can result in striking differences in the

magnitude and ordering of commonly used partial and general equilibrium welfare measures.

Keywords: Sorting; Housing supply; Housing demand; General equilibrium; Land use

JEL Codes: D5; D6; R2; R3

# Corresponding author: 208A Armsby Building, University Park, PA 16802. Email: klaiber.16@osu.edu. Phone:

614-247-4914.

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Linking Demand and Supply in a Housing Market Sorting Model

1. Introduction

The past decade has seen the rapid development of equilibrium sorting models for estimating

consumer preferences and welfare effects for a variety of public goods and environmental amenities. A

distinguishing characteristic of these models is the ability to measure general equilibrium feedback

effects, whereby price and non-price equilibria endogenously adjust to external shocks. Applications to

air quality (Sieg et al., 2004; Tra, 2010), open space (Klaiber and Phaneuf, 2010; Walsh, 2007), school

quality (Bayer et al., 2007; Klaiber and Smith, 2011), and recreation amenities (Timmins and Murdock,

2007; Phaneuf et al., 2009) have been used to show that feedback effects from price and other

endogenous variables can result in general equilibrium welfare impacts that are substantially different

than their partial equilibrium counterparts. This literature is reviewed by Kuminoff et al. (2010), and

Klaiber and Smith (2010) provide a detailed discussion of the importance of incorporating general

equilibrium effects in welfare measurement for changes in non-market goods.

Most equilibrium sorting models have focused on consumer behavior, implicitly or explicitly

assuming an exogenous supply of the commodity. This is particularly so in sorting models looking at

residential housing decisions, where the emphasis has been on understanding household demand for local

public goods. Many of these public goods are influenced either directly or indirectly by changes in

housing supply. For example, construction of new residential lots in existing school districts may

indirectly influence the sorting equilibrium through changes in the number of students attending local

schools, and thereby alter underlying school quality. As another example, changes in development

patterns may impact local air quality, which could in turn affect the underlying locational equilibrium.

For other applications that involve spatially delineated environmental amenities or land use

policies, the impact of supply responses may be more direct. These direct effects arise from the joint

determination of local amenities and housing. For example, local water quality is likely to be determined

in part by the spatial pattern of new housing construction and the consequent impact on urban storm water

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runoff. For local public goods/bads such as open space or road congestion, the combined behavior of

buyers and new home developers endogenously determines the amenity and externality levels. In these

instances predictions of the size and form of general equilibrium feedback effects will depend on how the

supply side of the market is treated. Nonetheless, there are few papers that examine supply side aspects

of residential sorting models, and fewer still that combine demand and supply models to examine the

latter's importance in measuring general equilibrium welfare effects.1

Our objective in this paper is to jointly examine the demand and supply sides of a residential

housing market using a horizontal sorting model, in order to demonstrate the extent to which accounting

for supply effects is important for predicting general equilibrium welfare measures in this class of models.

We build on our previous work (Klaiber and Phaneuf, 2009, 2010) on open space amenities in

Minnesota's Twin Cities area by adding an empirical model of new home builder behavior to our existing

model of household location choice. Integrating the two market sides allows us to conduct counterfactual

experiments in which home prices, the spatial distribution of new housing, and the amount of developable

land re-equilibrate in response to external or policy shocks. We find substantial differences in our

predicted welfare estimates between partial and general equilibrium measures, as has been shown in the

existing literature. However, we also show that including endogenous supply responses and various

degrees of endogenous feedbacks can lead to a large disparity between the general equilibrium measures

typically used in this literature (which hold supply fixed), and those that allow for more flexible supply

responses. Our results suggest that accounting for supply in residential sorting models is of first order

importance - particularly when the public good of interest evolves with new residential construction.

In some ways these findings are not surprising, in that research using reduced-form land

conversion models (Carrion-Flores and Irwin, 2004; Towe et al, 2008) has shown how landscapes evolve

in response to both households' preferences and builders' profit motives. Since this literature does not

take an equilibrium or structural perspective, welfare analysis is not possible, nor can one disentangle

1 Walsh (2007) endogenously determines the quantity of undeveloped land in a vertical sorting model, but does not

explicitly model the supply of new housing.

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supply and demand effects and predict endogenous feedback effects. As such we take the insights from

the micro-level land conversion literature as our starting point for constructing a simple, but nonetheless

structural, model of supply behavior.

Modeling the behavior of home builders is complicated for several reasons. Factors related to

dynamics, market power, economies of scale, and macroeconomic trends are all likely to play a role in the

level and spatial distribution of new home construction in a given market. Our sense, however, is that the

challenges associated with modeling supply behavior in a realistic way have prevented investigation of

the more fundamental question of how important supply impacts may be within the overall market (see

DiPasquale, 1999, for more discussion on this viewpoint). In order to focus on this question, our model

of supply abstracts from the difficulties listed above in order to isolate what we believe to be the key

behavioral dimension: the location of new construction based on home prices, vacant land prices, and the

availability of developable land, where the latter is potentially impacted by land use policy. Our decision

to simplify the supply model allows several important insights to emerge. First, including supply side

responses can result in general equilibrium welfare measures that differ from those that do not account for

a supply response by over 30%. Second, including endogenous feedback responses within supply - in our

case by changing the stock of developable land - can result in very large welfare implications of up to an

additional 30% change in the size of our welfare measures. Third, supply responses appear to be most

important for policies which directly impact the supply process, such as land use restrictions. Finally,

supply responses in general dampen the welfare implications of policy by lowering implied magnitudes as

greater degrees of market adjustment are available.

2. A model with supply and demand

Conceptual basis

Our analytical framework follows the demand side sorting models developed by Bayer et al

(2005) and Bayer and Timmins (2007). These structural models use agent's revealed location decisions to

recover preferences for spatially delineated goods, based on the assumption that the collection of

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observed outcomes is a Nash equilibrium in which each agent’s location choice is optimal conditional on

the choices of all other agents. In the current paper, we assume the urban landscape can be divided into

housing types indexed by h, where in our analysis h is broken into components that include location and

time, indexed by j and t respectively, so that h={j,t}. The housing stock at time t includes existing homes

as well as new construction provided by profit maximizing builders. There are I households that

maximize utility by choosing a housing type for their primary residence and B builders that each provide

a single home of type h. We denote the exogenous level of existing homes marketed in location j at time t

by Ejt=Eh and assume that all homes are eventually occupied, so that I=E+B, where E=hEh.

Household i's utility from choosing a particular house type h is

( , , , , ) ,i i i i

jt h h h h h hU U U S N I (1)

where the conditional indirect utility is a function of structural and neighborhood attributes Sh and Nh,

respectively, observable household characteristics Ii, price , a term capturing unobserved attributes of

the housing type , and an idiosyncratic error component . As is customary we use a linear

specification for (1) so that

,i i i i

h S h N h h h hU S N (2)

where and

are vectors whose individual elements consist of a mean parameter common across all

individuals and an individual component that varies with observable household characteristics, so that

0

1

, , ,Q

i i

X X qX q

q

I X S N

(3)

where Q is the number of household characteristics held in Ii. Household i selects the housing type h

* if

*

*, .i i

hhU U h h (4)

For home developers we assume there is a reduced form profit function describing the payoff to

builder b from providing a home of type h so that

( , , , ) ,b b b b

jt h h h h hF B (5)

where the payoff depends on the output price , observable factors affecting cost (such as the price of

5

developable land and land use restrictions), the builder's observable characteristics Bb, a term capturing

the type h unobserved determinants of payoff , and an idiosyncratic shock given by . We assume the

payoff function takes a linear form given by

,b b b

h F h h h hF (6)

where is a heterogeneous parameter given by

0

1

,L

b b

F F lF l

l

B

(7)

and L is the number observed builder characteristics. Builder b supplies a home of type h* if *

b b

hh

for all h≠h*.

There are two things to note about the model assumptions. First, price is common to both the

utility and profit functions in the same way that output price enters both demand and supply equations.

There may also be other common variables. For example, Nh will contain variables related to open space

such as undeveloped land and land use programs; these variables may enter Fh to the extent that they

affect the cost of new development. Other variables are likely to enter only one or the other function.

Whereas households receive utility directly from elements of Nh and disutility from price, firms care

about the former only to the extent that it increases the latter or affects costs. Likewise and are

likely to contain different factors, such as 'neighborhood appeal' for the utility function and 'permitting

costs' for the profit function. Second, assumptions on variables that are common or excluded from the

two functions will have ramifications for defining equilibria in the model and for identifying the primal

parameters.

To define an equilibrium in the model we note first that a household's probability of selecting

housing type h – also its expected demand for housing type h – is

Pr ( , , , , ),i I i

h hf I S N (7)

where the form of fhI(∙) arises from the assumption on the distribution of

, and bold letters indicate that

the probability of a particular choice is a function of all structural, neighborhood, price, and unobserved

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features of all the choices in the landscape. We obtain the expected market demand in share form for

housing type h by integrating the expression in (7) over the distribution of household characteristics so

that

( , , , ) ( , , , , ) ( ) ,d i i i

h h If I g I dI S N S N (8)

where gI() is the distribution of household characteristics in the population of I buyers.

Similarly note that the probability of a builder providing a new home of type h is

Pr ( , , , ),b B b

h hf B F (9)

where the form of fhB(∙) arises from the assumption on the distribution of

. The expected market share

of new homes of type h is obtained by integrating (9) over the values for Bb so that

( , , ) ( , , , ) ( ) ,ns B i b b

h h Bf B g B dB F F (10)

where gB() is the distribution of builder characteristics in the population of B home producers. The supply

share of housing type h is determined by combining the exogenous stock of existing type h marketed

homes with time t new construction. In particular, the expected supply share for type h is

( , , )

,ns

h hSh

E B

I

F (11)

where Eh is stock of existing housing offered for resale. If we ignore dynamics in the housing market - a

large assumption which we discuss in detail below - then we can denote the expected supply share by

, and equilibrium in the landscape is characterized by

(12)

which defines a vector of equilibrium prices as well as other endogenous outcomes, such as the amount

of developable land at each location j at each time t.

Econometric models

Our estimation objective is to identify the utility function and profit function parameters.

Estimation of the utility function follows closely our description in Klaiber and Phaneuf (2010), and so

7

we only sketch the approach here. We begin by rewriting the utility function in (2) as

,i i i

h h h hU (13)

where contains all terms that are common across people and

contains terms unique to household

i. Specifically,

0 0 ,h S h N h h hS N (14)

and

1 1

.Q Q

i i i

h qS q h qN q h

q q

I S I N

(15)

We estimate the model in two stages. First, we assume that is independent and identical extreme

value, so that the familiar conditional logit model arises in which equation (7) becomes

exp( )

Pr ,exp( )

ii h hh i

h h

h

(16)

and the log-likelihood function is

ln(Pr ),i i

h h

i h

ll Y (17)

where Yhi=1 if the individual chooses option h and zero otherwise. In addition, the empirical analog to

our equilibrium condition in (12) is

1

1 exp( ), ,

exp( )

iI h h

hi ih hh

hI

(18)

where is the empirical share of the I total homes in category h. The first stage of estimation maximizes

the log-likelihood function subject to (18) by searching for the parameters in

via a gradient method

and identifying the using Berry's (1994) contraction mapping routine. Because (18) is implied by

the first order conditions for maximizing the likelihood function, this process provides maximum

likelihood estimates of the and the parameters contained in

. The second stage of estimation

decomposes the into observed and unobserved components using a linear regression for equation

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(14). Because price is endogenous in this equation, we use the instrumental variables approach described

by Bayer et al. (2007) and implemented for this model by Klaiber and Phaneuf (2010).

To estimate the parameters of the profit function we first rewrite (6) as

,b b b

h h h h (19)

where contains all terms that are common across builders and

contains terms specific to builder

b. In particular,

0 ,h F h h hF (20)

and

1

.L

b b

h lF l h

l

B F

(21)

Estimation proceeds in two stages. We assume the idiosyncratic shock is distributed type I extreme value

and that each builder is observed building a single home on each observed choice occasion so that,

conditional on values for the , the probability that builder b provides a home of type h is

exp( )

Pr .exp( )

bb h hh b

h h

h

(22)

The empirical equilibrium condition that follows from (12) is

1

1 exp( ),

exp( )

bB h hh

h b bh hh

B E

I B I

(23)

which can be rewritten as

1

1 exp( ),

exp( )

bBh h h

h b bh hh

E

I I

(24)

recalling that is the empirical share of the I total homes marketed in category h and is the

exogenous number of type h marketed houses in the landscape. Further denoting Bh as the number of new

type h homes we define as the contribution of new homes to the overall

empirical share of homes in category h. With this the equilibrium condition for the empirical supply

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model can be written as

1

exp( )1.

exp( )

bBns h hh b

b h h

h

I

(25)

We estimate the parameters in

by a gradient search, and obtain the from (25) using a

contraction mapping. Once again, since (25) is derived from the first order conditions for the conditional

logit model, the estimates are maximum likelihood estimates.

In the second stage we estimate the linear model in (20) by instrumental variables using an

approach similar to that used on the demand side of the market. In particular, we add additional ring

variables to capture changes in development costs of surrounding areas, . Aside from this addition, the

instrumentation strategy proceeds in a similar fashion, where the key differentiating factor from the

demand instrument arises due to the different set of residuals obtained when estimating

(26)

where the tilde indicates additional ring variables are included, are additional housing, land use, and

census ring variables, prices have been moved to the left hand side, and is an initial conjecture at the

price coefficient. Setting the residuals from this regression to zero and solving for the set of prices which

clear the observed market equilibrium relationship between supply and demand provides our instrument

for housing prices on the supply side of the market.

3. Data

The Twin Cities area of Minnesota contains a wide variety of land uses interspersed within a

large housing stock containing both older, established neighborhoods near the city centers of Minneapolis

and St. Paul and more recent development in outlying areas. In addition, the Twin Cities is representative

of many major urban areas in the United States in that its population expanded rapidly during the 1990s

and early 2000s, which led to the construction of many new residential areas. Given the growth of

population in the Twin Cities, and its mix of old and extensive new residential development, the area

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provides an ideal laboratory for examining how the interactions between households and developers lead

to price and amenity level equilibria across the landscape.

Modeling household and developer behavior jointly requires specification of common temporal

and spatial dimensions in which both sets of actors make decisions. For this study, we use census block

groups as the spatial unit of analysis, so that agents choose to locate or build in one of J census block

grtoups, which proxy for neighborhoods.2 For the temporal dimension we focus on the years 1990

through 2004, taking as given the stock of housing in 1990 and assuming new households entering the

market are the result of large scale macroeconomic trends operating beyond the regional scale. We also

take as given the decision of homeowners to offer their existing houses for sale, choosing instead to focus

our modeling efforts on the supply of new housing by developers. As described above, our model and

data needs for the demand side of the market closely follow those described in Klaiber and Phaneuf

(2010), though in this analysis the choice elements are more aggregate in that they do not contain a home

size dimension. In the next subsections we first describe the motivations for how we have defined our

choice set, and then we briefly summarize the data sources we use to estimate the household sorting side

of our model. This is followed by a more detailed discussion of the data we use to estimate the home

developers objective function.

Transactions and choice set

Defining the choice set for a locational equilibrium model determines the scale of aggregation for

both housing and non-housing attributes that enter agents’ objective functions, as well as the set of

alternative specific unobservables captured by the model. As such, researchers face a tradeoff between

using small spatial and time dimensions to limit aggregation and the constraints of thin markets and data

availability. Using single family residential housing transactions purchased from Plat Research, a local

MLS company serving the Twin Cities, we observe 397,207 individual home sales transactions between

1990 and 2004 across the seven counties in our study area. Examining grantor and grantee names as well

2 Block groups are designed to contain between 600 and 3000 individuals.

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as construction years contained within these transactions, we identified 57,815 housing sales as initial

sales of new residential construction between developers and households. These transactions are

displayed in figure 1. As expected, the vast majority of new home construction is outside the established

central city areas and many of them are clustered, reflecting new subdivision development.

Given the long time period covered by our data, we choose to follow Klaiber and Phaneuf (2010)

and divide our choice set into three time periods, which are exogenous from the perspective of decision

makers in our models. These periods are 1990-1996, 1997-1999, and 2000-2004. The cutoff dates for

each exogenous time period were determined in part by the availability of land cover GIS data available

for each cutoff year. In treating the time dimension of choices as fixed, we allow the unobservable

components of utility and profit to vary over time, while maintaining the assumption that the observable

structure of preferences and profits remain constant.

We divide the landscape into nearly 2,000 unique spatial bins using Census 2000 block groups as

our spatial delineator. Unlike Klaiber and Phaneuf (2010), we omit house size as a choice set dimension

in order to limit the number of non-chosen alternatives in the supply model, for which the data are

necessarily much thinner. Our final choice set is formed by combining the three exogenous time periods

with Census 2000 block group spatial bins, resulting in a total of 5,563 choice alternatives containing at

least one housing transaction. These bins are the alternatives used for both household demand and

developer supply models.

Some refinement to the available supply alternatives is required which results in a reduction of

supply alternatives available to developers. Starting from the full set of 5,563 alternatives available to

households, we eliminated 866 of these alternatives if they involved block groups containing either no

new construction during our study period, many of which had no developable land, or were missing data

required for supply estimation. We further removed an additional 916 alternatives where the only new

housing construction was identified as either redevelopment, built in areas with no undeveloped land, or

as subdivisions of existing residential parcels with average lot sizes less than 0.05 acres and

predominately located in inner-city areas. After removing these alternatives, our choice set for home

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developers contains 3,781 alternatives. Of these alternatives, 2,170 experienced new construction,

representing approximately 60% of the total available alternatives. The block groups containing these

alternatives are shown in figure 2. Unlike demand estimation, the existence of non-chosen alternatives on

the supply side raises new challenges for estimation of the empirical model described in the previous

section.

Amenities, housing, and household characteristics

The amenities and housing characteristics distinguishing alternatives on the demand side of the

market were constructed following Klaiber and Phaneuf (2010). Detailed land use data was obtained

from the a local governing body, the Metropolitan Council, with each land use type converted to

percentages of total land area to reflect the likely proximity and accessibility of the land use type to

residents living in a particular location. Included in this analysis are land use categories of agricultural

preserves, agricultural and undeveloped lands, cemeteries, commercial properties, golf courses, highways,

industrial parks, protected natural areas, local parks, regional parks, small conservation easements, and

open water.

Housing characteristics were derived from data contained within the single family transactions

associated with each alternative in the choice set and calculated as the median of each housing attribute.

These variables include square footage, lot size, number of stories, bedrooms, bathrooms, and an indicator

for presence of a garage. Lastly, distance to CBD was calculated as the minimum distance to either

Minneapolis or St. Paul for the median household located in each choice set bin. Following Klaiber and

Phaneuf (2010), housing price indices are estimated for each alternative based on observed transaction

prices, controlling for adjacency to land use (dis)amenities and general levels of price appreciation within

each time period using yearly dummy variables. The results from these regressions are shown in table 1.

In addition to housing characteristics, census variables describing neighborhood characteristics, such as

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percentage of vacant houses, were obtained from both Census 1990 and Census 2000.3

To incorporate observable heterogeneity into the model, demographic characteristics of

households were obtained from Census 1990 and Census 2000 block demographic data which are the

smallest geographical delineation for which the census collects a 100% sample of the population. Each

geographical census block definition contains approximately 30 households. Data recorded at this

geographical level and made publicly available include statistics on household age composition and

household size. Using this data, we calculated the average number of retirees (65+), children (<18), and

working aged adults in a typical household for each block as well as the average household size. We

assigned these characteristics to each household observed purchasing a home in each block. For more

details and potential implications of this assignment process, see Klaiber and Phaneuf (2010). Summary

statistics for all demand side variables are shown in table 2.

Landscape and development cost characteristics

Modeling developer location decisions requires several additional data components in addition to

the output (housing) prices described above. While these equilibrium prices enter both demand and

supply decisions, additional variables characterizing potential costs and revenue generation for developers

reduced form profit functions are required. Building off of the existing land conversion literature we

develop a series of land suitability metrics to meet this need. As these measures exist primarily for

undeveloped land, likely as a result of the inability to measure suitability metrics for previously developed

areas, all of our data are based only on suitability measures falling within the undeveloped or agriculture

land use category.4

The suitability of land for residential development varies spatially and is likely a major

determinant of builders costs and hence location choices. To capture this aspect of the development

3 For the 1997-1999 time period we linearly interpolate the 1990 and 2000 data to year 1997.

4 Given that developers would require undeveloped land for new construction, we feel that creating suitability

measures based only on existing undeveloped land areas is appropriate.

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decision, we define four development suitability measures based on the publicly available soil survey

(SSURGO) database provided by the Natural Resources Conservation Service (NRCS) and available

online at http://soils.usda.gov. These variables include indicators for percentage of land in a block group

classified as poor drainage, limited development potential, poor agricultural potential and very high slope.

The SSURGO data provides a series of discrete indicators for each of these categories that we combine to

form the above four variables. We define poor drainage as any land area ranked in the lowest 3 out of 7

potential drainage classes. Limited development potential is defined as land falling into the lowest

category of development suitability, excluding basement construction suitability. Poor agricultural

potential is classified as any land falling within the lowest 2 of 8 potential non-irrigated agricultural

suitability rankings. Lastly, very high slope is defined as any areas with at least a sixteen degree slope.

In addition to the SSURGO derived suitability measures, we also obtained information on urban

services areas from the Metropolitan Council which outline the extent of sewer and water lines as well as

municipal trash service in our study area. Data on urban services were available for the years 1995, 1997,

and 2000 and we attach a measure of the percentage of land within the services boundary in each time

period. Lastly, we calculated distance to CBD for each alternative to proxy potential commuting costs to

work sites as well as other potentially spatially varying development cost characteristics. Summary

statistics for these variables as well as the development suitability measures described above are shown in

table 2.

To proxy land acquisition costs, we developed block group and time period specific vacant land

prices based on predictions from a semi-log land price regression using 30,499 vacant or agricultural land

sales occurring during our study period, and available in our transactions database. The location of these

sales is shown in figure 3 and reflects the greater extent of undeveloped land as one moves away from the

central city areas. In addition to including regressors for acres of available undeveloped land and acres

of water in each block group, we also include time period dummy variables and a set of 607 Census 2000

tract dummy variables. As expected, the impact of a larger number of undeveloped acres in an area is to

lower land prices in that area. Also as expected, increased open water acreage increases land prices,

15

likely due to the scarcity of undeveloped water-front lots and the price premium associated with those

lots. Using the land price regression results shown in table 3, we predict per acre land prices for each

block group and time period combination in our choice set. Summary statistics for the predicted land

prices in each time period are shown in table 2; comparing prices across time shows the intuitive increase

in prices as the urban fringe moves outwards.

In addition to output prices, vacant land prices, and development suitability proxies the

developer’s reduced form objective function includes variables measuring the percent of land in

agricultural preserves, percent of agricultural/undeveloped land, percent of protected natural areas, and

the number of Reinvest in Minnesota (RIM) conservation easements. These land use characteristics are

intended to reflect the relative availability of land for development and hence costs, while housing price

captures the revenue from selling the new structure. Thus the returns from new construction depend on

the value of local amenities, as determined by equilibrium sorting and housing prices. Summary statistics

for these variables are shown in table 2.

One advantage of the locational sorting framework we employ is the ability to estimate

heterogeneous objective functions. While only a small amount of literature exists regarding the role of

heterogeneity among developers, we hypothesize that costs are likely to vary with the size of developers.

Using the transactions data, we identify the names of developers from grantor name records attached to

each transaction. After manually inspecting grantor names and determining the likely variations of the

same name associated with a single developer, we create a measure reflecting the number of homes built

by each developer in our sample and use this variable as an indicator of builder size to incorporate

heterogeneity into the supply model.5 The summary statistics for this variable are shown in table 2 and

reflect a skewed distribution with the average developer constructing 588 houses, the largest developer

constructing 5,073, and numerous developers building a single home. A histogram of total houses

constructed by each developer is shown in figure 4.

5 It is likely that in some cases we underestimate the size of a developer due to difficulties in determining all

potential variations on a single developer’s name.

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4. Estimation results

To gauge the importance of supply responses in policy counterfactuals, we outlined a supply and

demand model which shared a common choice set. As described in section 2, both household and

developers are viewed as decision making agents choosing from a set of available housing types to either

purchase or construct. To recover preferences, we estimate two separate sorting models – one for supply

of new homes by developers and another for housing demand by households. These models are linked

through equilibrium prices, the market clearing equality of supply and demand, and potentially

endogenously determined levels of undeveloped land. As a similar demand-side only model is discussed

in detail in Klaiber and Phaneuf (2010), we only briefly discuss the estimation results for this model in the

following subsection.

Demand model results

Results from the estimated demand model are consistent with those reported in Klaiber and

Phaneuf (2010) and are shown in table 4. The model recovers mean preference parameters and

heterogeneity in those preferences using the two-stage estimator described in section 2. Interactions

included in the first stage capture potential differences in preferences across households with different age

composition and household sizes as shown in equation 15. From these results, it is clear that

heterogeneity plays an intuitive and important role in understanding household preferences for location

amenities. We find households with more retirees have stronger preferences for locations with golf

courses and water, as well as an aversion to multi-story housing. In addition, the presence of increasing

numbers of children results in an increase in household preferences for larger lot sizes and more

bedrooms while decreasing the willingness of households to live in more industrialized areas.

After instrumenting for price following Klaiber and Phaneuf (2010), the second stage of

estimation recovers the mean taste parameters shown in equation 14 which, combined with the first stage

parameters allows calculation of marginal willingness to pay measures. Examining the second stage

17

estimates, we find a negative coefficient on housing price, while other housing characteristics take on the

expected signs and significance.6 The final column of table 4 provides marginal willingness to pay values

which are based on the mean house price of $158,082 and combine both first-stage and second stage

estimates using mean household characteristics for variables interacted with household characteristics in

the first-stage. The marginal willingness to pay measures reflect a clear preference ordering for protected

open space over non-protected open space with a 1% increase in protected natural areas associated with a

willingness to pay of $1,740 compared with a willingness to pay of $661 for temporary agricultural

preserves and a negative willingness to pay of $727 for a 1% increase in agricultural and undeveloped

land. The negative willingness to pay for unprotected land potentially reflects the uncertainty of future

land use and perhaps existing negative externalities from farming activity in terms of congestion or

noise.7

Supply model results

Relatively little intuition has been developed in the existing literature regarding the micro-level

location decisions of developers in a structural supply model. However, we expect that characteristics of

the landscape which would lead to increased development costs, all else equal, would be undesirable

while characteristics associated with lower development costs or increased profit potential would be more

desirable. Provided that our characterization of landscape characteristics is sufficiently capable of

reflecting these costs we would expect our results to confirm this basic intuition. We estimate the discrete

choice model shown in equation 19, which allows developers' reduced form profit functions to vary by

developer size. We decompose the set of alternative specific fixed effects recovered using the Berry

(1994) contraction mapping into observable and unobservable components as shown in equation 20. To

6 When interpreting coefficients which are also included in the first stage, it is important to take the composite

effect. For example, numbers of bathrooms is negative in the second stage, but strongly positive in the first

providing an overall large positive effect.

7 For a more detailed discussion of these results, see Klaiber and Phaneuf (2010).

18

form an instrument for housing prices we use an instrumentation strategy which relies on the exogenous

determinants of housing prices in other, more distant alternatives. These price determinants are correlated

with the endogenous housing prices in a given neighborhood through equilibrium housing prices across

the broader housing market, but are unlikely to be correlated with locally unobservable determinants of

housing prices. In contrast to the demand model, estimation of supply raises additional challenges that

arise as a result of non-chosen alternatives in the developers’ choice set. We discuss the estimation

implications of non-chosen alternatives in a locational sorting model below.

Estimates from the first and second stage of the developer supply model are shown in table 5. To

identify heterogeneity in developer preferences, we include interactions between developer size and

percent of undeveloped land, percent of high slope land, and percent of metropolitan services. We expect

that larger developers would have stronger preferences for housing types located in areas with more

undeveloped land as those areas provide fewer constraints on the spatial configuration of subdivisions.

The positive and significant effect for this interaction term seems to support this intuition. While we do

not find a significant interaction between high slope and developer size, we do find a positive and

significant interaction effect between the existence of metropolitan services and developer size. We

hypothesize that the existence of water and sewer lines provides a substantial cost-savings for larger

developers relative to smaller developers due to the increased costs and regulatory hurdles of installing

community water systems for large developments.

In addition to heterogeneous interaction parameters, the first-stage model also recovers a

complete set of alternative specific constants, which are decomposed in the second stage of estimation.

Recovering these fixed effects is possible using a contraction mapping which derives from the structure of

the logit model. This algorithm equates observed empirical shares to predicted shares based on the first

order conditions for maximum likelihood. Due to the presence of non-chosen alternatives, which have a

zero share, it was necessary to employ a numerical patch. Following Timmins and Murdoch (2007), we

provided an initial share of 1e-10 for all non-chosen alternatives in the first stage of estimation which the

contraction mapping routine uses to recover these parameters.

19

The second stage of the model decomposes the estimated house type fixed effects into observable

and unobservable components as shown in equation 20. If we are concerned that the unobservable

component is correlated with an observable term, an instrumental variables strategy is needed. For our

application, it is very likely that higher housing prices are correlated with unobservable determinants of

costs and revenues facing developers. As with the demand side of the market, we use a strategy of

employing the exogenous characteristics of distant neighborhoods and land characteristics as instruments

following the approach outlined in Bayer et al (2007) and Klaiber and Phaneuf (2010) and described

previously. The instrument we create using this strategy for our supply model is derived from an iterative

set of auxiliary regressions which include a full set of housing characteristics, census controls,

development suitability data, and land use characteristics for overlapping ring variables in 1,2,3,4, and 5

mile rings surrounding each block group in our choice set.

Inclusion of non-chosen alternatives has potentially important implications for the consistency of

traditional instrumental variables strategies. Because of the numerical patch applied to estimate the fixed

effects associated with the non-chosen alternatives, we employ an instrumental variables quantile

regression (IVQR) estimation strategy following Chernozhukov and Hansen (2008) and used by Timmins

and Murdoch (2007) in the context of a sorting model. This estimation strategy allows us to recover

estimates based on a user provided quantile of the dependent variable rather ran rely on the estimates

from a traditional instrumental variables or least squares approach. The estimates we report are for the

median quantile, which falls within the range of fixed effects associated with housing supply alternatives

actually chosen by developers, and well identified. Furthermore, the median quantile reduces the

potential role of outliers resulting from weak identification of the numerically “patched” estimates of

fixed effects.

Returning to table 5, the IVQR estimates for the median quantile are reported in the bottom

panel.8 As described in section 3, the variables included can be divided into land availability parameters,

8 Results for a non-instrumental quantile regression of the second stage are reported in the appendix.

20

land suitability parameters, and price and proximity parameters. Focusing on the land availability

parameters, we find positive and significant coefficient estimates for percent of agricultural preserves and

percent of agricultural and undeveloped land. From these results we see that developers prefer locations

containing larger amounts of undeveloped land, all else equal. In addition, while the presence of

temporary easements associated with agricultural preserves necessarily prevents potential development,

these easements do not factor negatively in the location decisions of developers. In contrast, permanently

preserved natural areas have a large and negative coefficient, suggesting that developers avoid areas with

large numbers of preserved natural areas, all else equal (recall that the revenue premium from natural

areas is included in the output price). These results generally support our hypothesis that flexibility in

how undeveloped land can be used is attractive to developers. Nonetheless we find insignificant effects

for small conservation easements.

Turning to land suitability measures, we find the expected negative signs for poor drainage,

limited development potential, and very high slope which are likely capturing the increased development

costs faced by developers looking to build houses in these areas. We find a negative but insignificant

effect for poor agricultural potential. All developers have positive preferences associated with areas

providing metropolitan services. Lastly, the price and proximity variables reveal the expected negative

coefficient on land price (an input cost) and a positive and significant coefficient on housing price (the

output price). These are in line with our expectations and suggest that our instrumentation strategy for

housing prices is effective.9

5. Linking supply and demand for counterfactual simulation

The equilibrium condition in equation 11 defines market clearing quantities of housing in each

housing alternative that are required to equate housing supply and demand, given a set of prices and

spatial characteristics. The equality between demand and supply defines a locational equilibrium which

9 Supply results from a quantile regression with no instruments are shown in an appendix.

21

we exploit to perform counterfactual analyses and derive new market clearing quantities of housing,

prices, and endogenous landscape characteristics arising as a result of re-sorting following policy

interventions. Using the counterfactual equilibrium obtained by playing through the supply and demand

adjustments following a change, it is possible to calculate both partial and general equilibrium welfare

measures for policy changes.10

These welfare calculations follow the familiar log sum rule

, (27)

where the 0 and 1 superscripts reflect current and counterfactual levels of all the variables that change via

a policy or readjust in the new equilibrium.

To explore the implications of including an empirical model of developer supply of new housing

integrated with an existing model of household demand for policy analysis, we examine degrees of

general equilibrium re-sorting following a policy change. Each of these welfare measures is derived by

including or restricting various feedback dimensions present in the equilibrium framework outlined in

section 2. First, we calculate a partial equilibrium willingness to pay allowing demand to freely adjust in

response to a policy intervention using the baseline set of market clearing prices and landscape

characteristics. In this scenario, price does not respond to changes in demand, and as such does not result

in a market clearing equilibrium between supply and demand. The second welfare measurement includes

only a demand-side response, where households re-sort following a policy intervention and prices adjust

to clear the market at the initial level of housing supply of each housing type. The third welfare

calculation is obtained when both households and developers respond to the policy and prices adjust to

clear the market at potentially different housing supply quantities from the observed baseline supply.

Lastly, we calculate a market-wide general equilibrium willingness to pay where both households and

developers respond to the policy, treating the quantity of undeveloped land as endogenous to the supply

of new housing. To endogenously determine the quantity of undeveloped land, we calculate the per-

10

We do not calculate welfare associated with developers due to the reduced form nature of the estimated profit

function.

22

house acreage of land used by each housing type in our model and either increase or decrease the amount

of agricultural and undeveloped land in each alternative in response to changes in housing supply.11

To evaluate the implications of including supply responses in a general equilibrium framework

we present the results from three hypothetical welfare policies. Two of these policies are designed to

directly alter open space (dis)amenities to households while also directly impacting proxies for

development costs on the supply side of the market. The third policy is restricted to only directly

influence household amenities, where supply impacts are indirectly determined through changes in

housing prices resulting from demand shifts.

The first policy we examine converts 2.5% of agricultural and undeveloped land into preserved

open space in the 20 block groups shown in the left panel of figure 5. The second policy removes all

agricultural preserves in the 15 block groups shown in the right panel of figure 5 by converting those

areas into unprotected agricultural and undeveloped land. The third policy is designed to impact only the

demand side of the market and involves the creation of an additional conservation easement in the 30

block groups shown in the bottom panel of figure 5. For this we exclude the equivalent change in

conservation easements on the supply side of the market due to the highly insignificant coefficient on

conservation easements reported above. In so doing, we are able to form a comparison between policies

which directly impact both supply and demand through the reduced form profit and utility functions with

a policy which only indirectly influences supply through market adjustments caused by demand responses

to the policy.

Willingness to pay welfare measures associated with each policy for each of the four welfare

calculations are shown in table 6. For the open space conservation policy, willingness to pay measures

range from $100 for the partial equilibrium welfare measure to $51 for the market-wide general

equilibrium welfare measure that includes endogenously determined quantities of undeveloped land. For

this policy, the difference between the $78 demand-side only general equilibrium willingness to pay and

11

We also enforce a non-negative constraint on land in each alternative by increasing prices until available land

becomes non-negative.

23

the $74 market-wide general equilibrium willingness to pay ignoring undeveloped land adjustments is

small. We also find small differences between the two welfare approaches in terms of price increases for

the directly targeted alternatives experiencing the increase in open space. However, the inclusion of

endogenous adjustments in undeveloped land results in a willingness to pay that is nearly 35% lower than

the demand-only general equilibrium measure. Comparing the change in numbers of houses between the

market-wide supply models with and without endogenous undeveloped land reveals only slight

differences, suggesting that much of the difference in willingness to pay is driven by price adjustments.

Indeed, we see a difference of nearly $900 in housing price responses between the two market-wide

general equilibrium models in areas receiving additional open space.

The second policy removes agricultural preserves from selected block groups and converts those

lands into agricultural and undeveloped land. The welfare results from this policy reveal a similar pattern

of a dampening of the willingness to pay measure between the general equilibrium demand-only welfare

measure of a negative $372 and a loss of only $134 in the market-wide, endogenous undeveloped land

model. This magnitude reduction suggests that accounting for supply responses can mitigate some of the

direct impacts of policy changes to the demand-side of the market through changes in housing supply and

equilibrium prices. Overall, these results suggest that a demand-side only general equilibrium welfare

measure may exaggerate the impact of policy by limiting full market adjustments.12

In addition to these general equilibrium implications, a comparison between the partial and

general equilibrium willingness to pay measures reveals a very different implication for the agricultural

preserve policy compared to the first policy. Unlike the first policy, the difference between partial and

general equilibrium measures is non-monotonic. In fact, the willingness to pay for policy 2 increases in

magnitude (becomes more negative) between partial and general equilibrium demand-only models and

decreases in magnitude (becomes less negative) between the same partial equilibrium measure and the

general equilibrium models including supply responses. This result may be due in part to the much larger

12

In addition, the closed market assumptions commonly employed in the sorting literature may also contribute to

this result by excluding substitution to outside markets.

24

housing supply change experienced in the second policy (an average relocation of nearly 40 houses in

each of the targeted housing types) compared to an average of less than one house in the open space

conservation policy. This difference in welfare implications between demand-only models and full-

market models for this policy stands in contrast to much of the existing demand-only general equilibrium

insights regarding the relationship between partial and general equilibrium welfare measures.

The third policy we evaluate adds additional conservation easements to 30 block groups in our

choice set. To limit the direct impact of this policy to only the demand side, we omit the change in

conservation sites from the supply model, which given the highly insignificant coefficient on RIM sites in

the supply model seems reasonable. Comparing willingness to pay measures, there is virtually no

difference between the two market-wide general equilibrium supply approaches. As with each of the first

two policies, we find a fairly substantial difference between the partial and general equilibrium demand-

only welfare measures of 25%, with only an 8% difference between the demand only and supply

measures of general equilibrium. The similarity between these welfare approaches occurs despite the

non-trivial increase of an average of 7 houses in each impacted alternative. Comparing these results with

those from the first and second policies suggests a more limited role for supply responses when policy

does not directly target the supply side of the market.

Overall, these results highlight at least four key findings regarding the inclusion of supply

responses for welfare measurement using general equilibrium sorting models. First, supply responses are

the most relevant for policies directly impacting developer supply decisions. Second, supply effects

propagate primarily through price changes rather than large changes in the supply of housing in a

particular policy area. Third, comparisons between partial and demand-side only general equilibrium

welfare measures can potentially result in different ordinal implications relative to the partial versus

general equilibrium models including supply. Lastly, the importance of supply responses in the context

of welfare measurement appears to be highly case dependent, suggesting a one-size-fits-all rule may not

be easy to identify.

25

6. Conclusions

This paper describes and estimates one of the first micro-level equilibrium sorting models to

include both demand and supply models of housing. Drawing on the existing land conversion literature,

we estimated a reduced from profit function for developers that provides intuitive and plausible results.

In particular, we found negative profit effects for variables reflecting restrictions on developable land and

the expected positive effect of higher housing (output) prices. Thus our model is able to capture the cost

and revenue impacts on developers – the latter via higher sales prices – of efforts to conserve open space.

More generally our estimates suggest that a spatially explicit, micro-level reduced form profit function

used in a sorting context can capture policy relevant factors while providing a better understanding of

developers’ decision making processes.

Combining a micro-level model of housing supply with existing models of household sorting

raises several conceptual and modeling challenges. In order to connect the two market sides for

counterfactual analysis, a common choice set is needed to link the purchase and sale prices entering the

demand and supply models, respectively, into a single equilibrium outcome. We accomplished this by

relying on the locational equilibrium sorting framework which, at a minimum, defines a spatially

delineated set of housing alternatives. The equilibrium framework allows us to recover preferences

consistent with the empirically observed market shares of supply and demand that define the initial

market equilibrium. The model structure allows us to simulate new location, price, and amenity equilibria

following policy interventions.

Linking demand and supply sides of the housing market to recover general equilibrium

willingness to pay measures revealed the importance of accounting for supply responses when evaluating

policies targeting land use. Our results are striking. Using three hypothetical open space policies in

Minnesota’s Twin Cities, we find willingness to pay differences of over 60% between general equilibrium

models of demand assuming a fixed and exogenous supply, and models of supply and demand

incorporating endogenous quantities of undeveloped land. In addition, some preliminary regularities are

evident that suggest interventions directly impacting developers and households may lead to greater

26

differences between general equilibrium approaches, relative to policies that directly impact only

households.

Despite our early evidence on the importance of incorporating supply responses in micro-level

locational sorting models, much work still needs to be done to further evaluate the implications of supply

responses for policy analysis. In particular, we have relied on several strong assumptions to carry out the

analysis presented in this paper. These include the exclusion of dynamics by assuming exogenous time

periods for both households and developers, treating existing houses entering the market as exogenous,

and incorporating only one non-price feedback effect on the supply side of the model through changes in

undeveloped land. In addition, more theoretical work on incorporating non-chosen alternatives in

locational equilibrium models is needed to help address thin markets. Despite these limitations, we

believe this work helps to highlight the importance of considering supply side responses in the context of

micro-level models of equilibrium sorting.

Acknowledgements

We would like to thank Kerry Smith, Chris Timmins, Ray Palmquist, Roger von Haefen, and Elena

Irwin for their helpful comments and suggestions.

References

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Carrion-Flores, C. and E. G. Irwin. “Determinants of residential land use conversion and sprawl at the

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29

Table 1. Price index regressions for Census 2000 block groups by time period

Estimate Std Err t-statistic Estimate Std Err t-statistic Estimate Std Err t-statistic

On-Park 0.0544 0.0052 10.49 0.0627 0.0059 10.58 0.0444 0.0041 10.71

On-Golf 0.1672 0.0126 13.26 0.2375 0.0126 18.84 0.1977 0.0083 23.91

On-Cemetary -0.0416 0.0223 -1.87 -0.0394 0.0289 -1.37 -0.0104 0.0191 -0.55

On-Open Space 0.0416 0.0051 8.2 0.0383 0.0053 7.28 0.0320 0.0036 8.92

On-Water 0.2994 0.0052 57.24 0.3240 0.0067 48.64 0.2937 0.0049 59.62

Year 1990 n/a n/a

Year 1991 -0.0303 0.0036 -8.3

Year 1992 -0.0375 0.0034 -11.07

Year 1993 -0.0250 0.0033 -7.53

Year 1994 -0.0009 0.0035 -0.26

Year 1995 0.0133 0.0035 3.84

Year 1996 0.0480 0.0034 14.23

Year 1997 n/a n/a

Year 1998 0.0483 0.0028 17.48

Year 1999 0.1438 0.0028 50.94

Year 2000 n/a n/a

Year 2001 0.1124 0.0028 39.89

Year 2002 0.1920 0.0027 71.09

Year 2003 0.2659 0.0027 99.07

Year 2004 0.3362 0.0027 124.77

N

Model Information

157,299 88,065 152,273

Variables

Time Period

1990-1996 1997-1999 2000-2004

30

Table 2. Summary statistics for demand and supply variables

Variable Mean Std Min Max Variable Mean Std Min Max

% Agricultural Preserves 0.46% 2.98% 0.00% 51.05% % Agricultural Preserves 0.67% 3.57% 0.00% 51.05%

% Agricultural/Undeveloped 15.99% 23.60% 0.00% 96.74% % Agricultural/Undeveloped 22.79% 25.69% 0.00% 96.74%

% Cemetary 0.32% 3.11% 0.00% 58.43% % Open Space (non-park) 2.25% 4.43% 0.00% 47.87%

% Commercial 4.61% 7.50% 0.00% 69.41% RIM Sites 0.04 0.47 0 16

% Golf 0.89% 4.70% 0.00% 54.30% Distance to CBD 11.11 6.92 0.19 36.76

% 4-Lane Highways 2.55% 4.84% 0.00% 47.43% % Poor Drainage 20.48% 24.23% 0.00% 100.00%

% Industrial 3.85% 10.13% 0.00% 85.93% % Very Limited Development 26.92% 24.65% 0.00% 100.00%

% Open Space (non-park) 1.99% 4.21% 0.00% 47.87% % Metro Services 81.95% 36.05% 0.00% 100.00%

% Local Parks 2.45% 5.73% 0.00% 62.05% % Very Poor Ag Potential 5.79% 11.49% 0.00% 91.96%

% Regional Parks 1.96% 7.54% 0.00% 74.96% % Very High Slope 7.09% 12.99% 0.00% 100.00%

% Water 4.37% 10.34% 0.00% 88.74% Price ($) 163,309 65,457 38,636 586,431

# of RIM Sites 0.03 0.39 0 16 Land Price per Acre ($) 184,749 112,381 19,384 1,320,398

% Vacant Houses 3.21% 3.37% 0.00% 34.81%

Acreage 0.40 0.77 0.05 10.34

Age of House 44.33 28.81 1.00 116.00 Variable Mean Std Min Max

# of Baths 1.78 0.56 1.00 5.00 # of Retirees 0.22 0.20 0.00 3.00

Garage 0.94 0.22 0.00 1.00 # of Children 0.84 0.41 0.00 6.50

# of Stories 1.31 0.35 1.00 3.00 # of Working Aged Adults 1.78 0.32 0.00 8.00

# of Bedrooms 3.16 0.52 1.00 8.00 Household Size 2.84 0.54 0.30 15.00

Square Feet 1561 562 560 7644

Distance to CBD 9.11 6.70 0.00 36.76 Variable Mean Std Min Max

Price ($) 158,082 69,362 32,139 758,661 Developer Size 588.76 1143.46 1.00 5073.00

Demand Alternatives (N=5,563) Supply Alternatives (N=3,781)

Developer Characteristics (B=57,815)

Household Characteristics (I=397,207)

31

Table 3. Land price regression (Census 2000 tract dummyvariables not reported)

Variable Estimate Std Err t Value

Acres Agricultural/Undeveloped -0.00001 0.00000 -3.31

Acres Water 0.00007 0.00002 3.78

Time Period 1 (1990-1996)

Time Period 2 (1997-1999) 0.1175 0.0075 15.76

Time Period 3 (2000-2004) 0.4180 0.0090 46.67

omitted

32

Table 4: Estimates for household location model

Data Characteristics Counts

# of Alternatives 5,563

# of Chosen Alternatives 5,563

# of Individual Households 397,207

Interaction Variables Estimate Std Err t-Stat

% Golf-X-# of Retirees 5.1262 0.2464 20.8005

% Local Park-X-# of Children -0.0698 0.2158 -0.3236

% Regional Park-X-# of Working Age Adults 1.1152 0.3491 3.1949

% Water-X-# of Retirees 3.6199 0.1386 26.1243

% Industrial-X-# of Children -0.7303 0.1458 -5.0105

Acreage-X-# of Children 0.0860 0.0190 4.5222

# of Baths-X-Household Size 0.5005 0.0264 18.9451

# of Stories-X-# of Retirees -6.0003 0.0754 -79.5334

# of Bedrooms-X-# of Children 0.6221 0.0276 22.5386

Distance to CBD-X-# of Working Age Adults 0.1266 0.0026 48.0582

Variables Estimate Std Err t-Stat MWTP ($)

Constant 3.5670 0.3731 9.5600 n/a

% Agricultural Preserves 1.6553 1.2677 1.3058 661

% Agricultural/Undeveloped -1.8185 0.2592 -7.0164 -727

% Cemetary -0.1602 0.9506 -0.1685 -64

% Commercial -1.7786 0.4986 -3.5673 -711

% Golf 0.2186 0.7967 0.2744 530

% 4-Lane Highways -1.6664 0.7514 -2.2177 -666

% Industrial -0.3647 0.3275 -1.1138 -386

% Open Space (non-park) 4.3555 0.9356 4.6555 1740

% Local Parks 0.8345 0.5353 1.5590 304

% Regional Parks -1.9041 0.4545 -4.1892 51

% Water 0.3965 0.3745 1.0587 470

# of RIM Sites 0.1801 0.0856 2.1038 7196

% Vacant Houses -25.3035 1.5032 -16.8335 -10110

Acreage -0.3430 0.0559 -6.1372 -10811

Age of House -0.0002 0.0019 -0.1152 -9

# of Baths -0.9653 0.1052 -9.1751 18279

Garage 1.1759 0.1920 6.1248 46987

# of Stories 1.2948 0.1430 9.0545 -366

# of Bedrooms -0.5440 0.1012 -5.3736 -940

Square Feet (in 100s) 0.2285 0.0203 11.2537 9128

Distance to CBD -0.1833 0.0088 -20.8396 1666

Price (in $1000s) -0.0250 0.0023 -10.8951 -1000

First Stage Estimates

Second Stage Instrumental Variables Estimates

33

Table 5: Developer model of new housing supply

Data Characteristics Counts

# of Alternatives 3,781

# of Chosen Alternatives 2,170

# of Individual Builders 57,815

Interaction Variables Estimate Std Err t-Stat

% Ag/Undev-X-# of houses 0.0149 0.0023 6.5572

% High Slope-X-# of houses -0.0065 0.0043 -1.4989

% Metro Services-X-# of houses 0.0121 0.0015 5.142

Variables Estimate Std Err t-Stat MWTP ($)

constant -56.1659 2.6668 -21.0612 n/a

% Agricultural Preserves 36.8771 12.3618 2.9832 1,214

% Agricultural/Undeveloped 23.3247 2.7085 8.6118 771

% Open Space (non-park) -45.7602 9.3598 -4.8890 -1,506

RIM Sites 0.4522 0.5100 0.8867 1,488

Distance to CBD -0.0969 0.0984 -0.9847 -319

% Poor Drainage -7.4222 3.2785 -2.2639 -244

% Very Limited Development -11.0276 3.8377 -2.8735 -363

% Metro Services 9.7066 2.0565 4.7199 322

% Very Poor Ag Potential -0.2125 4.2385 -0.0501 -7

% Very High Slope -13.3026 4.6183 -2.8804 -439

Price 0.3038 0.0130 23.4463 1,000

Land Price -0.0539 0.0057 -9.4145 -177

Second Stage Instrumental Variables Quantile Regression

First Stage Estimates

34

Table 6. Household WTP for policy changes

GE/PE Supply Supply Feedbacks WTP ($) Overall Impacted Non-Impacted Mean Max (Abs)

PE No n/a 5987 59 n/a 100.30 0.00% 28.28% n/a n/a n/a

GE No n/a 5987 59 n/a 78.19 -22.04% 0.00% -16 3,940 -58

GE Yes None 5987 59 59 74.56 -25.66% -4.64% -12 3,814 -53 0.54 6.98

GE Yes Ag/Undev 5987 59 59 51.46 -48.69% -34.19% -9 2,908 -40 0.53 6.99

PE No n/a 7080 45 n/a -245.63 0.00% -33.97% n/a n/a n/a

GE No n/a 7080 45 n/a -372.01 51.45% 0.00% 204 -9,775 285

GE Yes None 7080 45 45 -262.89 7.03% -29.33% 75 -4,824 114 -39.23 -233.05

GE Yes Ag/Undev 7080 45 45 -134.91 -45.08% -63.73% 28 409 25 -39.63 -237.25

PE No n/a 6149 88 n/a 122.02 0.00% 34.67% n/a n/a n/a

GE No n/a 6149 88 n/a 90.61 -25.74% 0.00% 2 4,291 -67

GE Yes None 6149 88 83 100.69 -17.48% 11.12% -4 2,673 -47 7.41 39.45

GE Yes Ag/Undev 6149 88 83 100.22 -17.87% 10.61% -4 2,865 -50 7.34 38.44

Open Space Policy: 20 block groups receive additional 2.5% non-park open space, lose 2.5% Ag/UndevelopedReinvest in Minnesota

AGPR Policy: 15 block groups lose all Ag Preserves replaced by increase in Ag/Undeveloped

RIM Policy: Add 1 RIM Site in 30 block groups, do not alter the supply side RIM variable!

Housing Change (Impacted)

Welfare Results

Model Setup % Change

from PE

% Change from

GE, NO Supply

Supply

Alternatives

Demand

AlternativesHouseholds

Impacted Households/Alternatives

Welfare Policy

RIM

Open Space

Agricultural

Preserves

Mean Price Change ($)

35

Figure 1. New housing supply across block groups

36

Figure 2. Census 2000 block groups included as supply alternatives

37

Figure 3. Vacant land sales in Census 2000 tracts

38

Figure 4. Frequency histogram for developer size

39

Figure 5. Locations targeted by policy simulations

(a) Open Space (b) Agircultural Preserves

(c) Conservation Easements