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\textsf{\LARGE \hfill Welfare Economics of Land Use Regulation}

\vspace{0.75in}

\textsf{\Large \hfill Paul Cheshire and Stephen Sheppard}

\vspace{0.5in}

\hspace{2.25in}\textsf{\LARGE No. 42}

\newpage 

\vspace{1.7in}

\noindent
\textbf{Research Papers in Environmental and Spatial Analysis }have
been relaunched with a new subtitle reflecting the changing interests of
researchers in LSE: Geography. The papers aim to get findings to those who
may be interested quickly, even though that may be in a somewhat preliminary
form, and to present findings in depth. Comments on the contents of the
papers are one of the objectives of the series and authors value these
greatly.

\vspace{1in}

\hspace{1.5in}London School of Economics

\hspace{1.5in}Department of Geography

\hspace{1.5in}Houghton Street

\hspace{1.5in}London, WC2A 2AE

\vspace{0.5in}

\hspace{1.5in}
\begin{tabular}{lll}
Tel: & \hspace{0.5in} & +44 (0)171 955 7902 \\ 
Fax: &  & +44 (0)171 955 7412 \\ 
E-mail: &  & a.r.patterson@lse.ac.uk
\end{tabular}

\vspace{1in}

\noindent
\copyright \hspace{0.5in} \parbox[t]{14cm}{\sloppy The material contained in 
this Paper is the copyright of the
author. It can be quoted subject to normal copyright law, and should be
cited as: \textit{Research Papers in Environmental and Spatial Analysis }No.
42 (Department of Geography, London School of Economics).}

\vfill

\begin{tabular}{lll}
ISBN: & \hspace{0.36in} & 0 7530 017 5 \\ 
Published: &  & February, 1997
\end{tabular}

\newpage 

\quad

\vspace{2in}

\begin{center}
{\LARGE \bf The Welfare Economics of}
\vspace{.15in}
{\LARGE \bf Land Use Regulation}
\end{center}

\vspace{1.5in}

\begin{center}
{\large \textit{Paul Cheshire and Stephen Sheppard}}
\end{center}
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{\bf \Large The Welfare Economics of Land Use Regulation}%
\endnote{This paper draws upon research funded by the Economic and
Social Research Council under award No. D00 23 2044. This support is
gratefully acknowledged.}

\vspace{1in}

\parbox[t]{2.1875in}{\it {\large Paul Cheshire} 
\newline London School of Economics} 
and \quad \quad
\parbox[t]{3in}{\it {\large Stephen Sheppard} 
\newline Oberlin College} \hfill

\vspace{1.5in}

\noindent
\textbf{\large Abstract}
%\addcontentsline{toc}{Abstract}{\hspace{0.19in} Abstract \dotfill \ \  }

\vspace{.35in}
\noindent
Despite the pervasive nature of land use planning and land use regulation,
evaluation of the costs and benefits of these policies has received only
limited attention. This paper presents an empirical methodology, based on
clear microeconomic foundations, for the evaluation of benefits and costs of
land use planning. The technique is applied to the Town and Country Planning
System of the UK. Evaluation is presented of gross benefits from several
land use planning activities, the net costs of land use planning, and the
distributional consequences of these policies. The results show that these
welfare and distributional impacts are considerable.

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\section{Introduction}

A central focus of economics is evaluation of the consequences of public
policy. From Corn Laws to Airline regulation, the tools of the profession
have been applied to determine the costs and benefits of acts of government.
This continues to the present, with examples such as consideration of
environmental regulation \cite{HazillaKopp:1990:JPE}, occupational safety
regulation \cite{French:1988:SEJ} and noise regulation \cite
{HollandCross:1995:ELRR}. Curiously, one of the most pervasive forms of
government regulation has received much less attention from economists: land
use planning. While the theoretical properties of land use controls have
received some attention\endnote{For example, see \cite{Sheppard:1988:JUE}, 
\cite{Fischel:1990:GrowthControls}, \cite{EppleRomerFilimon:1988:JPubE}, 
\cite{Brueckner:1990:LandEcon}, \cite{Brueckner:1995:JPubE}, and \cite
{Brueckner:1996:JRS}.}, there are no studies which have estimated the net
costs and distributional consequences.

Virtually every urban area in the developed world exercises some control
over the use of land and the type or extent of residential building. Such
regulation serves a variety of purposes:\ control of the spatial structure
of residential development can reduce the cost of providing some local
public goods and serve to isolate land uses which are likely to generate
costly external effects; regulation of building types can serve to limit the
deadweight loss from property taxation; regulation of land use can be a
method of providing valued public goods and amenities by fiat rather than
through imposition of taxes and purchase of land in particular uses.

Of course, the types of regulation which have been the subject of extensive
analysis also serve a variety of goals and can reasonably be claimed to
generate benefits as well as costs. The question of interest is not whether
these public policies generate benefits, but rather what is the value of the
benefit and how do these benefits compare with the costs associated with the
policies. In this paper we develop and test an approach for such an
evaluation of land use planning. We apply this method to evaluate (at least
some of the) benefits and the net costs of land use planning, and the
distributional incidence of these benefits and costs. The methodology is
applied to the British Town and Country Planning System.

The British land use planning system is the archetype for one of the three
main types of planning system that operate around the world; the others
being the `master planning' system of continental Europe and the zoning
system of the USA. In the British system every action that legally
constitutes development requires individual consideration by the planning
authority of the local community.

Several previous papers\endnote{For example, see \cite
{MayoSheppard:1991:OCDP}, \cite{CheshireSheppard:1989:UrbanStudies}, \cite
{Bramley:1993:EandP}, \cite{Bramley:1993:UrbanStudies}, \cite
{GatzlaffSmith:1993:JREFE}, and again \cite{Fischel:1990:GrowthControls}.}
have shown that these systems of `development control' act to restrict the
supply of urban land by category of land use. The British and other land use
planning systems generate benefits in the form of unpriced local public
goods. Unlike some other public goods, these are not made available by
imposing taxes on local residents and then using the proceeds to pay for
production. Rather, they are produced by using the power of the state to
require land to be used in particular ways, or neighbourhoods to be of a
particular type. The absence of taxes does not imply the absence of costs.
These policies can generate significant changes in land prices. This
generates both welfare costs, measurable in terms of the equivalent
variation associated with the price change, and distributional effects.

This paper draws on previous results which have estimated implicit prices
and identified the structure of demand for land and planning benefits to
develop a methodology for quantifying the net welfare and distributional
impacts this system of land use planning can have. Using analysis of land
values and housing markets in cities chosen to represent the full range of
possible levels of planning restrictiveness, we calculate the changes in
land values attributable to the planning system. This permits us to
calculate the equivalent variation in income associated with the policies,
and to assess the effective distributional consequences.

Such analysis has been undertaken for many of the other productive
activities of local governments, but has not generally been undertaken for
land use planning because of the lack of explicit taxes and payments. We
view this paper as providing the first results of this sort for the British
system, and believe that the methodology might be quite useful in assessing
the implications of land use planning on the distribution of welfare and
equity in other contexts.

All planning systems work to some extent to provide local amenities without
collecting taxes to pay for them. Thus, in principle, the techniques we
employ should be applicable to analysis of other types of planning systems.
To the extent that the distribution of burdens and benefits arising out the
planning system differs from that associated with local tax structures, our
analysis can also shed light on the distributional consequences of recent
legal debates concerning `takings' in the U.S., and the associated proposals
to provide greater compensation (obtained presumably from tax revenues) to
land owners whose property values are affected by planning and environmental
policies.

\subsection{Outline approach}

The methodology we implement proceeds through a series of straightforward
steps. We begin by identifying a structurally and geographically comparable
pair of urban areas which appear to represent extremes, or near extremes, in
the operation of land use planning constraints. For each urban area, sample
data concerning the housing market is collected, including land, location,
neighbourhood amenities, and incomes of households occupying the houses in
the sample. An hedonic price function and demand system is estimated for
each urban area which permits the construction of an expenditure function
for consumers in each city. Using the expenditure function we estimate the
utility level experienced by a `typical' household in each city.

Taking this average household as representative of all households in each
urban area, we use the standard characterization of land market equilibrium
to determine the extent to which the local planning authority makes land
available for residential use in each city, and use observed patterns of
residential development to determine the innermost and outermost extent of
residential land use

To estimate the gross benefits of land use planning, we use the demand
system to determine the `reservation price' for each amenity attributable to
the planning system by calculating the price at which demand for the good
would be reduced to zero. We can then estimate gross benefit to each
household by calculating the variation in income associated with increasing
the price of each amenity to the reservation price.

Estimation of the net costs of land use planning is somewhat more complex,
since we must examine not only the change in benefits resulting from a
change in planning regime (again using the demand system) but also the
costs. The costs of land use planning come primarily in the form of
increased prices for residential land and hence for housing. We estimate the
equilibrium land rents under alternative planning regimes and calculate the
equivalent variation in income associated with the combined reduction in
residential land prices and effective increase in the price of the amenities
produced by the planning system.

This approach permits us to examine the distribution among households of
costs and benefits, and to provide tentative answers concerning the
efficiency of the land use planning system as implemented in the UK. We find
that considerable value is attached to the amenities produced by the
planning system. These amenities, however, come at a very high cost, and we
estimate considerable net costs associated with the most restrictive
planning regime. The distributional consequences of the land use planning
system are seen to depend on which aspects of planning are being considered.
Taken as a bundle, we find the planning system to be somewhat
`redistributive', generally comparable to other public sector provision of
in-kind benefits.

\section{The Data}

\subsection{Planning restrictiveness}

The data for this study are drawn from two cities: Reading (located in
Berkshire and one of the most prosperous local economies in the South of
England) and Darlington (located in Durham and one of the most prosperous
local economies in the North of England). Both are relatively stable,
intermediate sized cities with an essentially monocentric structure, and
therefore plausible cities to which to apply the standard urban economic
location model. Reading and Darlington also represent very different
planning regimes. For example, consider the information presented in table 
\ref{UK planning data}. The table presents information on the rate of
residential planning applications and the acceptance rate of those
applications for five English cities.

%TCIMACRO{\TeXButton{B}{\begin{table}[tbp] \centering}}
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\begin{tabular}{|l|lrlll|}
\hline
Development Type & Darlington & Hull & Norwich & Oxford & Reading \\ \hline
\multicolumn{6}{|c|}{\textit{Acceptance Rates}} \\ 
Minor Residential & \multicolumn{1}{|r}{.80} & .78 & \multicolumn{1}{r}{.70}
& \multicolumn{1}{r}{.66} & \multicolumn{1}{r|}{.52} \\ 
Major Residential & \multicolumn{1}{|r}{.86} & .78 & \multicolumn{1}{r}{.74}
& \multicolumn{1}{r}{.78} & \multicolumn{1}{r|}{.54} \\ 
All Minor & \multicolumn{1}{|r}{.88} & .84 & \multicolumn{1}{r}{.82} & 
\multicolumn{1}{r}{.78} & \multicolumn{1}{r|}{.66} \\ 
All Major & \multicolumn{1}{|r}{.82} & .80 & \multicolumn{1}{r}{.80} & 
\multicolumn{1}{r}{.78} & \multicolumn{1}{r|}{.62} \\ 
\multicolumn{6}{|c|}{\textit{Application Rate}} \\ 
Minor Residential & \multicolumn{1}{|r}{.045} & .06 & \multicolumn{1}{r}{.085
} & \multicolumn{1}{r}{.09} & \multicolumn{1}{r|}{.095} \\ 
Major Residential & \multicolumn{1}{|r}{.006} & .008 & \multicolumn{1}{r}{
.0055} & \multicolumn{1}{r}{.0105} & \multicolumn{1}{r|}{.0125} \\ \hline
\end{tabular}
\caption{Planning data for select UK cities: 1982-83\label{UK planning data}}%
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The data in the table show striking differences in the acceptance rates and
application rates between the cities, with Reading being much more
restrictive than Darlington. Reading is also subject to much greater
pressure for development as indicated by the much higher application rates.
Comparative analysis of the two urban areas thus affords the possibility to
explore the economic consequences of significant differences in land use
planning regimes.

\subsection{Observed Characteristics}

The samples were collected in the second and third quarters of 1984. The
data are described in more detail in \cite{CheshireSheppard:1995:Economica}.
Approximately 350 structures in Darlington, and 490 in Reading were included
but some observations had to be dropped because particular variables were
missing.

While a variety of hedonic studies have been undertaken for UK cities, none
of which we are aware have had access to data which included the amount of
land included with each structure and/or the precise location. Without such
information, of course, it is impossible to obtain estimates of land values
or land rent gradients in the sense embodied in standard economic theory:
that is land as pure space with accessibility. As was shown in \cite
{CheshireSheppard:1995:Economica}, since the value of neighbourhood
amenities is largely capitalised into land values, the market price of
cleared sites does not reflect the appropriate concept. Since the economic
effects of land use planning are primarily experienced as changes in the
equilibrium price of land, with consequent implications for housing prices
and land development.

The samples collected for Reading and Darlington include location, land
area, plus a variety of structure and neighborhood characteristics. Table 
\ref{Variable Descriptions} in the appendix provides a list of variables
used in the estimation of the hedonic and the subsequent analysis of demand,
along with brief descriptions.

The mean values and standard deviations for these variables are presented in
table \ref{DescripStat}. Darlington is a city with lower average incomes and
significantly less costly housing than Reading. It is also smaller, with a
built-up area consisting of about 36,000 households compared to Reading's
80,000.

\section{Structure of Demand}

Our analysis builds upon the previous work \cite
{CheshireSheppard:1995:Economica}, \cite{CheshireSheppard:1995:OCDP} which
obtained for these two cities estimates of hedonic prices and the structure
of demand for housing and neighbourhood characteristics. Here we summarize
those results.

\subsection{Hedonic price function and land rents}

Using the data described above, we estimate characteristics prices by
estimating the coefficients of a `Box-Cox' hedonic price function. We allow
three different `transformation parameters': one for the structure price,
one for land area, and one for all other non-dichotomous variables. The
final hedonic price function to be estimated is given by:

\begin{equation}
\frac{p^\psi -1}\psi =K+\sum_{i\in D}\beta _i\cdot q_i+\sum_{j\in C}\beta
_j\cdot \left( \frac{q_j^\lambda -1}\lambda \right) +r(x,\theta )\cdot \frac{%
L^\xi -1}\xi  \label{Hedonic}
\end{equation}

where:

\begin{tabular}{rcl}
$p$ & = & rentalised price of structure \\ 
$q_i,q_j$ & = & structure or location specific characteristics \\ 
$K,\beta _i,\beta _j,\psi ,\lambda ,\xi $ & = & parameters to be estimated
\\ 
$L$ & = & quantity of land included with structure \\ 
$D$ & = & set of indices of characteristics which are dichotomous \\ 
$C$ & = & set of indices of characteristics which are continuously variable
\\ 
$r(x,\theta )$ & = & land rent function defined below \\ 
$\psi ,\lambda ,\xi $ &  & are the standard parameters of the Box-Cox
functional form.
\end{tabular}

Since land rents are critical in what follows, the land rent function
warrants particular comment. Because much of the data used in hedonic
analyses lacks land and location information, the form of the `land value'
component of a hedonic function has not received much attention. Perhaps the
most obvious exception to this observation is \cite
{JacksonJohnsonKaserman:1984:JUE} who use a third degree polynomial in two
dimensions to model land prices. To economize on the number of required
parameters, we use the following land rent function:

\begin{equation}
r(x,\theta )=\beta _1\cdot e^{x\cdot \,\left( \beta _2\,+\ \beta _3\cdot
\sin (n\cdot \theta \ -\ \beta _4)\right) }  \label{Rent function}
\end{equation}

where:

\begin{tabular}{rcl}
$x$ & = & distance from town centre, \\ 
$\theta $ & = & angle of deflection from East, \\ 
$\beta _i$ & = & parameters to be estimated, and \\ 
$n$ & = & an integer which determines the number of radial asymmetries
\end{tabular}

This rent function possesses the advantage of considerable flexibility while
requiring estimation of relatively few parameters\endnote{Fewer than half
the ten parameters used in Jackson, \textit{et al.}}. The function allows
estimation of asymmetries in land values which may be due to transport
networks or topography. The form does not require that land values decrease
from the urban center. It is `monocentric' only in the sense that along any
linear path from the city centre land rents will increase or decrease at a
constant rate.

Estimates of the parameters of the hedonic price function specified in
equations \ref{Hedonic} and \ref{Rent function} are given in Appendix table 
\ref{Hedonic Table}. From these functions we obtain estimates of the hedonic
price of structure and neighborhood characteristics as well as land. Note
that neighbourhood characteristics, as discussed in more detail in section 
\ref{BenOfPlanAmen} below, are formulated to reflect the main amenity
outputs produced by the planning system.

The estimated structure price from the hedonic equation, $\widehat{P}$, is a
function of the vector of observed characteristics and location. The hedonic
price of a continuously variable characteristic $q_i$ is obtained by simple
differentiation: 
\begin{equation}
p_i=\frac{\partial \widehat{P}}{\partial q_i}=\widehat{\beta }_i\frac{%
q_i^{\lambda -1}}{\widehat{P}^{\psi -1}}  \label{Continuous hedonic price}
\end{equation}
Similarly, for a dichotomous variable, the hedonic price is: 
\begin{equation}
p_i=\frac{\partial \widehat{P}}{\partial q_i}=\frac{\widehat{\beta }_i}{%
\widehat{P}^{\psi -1}}  \label{Dichot hedonic price}
\end{equation}
Finally, letting $\widehat{R}$ represent the estimated price of land (again
a function of other characteristics and location), we obtain: 
\begin{equation}
\widehat{R}=\frac{\partial \widehat{P}}{\partial L}=r(x,\theta )\cdot \frac{%
L^{\xi -1}}{\widehat{P}^{\psi -1}}  \label{Price of land}
\end{equation}
These prices are then combined with observed household incomes available,
for a subset of the sample, to estimate the structure of demand.

\subsection{Almost Ideal Demand System}

The Almost Ideal Demand System developed by \cite{DeatonMuellbauer:1980:AER}
is well suited for our purposes for two reasons. First, it provides a
flexible and theoretically well-grounded framework within which to analyze
individual demand data. Second, because it is derived explicitly from a
particular expenditure function whose parameters are estimated (or
approximated) as part of the estimation of the demand system, it provides
for simple implementation of welfare analysis. Once the demand system is
estimated, we will also have an expenditure function which can be used to
determine the equivalent variation in income associated with changes in land
prices.

Making use of the linear approximation of the budget share equations
suggested by Deaton and Muellbauer and widely used, we can adapt their model
to the present circumstances and obtain a budget share equation of the form:%
\endnote{In the budget share equation we regard land as one of the
continuously variable characteristics of a house, and its price $\widehat{R}$
would be one of the prices denoted $p_j$.}: 
\begin{equation}
w_i=\left( \alpha _i-\delta _i\alpha _0\right) +\sum_{j\in C}\gamma
_{i,j}\cdot \ln p_j+\sum_{k\in D}\gamma _{i,k}\cdot \ln p_k+\delta _i\cdot
\ln \left( \frac M{I^{*}}\right)  \label{Budget share}
\end{equation}

where:

\begin{tabular}{rcl}
$w_i$ & = & expenditure share on characteristic i, \\ 
$p_j,p_k$ & = & prices of characteristics, \\ 
$D$ & = & set of indices of dichotomous characteristics, \\ 
$C$ & = & set of indices of continuous characteristics, \\ 
$M$ & = & income, \\ 
$I^{*}$ & = & Stone's price index, defined by $\ln I^{*}=\tsum_iw_i\ln p_i$
\\ 
$\alpha _i,\alpha _0,\delta _i,\gamma _{i,j},\gamma _{i,k}$ & = & parameters
to be estimated.
\end{tabular}

Then using the hedonic prices given in equations \ref{Continuous hedonic
price} and \ref{Dichot hedonic price} above, equation \ref{Budget share} can
be adapted to: 
\begin{equation}
w_i=\overline{\alpha }_i+\overline{\gamma }_i\cdot \ln \widehat{P}+\delta
_i\cdot \ln \left( \frac M{I^{*}}\right) +\sum_{j\in C}\gamma _{i,j}\cdot
\ln p_j  \label{Budget share model}
\end{equation}

where: 
\begin{eqnarray*}
\widehat{P} &=&\text{structure value predicted from the hedonic price
function,} \\
\overline{\alpha }_i &=&\left( \alpha _i-\delta _i\alpha _0\right)
+\sum_{k\in D}\gamma _{i,k}\cdot \ln \widehat{\beta }_k \\
\overline{\gamma }_i &=&\left( 1-\widehat{\psi }\right) \cdot \sum_{k\in
D}\gamma _{i,k} \\
\widehat{\beta }_k,\widehat{\psi }\text{ } &\text{are}&\text{ estimated
parameters from the hedonic price function.}
\end{eqnarray*}

\subsection{Estimated Demand System}

The estimated parameters for the demand system identified in equation \ref
{Budget share model} are presented in the appendix tables \ref{Reading
Demand Non Plan}, \ref{Reading Demand Plan}, \ref{Darlington Demand Non Plan}
 and \ref{Darlington Demand Plan}. Estimation of housing and neighbourhood
characteristics demand using hedonic prices intrinsically involves the
problem of correlation between `independent variables' (the hedonic prices)
and disturbances (fluctuations in the quantities of characteristics). This
problem has been thoroughly explained in \cite{Murray:1983:JUE}, \cite
{Bartik:1987:JPE} and \cite{Epple:1987:JPE}. As discussed in \cite
{CheshireSheppard:1995:OCDP}, the demand system estimates used for this
study have been obtained using an instrumental variables approach to address
issues of independent variable endogeneity.

The tables present estimated budget share equations only for those
characteristics which are not dichotomous. As indicated in equation \ref
{Budget share model} the prices of dichotomous variables are not used in the
demand system, since they are constant across the sample. It is possible to
estimate budget share equations for the dichotomous variables using the same
functional structure as used for the `continuous' variables. These were
obtained so that the estimated parameters could be used in the expenditure
function for evaluation of the welfare effects of land use controls.

Overall, the estimated budget share equations perform well. While some
individual parameters are estimated with high standard errors (and are not
statistically significant) this is at least in part due to colinearity
between characteristics prices. Furthermore, it is to be expected that not
all prices will affect demand for a particular characteristic in a
significant way.

\section{Equilibrium Utilities and Planning Restrictiveness}

The demand system presented in the preceding section includes three
neighbourhood characteristics which are intimately connected with operation
of land use regulations: the availability of open space which is generally
accessible to the public (either through public ownership or extensive
public rights-of-way), the availability of open space which is inaccessible,
but nevertheless valuable for visual amenity and is used as an instrument to
contain the spread of the built-up area, and the limitation of the extent of
industrial land use and its separation from industrial areas. Our analysis
below will focus on the value of these benefits produced by planning
policies, and the costs associated with land use restrictions imposed to
produce these amenities, particularly the open space amenities.

The first step in this analysis is to parametrize and determine a utility
level for households in the existing equilibrium, and determine the prices
which would be faced by households under alternative policy scenarios.
Following this we can use a model of land market equilibrium to characterize
the extent of planning restrictiveness in each community.

\subsection{Utility level}

The expenditure function associated with the demand system used above is
given by\endnote{In this equation and those that follow, we use the notation 
$I^{*}$ to denote the price index. In the original presentation of Deaton
and Muellbauer, this index was given by: 
\[
\alpha _0+\sum \alpha _k\ln p_k+\frac 12\stackunder{k}{\sum }\stackunder{l}{%
\sum }\gamma _{k,l}\ln p_k\ln p_l 
\]
In our calculations we have followed the same procedure used in estimation,
and used Stone's price index as an approximation.} 
\begin{equation}
\ln c(u,p)=I^{*}+u\cdot \prod p_i^{\delta _i}  \label{Expenditure function}
\end{equation}
Households have a given after tax income $M$, and spend part of this income
on transport costs $t(x,\theta )$, leaving $M-t(x,\theta )$ available for
expenditures on goods and services from which utility is derived. This
implies an indirect utility function for each household having the form%
\endnote{Clearly, any monotonic transformation of the right hand side of \ref
{uhat} would serve as well. In our calculations we take this \emph{particular%
} representation.}: 
\begin{equation}
\widehat{u}=\frac{\ln \left( M-t(x,\theta )\right) -I^{*}}{\prod p_i^{\delta
_i}}  \label{uhat}
\end{equation}

To utilize this for estimating utility levels, we must determine the
transport costs faced by a household located at location $(x,\theta ).$ The
first thing to note is that estimates of the land values obtained from the
hedonic function discussed above and shown in appendix table \ref{Hedonic
Table} indicated considerable radial asymmetries. These are to be expected
given the fact that roadways and other components of transport
infrastructure are not radially symmetric, and it was shown in \cite
{CheshireSheppard:1995:Economica} that these asymmetries faithfully reflect
those of the transport system. In determining the transport cost function,
we expect that the function $t$ would exhibit asymmetries and a directional
orientation that would be associated with the land value surface which has
been estimated from the data.

We take transport costs per mile per annum to be:

\begin{eqnarray}
t(x,\theta ) & = & \tau x\left( 1+\nu \sin \left( n\theta -\beta _4-\pi \right)
\right)
\label{transport costs}
\\
& \text{where } & \left\{ 
\begin{array}{clll}
n=2 & \tau =403.49 & \upsilon =0.46156 & \text{for Reading} \\ 
n=1 & \tau =288.4983 & \upsilon =0.28451 & \text{for Darlington}
\end{array}
\right.  
\nonumber
\end{eqnarray}
and the parameter $\beta _4$ is taken from the estimated hedonic price
function for each city, as reported in table \ref{Hedonic Table}. The
parameter values shown capture (via parameters $n$ and $\nu $ and $\beta _4)$
the asymmetries observed in the estimated land values, and are based upon
estimated vehicle running costs\endnote{As reported by the Automobile
Association for 1984.} and the value of time (as estimated by the sample
mean income levels and mean travel speeds).

Beyond structural asymmetries, the overall level of transport costs is
determined by two factors: actual operating costs (or fares if using public
transport) and the time costs of travel. The parameter $\tau $ determines
the overall level of transport costs, and is chosen so that the average
transport cost per mile equals the amount expected from available estimates
of vehicle running costs plus time costs.\endnote{Based on estimated mean
travel speeds and sample mean incomes within each city.}

Given these transport costs we calculate, for each household, a vector of
utility levels\endnote{We use bold face to denote vectors or matrices with
each row corresponding to an observation in our sample. A bar over the
variable such as $\mathbf{\bar{u}}_1$ denotes the mean of the corresponding
vector.} $\mathbf{u}_1$ with each component determined by equation \ref{uhat}%
. For Reading, this calculation indicates a mean utility level of $21.585$
and for Darlington, the mean utility level is estimated to be $19.797.$

\subsection{Levels of planning restriction}

The expenditure function given in equation \ref{Expenditure function} can
also be used to derive the general form of the equilibrium land value. An
optimising consumer makes a choice which satisfies: 
\begin{equation}
\ln \left( M-t(x,\theta )\right) =I^{*}+u\cdot \prod p_i^{\delta _i}
\label{ExpFuncTranspCost}
\end{equation}
Assuming without loss of generality that land area is indexed as good 1, we
have: 
\begin{equation}
r(u,x,\theta ,p\mathbf{,}M)=\left( \frac{\ln \left( M-t(x,\theta )\right)
-I^{*}}{u\cdot \stackunder{i\geq 2}{\prod }p_i^{\delta _i}}\right) ^{\frac
1{\delta _1}}  \label{BidRentFunction}
\end{equation}
Given estimated parameters for the demand system, and a utility level, we
can use this to calculate bid-rents for a typical household at any location.

It is then possible to make use of this land value within the context of a
standard monocentric urban model. Let $h(u,r,p)$ be the compensated demand
for land for a consumer whose preferences generate an expenditure function
of the form \ref{Expenditure function}, where $r$ is land rent and $p$ is
the vector of all prices. If the city were occupied by a single class of
identical individuals, then equilibrium in the land market would require: 
\begin{equation}
N=\stackrel{\chi _2}{\stackunder{\chi _1}{\int }\ }\stackunder{0}{\stackrel{%
2\pi }{\int }}\frac{\omega \cdot x}{h(u,r(u,x,\theta ,p\mathbf{,}M),p)}\
d\theta \,dx  \label{LandMarketEquilib}
\end{equation}
where:

$
\begin{array}{cl}
N & \text{is the total number of households to be accomodated within the
urban area} \\ 
\omega & \text{is the share of space internal to the urban area made
available for residential use;} \\ 
\chi _1 & \text{is the inner boundary of allowed residential
development;} \\ 
\chi _2 & \text{is the outer boundary of residential development,
and of the urban area.}
\end{array}
$

The parameters $\omega $, $\chi _1$, and $\chi _2$ are determined by
planning policy, and are of central interest in the evaluations below. The
parameters $\chi _1$ and $\chi _2$ are estimated from the observed structure
of each urban area. Given these estimates for the residential boundaries, we
estimate the parameter $\omega $ by adapting equation \ref{LandMarketEquilib}
to obtain: 
\begin{equation}
\hat{\omega}=\frac N{\stackrel{\chi _2}{\stackunder{\chi _1}{\int }\ }%
\stackunder{0}{\stackrel{2\pi }{\int }}\frac x{h(\mathbf{\bar{u}},r(\mathbf{%
\bar{u}},x,\theta ,\mathbf{\bar{p},}\overline{\mathbf{M}}),\mathbf{\bar{p}}%
)}\ d\theta \,dx}  \label{omegahat}
\end{equation}
and evaluating at sample mean levels of utility, income, and non-land
prices: $\mathbf{\bar{u}}$, $\overline{\mathbf{M}}$, and $\mathbf{\bar{p}}$.
That is, we estimate the implicit level of planning restrictiveness by
solving for the equilibrium of a land market accommodating $N$ households
who have identical incomes, face identical non-land prices, and achieve
identical utility levels - with each of these determined by the sample mean.

The parameter $\omega $ represents the share of land area made available for
residential development between the inner and outer boundaries $\chi _1$ and 
$\chi _2$. This parameter will always be less than one, since some land is
used for transport infrastructure and other land uses. Local land use policy
concerning the provision of internal open space - whether accessible in the
form of parkland or inaccessible, `visual amenity' open space like pasture
and other agricultural use - will be the major determinant of differences in 
$\omega $ between topographically similar cities.

Table \ref{PlanningRest} presents the estimates of $\hat{\omega}$ along with
the parameters $\overline{\mathbf{u}}$ (the mean utility levels), $N$ (the
number of households), $\chi _1$ and $\chi _2$ (inner and outer limits of
the built-up area, in feet). The number of households is estimated from
Census small area statistics for the built-up area, the inner limit $\chi _1$
is estimated from the sample as the minimum observed distance from the urban
centre, and the outer limit $\chi _2$ is estimated from Ordnance Survey maps
showing the extent of each city.

%TCIMACRO{\TeXButton{B}{\begin{table}[tbp] \centering}}
%BeginExpansion
\begin{table}[tbp] \centering%
%EndExpansion
\begin{tabular}{|l|l|l|l|l|l|}
\hline
\textbf{City} & $\widehat{\mathbf{\omega }}$ & $\overline{\mathbf{u}}$ & $N$
& $\mathbf{\chi }_1$ & $\mathbf{\chi }_2$ \\ \hline
Reading & $.384125$ & $21.585$ & $80000$ & $1525.927$ & $23047$ \\ 
Darlington & $.427157$ & $19.797$ & $36000$ & $1562.839$ & $11979$ \\ \hline
\end{tabular}
\caption{Estimated utility and level of planning restriction
\label{PlanningRest}}%
%TCIMACRO{\TeXButton{E}{\end{table}}}
%BeginExpansion
\end{table}%
%EndExpansion

Note that as expected, Reading makes less land available for private
residential use than Darlington. Note that the estimated levels of $\hat{%
\omega}$ are based on the estimated demand system in each city, and thus
correct for most of the other differences between these two areas (such as
income levels or the prices and availability of other amenities and
structure characteristics). These utility levels and measures of planning
policy are taken as the basis from which changes in planning policy will be
evaluated.

\section{Benefits of Planning Amenities\label{BenOfPlanAmen}}

We focus on the community with the more restrictive planning regime,
utilising the demand system to provide some estimates of the gross value of
benefits from these amenities, and the distribution of these benefits
amongst households.

\subsection{Estimation of benefits}

To obtain an estimate of the `gross benefits' of planning amenities, we
assume that effectively none of the amenity would be produced in the absence
of planning. This is most reasonable in the case of inaccessible open space,
and is probably less acceptable in the case of absence of industrial uses in
conjunction with residential use. For each household, we can then calculate
the variation in income which would be sufficient to achieve the current
utility level if it faced the amenity price associated with the absence of
land use planning. In this way an estimate of the benefit received by each
household is calculated. We analyze both the distribution of this benefit
alone, and since we have observed household income the effect on the
distribution of income as augmented by the value of these benefits.

For the two types of open space, we assume that essentially zero would be
produced in the absence of the planning system and that land would instead
be allocated to various types of private consumption. Using the demand
system evaluated for a `typical' household (that is a household with income
equal to the sample mean facing sample mean prices for other
characteristics), we make a separate determination of the price at which
demand for each amenity would be reduced to zero. For open space amenities,
we used the following procedure: let $p_1$ denote the vector of prices in
which all characteristics take prices as estimated via equations \ref
{Continuous hedonic price}, \ref{Dichot hedonic price}, and \ref{Price of
land}. Let $p_2$ denote the vector of prices in which all prices remain the
same except the price of the given open space amenity is increased to this
`reservation price'. Then for each household, we estimate the gross benefit
from the given amenity by: 
\begin{equation}
c(u_1,p_2)-c(u_1,p_1)  \label{GrossBenefit}
\end{equation}
where the utility level $u_1$ is obtained for each household via equation 
\ref{uhat}. This provides the increase in income required to achieve the
current level of welfare if the price of the amenity were increased to its
reservation price.

For limitation of industrial land use, the `reservation price' was taken to
be the highest price for limiting industrial land use observed in the
sample. This is seen to provide a more reasonable measure of the benefits
from limiting industrial land use once we recall the interpretation of each
variable. When the measure of open space amenity reaches zero, the
interpretation is zero open space and more land available for private
residential or commercial uses, and we expect this outcome in the absence of
any planning or zoning constraints. When the industrial land use variable
reaches zero, the interpretation is that 100 percent of the land in the
surrounding square kilometer is in industrial use. This extreme scenario
would not describe the absence of a planning system. As a reasonable
alternative datum, we therefore assume a scenario in which all households
face the same exposure to industrial land use as the most exposed property
in the sample.

Table \ref{GrossBenefitTable} presents the results for each planning
amenity. The second column of the table lists the mean value of estimated
gross benefits\endnote{These and all monetary figures given below are in
1984 pounds per annum unless otherwise noted.} for each amenity, followed by
the standard deviation, minimum and maximum values, correlation with
household income, correlation with plot size, and correlation with the price
of the house.

%TCIMACRO{\TeXButton{B}{\begin{table}[tbp] \centering}}
%BeginExpansion
\begin{table}[tbp] \centering%
%EndExpansion
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}
\hline
\textbf{Amenity} & \textbf{Mean \pounds } & \textbf{$\sigma$} & $\min $ & $%
\max $ & \textbf{r}$_{\text{Y}}$ & \textbf{r}$_{\text{area}}$ & \textbf{r}$_{%
\text{value}}$ & \textbf{gini} & \textbf{gini}$_{\text{Y}}$ \\ \hline
Accessible Space & 3606.66 & 1505.37 & 1169.8 & 10838.5 & .696 & .786 & .848
& 22.51 & 20.75 \\ 
Inaccessible Space & 1275.23 & 1120.82 & 233.43 & 6909.99 & .450 & .451 & 
.559 & 44.32 & 21.54 \\ 
Industrial Land & 1919.32 & 691.78 & 0 & 3495.95 & .674 & .486 & .524 & 
20.03 & 19.78 \\ \hline
\end{tabular}
\caption{Value of Benefits from Planning Amenities\label{GrossBenefitTable}}%
%TCIMACRO{\TeXButton{E}{\end{table}}}
%BeginExpansion
\end{table}%
%EndExpansion

\subsection{Distributional consequences}

We focus on two separate issues regarding the distributional consequences of
land use planning. The first concerns the equity, or lack thereof, with
which the benefits (and later the net costs) are distributed. The second
concerns the distribution of `effective' income after consideration of the
benefits or costs. The issues deserve separate consideration and each seems
of interest. The value of planning benefits might be quite equally
distributed but, depending on the correlation between household income and
benefit received, might increase or decrease the overall level of inequality
within the society.

The assessment made concerns the distribution of benefits within our sample.
Since it is drawn exclusively from the population home owners, the level of
inequality is much less than that observed in the entire UK population. The
gini coefficient for after tax income in the Reading sample is 20.52. For
this time period the index for after tax income for the entire UK was
approximately 38.1. For more details, see \cite{CSO:1985:EconTrends} and 
\cite{CSO:1986:EconTrends}.

The last two columns of table \ref{GrossBenefitTable} provide information on
how these benefits are distributed. The penultimate column presents the
calculated gini coefficient for distribution of the gross benefit alone, and
the last column gives the gini index of household income augmented by the
value of the benefit. Thus provision of open space generates a slight
increase in inequality in society, while limitations on industrial land use
might be said to generally reduce inequality.

Figure \ref{PlanBenLorenz} shows Lorenz curves for the distribution of gross
benefits from each of the three amenities. This makes the differences in
distributional equity quite clear. It is not surprising that the benefits
from inaccessible open space are much less equally shared among households
than benefits from the other amenities, since most of this type of open
space is available at the urban fringe as part of the `greenbelt' which
contains the urban area.

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An interesting comparison can be made with the distributional consequences
of `in kind benefits' in Britain, made available in the annual reports from
the treasury. The analysis covers a variety of benefits, including state
education, school meals and other meal subsidies, the national health
service, rail, bus, and other travel subsidies. Collectively, these lower
the gini coefficient of income after direct and indirect taxes by about
10.11 percent. Our calculations suggest that the combined consequences of
planning amenities is almost distributionally neutral, with a 3.6 percent
decline in the gini resulting from limiting industrial land use generally
offsetting the 4.97 percent increase resulting from inaccessible open space,
and the 1.12 percent increase from accessible open space. Although these
combine to yield little change in the aggregate distribution of welfare,
individually they are quite significant, and likely to be as large as many
of the public services traditionally structured with at least a partly
egalitarian objective.

Figure \ref{AccessOpenHist} shows the distribution of gross benefit levels
from accessible open space, and figure \ref{Amen1BenefitToQuintiles} shows
how these benefits are distributed between income quintiles (with quintiles
defined on income after taxes but exclusive of any imputed planning
benefit). The numeric labels at the top of each bar show the actual
percentage of total benefits realized by each quintile, and the line
superimposed over the bars shows the actual distribution of income going to
each quintile.

\FRAME{ftbpFU}{4.9502in}{3.4437in}{0pt}{\Qcb{Distribution of benefits from
accessible open space}}{\Qlb{AccessOpenHist}}{sod2benamen1.wmf}{%
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\FRAME{ftbphFU}{393.375pt}{257.375pt}{0pt}{\Qcb{Share of gross benefit from
accessible open space to each income quintile}}{\Qlb{Amen1BenefitToQuintiles}%
}{Figure }{\special{language "Scientific Word";type
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263.375pt;cropleft "0";croptop "1";cropright "1";cropbottom "0";tempfilename
'/document/E5PYHC00.wmf';tempfile-properties "XP";}}Thus for
accessible open space, we see that the change in effective income
distribution mostly arises by the poorest quintile getting a share of
benefits larger than their corresponding income share, and `paying' for this
primarily by the fourth quintile getting less than their income share.

Figures \ref{InaccOpenHist} and \ref{Amen2BenefitToQuintile} present the
same information for inaccessible open space. The less equal distribution of
these benefits, and their more regressive final impact, is immediately
apparent. Figure \ref{Amen2BenefitToQuintile} clearly shows the regressive
nature of the benefit with the benefit shares rising more rapidly than
income shares.

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\FRAME{ftbphFU}{393.375pt}{257.375pt}{0pt}{\Qcb{Share of gross benefits from
inaccessible open space to each income quintile}}{\Qlb{Amen2BenefitToQuintile%
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263.375pt;cropleft "0";croptop "1";cropright "1";cropbottom "0";tempfilename
'/document/E5PYHC01.wmf';tempfile-properties "XP";}}Finally, the
distribution of benefits from limiting industrial land use below the most
industrialized area found in Reading is shown in figures \ref{BenIndHist}
and \ref{IndusBenefitToQuintile}. Note that while the benefits of limiting
industrial land use are, by themselves, distributed regressively with
disproportionate amounts going to upper income persons, nevertheless this
amenity contributes to a reduction in inequality because it is less
unequally distributed than after tax income. Limitation of industrial land
use is seen to be the most redistributive of the benefits, with the first
and second quintiles getting clearly a larger share of benefits than their
income shares, with the fourth and fifth getting clearly less.

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\FRAME{ftbpFU}{406.1875pt}{266.0625pt}{0pt}{\Qcb{Share of benefit to income
quintiles from limiting industrial land use}}{\Qlb{IndusBenefitToQuintile}}{%
Figure }{\special{language "Scientific Word";type
"GRAPHIC";maintain-aspect-ratio TRUE;display "USEDEF";valid_file "T";width
406.1875pt;height 266.0625pt;depth 0pt;original-width 213pt;original-height
212.9375pt;cropleft "0";croptop "1";cropright "1";cropbottom
"0";tempfilename '/document/E5PYHC02.wmf';tempfile-properties
"XP";}}The gross benefit estimates for the three planning amenities are
quite large and from a political economic perspective help to explain the
widespread appeal and general support given to implementation of land use
planning restrictions. These activities produce amenities which are highly
valued by a large number of residents. A further point is that households
are financially locked into the system. Since planning amenities are
capitalised into the price of the aggregate `house-land bundle', a reduction
in amenities by, say, permitting development on inaccessible open land would
produce a capital loss for existing house owners (although, as we see below,
it would be consistent with increasing overall community welfare).

The estimates show that planning benefits are certainly not distributed
equally. Furthermore, the benefits arising from all three types of amenities
flow disproportionately to upper income groups, although only inaccessible
open space produces benefits which are more unequally distributed than
income itself. Our findings seem to suggest that the greatest inequities are
not in those benefits traditionally associated with high exposure to
pollutants (industrial land use) but rather in the provision of `green'
amenities like open space.

We next turn attention to the net welfare costs of planning in efficiency
terms. We do this by using the estimated parameter values to simulate the
effects of alternative planning regimes.

\section{Net Costs of Land Use Planning}

To acknowledge that the amenities produced by the planning system are
valuable to some, even all, persons in the community is not to establish
that the quantity provided is efficient. The marginal units of amenities
provided may still fail a benefit-cost test. Application of such a test, as
noted above, is made more difficult by the fact that the amenities are
provided through regulation rather than through a market transaction. The
latter would involve explicit taxation of some sort and collective purchase
of the inputs required to produce the public good. We could then compare the
costs with estimates of the benefits. With land use planning the costs come
in the form of distortions in land and housing prices, and we must attempt
to estimate the price distortions that result from the policy, and compare
the value of this change with the value of the change in amenity provided.

A fundamental difficulty which confronts this approach is to determine what
changes in land prices might actually be attributable to the policy. The
very pervasiveness of land use planning makes observing an economy with no
land use regulation very difficult. We adopt an approach which will provide,
we argue, a lower bound estimate of the net costs of land use planning in a
highly constrained community: it is thus a lower bound estimate of the
maximum cost in the economy under investigation -- Britain. At a minimum our
approach can be said to provide an evaluation of the potential costs and
benefits of reforming an existing land use planning system.

We have identified two comparable urban areas which, though subject to the
same land use regulation system, operate these regulatory constraints very
differently. Through careful analysis of what appears to be one of the least
restrictive planning regimes, and comparison with what appears to be one of
the most restrictive, we can provide an evaluation of the changes in land
prices which may be attributed to the more restrictive planning regime.
Combining this with an evaluation of the reduction in the level of benefits
from open space will provide a measure of the net costs of land use planning.

\subsection{Provision of open space within urbanized area}

In table \ref{PlanningRest} above we presented results of estimates of the
parameter $\omega $ which represents the extent to which land is made
available for private residential consumption in each city. The data
presented in table \ref{UK planning data} suggests that the two cities
represent extreme implementations of the Town and Country Planning system,
with Reading being the most restrictive and Darlington the least. We
attribute the differences in estimated levels of $\omega $ to the difference
in land use planning regimes in the two cities.

The impact of two possible policy changes is evaluated. In this section we
provide estimates of the impact which would result if the more constrained
community -- Reading -- adopted the more relaxed regime of internal open
space availability observed in Darlington. In the next section the effects
of relaxing the constraint on building beyond the present boundary of the
built-up area are estimated.

The first policy change -- Reading adopting Darlington's `permissive' regime
on internal space availability -- itself would generate at least two major
changes: first there will be an increase in availability of residential land
-- an increase in $\omega $ from $\omega _1=0.384$ to $\omega _2=0.427$.
Equilibrium in the urban land market will then require a reduction in land
rents, with an associated increase in household utility levels. Associated
with such a policy shift would be a reduction in internal open space
available to the community. We assume that the reduction in open space is
taken from both accessible and inaccessible open space so that the ratio of
the two types of open space provided remains constant. The change in
consumption of private residential land resulting from implementation of $%
\omega _2$ in place of $\omega _1$ amounts (over the allowed range of
residential construction) to approximately $71.5$ million square feet of land%
\endnote{This amounts to about 894 square feet per household.}. To release
this much land to private consumption would require an $11.45$ percent
reduction in the amount of available open space in the urban area.

Using elasticities estimated from the demand system, we estimate that such a
reduction in open space would increase the price of accessible open space by
10.2 percent, and the price of inaccessible open space would increase by
10.1 percent. Let the price vector $\mathbf{p}_2$ represent, for each
household, the prices of housing and neighbourhood characteristics with the
price of open space increased by these amounts. Let $\overline{\mathbf{p}}_2$
be the vector of mean prices for the sample, reflecting the increased price
for open space. The associated price vectors before any change (representing
the \textit{status quo}) are $\mathbf{p}_1$ and $\mathbf{\bar{p}}_1.$

If the level of planning restrictiveness were reduced, and the price of
internal open space were increased to release the associated amount of land
for private consumption, a new equilibrium would be reached with utility
level $u_2$. This utility level can be determined by solving: 
\begin{equation}
N=\stackrel{\chi _2}{\stackunder{\chi _1}{\int }\ }\stackunder{0}{\stackrel{%
2\pi }{\int }}\frac{\omega _2\cdot x}{h(u_2,r(u_2,x,\theta ,\overline{%
\mathbf{p}}_2\mathbf{,}\overline{\mathbf{M}}),\overline{\mathbf{p}}_2)}\
d\theta \,dx  \label{LandEquilibForU2}
\end{equation}
for utility level $u_2$. This utility level would be achieved, \emph{on
average}, for households in the sample. The utility level can be used to
provide an estimate of the new level of land rent at each location $%
r(u_2,x,\theta ,\overline{\mathbf{p}}_2\mathbf{,}\overline{\mathbf{M}})$, so
that for each actual household in the sample, we have an estimate of the
change in the price of land as well as the change in the price of open space.

For each household, actual income would remain unchanged. Implicit
differentiation of the expenditure function allows us to determine the
marginal indirect utility of a change in price: 
\begin{equation}
\frac{\partial u}{\partial p_i}=-\frac{\frac{\partial c(u,r,p)}{\partial p_i}%
}{\frac{\partial c(u,r,p)}{\partial u}}=-\frac{h_i(u,r,p)}\lambda
\label{MarginalUtilityofPrice}
\end{equation}
Thus the marginal indirect utility of a change in price is proportional to
consumption of the good, with the factor of proportionality $-\frac 1\lambda 
$ equal to minus the reciprocal of the `marginal cost of utility'. This
observation suggests the following approach for estimating the change in
utility for each individual household. Determine a vector of utilities $%
\mathbf{u}_2$ by solving for $\varphi $ to satisfy: 
\begin{eqnarray}
\mathbf{u}_2 &=&\mathbf{u}_1+\varphi \left( \mathbf{L\Delta r}+\mathbf{q}_a%
\mathbf{\Delta p}_a+\mathbf{q}_i\mathbf{\Delta p}_i\right)
\label{UtilityChangeEquation} \\
\overline{\mathbf{u}}_2 &=&u_2  \nonumber
\end{eqnarray}

where:

$
\begin{array}[t]{lll}
\overline{\mathbf{u}}_2 & = & \text{mean of vector }\mathbf{u}_2 \\ 
\mathbf{L} & = & \text{quantity of land consumed by an individual household}
\\ 
\mathbf{\Delta r} & = & \text{change in land rent at the household's location%
} \\ 
\mathbf{q}_a & = & \text{quantity of accessible open space consumed by the
household}
\end{array}
$

$
\begin{array}[t]{lll}
\mathbf{\Delta p}_a & = & \text{change in price of accessible open space at
the household's location} \\ 
\mathbf{q}_i & = & \text{quantity of inaccessible open space consumed by the
household} \\ 
\mathbf{\Delta p}_i & = & \text{change in price of inaccessible open space
at the household's location} \\ 
\varphi & = & \text{factor of proportionality to determine change in utility
level}
\end{array}
$

Using equation \ref{UtilityChangeEquation} we solve for the factor of
proportionality $\varphi $, and obtain an estimated vector of new utilities
for each household $\mathbf{u}_2$. We use this to calculate a vector of net
costs of planning for the sample\endnote{In equation \ref{NetCostEqVar1} we
abuse the notation somewhat. We have written the price vector with the price
of land separately, so that the expenditure function, which depends on the
utility level and prices is written $c(u,r,p)$.}: 
\begin{equation}
c\left( \mathbf{u}_2,r\left( u_1,\mathbf{x},\mathbf{\theta },\overline{%
\mathbf{p}}_1\mathbf{,}\overline{\mathbf{M}}\right) ,\mathbf{p}_1\right)
-c\left( \mathbf{u}_2,r\left( u_2,\mathbf{x},\mathbf{\theta },\overline{%
\mathbf{p}}_2\mathbf{,}\overline{\mathbf{M}}\right) ,\mathbf{p}_2\right)
\label{NetCostEqVar1}
\end{equation}
In equation \ref{NetCostEqVar1} we generate a vector of rents by evaluating $%
r\left( \cdot \right) $ at every location given by the vectors $\mathbf{x}$
and $\mathbf{\theta }$. We then have a vectors of utilities $\mathbf{u}_2$
and rents, and a matrix of prices $\mathbf{p}_i$ with one row for each
observation.

Evaluating the expenditure function at each row then gives income net of
transport costs required to achieve the utility level associated with the
permissive planning regime under the two alternative sets of land and
amenity prices. The difference gives the equivalent variation associated
with the change in planning policy. A positive number indicates that greater
expenditures would be required under the observed restrictive planning
policies to achieve utility level $\mathbf{u}_2.$ Table \ref
{NetCostOpenSpaceTable} provides a summary of these calculations.

%TCIMACRO{\TeXButton{B}{\begin{table}[h] \centering}}
%BeginExpansion
\begin{table}[h] \centering%
%EndExpansion
\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
\multicolumn{9}{|l|}{\emph{Provision of open space within urban area}} \\ 
\hline
$\mathbf{\mu }$ & $\mathbf{\sigma }$ & $\min $ & $\max $ & \textbf{r}$_{%
\text{income}}$ & \textbf{r}$_{\text{area}}$ & \textbf{r}$_{\text{value}}$ & 
\textbf{gini} & \textbf{gini}$_{\text{Y}}$ \\ \hline
159.69 & 84.14 & 48.86 & 698.62 & .649 & .858 & .832 & 26.30 & 20.55 \\ 
\hline
\end{tabular}
\caption{Net Costs of Internal Land Availability
Policies\label{NetCostOpenSpaceTable}}%
%TCIMACRO{\TeXButton{E}{\end{table}}}
%BeginExpansion
\end{table}%
%EndExpansion

As indicated, all households in the sample appear to experience positive net
costs from the current land use planning policy. On average, a relaxation of
the policy would be equivalent to an increase in income of nearly \pounds
160 per annum. There is considerable variation in the levels of net costs
experienced by different households. Figure \ref{NetCostInternalSpace} shows
the distribution of costs, giving the proportion of households who
experience costs at various levels. The fifth, sixth, and seventh columns of
table \ref{NetCostOpenSpaceTable} show the correlation between net cost of
providing such a large supply of internal open space and household income,
land consumption, and house value respectively. The correlation with income
is positive but, unsurprisingly, not as strong as is that with land
consumption.\FRAME{ftbpFU}{4.8386in}{3.4428in}{0pt}{\Qcb{Net costs of
constraints on supply of residential land}}{\Qlb{NetCostInternalSpace}}{%
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Figure \ref{NetCostInternalSpaceQuintiles} shows the distribution of net
costs by income quintiles, along with income shares received by each
quintile. In contrast to the discussion of gross benefits presented above,
we are here looking at costs net of benefits. If upper income groups
experiences greater cost shares than their income share, then the policy may
be viewed as generally redistributive.

\FRAME{ftbpFU}{405.375pt}{265.25pt}{0pt}{\Qcb{Net cost shares to income
quintiles from internal open space constraint}}{\Qlb{%
NetCostInternalSpaceQuintiles}}{Figure }{\special{language "Scientific
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'/document/E5PYHC03.wmf';tempfile-properties "XP";}}

The penultimate column of table \ref{NetCostOpenSpaceTable} presents a gini
coefficient for the distribution of costs, indicating the inequality with
which the costs themselves are shared over observations in our sample. The
final column presents what might be called an `income equivalent' gini
coefficient for income. That is, we take household income and add the income
which would be equivalent to adopting the less restrictive land use planning
regime. Both figure \ref{NetCostInternalSpaceQuintiles} and the `equivalent
income gini' show internal open space policies to be generally neutral. The
middle quintile comes out about even. The second and third quintiles gain
somewhat at the expense of the richest and poorest quintile. Without
affecting the overall gini much, internal open space policies appear
relatively to benefit the middle class at the expense of the rich \emph{and}
the poor. This is an observation about relative position only. All income
groups experience positive net costs and, the evidence suggests, would
benefit from adoption of the more permissive planning regime.

While the net costs of providing a higher level of internal open space are
not small over the entire urban area, amounting to about $\pounds 12.775$
million per annum, they are moderate for individual households. By way of
comparison, the mean level of net costs are about $53.5$ percent of the then
current level of local rates,\endnote{A tax on real property which was tied
to property values. The tax was eliminated in favor of the `community
charge', which itself was eliminated and replaced in 1992 by a modified
property tax.} so the net costs are significant relative to the level of tax
paid to local government. We next turn attention to the net cost associated
with a more comprehensive view of what constitutes land use planning.

\subsection{Containment of urbanized area}

In the preceding section, we provided estimates of the net costs associated
with policies designed to provide open space within the residential area of
the city. Next we consider not only this `interior open space' component of
planning, but also the `containment' policies whereby planners seek to
contain the urban area within the existing boundaries of the built-up area
(or `settlement envelopes') preventing urbanisation spreading to existing
agricultural land. So called `greenbelts' represent the best known but most
expensive instrument of this policy. The approach is generally similar to
that used previously. We consider replacing the \textit{status quo} planning
regime with one in which the internal open space parameter $\omega $ is
raised from $\omega _1=0.384$ to $\omega _2=0.427$, \emph{and} the maximum
extent of residential development is not constrained at $\chi _2$ but is
allowed to expand until the price of developed residential land is equal to
the price of vacant agricultural land plus some essential premium required
to bring such land into urban use.

As in the previous case, we must determine the change in land rents and the
change in the effective price of open space. This latter price will
naturally increase for two reasons: first is the reduction in internal open
space which is associated with the increase in $\omega .$ Second, the
increase in the spatial extent of residential development implies that fewer
households will live within a kilometer of the settlement envelope, and will
therefore experience reduced access to open space. The first factor, with
its associated $11.45$ percent decrease in open space, is handled as in the
previous section.

To capture the effect of the second factor, we further reduce all open space
consumption by a factor which reflects the difference between open space
consumption of those households in the sample which live within one
kilometer of the urban periphery and those living closer to the centre. This
results in a further $1.17$ percent reduction in accessible open space, and
a $13.74$ percent reduction in inaccessible open space. The larger reduction
in inaccessible open space is to be expected, since much of the open land
beyond the urban periphery is not open to the general public. Let the matrix 
$\mathbf{p}_3$ provide a price vector for each household which reflects
these higher prices for open space, and $\mathbf{\bar{p}}_3$ represent the
associated vector of sample mean prices.

If we are to replace $\chi _2$ with the distance $\widetilde{x}$ at which
residential land values equal the price of vacant land, we must determine a
price for vacant land. The appropriate price for vacant land should be
several times the price of agricultural land for several reasons. First,
land that is cleared and prepared for development has some investment
applied which already raises its value above vacant land in agricultural
use. Second, as discussed in \cite{Titman:1980:AER}, \cite
{CapozzaHelsley:1990:JUE}, and \cite{CapozzaSick:1994:JUE} \textit{inter alia%
}, the price at which land will be held vacant depends in part on the
stochastic structure of the price of residential property. As noted in \cite
{MayoSheppard:1991:OCDP}, the vacant land price can therefore depend upon
the nature of `development controls' and land use planning.

The estimates presented below are based on a vacant land purchase price of $%
\pounds 20000$ per acre. This level represents a multiple of agricultural
land values which is similar to that observed in North American cities%
\endnote{About 6 or 7 times agricultural land values.}. It also results in
eventual population densities which are similar to those observed in North
American cities\endnote{Somewhat less than three households per acre within
the urban area.} of the size being considered here.

For a mean utility level experienced within the urban area of $u_3$, the
maximum extent of residential development will be 
\begin{equation}
\widetilde{x}=r^{-1}\left( u_3,20000,\theta ,\overline{\mathbf{p}}_3\mathbf{,%
}\overline{\mathbf{M}}\right) =\left\{ x\left| \ r\left( u_3,x,\theta ,%
\overline{\mathbf{p}}_3\mathbf{,}\overline{\mathbf{M}}\right) =20000\right.
\right\}  \label{MaxExten}
\end{equation}
The utility level which equilibrates the urban land market in this case can
be determined by solving for $u_3$ in the equation: 
\begin{equation}
N=\stackrel{r^{-1}\left( u_3,20000,\theta ,\overline{\mathbf{p}}_3\mathbf{,}%
\overline{\mathbf{M}}\right) }{\stackunder{\chi _1}{\int }\ }\stackunder{0}{%
\stackrel{2\pi }{\int }}\frac{\omega _2\cdot x}{h(u_3,r(u_3,x,\theta ,%
\overline{\mathbf{p}}_3\mathbf{,}\overline{\mathbf{M}}),\overline{\mathbf{p}}%
_3)}\ d\theta \,dx  \label{LandEquilibForU3}
\end{equation}

After solving for the mean utility level $u_3$, we obtain a vector of
estimated utilities $\mathbf{u}_3$ using a procedure similar to that
outlined in equation \ref{UtilityChangeEquation}. We then estimate the net
cost of the combined land use planning policies by: 
\begin{equation}
c\left( \mathbf{u}_3,r\left( u_1,\mathbf{x},\mathbf{\theta },\overline{%
\mathbf{p}}_1\mathbf{,}\overline{\mathbf{M}}\right) ,\mathbf{p}_1\right)
-c\left( \mathbf{u}_3,r\left( u_3,\mathbf{x},\mathbf{\theta },\overline{%
\mathbf{p}}_3\mathbf{,}\overline{\mathbf{M}}\right) ,\mathbf{p}_3\right)
\label{NetCostEqVar2}
\end{equation}
Table \ref{NetCostAllPlanTable} presents a summary of these calculations.
The net cost per household is much larger when we consider this more
complete picture of what constitutes the restrictiveness of land use
planning policies on the supply of urban land. It amounts to nearly $13$
percent of household income. It must be stressed that these are net costs,
taking into account the reduction in open space which households experience.
While this amenity is valuable to households, the decrease in land (and
hence housing) costs overwhelms the increase in effective price of open
space.

%TCIMACRO{\TeXButton{B}{\begin{table}[tbp] \centering}}
%BeginExpansion
\begin{table}[tbp] \centering%
%EndExpansion
\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
\multicolumn{9}{|l|}{\emph{Provision of internal open space and containment}}
\\ \hline
$\mathbf{\mu }$ & $\mathbf{\sigma }$ & $\min $ & $\max $ & \textbf{r}$_{%
\text{income}}$ & \textbf{r}$_{\text{area}}$ & \textbf{r}$_{\text{value}}$ & 
\textbf{gini} & \textbf{gini}$_{\text{Y}}$ \\ \hline
1356.63 & 1301.91 & 349.69 & 13688.10 & .409 & .918 & .700 & 34.01 & 21.39
\\ \hline
\end{tabular}
\caption{Net Costs of Open Space and Containment
Policies\label{NetCostAllPlanTable}}%
%TCIMACRO{\TeXButton{E}{\end{table}}}
%BeginExpansion
\end{table}%
%EndExpansion

As before, note that the correlation between net costs and income is weaker
than the correlation between land consumption or overall house value. The
gini index for distribution of the net costs of land use planning indicates
considerable inequality between households in bearing these costs. This is
further illustrated in figure \ref{NetCostAllPlanConstraints}, which shows a
highly skewed distribution of net costs.

\FRAME{ftbpFU}{4.9199in}{3.4428in}{0pt}{\Qcb{Net cost of `containment' and
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Figure \ref{NetCostAllPlanToQuintiles} shows the distribution of net costs
between income quintiles. Upper income households bear a disproportionate
share of the costs of planning, with middle class quintiles 2 and 4 again
being relatively favored. As in the preceding sections, all income groups
experience net costs and would appear to benefit from a regime of land use
regulation that while producing fewer amenity benefits was less restrictive
on urban land supply.

\FRAME{ftbpFU}{406.1875pt}{266.0625pt}{0pt}{\Qcb{Net cost shares to income
quintiles from internal open space and containment}}{\Qlb{%
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'/document/E5PYHC04.wmf';tempfile-properties "XP";}}

This is further substantiated by examination of the `income equivalent'
distribution obtained by adding observed household income to the income
equivalent associated with adoption of an unconstrained land use planning
policy. The resulting gini coefficient of $21.39$ represents a $4.2$ percent
increase in income inequality compared with the distribution of income
observed in our sample. In this sense, land use planning is generally
redistributive, comparing (as noted above) with a variety of other `in kind'
benefits distributed to consumers. This increase in overall equality is,
however, purchased at a considerable price - with total net costs amounting
to nearly $\pounds 109$ million pounds per annum for the Reading urban area,
or nearly three times the amount of local rates. Another way of expressing
it is as a tax on household incomes of around 10\%.

The net costs of this more comprehensive view of land use planning are also
considerably less equally borne by residents than the costs of internal open
space provision alone. This is illustrated graphically in figure \ref
{PlanCostLorenz}, which shows Lorenz curves for the distribution of the net
costs of planning constraints, independent of household income. The observed
differences reflect the increase in the gini associated with the
distribution of these costs from $26.30$ for the internal open space
provision to $34.01$ for open space provision plus containment.

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\section{Concluding remarks}

How does this methodology compare with others that might be available? \cite
{Horowitz:1984:EconLet}, for example, presents a method for calculating
equivalent variations in income directly from estimated hedonic price
functions. One difference which characterizes the approach of this paper is
the use of equilibrium in the urban land market. Since changes in planning
regimes are `system wide' phenomena, they will certainly result in
significant changes in the overall structure of land market equilibrium in
the city, changes which are not observed in the estimation of a hedonic
price function. While Horowitz's approach may be useful for measurement of
the gross benefits from planning amenities, evaluation of the costs requires
estimation and evaluation of the new equilibrium.

We have presented an approach for evaluation of some of the economic
consequences of land use planning. In particular, we have considered the
income-equivalent costs of land use restrictions with their consequent
associated increase in land and housing prices. By focusing on two urban
areas with contrasting planning regimes, we obtain estimates of these
effects as a test of our methodology.

We find the net costs to be significant, as much as 13 percent of annual
household income. We find perverse distributional consequences for some
parts of the land use planning system. Distribution of benefits from
planning amenities tends to favor upper income groups. This is particularly
true of the benefits associated with containment. Interestingly, given
expressed public and `official' concern about the impact of environmental
policies on low income neighbourhoods, we find benefits from limiting
industrial land use to be the most equitably distributed of all land use
planning amenities.

A variety of extensions to the research might be pursued. It would be useful
to verify that there are not other benefits produced by land use planning
which have not been measured in this study and which might alter the
estimated net costs. It would be of further interest to embed the analysis
within a more comprehensive general equilibrium model, as done by \cite
{HazillaKopp:1990:JPE} which may identify additional economic costs of
planning\endnote{For example, increases in prices of other goods resulting
from increased land prices or suboptimal location of production.} which need
to be considered. The analysis presented here concentrates on the costs that
arise through operation of the market for residential land which comes as
part of owner-occupied properties. Land use regulation obviously affects
several other sectors of the economy.

In any event, the methods we develop are computationally feasible and could
be widely applied. They do, however, require data which provide information
on residential structure values and characteristics, including land and
location as well as the incomes of the households occupying the sample
houses. Given such data, the analysis could be of benefit to planners and
policy makers. The results also reinforce the often repeated advice of
economists that the provision of public goods by regulation has the
additional disadvantage from a liberal viewpoint: the real costs are not
directly visible, but require some effort and ingenuity even to approximate.
That they are not visible, however, does not mean that they are not real
nor, in the case at least of British land use planning, that they cannot be
substantial.

\bibliographystyle{Economet}
\bibliography{sod}

\newpage

\appendix 

\section{Variables and descriptive statistics}

%TCIMACRO{\TeXButton{B}{\begin{table}[b] \centering}}
%BeginExpansion
\begin{table}[b] \centering%
%EndExpansion

\begin{tabular}{|lc|}
\hline
\textbf{Variable Name} & \textbf{Description} \\ \hline
Income after tax & \multicolumn{1}{l|}{{\small After tax household income
obtained from survey in }$\pounds ${\small 's}} \\ 
Price$^1$ & \multicolumn{1}{l|}{{\small Rentalised after-tax annual cost of
structure in thousands of }$\pounds ${\small 's}} \\ 
Bedrooms$^1$ & \multicolumn{1}{l|}{\small Number of bedrooms in the structure%
} \\ 
WC's$^1$ & \multicolumn{1}{l|}{\small Number of WC's in the structure} \\ 
Terrace$^1$ & \multicolumn{1}{l|}{\small 1 if property is Terrace style} \\ 
Semi$^1$ & \multicolumn{1}{l|}{\small 1 if property is Semi-detached} \\ 
Flat$^1$ & \multicolumn{1}{l|}{\small 1 if property is a Flat} \\ 
Parking$^1$ & \multicolumn{1}{l|}{\small 1 if property has off-street parking%
} \\ 
Garage$^1$ & \multicolumn{1}{l|}{\small 1 if property has a garage} \\ 
Central Heat$^1$ & \multicolumn{1}{l|}{\small 1 if structure has central
heating} \\ 
Floors$^1$ & \multicolumn{1}{l|}{\small Defined as (5 - number of floors in
structure)} \\ 
Plot Width$^2$ & \multicolumn{1}{l|}{\small Width of plot in feet} \\ 
Sq. Feet$^1$ & \multicolumn{1}{l|}{\small Square feet of living area in
structure} \\ 
Land (L)$^2$ & \multicolumn{1}{l|}{\small Area of land in square feet
associated with the structure} \\ 
Distance$^2$ & \multicolumn{1}{l|}{\small Distance in miles from city centre}
\\ 
Theta$^2$ & \multicolumn{1}{l|}{\small Angle in radians from East} \\ 
School A$^3$ & \multicolumn{1}{l|}{\small 1 if located in `premium'
secondary school A catchment area} \\ 
School B$^3$ & \multicolumn{1}{l|}{\small 1 if located in `premium'
secondary school B catchment area} \\ 
School C$^3$ : Reading only & \multicolumn{1}{l|}{\small 1 if located in
`premium' secondary school C catchment area} \\ 
Street 1$^2$ & \multicolumn{1}{l|}{\small 1 if located on minor road} \\ 
Street 2$^2$ & \multicolumn{1}{l|}{{\small 1 if located on road with }$>$%
{\small \ 4.3 metres metalling : Datum in Darlington}} \\ 
Street 3$^2$ & \multicolumn{1}{l|}{\small 1 if located on a `B-class'
roadway : Datum in Reading} \\ 
Street 4$^2$ & \multicolumn{1}{l|}{\small 1 if located on an `A-class'
roadway} \\ 
Bus$^{2,4}$ & \multicolumn{1}{l|}{\small 1 if property within 3 mile of
local bus route} \\ 
Blue Collar$^5$ & \multicolumn{1}{l|}{\small \ (100 - fraction of ward
labour force in blue collar occupations)} \\ 
Ethnic$^5$ : Reading & \multicolumn{1}{l|}{\small (15 - \% of urban area's
afro-caribbean population located in ward)} \\ 
Ethnic$^5$ : Darlington & \multicolumn{1}{l|}{\small (20 - \% of area's
asian population located in ward)} \\ 
Altitude$^2$ & \multicolumn{1}{l|}{\small Maximum altitude (metres) in 1 km
OS square containing address} \\ 
Industrial Land$^{2,6}$ & \multicolumn{1}{l|}{\small (100 - Percent of land
in Industrial use within 1km OS square)} \\ 
New Construction$^{2,6}$ & \multicolumn{1}{l|}{$\left\{ 
\begin{array}{l}
\text{{\small For Darlington: 1 if majority of observations}} \\ 
\qquad \text{{\small in 1km OS square are new construction; }} \\ 
\text{{\small For Reading, 1 if majority of observations}} \\ 
\qquad \text{{\small \ in 1km OS square are NOT new construction}}
\end{array}
\right. $} \\ 
Open Land Amenity$^{2,6}$ & \multicolumn{1}{l|}{\small Percent of land in
accessible open space in 1km OS square} \\ 
Closed Land Amenity$^{2,6}$ & \multicolumn{1}{l|}{\small Percent of land in
inaccessible open space 1km OS square} \\ 
\multicolumn{2}{|l|}{$
\begin{array}{l}
\text{Sources:}^1\text{Estate Agents Particulars; }^2\text{Ordnance Survey; }%
^3\text{Local Education Authority} \\ 
^4\text{Reading Transport; }^5\text{1981Population Census, Ward Data; }^6%
\text{Aerial Photographs}
\end{array}
$} \\ \hline
\end{tabular}
\caption{Variable Descriptions\label{Variable Descriptions}}%

%TCIMACRO{\TeXButton{E}{\end{table}}}
%BeginExpansion
\end{table}%
%EndExpansion

\pagebreak

%TCIMACRO{\TeXButton{B}{\begin{table}[b] \centering}}
%BeginExpansion
\begin{table}[b] \centering%
%EndExpansion
\begin{tabular}{|ccccc|}
\hline
& \multicolumn{2}{c}{\textbf{Reading}} & \multicolumn{2}{c|}{\textbf{%
Darlington}} \\ 
\textbf{Variable} & $\mu $ & $\sigma $ & $\mu $ & $\sigma $ \\ \hline
\multicolumn{5}{|c|}{\textit{Continuous Characteristics}} \\ 
\multicolumn{1}{|l}{Income After Tax} & \multicolumn{1}{r}{10577.57} & 
\multicolumn{1}{r}{3862.51} & \multicolumn{1}{r}{8869.79} & 
\multicolumn{1}{r|}{4006.08} \\ 
\multicolumn{1}{|l}{Asking Price} & \multicolumn{1}{r}{51065.99} & 
\multicolumn{1}{r}{20767.35} & \multicolumn{1}{r}{23852.7} & 
\multicolumn{1}{r|}{13996.06} \\ 
\multicolumn{1}{|l}{Rentalized Price} & \multicolumn{1}{r}{4.468} & 
\multicolumn{1}{r}{1.817} & \multicolumn{1}{r}{2.087} & \multicolumn{1}{r|}{
1.225} \\ 
\multicolumn{1}{|l}{Bedrooms} & \multicolumn{1}{r}{3.113} & 
\multicolumn{1}{r}{0.949} & \multicolumn{1}{r}{2.823} & \multicolumn{1}{r|}{
0.911} \\ 
\multicolumn{1}{|l}{WC's} & \multicolumn{1}{r}{1.49} & \multicolumn{1}{r}{
0.664} & \multicolumn{1}{r}{1.122} & \multicolumn{1}{r|}{0.543} \\ 
\multicolumn{1}{|l}{Square Feet} & \multicolumn{1}{r}{832.463} & 
\multicolumn{1}{r}{356.581} & \multicolumn{1}{r}{794.483} & 
\multicolumn{1}{r|}{333.209} \\ 
\multicolumn{1}{|l}{Floors$^1$} & \multicolumn{1}{r}{3.074} & 
\multicolumn{1}{r}{0.442} & \multicolumn{1}{r}{3} & \multicolumn{1}{r|}{0.29}
\\ 
\multicolumn{1}{|l}{Land Area} & \multicolumn{1}{r}{4340.436} & 
\multicolumn{1}{r}{4546.668} & \multicolumn{1}{r}{2296.004} & 
\multicolumn{1}{r|}{1905.702} \\ 
\multicolumn{1}{|l}{Plot Width} & \multicolumn{1}{r}{35.768} & 
\multicolumn{1}{r}{27.106} & \multicolumn{1}{r}{27.398} & 
\multicolumn{1}{r|}{17.058} \\ 
\multicolumn{1}{|l}{Distance to CBD} & \multicolumn{1}{r}{2.195} & 
\multicolumn{1}{r}{1.018} & \multicolumn{1}{r}{1.01} & \multicolumn{1}{r|}{
0.464} \\ 
\multicolumn{1}{|l}{Blue Collar$^1$} & \multicolumn{1}{r}{55.078} & 
\multicolumn{1}{r}{14.987} & \multicolumn{1}{r}{39.603} & 
\multicolumn{1}{r|}{21.82} \\ 
\multicolumn{1}{|l}{Ethnic$^1$} & \multicolumn{1}{r}{10.781} & 
\multicolumn{1}{r}{3.655} & \multicolumn{1}{r}{14.12} & \multicolumn{1}{r|}{
3.288} \\ 
\multicolumn{1}{|l}{Altitude} & \multicolumn{1}{r}{68.669} & 
\multicolumn{1}{r}{16.097} & \multicolumn{1}{r}{} & \multicolumn{1}{r|}{} \\ 
\multicolumn{1}{|l}{Amenity Land I (open)} & \multicolumn{1}{r}{18.169} & 
\multicolumn{1}{r}{12.507} & \multicolumn{1}{r}{8.619} & \multicolumn{1}{r|}{
7.806} \\ 
\multicolumn{1}{|l}{Amenity Land II (closed)} & \multicolumn{1}{r}{8.330} & 
\multicolumn{1}{r}{16.322} & \multicolumn{1}{r}{9.643} & \multicolumn{1}{r|}{
15.543} \\ 
\multicolumn{1}{|l}{Industrial Land} & \multicolumn{1}{r}{95.522} & 
\multicolumn{1}{r}{7.140} & \multicolumn{1}{r}{90.382} & \multicolumn{1}{r|}{
13.984} \\ 
\multicolumn{5}{|c|}{\textit{Dichotomous Characteristics}} \\ 
\multicolumn{1}{|l}{Terrace} & \multicolumn{1}{r}{0.133} & 
\multicolumn{1}{r}{0.34} & \multicolumn{1}{r}{0.434} & \multicolumn{1}{r|}{
0.496} \\ 
\multicolumn{1}{|l}{Semi} & \multicolumn{1}{r}{0.345} & \multicolumn{1}{r}{
0.476} & \multicolumn{1}{r}{0.392} & \multicolumn{1}{r|}{0.489} \\ 
\multicolumn{1}{|l}{Flat} & \multicolumn{1}{r}{0.097} & \multicolumn{1}{r}{
0.296} & \multicolumn{1}{r}{0.006} & \multicolumn{1}{r|}{0.08} \\ 
\multicolumn{1}{|l}{Parking} & \multicolumn{1}{r}{0.21} & \multicolumn{1}{r}{
0.408} & \multicolumn{1}{r}{0.228} & \multicolumn{1}{r|}{0.42} \\ 
\multicolumn{1}{|l}{Garage} & \multicolumn{1}{r}{0.641} & \multicolumn{1}{r}{
0.48} & \multicolumn{1}{r}{0.437} & \multicolumn{1}{r|}{0.497} \\ 
\multicolumn{1}{|l}{Central Heat} & \multicolumn{1}{r}{0.801} & 
\multicolumn{1}{r}{0.399} & \multicolumn{1}{r}{0.54} & \multicolumn{1}{r|}{
0.499} \\ 
\multicolumn{1}{|l}{School A} & \multicolumn{1}{r}{0.149} & 
\multicolumn{1}{r}{0.356} & \multicolumn{1}{r}{0.154} & \multicolumn{1}{r|}{
0.362} \\ 
\multicolumn{1}{|l}{School B} & \multicolumn{1}{r}{0.093} & 
\multicolumn{1}{r}{0.29} & \multicolumn{1}{r}{0.164} & \multicolumn{1}{r|}{
0.371} \\ 
\multicolumn{1}{|l}{School C} & \multicolumn{1}{r}{0.081} & 
\multicolumn{1}{r}{0.274} & \multicolumn{1}{r}{0.238} & \multicolumn{1}{r|}{
0.427} \\ 
\multicolumn{1}{|l}{School D} & \multicolumn{1}{r}{} & \multicolumn{1}{r}{}
& \multicolumn{1}{r}{0.244} & \multicolumn{1}{r|}{0.43} \\ 
\multicolumn{1}{|l}{Street 1$^1$} & \multicolumn{1}{r}{0.291} & 
\multicolumn{1}{r}{0.455} & \multicolumn{1}{r}{0.637} & \multicolumn{1}{r|}{
0.482} \\ 
\multicolumn{1}{|l}{Street 2$^1$} & \multicolumn{1}{r}{0.12} & 
\multicolumn{1}{r}{0.325} & \multicolumn{1}{r}{0.074} & \multicolumn{1}{r|}{
0.262} \\ 
\multicolumn{1}{|l}{Street 3$^1$} & \multicolumn{1}{r}{0.016} & 
\multicolumn{1}{r}{0.125} & \multicolumn{1}{r}{0.013} & \multicolumn{1}{r|}{
0.113} \\ 
\multicolumn{1}{|l}{Street 4$^1$} & \multicolumn{1}{r}{0.059} & 
\multicolumn{1}{r}{0.235} & \multicolumn{1}{r}{0.026} & \multicolumn{1}{r|}{
0.159} \\ 
\multicolumn{1}{|l}{New Construction} & \multicolumn{1}{r}{0.820} & 
\multicolumn{1}{r}{0.384} & \multicolumn{1}{r}{0.052} & \multicolumn{1}{r|}{
0.221} \\ 
\multicolumn{5}{|l|}{$
\begin{array}{l}
^1\text{{\small These variables were defined so that an increase in the
variable was expected }} \\ 
\text{{\small to be more desirable. See table \ref{Variable Descriptions}
above for variable definitions.}}
\end{array}
$} \\ \hline
\end{tabular}
\caption{Descriptive Statistics for Sample\label{DescripStat}}%
%TCIMACRO{\TeXButton{E}{\end{table}}}
%BeginExpansion
\end{table}%
%EndExpansion

\clearpage

\newpage

\section{Estimated hedonic price function}

%TCIMACRO{\TeXButton{B}{\begin{table}[b] \centering}}
%BeginExpansion
\begin{table}[b] \centering%
%EndExpansion
\begin{tabular}{|cllll|}
\hline
& \multicolumn{2}{c}{\textbf{Reading}} & \multicolumn{2}{c|}{\textbf{%
Darlington}} \\ 
\multicolumn{1}{|l}{\textbf{Variable}} & estimate & t & estimate & t \\ 
\hline
\multicolumn{1}{|l}{Constant} & \multicolumn{1}{c}{-0.89318} & 
\multicolumn{1}{c}{-5.51} & \multicolumn{1}{c}{-1.79801} & 
\multicolumn{1}{c|}{-5.78} \\ 
\multicolumn{5}{|c|}{\textit{Continuous Structure Characteristics}} \\ 
\multicolumn{1}{|l}{Bedrooms} & \multicolumn{1}{c}{0.07369} & 
\multicolumn{1}{c}{4.08} & \multicolumn{1}{c}{0.30587} & \multicolumn{1}{c|}{
4.50} \\ 
\multicolumn{1}{|l}{WC} & \multicolumn{1}{c}{0.07654} & \multicolumn{1}{c}{
4.50} & \multicolumn{1}{c}{0.11219} & \multicolumn{1}{c|}{1.78} \\ 
\multicolumn{1}{|l}{Floors} & \multicolumn{1}{c}{0.08409} & 
\multicolumn{1}{c}{2.65} & \multicolumn{1}{c}{0.42815} & \multicolumn{1}{c|}{
4.57} \\ 
\multicolumn{1}{|l}{Plot Width} & \multicolumn{1}{c}{0.01943} & 
\multicolumn{1}{c}{2.02} & \multicolumn{1}{c}{0.01297} & \multicolumn{1}{c|}{
0.68} \\ 
\multicolumn{1}{|l}{Square Feet} & \multicolumn{1}{c}{0.07409} & 
\multicolumn{1}{c}{3.62} & \multicolumn{1}{c}{0.01010} & \multicolumn{1}{c|}{
0.46} \\ 
\multicolumn{5}{|c|}{\textit{Dichotomous Structure Characteristics}} \\ 
\multicolumn{1}{|l}{Terrace} & \multicolumn{1}{c}{0.02788} & 
\multicolumn{1}{c}{1.43} & \multicolumn{1}{c}{0.07337} & \multicolumn{1}{c|}{
0.47} \\ 
\multicolumn{1}{|l}{Semi} & \multicolumn{1}{c}{0.03278} & \multicolumn{1}{c}{
1.82} & \multicolumn{1}{c}{0.28446} & \multicolumn{1}{c|}{1.88} \\ 
\multicolumn{1}{|l}{Detached} & \multicolumn{1}{c}{0.11230} & 
\multicolumn{1}{c}{4.84} & \multicolumn{1}{c}{0.55044} & \multicolumn{1}{c|}{
3.57} \\ 
\multicolumn{1}{|l}{Parking} & \multicolumn{1}{c}{0.01982} & 
\multicolumn{1}{c}{1.39} & \multicolumn{1}{c}{0.01855} & \multicolumn{1}{c|}{
0.64} \\ 
\multicolumn{1}{|l}{Garage} & \multicolumn{1}{c}{0.05230} & 
\multicolumn{1}{c}{3.28} & \multicolumn{1}{c}{0.07368} & \multicolumn{1}{c|}{
2.06} \\ 
\multicolumn{1}{|l}{Central Heating} & \multicolumn{1}{c}{0.04771} & 
\multicolumn{1}{c}{4.08} & \multicolumn{1}{c}{0.11683} & \multicolumn{1}{c|}{
4.78} \\ 
\multicolumn{5}{|c|}{\textit{Schools}} \\ 
\multicolumn{1}{|l}{School A} & \multicolumn{1}{c}{0.08368} & 
\multicolumn{1}{c}{4.52} & \multicolumn{1}{c}{0.12076} & \multicolumn{1}{c|}{
2.35} \\ 
\multicolumn{1}{|l}{School B} & \multicolumn{1}{c}{0.05902} & 
\multicolumn{1}{c}{3.35} & \multicolumn{1}{c}{0.10965} & \multicolumn{1}{c|}{
3.24} \\ 
\multicolumn{1}{|l}{School C} & \multicolumn{1}{c}{0.02440} & 
\multicolumn{1}{c}{1.34} & \multicolumn{1}{c}{not included} & 
\multicolumn{1}{c|}{} \\ 
\multicolumn{5}{|c|}{\textit{Socio-Economic Characteristics}} \\ 
\multicolumn{1}{|l}{Blue Collar} & \multicolumn{1}{c}{0.01193} & 
\multicolumn{1}{c}{0.98} & \multicolumn{1}{c}{0.06146} & \multicolumn{1}{c|}{
1.21} \\ 
\multicolumn{1}{|l}{Ethnic} & \multicolumn{1}{c}{0.02630} & 
\multicolumn{1}{c}{2.92} & \multicolumn{1}{c}{0.04462} & \multicolumn{1}{c|}{
1.73} \\ 
\multicolumn{5}{|c|}{\textit{Transport infrastructure}} \\ 
\multicolumn{1}{|l}{Street 0} & \multicolumn{1}{c}{0.05131} & 
\multicolumn{1}{c}{1.52} & \multicolumn{1}{c}{0.05063} & \multicolumn{1}{c|}{
1.14} \\ 
\multicolumn{1}{|l}{Street 1} & \multicolumn{1}{c}{0.04797} & 
\multicolumn{1}{c}{1.41} & \multicolumn{1}{c}{0.01463} & \multicolumn{1}{c|}{
0.37} \\ 
\multicolumn{1}{|l}{Street 2} & \multicolumn{1}{c}{0.04803} & 
\multicolumn{1}{c}{1.39} & \multicolumn{1}{c}{datum} & \multicolumn{1}{c|}{}
\\ 
\multicolumn{1}{|l}{Street 3} & \multicolumn{1}{c}{datum} & 
\multicolumn{1}{c}{} & \multicolumn{1}{c}{0.19120} & \multicolumn{1}{c|}{1.87
} \\ 
\multicolumn{1}{|l}{Street 4} & \multicolumn{1}{c}{0.07527} & 
\multicolumn{1}{c}{1.99} & \multicolumn{1}{c}{0.05144} & \multicolumn{1}{c|}{
0.64} \\ 
\multicolumn{1}{|l}{Bus Access} & \multicolumn{1}{c}{0.00652} & 
\multicolumn{1}{c}{0.82} & \multicolumn{1}{c}{not available} & 
\multicolumn{1}{c|}{} \\ 
\multicolumn{5}{|c|}{\textit{Planning and topography}} \\ 
\multicolumn{1}{|l}{Altitude} & \multicolumn{1}{c}{0.00843} & 
\multicolumn{1}{c}{0.68} & \multicolumn{1}{c}{not included} & 
\multicolumn{1}{c|}{} \\ 
\multicolumn{1}{|l}{Amenity Land I} & \multicolumn{1}{c}{0.00664} & 
\multicolumn{1}{c}{1.52} & \multicolumn{1}{c}{0.01843} & \multicolumn{1}{c|}{
2.51} \\ 
\multicolumn{1}{|l}{Amenity Land II} & \multicolumn{1}{c}{0.00625} & 
\multicolumn{1}{c}{3.52} & \multicolumn{1}{c}{0.00021} & \multicolumn{1}{c|}{
0.04} \\ 
\multicolumn{1}{|l}{Industrial Land} & \multicolumn{1}{c}{0.05184} & 
\multicolumn{1}{c}{1.77} & \multicolumn{1}{c}{0.00406} & \multicolumn{1}{c|}{
0.28} \\ 
\multicolumn{1}{|l}{New Construction*} & \multicolumn{1}{c}{0.02260} & 
\multicolumn{1}{c}{1.94} & \multicolumn{1}{c}{0.15881} & \multicolumn{1}{c|}{
2.58} \\ 
\multicolumn{5}{|c|}{\textit{Land value function}} \\ 
\multicolumn{1}{|l}{$\beta _1$} & \multicolumn{1}{c}{0.03299} & 
\multicolumn{1}{c}{3.26} & \multicolumn{1}{c}{0.00006} & \multicolumn{1}{c|}{
7.27} \\ 
\multicolumn{1}{|l}{$\beta _2$} & \multicolumn{1}{c}{-0.11966} & 
\multicolumn{1}{c}{-3.58} & \multicolumn{1}{c}{-0.17655} & 
\multicolumn{1}{c|}{-0.95} \\ 
\multicolumn{1}{|l}{$\beta _3$} & \multicolumn{1}{c}{0.05523} & 
\multicolumn{1}{c}{3.39} & \multicolumn{1}{c}{-0.05023} & 
\multicolumn{1}{c|}{-0.48} \\ 
\multicolumn{1}{|l}{$\beta _4$} & \multicolumn{1}{c}{4.31092} & 
\multicolumn{1}{c}{27.75} & \multicolumn{1}{c}{3.99973} & 
\multicolumn{1}{c|}{2.82} \\ 
\multicolumn{5}{|c|}{\textit{Transformation variables}} \\ 
\multicolumn{1}{|l}{$\lambda $} & \multicolumn{1}{c}{0.21918} & 
\multicolumn{1}{c}{5.56} & \multicolumn{1}{c}{0.31712} & \multicolumn{1}{c|}{
1.32} \\ 
\multicolumn{1}{|l}{$\psi $} & \multicolumn{1}{c}{-0.31622} & 
\multicolumn{1}{c}{-3.37} & \multicolumn{1}{c}{0.24335} & 
\multicolumn{1}{c|}{2.96} \\ 
\multicolumn{1}{|l}{$\xi $} & \multicolumn{1}{c}{0.12286} & 
\multicolumn{1}{c}{2.9} & \multicolumn{1}{c}{1.02445} & \multicolumn{1}{c|}{
34.15} \\ \hline
\end{tabular}
\caption{Hedonic Functions for Reading and Darlington\label{Hedonic Table}}%
%TCIMACRO{\TeXButton{E}{\end{table}}}
%BeginExpansion
\end{table}%
%EndExpansion

\clearpage

\newpage

\section{Demand system estimates}

%TCIMACRO{\TeXButton{B}{\begin{table}[ht] \centering}}
%BeginExpansion
\begin{table}[ht] \centering%
%EndExpansion
\begin{tabular}{c|ccccccccc}
& Area & Bedrms & WC's & Width & Sq. Ft. & Floors & Ethnic & Bl Collar & 
Altitude \\ \hline
$\alpha $ & \multicolumn{1}{|r}{37.079} & \multicolumn{1}{r}{6.383} & 
\multicolumn{1}{r}{6.542} & \multicolumn{1}{r}{3.762} & \multicolumn{1}{r}{
6.306} & \multicolumn{1}{r}{6.682} & \multicolumn{1}{r}{2.424} & 
\multicolumn{1}{r}{1.244} & \multicolumn{1}{r}{-0.086} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{2.54}} & \multicolumn{1}{r}{\textit{%
0.58}} & \multicolumn{1}{r}{\textit{0.63}} & \multicolumn{1}{r}{\textit{0.98}
} & \multicolumn{1}{r}{\textit{0.30}} & \multicolumn{1}{r}{\textit{0.49}} & 
\multicolumn{1}{r}{\textit{0.45}} & \multicolumn{1}{r}{\textit{0.45}} & 
\multicolumn{1}{r}{\textit{-0.04}} \\ 
$\gamma $ & \multicolumn{1}{|r}{-12.856} & \multicolumn{1}{r}{-3.915} & 
\multicolumn{1}{r}{-3.279} & \multicolumn{1}{r}{-1.814} & \multicolumn{1}{r}{
-8.143} & \multicolumn{1}{r}{-3.772} & \multicolumn{1}{r}{-1.264} & 
\multicolumn{1}{r}{-0.879} & \multicolumn{1}{r}{-0.524} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{-5.33}} & \multicolumn{1}{r}{%
\textit{-2.03}} & \multicolumn{1}{r}{\textit{-1.86}} & \multicolumn{1}{r}{%
\textit{-2.80}} & \multicolumn{1}{r}{\textit{-2.21}} & \multicolumn{1}{r}{%
\textit{-1.58}} & \multicolumn{1}{r}{\textit{-1.40}} & \multicolumn{1}{r}{%
\textit{-1.89}} & \multicolumn{1}{r}{\textit{-1.52}} \\ 
$\delta $ & \multicolumn{1}{|r}{3.517} & \multicolumn{1}{r}{3.862} & 
\multicolumn{1}{r}{3.623} & \multicolumn{1}{r}{1.331} & \multicolumn{1}{r}{
7.680} & \multicolumn{1}{r}{4.278} & \multicolumn{1}{r}{1.527} & 
\multicolumn{1}{r}{0.855} & \multicolumn{1}{r}{0.637} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{14.52}} & \multicolumn{1}{r}{%
\textit{23.03}} & \multicolumn{1}{r}{\textit{22.87}} & \multicolumn{1}{r}{%
\textit{22.74}} & \multicolumn{1}{r}{\textit{23.73}} & \multicolumn{1}{r}{%
\textit{21.45}} & \multicolumn{1}{r}{\textit{18.50}} & \multicolumn{1}{r}{%
\textit{20.51}} & \multicolumn{1}{r}{\textit{22.35}} \\ 
P$_{Land}$ & \multicolumn{1}{|r}{-1.019} & \multicolumn{1}{r}{0.409} & 
\multicolumn{1}{r}{0.296} & \multicolumn{1}{r}{0.065} & \multicolumn{1}{r}{
0.848} & \multicolumn{1}{r}{0.213} & \multicolumn{1}{r}{0.071} & 
\multicolumn{1}{r}{0.059} & \multicolumn{1}{r}{0.031} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{-1.84}} & \multicolumn{1}{r}{%
\textit{1.34}} & \multicolumn{1}{r}{\textit{0.99}} & \multicolumn{1}{r}{%
\textit{0.58}} & \multicolumn{1}{r}{\textit{1.37}} & \multicolumn{1}{r}{%
\textit{0.54}} & \multicolumn{1}{r}{\textit{0.48}} & \multicolumn{1}{r}{%
\textit{0.75}} & \multicolumn{1}{r}{\textit{0.55}} \\ 
P$_{Beds}$ & \multicolumn{1}{|r}{2.111} & \multicolumn{1}{r}{0.011} & 
\multicolumn{1}{r}{0.497} & \multicolumn{1}{r}{0.284} & \multicolumn{1}{r}{
1.632} & \multicolumn{1}{r}{0.552} & \multicolumn{1}{r}{0.170} & 
\multicolumn{1}{r}{0.108} & \multicolumn{1}{r}{0.120} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{2.51}} & \multicolumn{1}{r}{\textit{%
0.02}} & \multicolumn{1}{r}{\textit{0.84}} & \multicolumn{1}{r}{\textit{1.28}
} & \multicolumn{1}{r}{\textit{1.33}} & \multicolumn{1}{r}{\textit{0.76}} & 
\multicolumn{1}{r}{\textit{0.58}} & \multicolumn{1}{r}{\textit{0.68}} & 
\multicolumn{1}{r}{\textit{1.09}} \\ 
P$_{WC}$ & \multicolumn{1}{|r}{0.318} & \multicolumn{1}{r}{-0.295} & 
\multicolumn{1}{r}{-1.216} & \multicolumn{1}{r}{-0.090} & \multicolumn{1}{r}{
-0.336} & \multicolumn{1}{r}{-0.286} & \multicolumn{1}{r}{-0.105} & 
\multicolumn{1}{r}{-0.030} & \multicolumn{1}{r}{-0.065} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{0.48}} & \multicolumn{1}{r}{\textit{%
-0.75}} & \multicolumn{1}{r}{\textit{-3.26}} & \multicolumn{1}{r}{\textit{%
-0.63}} & \multicolumn{1}{r}{\textit{-0.42}} & \multicolumn{1}{r}{\textit{%
-0.59}} & \multicolumn{1}{r}{\textit{-0.56}} & \multicolumn{1}{r}{\textit{%
-0.29}} & \multicolumn{1}{r}{\textit{-0.93}} \\ 
P$_{Width}$ & \multicolumn{1}{|r}{-0.671} & \multicolumn{1}{r}{0.338} & 
\multicolumn{1}{r}{0.353} & \multicolumn{1}{r}{-0.187} & \multicolumn{1}{r}{
0.624} & \multicolumn{1}{r}{0.752} & \multicolumn{1}{r}{0.282} & 
\multicolumn{1}{r}{0.130} & \multicolumn{1}{r}{0.102} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{-1.26}} & \multicolumn{1}{r}{%
\textit{0.86}} & \multicolumn{1}{r}{\textit{0.91}} & \multicolumn{1}{r}{%
\textit{-1.28}} & \multicolumn{1}{r}{\textit{0.83}} & \multicolumn{1}{r}{%
\textit{1.61}} & \multicolumn{1}{r}{\textit{1.51}} & \multicolumn{1}{r}{%
\textit{1.39}} & \multicolumn{1}{r}{\textit{1.47}} \\ 
P$_{SqFt}$ & \multicolumn{1}{|r}{1.197} & \multicolumn{1}{r}{1.161} & 
\multicolumn{1}{r}{1.450} & \multicolumn{1}{r}{0.582} & \multicolumn{1}{r}{
0.668} & \multicolumn{1}{r}{1.718} & \multicolumn{1}{r}{0.795} & 
\multicolumn{1}{r}{0.400} & \multicolumn{1}{r}{0.216} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{1.14}} & \multicolumn{1}{r}{\textit{%
1.54}} & \multicolumn{1}{r}{\textit{2.02}} & \multicolumn{1}{r}{\textit{2.17}
} & \multicolumn{1}{r}{\textit{0.45}} & \multicolumn{1}{r}{\textit{1.95}} & 
\multicolumn{1}{r}{\textit{2.13}} & \multicolumn{1}{r}{\textit{2.13}} & 
\multicolumn{1}{r}{\textit{1.61}} \\ 
P$_{Floors}$ & \multicolumn{1}{|r}{1.160} & \multicolumn{1}{r}{0.979} & 
\multicolumn{1}{r}{0.773} & \multicolumn{1}{r}{0.356} & \multicolumn{1}{r}{
2.057} & \multicolumn{1}{r}{0.083} & \multicolumn{1}{r}{0.262} & 
\multicolumn{1}{r}{0.253} & \multicolumn{1}{r}{0.125} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{1.14}} & \multicolumn{1}{r}{\textit{%
1.23}} & \multicolumn{1}{r}{\textit{1.05}} & \multicolumn{1}{r}{\textit{1.30}
} & \multicolumn{1}{r}{\textit{1.32}} & \multicolumn{1}{r}{\textit{0.08}} & 
\multicolumn{1}{r}{\textit{0.67}} & \multicolumn{1}{r}{\textit{1.27}} & 
\multicolumn{1}{r}{\textit{0.87}} \\ 
P$_{Ethnic}$ & \multicolumn{1}{|r}{1.017} & \multicolumn{1}{r}{-0.265} & 
\multicolumn{1}{r}{-0.206} & \multicolumn{1}{r}{-0.006} & \multicolumn{1}{r}{
-0.476} & \multicolumn{1}{r}{-0.346} & \multicolumn{1}{r}{-0.318} & 
\multicolumn{1}{r}{-0.050} & \multicolumn{1}{r}{-0.040} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{3.57}} & \multicolumn{1}{r}{\textit{%
-1.33}} & \multicolumn{1}{r}{\textit{-1.07}} & \multicolumn{1}{r}{\textit{%
-0.08}} & \multicolumn{1}{r}{\textit{-1.19}} & \multicolumn{1}{r}{\textit{%
-1.43}} & \multicolumn{1}{r}{\textit{-4.07}} & \multicolumn{1}{r}{\textit{%
-1.06}} & \multicolumn{1}{r}{\textit{-1.21}} \\ 
P$_{BlCollar}$ & \multicolumn{1}{|r}{0.228} & \multicolumn{1}{r}{0.432} & 
\multicolumn{1}{r}{0.364} & \multicolumn{1}{r}{0.127} & \multicolumn{1}{r}{
0.876} & \multicolumn{1}{r}{0.444} & \multicolumn{1}{r}{0.168} & 
\multicolumn{1}{r}{-0.117} & \multicolumn{1}{r}{0.055} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{0.48}} & \multicolumn{1}{r}{\textit{%
1.24}} & \multicolumn{1}{r}{\textit{1.12}} & \multicolumn{1}{r}{\textit{1.01}
} & \multicolumn{1}{r}{\textit{1.28}} & \multicolumn{1}{r}{\textit{1.06}} & 
\multicolumn{1}{r}{\textit{1.00}} & \multicolumn{1}{r}{\textit{-1.39}} & 
\multicolumn{1}{r}{\textit{0.89}} \\ 
P$_{Altitude}$ & \multicolumn{1}{|r}{-0.755} & \multicolumn{1}{r}{0.305} & 
\multicolumn{1}{r}{0.099} & \multicolumn{1}{r}{-0.040} & \multicolumn{1}{r}{
0.541} & \multicolumn{1}{r}{0.264} & \multicolumn{1}{r}{0.046} & 
\multicolumn{1}{r}{0.036} & \multicolumn{1}{r}{-0.112} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{-1.61}} & \multicolumn{1}{r}{%
\textit{1.07}} & \multicolumn{1}{r}{\textit{0.37}} & \multicolumn{1}{r}{%
\textit{-0.36}} & \multicolumn{1}{r}{\textit{0.97}} & \multicolumn{1}{r}{%
\textit{0.78}} & \multicolumn{1}{r}{\textit{0.36}} & \multicolumn{1}{r}{%
\textit{0.51}} & \multicolumn{1}{r}{\textit{-2.20}} \\ 
P$_{Amen1}$ & \multicolumn{1}{|r}{0.028} & \multicolumn{1}{r}{0.058} & 
\multicolumn{1}{r}{0.065} & \multicolumn{1}{r}{0.015} & \multicolumn{1}{r}{
0.080} & \multicolumn{1}{r}{0.119} & \multicolumn{1}{r}{0.082} & 
\multicolumn{1}{r}{0.031} & \multicolumn{1}{r}{0.018} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{0.17}} & \multicolumn{1}{r}{\textit{%
0.54}} & \multicolumn{1}{r}{\textit{0.66}} & \multicolumn{1}{r}{\textit{0.38}
} & \multicolumn{1}{r}{\textit{0.38}} & \multicolumn{1}{r}{\textit{0.94}} & 
\multicolumn{1}{r}{\textit{1.65}} & \multicolumn{1}{r}{\textit{1.17}} & 
\multicolumn{1}{r}{\textit{0.98}} \\ 
P$_{Amen2}$ & \multicolumn{1}{|r}{0.087} & \multicolumn{1}{r}{-0.008} & 
\multicolumn{1}{r}{-0.003} & \multicolumn{1}{r}{0.001} & \multicolumn{1}{r}{
-0.015} & \multicolumn{1}{r}{-0.002} & \multicolumn{1}{r}{-0.003} & 
\multicolumn{1}{r}{0.000} & \multicolumn{1}{r}{-0.001} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{3.65}} & \multicolumn{1}{r}{\textit{%
-0.44}} & \multicolumn{1}{r}{\textit{-0.16}} & \multicolumn{1}{r}{\textit{%
0.07}} & \multicolumn{1}{r}{\textit{-0.42}} & \multicolumn{1}{r}{\textit{%
-0.08}} & \multicolumn{1}{r}{\textit{-0.41}} & \multicolumn{1}{r}{\textit{%
0.00}} & \multicolumn{1}{r}{\textit{-0.16}} \\ 
P$_{Indus}$ & \multicolumn{1}{|r}{5.703} & \multicolumn{1}{r}{-1.082} & 
\multicolumn{1}{r}{-0.841} & \multicolumn{1}{r}{0.051} & \multicolumn{1}{r}{
-1.955} & \multicolumn{1}{r}{-1.424} & \multicolumn{1}{r}{-0.636} & 
\multicolumn{1}{r}{-0.255} & \multicolumn{1}{r}{-0.191} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{4.16}} & \multicolumn{1}{r}{\textit{%
-1.47}} & \multicolumn{1}{r}{\textit{-1.17}} & \multicolumn{1}{r}{\textit{%
0.18}} & \multicolumn{1}{r}{\textit{-1.33}} & \multicolumn{1}{r}{\textit{%
-1.61}} & \multicolumn{1}{r}{\textit{-1.56}} & \multicolumn{1}{r}{\textit{%
-1.38}} & \multicolumn{1}{r}{\textit{-1.45}} \\ 
Adj. $R^2$ & \multicolumn{1}{|r}{0.95} & \multicolumn{1}{r}{0.97} & 
\multicolumn{1}{r}{0.98} & \multicolumn{1}{r}{0.98} & \multicolumn{1}{r}{0.98
} & \multicolumn{1}{r}{0.97} & \multicolumn{1}{r}{0.97} & \multicolumn{1}{r}{
0.97} & \multicolumn{1}{r}{0.97}
\end{tabular}
\caption{Reading Demand System - Non-Planning Characteristics \label{Reading
Demand Non Plan}}%
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\begin{tabular}{cccc}
& Amenity 1 & Amenity 2 & Ind Land \\ \hline
$\alpha $ & \multicolumn{1}{r}{-1.304} & \multicolumn{1}{r}{-2.303} & 
\multicolumn{1}{r}{3.919} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-0.92}} & \multicolumn{1}{r}{\textit{%
-1.17}} & \multicolumn{1}{r}{\textit{0.32}} \\ 
$\gamma $ & \multicolumn{1}{r}{-0.106} & \multicolumn{1}{r}{0.247} & 
\multicolumn{1}{r}{-3.844} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-0.43}} & \multicolumn{1}{r}{\textit{%
0.73}} & \multicolumn{1}{r}{\textit{-1.80}} \\ 
$\delta $ & \multicolumn{1}{r}{0.426} & \multicolumn{1}{r}{0.183} & 
\multicolumn{1}{r}{4.073} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{22.36}} & \multicolumn{1}{r}{\textit{%
5.05}} & \multicolumn{1}{r}{\textit{22.42}} \\ 
P$_{Land}$ & \multicolumn{1}{r}{0.004} & \multicolumn{1}{r}{-0.084} & 
\multicolumn{1}{r}{0.317} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{0.09}} & \multicolumn{1}{r}{\textit{%
-1.11}} & \multicolumn{1}{r}{\textit{0.91}} \\ 
P$_{Beds}$ & \multicolumn{1}{r}{0.063} & \multicolumn{1}{r}{0.126} & 
\multicolumn{1}{r}{0.581} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{1.00}} & \multicolumn{1}{r}{\textit{%
1.11}} & \multicolumn{1}{r}{\textit{0.86}} \\ 
P$_{WC}$ & \multicolumn{1}{r}{-0.082} & \multicolumn{1}{r}{-0.134} & 
\multicolumn{1}{r}{-0.256} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-1.79}} & \multicolumn{1}{r}{\textit{%
-1.65}} & \multicolumn{1}{r}{\textit{-0.58}} \\ 
P$_{Width}$ & \multicolumn{1}{r}{0.075} & \multicolumn{1}{r}{0.113} & 
\multicolumn{1}{r}{0.565} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{1.39}} & \multicolumn{1}{r}{\textit{%
1.34}} & \multicolumn{1}{r}{\textit{1.34}} \\ 
P$_{SqFt}$ & \multicolumn{1}{r}{0.073} & \multicolumn{1}{r}{-0.021} & 
\multicolumn{1}{r}{1.461} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{0.81}} & \multicolumn{1}{r}{\textit{%
-0.14}} & \multicolumn{1}{r}{\textit{1.80}} \\ 
P$_{Floors}$ & \multicolumn{1}{r}{-0.037} & \multicolumn{1}{r}{-0.117} & 
\multicolumn{1}{r}{0.964} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-0.38}} & \multicolumn{1}{r}{\textit{%
-0.82}} & \multicolumn{1}{r}{\textit{1.08}} \\ 
P$_{Ethnic}$ & \multicolumn{1}{r}{-0.009} & \multicolumn{1}{r}{0.050} & 
\multicolumn{1}{r}{-0.317} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-0.44}} & \multicolumn{1}{r}{\textit{%
1.45}} & \multicolumn{1}{r}{\textit{-1.45}} \\ 
P$_{BlCollar}$ & \multicolumn{1}{r}{0.009} & \multicolumn{1}{r}{-0.094} & 
\multicolumn{1}{r}{0.404} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{0.21}} & \multicolumn{1}{r}{\textit{%
-1.46}} & \multicolumn{1}{r}{\textit{1.05}} \\ 
P$_{Altitude}$ & \multicolumn{1}{r}{0.007} & \multicolumn{1}{r}{-0.149} & 
\multicolumn{1}{r}{0.274} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{0.19}} & \multicolumn{1}{r}{\textit{%
-2.31}} & \multicolumn{1}{r}{\textit{0.88}} \\ 
P$_{Amen1}$ & \multicolumn{1}{r}{-0.082} & \multicolumn{1}{r}{0.022} & 
\multicolumn{1}{r}{0.106} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-6.11}} & \multicolumn{1}{r}{\textit{%
0.95}} & \multicolumn{1}{r}{\textit{0.92}} \\ 
P$_{Amen2}$ & \multicolumn{1}{r}{-0.001} & \multicolumn{1}{r}{-0.052} & 
\multicolumn{1}{r}{-0.004} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-0.28}} & \multicolumn{1}{r}{\textit{%
-13.99}} & \multicolumn{1}{r}{\textit{-0.20}} \\ 
P$_{Indus}$ & \multicolumn{1}{r}{-0.121} & \multicolumn{1}{r}{0.040} & 
\multicolumn{1}{r}{-2.022} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-1.36}} & \multicolumn{1}{r}{\textit{%
0.21}} & \multicolumn{1}{r}{\textit{-2.42}} \\ 
Adj. $R^2$ & \multicolumn{1}{r}{0.97} & \multicolumn{1}{r}{0.85} & 
\multicolumn{1}{r}{0.97}
\end{tabular}
\caption{Reading Demand -- Planning Amenities \label{Reading Demand Plan}}%
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\begin{tabular}{c|cccccccc}
& Area & Bedrms & WC's & Width & Sq. Ft. & Floors & Ethnic & Bl Collar \\ 
\hline
$\alpha $ & \multicolumn{1}{|r}{26.717} & \multicolumn{1}{r}{65.090} & 
\multicolumn{1}{r}{29.234} & \multicolumn{1}{r}{3.634} & \multicolumn{1}{r}{
3.929} & \multicolumn{1}{r}{57.534} & \multicolumn{1}{r}{13.623} & 
\multicolumn{1}{r}{31.863} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{0.63}} & \multicolumn{1}{r}{\textit{%
0.55}} & \multicolumn{1}{r}{\textit{0.94}} & \multicolumn{1}{r}{\textit{0.37}
} & \multicolumn{1}{r}{\textit{0.18}} & \multicolumn{1}{r}{\textit{0.34}} & 
\multicolumn{1}{r}{\textit{0.50}} & \multicolumn{1}{r}{\textit{0.58}} \\ 
$\gamma $ & \multicolumn{1}{|r}{-13.738} & \multicolumn{1}{r}{9.748} & 
\multicolumn{1}{r}{0.566} & \multicolumn{1}{r}{0.550} & \multicolumn{1}{r}{
2.001} & \multicolumn{1}{r}{16.581} & \multicolumn{1}{r}{2.146} & 
\multicolumn{1}{r}{2.726} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{-2.72}} & \multicolumn{1}{r}{%
\textit{0.83}} & \multicolumn{1}{r}{\textit{0.18}} & \multicolumn{1}{r}{%
\textit{0.52}} & \multicolumn{1}{r}{\textit{0.88}} & \multicolumn{1}{r}{%
\textit{0.90}} & \multicolumn{1}{r}{\textit{0.73}} & \multicolumn{1}{r}{%
\textit{0.49}} \\ 
$\delta $ & \multicolumn{1}{|r}{11.011} & \multicolumn{1}{r}{6.686} & 
\multicolumn{1}{r}{1.809} & \multicolumn{1}{r}{0.748} & \multicolumn{1}{r}{
1.395} & \multicolumn{1}{r}{9.463} & \multicolumn{1}{r}{1.609} & 
\multicolumn{1}{r}{3.754} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{7.06}} & \multicolumn{1}{r}{\textit{%
2.84}} & \multicolumn{1}{r}{\textit{2.93}} & \multicolumn{1}{r}{\textit{3.79}
} & \multicolumn{1}{r}{\textit{3.05}} & \multicolumn{1}{r}{\textit{2.78}} & 
\multicolumn{1}{r}{\textit{2.79}} & \multicolumn{1}{r}{\textit{3.23}} \\ 
P$_{Land}$ & \multicolumn{1}{|r}{3.460} & \multicolumn{1}{r}{13.957} & 
\multicolumn{1}{r}{4.250} & \multicolumn{1}{r}{1.244} & \multicolumn{1}{r}{
2.590} & \multicolumn{1}{r}{20.385} & \multicolumn{1}{r}{3.502} & 
\multicolumn{1}{r}{6.998} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{1.10}} & \multicolumn{1}{r}{\textit{%
1.97}} & \multicolumn{1}{r}{\textit{2.23}} & \multicolumn{1}{r}{\textit{2.07}
} & \multicolumn{1}{r}{\textit{1.92}} & \multicolumn{1}{r}{\textit{2.01}} & 
\multicolumn{1}{r}{\textit{2.12}} & \multicolumn{1}{r}{\textit{2.13}} \\ 
P$_{Beds}$ & \multicolumn{1}{|r}{3.092} & \multicolumn{1}{r}{-14.364} & 
\multicolumn{1}{r}{-2.070} & \multicolumn{1}{r}{-0.653} & \multicolumn{1}{r}{
-1.836} & \multicolumn{1}{r}{-13.084} & \multicolumn{1}{r}{-2.258} & 
\multicolumn{1}{r}{-4.607} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{1.20}} & \multicolumn{1}{r}{\textit{%
-2.99}} & \multicolumn{1}{r}{\textit{-1.57}} & \multicolumn{1}{r}{\textit{%
-1.65}} & \multicolumn{1}{r}{\textit{-1.98}} & \multicolumn{1}{r}{\textit{%
-1.96}} & \multicolumn{1}{r}{\textit{-2.10}} & \multicolumn{1}{r}{\textit{%
-2.10}} \\ 
P$_{WC}$ & \multicolumn{1}{|r}{-0.051} & \multicolumn{1}{r}{-0.544} & 
\multicolumn{1}{r}{-0.416} & \multicolumn{1}{r}{-0.060} & \multicolumn{1}{r}{
-0.120} & \multicolumn{1}{r}{-0.935} & \multicolumn{1}{r}{-0.143} & 
\multicolumn{1}{r}{-0.368} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{-0.19}} & \multicolumn{1}{r}{%
\textit{-0.93}} & \multicolumn{1}{r}{\textit{-3.51}} & \multicolumn{1}{r}{%
\textit{-1.23}} & \multicolumn{1}{r}{\textit{-1.07}} & \multicolumn{1}{r}{%
\textit{-1.12}} & \multicolumn{1}{r}{\textit{-1.04}} & \multicolumn{1}{r}{%
\textit{-1.21}} \\ 
P$_{Width}$ & \multicolumn{1}{|r}{-3.348} & \multicolumn{1}{r}{3.535} & 
\multicolumn{1}{r}{0.865} & \multicolumn{1}{r}{-0.172} & \multicolumn{1}{r}{
0.629} & \multicolumn{1}{r}{4.074} & \multicolumn{1}{r}{0.712} & 
\multicolumn{1}{r}{1.367} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{-1.29}} & \multicolumn{1}{r}{%
\textit{0.69}} & \multicolumn{1}{r}{\textit{0.67}} & \multicolumn{1}{r}{%
\textit{-0.40}} & \multicolumn{1}{r}{\textit{0.63}} & \multicolumn{1}{r}{%
\textit{0.56}} & \multicolumn{1}{r}{\textit{0.58}} & \multicolumn{1}{r}{%
\textit{0.57}} \\ 
P$_{SqFt}$ & \multicolumn{1}{|r}{0.244} & \multicolumn{1}{r}{9.181} & 
\multicolumn{1}{r}{2.024} & \multicolumn{1}{r}{0.652} & \multicolumn{1}{r}{
0.775} & \multicolumn{1}{r}{10.533} & \multicolumn{1}{r}{2.009} & 
\multicolumn{1}{r}{4.534} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{0.10}} & \multicolumn{1}{r}{\textit{%
1.90}} & \multicolumn{1}{r}{\textit{1.52}} & \multicolumn{1}{r}{\textit{1.59}
} & \multicolumn{1}{r}{\textit{0.86}} & \multicolumn{1}{r}{\textit{1.59}} & 
\multicolumn{1}{r}{\textit{1.93}} & \multicolumn{1}{r}{\textit{2.09}} \\ 
P$_{Floors}$ & \multicolumn{1}{|r}{2.727} & \multicolumn{1}{r}{-17.055} & 
\multicolumn{1}{r}{-3.627} & \multicolumn{1}{r}{-1.475} & \multicolumn{1}{r}{
-3.465} & \multicolumn{1}{r}{-31.132} & \multicolumn{1}{r}{-4.150} & 
\multicolumn{1}{r}{-7.422} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{0.67}} & \multicolumn{1}{r}{\textit{%
-2.32}} & \multicolumn{1}{r}{\textit{-1.75}} & \multicolumn{1}{r}{\textit{%
-2.16}} & \multicolumn{1}{r}{\textit{-2.32}} & \multicolumn{1}{r}{\textit{%
-2.71}} & \multicolumn{1}{r}{\textit{-2.21}} & \multicolumn{1}{r}{\textit{%
-2.20}} \\ 
P$_{Ethnic}$ & \multicolumn{1}{|r}{-1.588} & \multicolumn{1}{r}{-1.961} & 
\multicolumn{1}{r}{-0.505} & \multicolumn{1}{r}{-0.234} & \multicolumn{1}{r}{
-0.429} & \multicolumn{1}{r}{-3.874} & \multicolumn{1}{r}{-1.431} & 
\multicolumn{1}{r}{-0.962} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{-0.80}} & \multicolumn{1}{r}{%
\textit{-0.69}} & \multicolumn{1}{r}{\textit{-0.67}} & \multicolumn{1}{r}{%
\textit{-0.91}} & \multicolumn{1}{r}{\textit{-0.75}} & \multicolumn{1}{r}{%
\textit{-0.92}} & \multicolumn{1}{r}{\textit{-2.23}} & \multicolumn{1}{r}{%
\textit{-0.72}} \\ 
P$_{BlCollar}$ & \multicolumn{1}{|r}{1.729} & \multicolumn{1}{r}{-0.514} & 
\multicolumn{1}{r}{-0.047} & \multicolumn{1}{r}{-0.056} & \multicolumn{1}{r}{
-0.130} & \multicolumn{1}{r}{-0.953} & \multicolumn{1}{r}{-0.131} & 
\multicolumn{1}{r}{-2.309} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{1.26}} & \multicolumn{1}{r}{\textit{%
-0.24}} & \multicolumn{1}{r}{\textit{-0.09}} & \multicolumn{1}{r}{\textit{%
-0.29}} & \multicolumn{1}{r}{\textit{-0.31}} & \multicolumn{1}{r}{\textit{%
-0.30}} & \multicolumn{1}{r}{\textit{-0.26}} & \multicolumn{1}{r}{\textit{%
-2.31}} \\ 
P$_{Amen1}$ & \multicolumn{1}{|r}{0.028} & \multicolumn{1}{r}{0.170} & 
\multicolumn{1}{r}{0.063} & \multicolumn{1}{r}{0.012} & \multicolumn{1}{r}{
0.035} & \multicolumn{1}{r}{0.237} & \multicolumn{1}{r}{0.052} & 
\multicolumn{1}{r}{0.053} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{0.26}} & \multicolumn{1}{r}{\textit{%
0.67}} & \multicolumn{1}{r}{\textit{0.93}} & \multicolumn{1}{r}{\textit{0.59}
} & \multicolumn{1}{r}{\textit{0.70}} & \multicolumn{1}{r}{\textit{0.63}} & 
\multicolumn{1}{r}{\textit{0.82}} & \multicolumn{1}{r}{\textit{0.43}} \\ 
P$_{Amen2}$ & \multicolumn{1}{|r}{0.054} & \multicolumn{1}{r}{-0.313} & 
\multicolumn{1}{r}{-0.078} & \multicolumn{1}{r}{-0.026} & \multicolumn{1}{r}{
-0.060} & \multicolumn{1}{r}{-0.479} & \multicolumn{1}{r}{-0.077} & 
\multicolumn{1}{r}{-0.143} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{0.73}} & \multicolumn{1}{r}{\textit{%
-2.00}} & \multicolumn{1}{r}{\textit{-1.97}} & \multicolumn{1}{r}{\textit{%
-2.10}} & \multicolumn{1}{r}{\textit{-2.01}} & \multicolumn{1}{r}{\textit{%
-2.14}} & \multicolumn{1}{r}{\textit{-2.08}} & \multicolumn{1}{r}{\textit{%
-1.94}} \\ 
P$_{Indus}$ & \multicolumn{1}{|r}{3.616} & \multicolumn{1}{r}{-11.292} & 
\multicolumn{1}{r}{-2.235} & \multicolumn{1}{r}{-0.765} & \multicolumn{1}{r}{
-2.064} & \multicolumn{1}{r}{-16.927} & \multicolumn{1}{r}{-2.507} & 
\multicolumn{1}{r}{-4.724} \\ 
\textit{t} & \multicolumn{1}{|r}{\textit{1.58}} & \multicolumn{1}{r}{\textit{%
-1.93}} & \multicolumn{1}{r}{\textit{-1.60}} & \multicolumn{1}{r}{\textit{%
-1.59}} & \multicolumn{1}{r}{\textit{-1.85}} & \multicolumn{1}{r}{\textit{%
-1.89}} & \multicolumn{1}{r}{\textit{-1.81}} & \multicolumn{1}{r}{\textit{%
-1.71}} \\ 
Adj. $R^2$ & \multicolumn{1}{|r}{0.89} & \multicolumn{1}{r}{0.53} & 
\multicolumn{1}{r}{0.60} & \multicolumn{1}{r}{0.70} & \multicolumn{1}{r}{0.54
} & \multicolumn{1}{r}{0.48} & \multicolumn{1}{r}{0.50} & \multicolumn{1}{r}{
0.64}
\end{tabular}
\caption{Darlington Demand System -- Non-Planning Characteristics
\label{Darlington Demand Non Plan}}%
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\begin{tabular}{cccc}
& Amenity 1 & Amenity 2 & Ind Land \\ \hline
$\alpha $ & \multicolumn{1}{r}{-0.141} & \multicolumn{1}{r}{-0.070} & 
\multicolumn{1}{r}{1.496} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-0.01}} & \multicolumn{1}{r}{\textit{%
-0.54}} & \multicolumn{1}{r}{\textit{0.31}} \\ 
$\gamma $ & \multicolumn{1}{r}{0.974} & \multicolumn{1}{r}{0.011} & 
\multicolumn{1}{r}{0.404} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{0.89}} & \multicolumn{1}{r}{\textit{%
0.66}} & \multicolumn{1}{r}{\textit{0.79}} \\ 
$\delta $ & \multicolumn{1}{r}{0.608} & \multicolumn{1}{r}{0.004} & 
\multicolumn{1}{r}{0.266} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{2.38}} & \multicolumn{1}{r}{\textit{%
1.21}} & \multicolumn{1}{r}{\textit{2.77}} \\ 
P$_{Land}$ & \multicolumn{1}{r}{0.696} & \multicolumn{1}{r}{0.004} & 
\multicolumn{1}{r}{0.593} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{1.16}} & \multicolumn{1}{r}{\textit{%
0.55}} & \multicolumn{1}{r}{\textit{2.07}} \\ 
P$_{Beds}$ & \multicolumn{1}{r}{-0.895} & \multicolumn{1}{r}{0.003} & 
\multicolumn{1}{r}{-0.411} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-2.13}} & \multicolumn{1}{r}{\textit{%
0.70}} & \multicolumn{1}{r}{\textit{-2.16}} \\ 
P$_{WC}$ & \multicolumn{1}{r}{-0.036} & \multicolumn{1}{r}{0.000} & 
\multicolumn{1}{r}{-0.027} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-0.70}} & \multicolumn{1}{r}{\textit{%
0.47}} & \multicolumn{1}{r}{\textit{-1.11}} \\ 
P$_{Width}$ & \multicolumn{1}{r}{0.315} & \multicolumn{1}{r}{0.004} & 
\multicolumn{1}{r}{0.111} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{0.68}} & \multicolumn{1}{r}{\textit{%
0.74}} & \multicolumn{1}{r}{\textit{0.54}} \\ 
P$_{SqFt}$ & \multicolumn{1}{r}{0.721} & \multicolumn{1}{r}{-0.004} & 
\multicolumn{1}{r}{0.346} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{1.74}} & \multicolumn{1}{r}{\textit{%
-0.92}} & \multicolumn{1}{r}{\textit{1.84}} \\ 
P$_{Floors}$ & \multicolumn{1}{r}{-1.121} & \multicolumn{1}{r}{-0.010} & 
\multicolumn{1}{r}{-0.712} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-1.72}} & \multicolumn{1}{r}{\textit{%
-0.90}} & \multicolumn{1}{r}{\textit{-2.28}} \\ 
P$_{Ethnic}$ & \multicolumn{1}{r}{-0.125} & \multicolumn{1}{r}{-0.003} & 
\multicolumn{1}{r}{-0.097} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-0.52}} & \multicolumn{1}{r}{\textit{%
-1.40}} & \multicolumn{1}{r}{\textit{-0.82}} \\ 
P$_{BlCollar}$ & \multicolumn{1}{r}{-0.008} & \multicolumn{1}{r}{0.003} & 
\multicolumn{1}{r}{-0.032} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-0.03}} & \multicolumn{1}{r}{\textit{%
1.37}} & \multicolumn{1}{r}{\textit{-0.37}} \\ 
P$_{Amen1}$ & \multicolumn{1}{r}{-0.139} & \multicolumn{1}{r}{0.001} & 
\multicolumn{1}{r}{0.008} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-6.23}} & \multicolumn{1}{r}{\textit{%
1.83}} & \multicolumn{1}{r}{\textit{0.72}} \\ 
P$_{Amen2}$ & \multicolumn{1}{r}{-0.029} & \multicolumn{1}{r}{-0.002} & 
\multicolumn{1}{r}{-0.013} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-2.13}} & \multicolumn{1}{r}{\textit{%
-10.90}} & \multicolumn{1}{r}{\textit{-2.07}} \\ 
P$_{Indus}$ & \multicolumn{1}{r}{-1.080} & \multicolumn{1}{r}{-0.009} & 
\multicolumn{1}{r}{-0.589} \\ 
\textit{t} & \multicolumn{1}{r}{\textit{-1.85}} & \multicolumn{1}{r}{\textit{%
-1.28}} & \multicolumn{1}{r}{\textit{-2.31}} \\ 
Adj. $R^2$ & \multicolumn{1}{r}{0.66} & \multicolumn{1}{r}{0.75} & 
\multicolumn{1}{r}{0.49}
\end{tabular}
\caption{Darlington Demand -- Planning Amenities \label{Darlington Demand
Plan}}%
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