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THESIS
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LIBRARY ‘1
Michigan Slater
Univemég‘g}; 4

This is to certify that the

dissertation entitled

ECONOMIC ANALYSIS
OF THE GREENBELT AMENITY
IN SEO
mama

presen

Joo An Kwon

has been accepted towards fulfillment
of the requirements for

w; degree in Econom i 95

Major pr essor

21 4f

Date

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PLACE IN RETURN BOX to remove this checkout from your record.
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DATE DUE DATE DUE DATE DUE

 

 

 

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ll 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

i.

ans-9.1

 

T—i

MSU Is An Affirmative Action/Equal Opportunity Institution
W

 

 

 

ECONOMIC ANALYSIS
OF THE GREENBELT AMENITY
INSEOUL,KOREA
By

Joo An Kwon

A DISSERTATION

submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

1995

 

ABSTRACT

ECONOMIC ANALYSIS
OF THE GREENBELT AMENITY
IN SEOUL, KOREA

By

Joo An Kwon

In Korea the metropolitan area of Seoul is surrounded by the restricted area,
which is called as the Greenbelt, and starts at 10-18 km from the CBD. As the
economic growth continues with high income, there has been a strong pressure from the
demand side of the housing and land markets to demand more of urban residential land
and floor space. The Greenbelt has been blamed as restraining physically the area from
being developed into urban uses and has to be adjusted to meet the increasing demand
pressure in Seoul. Along with the deregulation mood in Korea, attacks to the Greenbelt
seem to lead the total abolition of the system. Kim(l987) asserted that if the Greenbelt
is released by 1 km wide, then 7.7% decrease of land rent is estimated by using 1976
survey data.

If the Greenbelt has an amenity effect and makes a positive environmental
contribution to the areas adjacent to the Greenbelt, then the net social gain must
consider these positive externalities of the Greenbelt. In order to find the net social gain
of releasing the land from the Greenbelt, we have to estimate the rent gradient with the
amenity effect considered as a function of the distance from the Greenbelt. Using the
linear spline estimation with the semi-log specification of the rent gradient, the rent
gradient with the amenity effect of the Greenbelt is estimated. Based on these results,

we calculate the new net social gain of releasing the land from the Greenbelt; and if the

 

width of the Greenbelt matters, it is found to be smaller than previously without
considering the amenity effect.

Amenity effect of the Greenbelt illustrates that it is desirable not to abolish all
the Greenbelt system but to adjust the present system to produce the same amenity
effect. We introduced the Green Disks as an alternative to the Greenbelt, and the Green
Disks are preferrable to the Greenbelt because they spend less land for restriction. Also,
Urban Disks are considered, but the Green Disks are superior. According to our
findings of net social gain and the Green Disks, we build an examplary alternative form

of the Greenbelt.

 

dedicated to
my grandparents, parents, wife and son

iv

 

ACKNOWLEDGEMENTS

My first thanks should be devoted to Professor Paul Strassmann, my dissertation
chairman for his incomparable guidance of this dissertation. I appreciate his kindness,
sincerity, patience and wit all the time. He has supported me in many ways and
suggested many ideas developed in this dissertation. I have really enjoyed working with
him. I also thank the other dissertation committee members, John Strauss and Lawrence
Martin for their helpful comments. Finally, I appreciate assistance by many friends and
faculties in department of economics. Also without help of Dr. Yong Taek Kim, Dr. Mak
Joong Choi and Dr. Gill-Chin Lim in collecting data, the empirical studies are not
possible at all.

My best thanks must go to my parents, parents-in-laws and my wife, Eunwha for
their invaluable support and patience. I also wish to express my greatest delight to my

beloved son, Andrew.

 

TABLE OF CONTENTS

List of Tables ......................................... vfii
List of Figures ........................................ ix
Chapter I. Introduction ................................ l
l. The Greenbelt ................................. 2
2. The Greenbelt in the Capital Region ........... 4
3. Previous Studies .............................. 11

Chapter II. Theoretical Analysis of the Effect of the

Greenbelt ................................. 16

1. Land Market ................................... 16

1—1. Model without Amenity ................... 16

1-2. Model with Amenity ...................... 21

2. Housing Market ................................ 25
Chapter III. Empirical Analysis of Amenity Effect ..... 31
1 Data .......................................... 32

2. Empirical Model ............................... 35

3. Rent Gradient Estimation ...................... 37

4. Population Gradient ........................... 48

vi

 

Chapter IV. Welfare Analysis of Releasing the Greenbelt

Restriction ...............................

l. Releasing the Land from the Greenbelt .........

2. Social Gain from Releasing Land ...............

3. Social Gain in case of No Amenity Effect ......

Chapter V. Green Disks for an Alternative to the
Greenbelt ..................................

1. Greenbelt and Green Disks .....................

2. Changes of Welfare and Rent Gradients under the

Green Disks ...................................

3. Urban Disks; Seoul and Satellite Cities .......

Chapter VI. Conclusions ...............................

List of References

vfi

51

51

59

63

66

67

73

79

85

9O

 

Table

Table
Table

Table

Table

Table
Table

Table
Table

Table

Table
Table

List of Tables

Greenbelts in the Capital Region and
Kyonggi Province as of 1988
Descriptive Statistics of Data ............
Definition of Variables used in Spline
Estimation
Linear Spline Estimation
Gradient
Linear Spline Estimation II of Rent
Gradient
Population Gradient Estimation ............
Rent Gradient Intercepts before and after
the Land Release
Net Social Gains
Linear Spline Estimation of Rent Gradient
; No Amenity Effect
Change in Intercepts and Net Social Gains
; No Amenity Effect
Greenbelt and Green Disks
Social Gains of Releasing Land and Amenity
Effect

I of Rent

\lili

 

Figure
Figure

Figure

Figure
Figure
Figure

Figure
Figure
Figure
Figure
Figure
Figure

List of Figures

1 Seoul in Korean History ...................
l-l

Capital Region and Greenbelt ..............
2 Population Densities and Residential Land

in Seoul ..................................
3 Rent Gradients ............................
4 Rent Gradient with Greenbelt ..............
2— (d)

Fitted Value of Imputed Rent ...............
5 Change of Rent Gradient ...................
6 Greenbelt and Green Disks .................
7 Amenity Effect of Green Disks .............
8 Rent Gradients in case of the Green Disks
9 Seoul and Satellite Cities ................
10 Examplary Scattered Reserve Areas in Seoul.

ix

9-10
20
22

47
53-55
68-69

74
77-78
82—84

89

 

Chapter I

 

I. Introduction

The simplest model in urban economics assumes that a city is monocentric. It is a
long-run equilibrium model and built up with the assumption of homogeneous housing
services. Various implications stem from the basic trade-off between accessibility and
residential space. It has strong analytical power but ignores the heterogeneity of housing
services in the real world. Introducing heterogeneity cannot guarantee trouble-free
models since we have to bear some costs: losses in analytical simplicity and empirical
application. The best way to deal with such problems is a compromise between realism
and analytical power.

Greenbelts may introduce some heterogeneity in urban economics with other
attribute variables. If an amenity from the Greenbelt varies with the distance to the
Greenbelt, housing on different parcels will provide a different degree of amenity. It
brings the simple monocentric model closer to reality. On the other hand, because the
Greenbelt is established around the urban areas, the monocentric model could exhibit its
full analytical power in explaining the amenity effect of the Greenbelt. Therefore, our
analytical model is basically monocentric with some heterogeneity of the amenity effect.

In Korea the deregulation movement seems to flourish since the first civilian
president was elected in 1993. In line with the deregulation movement, the Greenbelt is
criticized for its pervasive effect on the urban land supply in Seoul and other major cities.
In this study we analyze the amenity effect of the Greenbelt and reconsider the validity of

the deregulation movement.

 

2

First, we show that the amenity effect of the Greenbelt exists in the land market.
Amenity effects basically depend on the distance from the Greenbelt boundary. Second,
if the amenity effect exists, then the social gain from releasing the Greenbelt restriction
may be less than expected since the amenity gives a positve benefit to the residents near
the Greenbelt. These amenity benefits depend on how thick the Greenbelt is and how
wide the restricted area is released. Because the Greenbelt is not changed yet, we cannot
observe the amenity changes or rent gradient after the land release and do not have clear
information about how the amenity benefit should be specified. For calculation of the net
social gain, we simply assume that amenity benefit can be calculated from the rent
gradient, and the rent gradient shifts vertically due to land release. Third, we introduce
the Green Disks and urban disks as an alternative system to the Greenbelt. The
deregulation movement of the Greenbelt leads many to conclude that it must be
abolished. However, if the Greenbelt has some merits, then it may be better to adjust the

system partially to preserve such merits than to abolish it entirely.

1. The Greenbelt

The Greenbelt restriction is one of many growth controls. The Greenbelt is
designed to contain the growth of urban areas. The Greenbelt has a long but intermittent
history. The first idea ever of the Greenbelt may be found in the Old Testament which
describes towns and cities with inviolable rural hinterlands -- Numbers 3521-4 and

Leviticus 25:34 (see Osborn, 1946, pp.167-180).

On the plains of Moab by the Jordan across from Jericho, the Lord said to Moses,

"Command the Israelites to give the Levites towns to live in from the inheritance and

 

3
Israelites will possess. And give them pasturelands around the towns. Then they will

have towns to live in and pasture lands for their cattle, flocks and all their other livestock.
The pasturelands around the towns that you give the Levites will extend out fifteen
hundred feet from the town wall. ----- " -- Numbers 35:1-4

But the pastureland belonging to their towns must not be sold; it is their permanent

possession. -- Leviticus 25:34

Later authors, such as Sir Thomas More (Utopia), Robert Owen and J. S. Buckingham
contributed to the idea that town and country should be functionally related but physically
distinct (see Thomas, 1970, p.72). The first systematic concern of the Greenbelt was
introduced in London -- the 1580 proclamation of Elizabeth established a cordon sanitaire
three miles wide around London -- to check the further growth of a large built-up area, to
prevent neighboring towns from merging into one another and to preserve the special
character of a town (see Munton, 1983, pp.15-29; Thomas, 1970, pp.72-96; Mandelker,
1962, p.31).

The Greenbelts were also introduced in the United States as a Garden City or
Greenbelt Town; Greenbelt in Maryland outside Washington DC, Greendale in
Wisconsin outside Milwaukee and Greenhills in Ohio outside Cincinnati, three Greenbelt
Towns begun by the New Deal's Resettlement Administration in 1936. At that time the
Greenbelt Towns were an experiment in urban living. Different from the Greenbelt in
London, the three Greenbelt Towns were very small in population and urban area. In the
late 1970's and early 1980's another application was done in Boulder, Colorado; Portland,

Oregon and California as an urban growth boundary or one of grth controls.

 

2. The Greenbelt in the Capital Region

Once called Wiryesong, the capital of Baekje Kingdom, Seoul has been the most
important geo-political center in Korean history. As the town expanded and formed its
rudimentary structure during the Koryo Dynasty, Seoul was one of three capital towns
called Namgyong. Six hundred years have passed since Seoul became the capital of the
Choson Dynasty in 1394. Hansongbu, another old name of Seoul, had a hundred
thousand population at that time, but has reached 1.4 million in 1945 and ten million
now. Also the city area has expanded from 16.5 km? in 1394 to 627.06 km? in 1994.
Seoul has changed from a fortress town into a gigantic metropolis (see <Figure 1>.).

At the beginning of the 1970's the city planning began to focus on the control of
growth as the overconcentration problem became a major planning issue among large
cities. The period after the 1970's was a transition toward a modern city. Bristling high-
rise office buildings appeared in the urban renewal areas and Kangnarn (southern part of
Han River in Seoul) was developing with construction of many apartments. Subcenters
or secondary centers also grew in Seoul and small satellite cities such as Euijongbu,
Songnam, Kwangmyung, Buchon and Anyang began to form.

The Greenbelt was designated in major cities in Korea between 1971 and 1977 for
the purposes of land use control and containment. The total area of the Greenbelt was
5397.1 km2 as of 1988 and about 5.5% of the total area of Korea. This number is
relatively small compared with the total area but since it is imposed around the urban
boundaries, the physical restriction is quite large. The Greenbelts are designed to serve
the functions of preventing irregular physical expansion of cities, protecting the
environment and securing national defense. The Urban Planning Law prohibits land use
conversions and construction activities other than rebuilding or altering an existing

structure inside the Greenbelt.

 

Figure 1. Seoul in Korean History

 

Kokuryo
Wirygonglg ......
‘\,I ........ O
the Yellow
Sea the Sea
Baekje Silla of Japan
(a) Three lGngdoms:
Kokuryo, Baekje and Silla (AB. SC)
.I"
r j
’7
j Japan
i
Haneongbu
ix.) 0
the Yellow
Sea Choson the Sea
of Japan
(b) Choson Dynasty
(A.D. 14c) .,_
e"
r j
/' Japan
i

 

6
As noted, the Greenbelt has had a pervasive effect on the urban land supply.
Population kept on increasing steadily in Seoul with rapid economic growth and
urbanization while the boundary of Seoul is fixed by the Greenbelt. Population grth
has consequently brought a highly dense development in Seoul. The shortage of

residential land in Seoul has been partially filled by decreasing other land uses.

< Table 1 > Greenbelts in the Capital Region and Kyonggi Province as of 1988 (km2)

 

 

 

Region Total Area (1) Greenbelt (2) (2)/(1) (%) (2)/{(1)-(2)}(%)
(a) Seoul 605.4 166.8 27.6 38.0
(b) Inchon 310.8 55.2 17.8 21.6
(c) Other Cities 1178.2 670.8 56.9 132.2
(a)+(b)+(c) 2094.4 892.8 42.6 74.3
Rest of Kyonggi* 9584.3 658.9 6.9 7.4
Total 11678.7 1551.7 13.3 15.3

 

 

 

 

 

 

 

Source : Municipal Yearbook of Korea, MOHA, Seoul, 1989.
"' : Kyonggi Province is one of nine provinces in Korea and it encompasses Seoul.

<1“ able l> illustrates the current status of the Greenbelt in the capital region. The
Greenbelt in the capital region starts at 10-18 km from the center of Seoul and expands
10-
15 km outward to cover parts of Inchon, 14 other cities and 8 counties. The Greenbelt is
42.6% in the total urban area and 27.6% in Seoul. Most area in the Greenbelt is
composed of forest and arable land, and only 5.6% (4.0% and 4.4%) is developed for
residential use in the capital region (Seoul and all urban areas respectively). <Figure 1-
1> illustrates the locations and areas of the Greenbelt around the capital region. The
Greenbelt is established around the Seoul area, and its inner boundary shows a shape
similar to the administrative boundary. Also the satellite cities are surrounded by the

Greenbelt.

 

mmthd

 

Figure 1-1. Capital Region and Greenbelt

  
     

 
   

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Gun'

8 Gunpo
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Hannam
Sungnam
Kwachon

Euwang
10 Kwangmyung
1" Slheung
12 Buchon

 

 

 

 

8

Before going on to the theoretical analysis, it is desirable to see the spatial
distribution of population and residential area in Seoul. <Figure 2-(a)> shows the total
population and the proportion of the residential area to the total developed area in the
corresponding circular area according to the distance from the central business district.
The proportion of the residential area increases steadily until 8 km and remains about
45% afterwards. The population shows an inverse U-shape. It increases until 10 km
where it reaches the maximum and after 10 km, it decreases. Considering that the
Greenbelt starts at 10-18 km from the CBD and the proportion of the residential area
remains steady around 45% after 8 km from the CBD, the population is concentrated
relatively in the adjacent area to the Greenbelt.

Even though the proportion of residential land does not show any decreases at
locations of 11 km from the CBD, the density on residential land may actually increase as
the total developed area falls more than population declines with distance from the CBD.
In <Figure 2-(b)>, we show the two different population densities with respect to the total
developed area (density 2) and the residential area (density 1). While the density to
the residential area increases so sharply that it reaches the highest level at the range of 2-3
km, the density to the total developed area reaches the highest level at the range of 13-14
km. In case of the density 7, the residential area is relatively small to the total
developed area at the range of 2-3 km, and this makes the density 1 high and the
density 2 low. Two densities are high at the range of 13-14 km since the residential and
commercial areas are developed more densely (especially in the southern part of Seoul),
and population size is higher than the residential area relatively to the other areas in
Seoul. We can see that population is concentrated relatively heavily in the areas adjacent

to the Greenbelt.

 

Figure 2. Population Densities and Residential Land in Seoul (1988), and
Average Land Rent in Selected Years

(a) Population Distribution and Residential Land

1200 -- -- 50

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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0 Eli]: l i l % 1L: i 4 i l i ' i :H: ' i O
12 3 4 5 6 7 8 91011121314151617181920
Distance from the CBD(km)
I: population ———I— residential land
Note : The Greenbelt begins at 10 - 18 km from the CBD.
(b) Two Population Densities
160
E 140 /F"\\
120
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20 P73
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

distance from CBD(km)

 

I ——I— population density 1 ——{:~—— population density 2

 

 

Note : population density 1 = population + residential area
population density 2 = population + total developed area.

 

10

 

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<Figure 2-(c)> shows the average land rent of Seoul in selected years. Land rent
is decreasing with the distance from the CBD in all selected years. When we compare the
land rent in 1980 and 1984, the average land rent is shown to rotate counter-clockwise
around the area of 9-10 km from the CBD. The Greenbelt starts at 10 km from the CBD,
and during the period of 1980-1984 land rent increases relatively higher at the areas

adjacent to the Greenbelt.

3. Previous Studies

The Greenbelt is one of many measures for growth controls. Brueckner (1990)
illustrates the effect of growth controls on the land values in an open city setting. In an
open city model population changes to restore the previous equilibrium. Pogodzinski and
Sass (1992), Engle et a1. (1992), Landis (1992), and Fischel (1989) provide a good survey
of grth controls, and they tried to illustrate the goods and bads of many growth
controls measures. Cheshire and Sheppard (1989), Zorn et a1. (1986), Knapp (1985), and
Ohls et al. (1974) are a few of many empirical studies about effects of growth controls on
land and property values.

Growth controls are designed to check and adjust the urban growth in the long
run. Capozza and Helsley (1989) provide the fundamental factors of land prices in the
long run. Land prices are composed of discounted value of urban land rent, conversion
costs, and agricultural rent. For area near the Greenbelt there is one more factor to be
considered, and it is an amenity effect of the Greenbelt. As Nelson (1988) pointed out,
the rent gradient is higher near the Greenbelt due to amenity effect. Polinsky and Shavell
(1976) considered the amenity effect in the closed and Open city models. Utility fimction
is defined to include the amenity variable, and because land rent gradient carries enough

information about the amenity effect in utility function, the amenity effect can be traced

 

12

out from the estimated rent gradient in both closed and open models. Diamond (1980)
used a modified Box-Cox specification to estimate the amenity effect on the urban land
prices. He found that the specification of functional form is very important in estimating
the amenity effect. General Box-Cox functional form is chosen and preferred by most
researchers of the amenity effect. But maximum likelihood estimation does not
necessarily guarantee the global maximization. We choose a simple linear estimation
over the nonlinear maximum likelihood estimation because it is easier to estimate and
interpret.

Most Greenbelt studies have been done on the London's Greenbelt because
London has the longest history of the Greenbelt. Thomas (1970) attempted to show how
the stricter controls over land usage, implicit in the Greenbelts, have led to modifications
in the use of land over the zone surrounding London. He illustrated the changes in
population, land uses, and industrial redeployment. He emphasized the containment role
of the London's Greenbelt, and it was found to be successful by using 1960 data. Munton
(1983) pointed that the implementation of the Greenbelt restriction raises many complex
issues. This is partly because the purpose of the Greenbelt in London can be interpreted
in widely differing ways and partly because today's substantial Greenbelt encompass a
great range of local planning situations. Interpretative gaps between local and central
government were found to be critical in the size of the Greenbelt, determining the
Greenbelt boundaries, and environmental issues. Under these confusion of practising the
Greenbelt farmland has been maintained very poorly. Elson (1986) pointed that the
Greenbelt in London is a successfirl example of reconciliation invented for planning
profession. He also sorted out several effects of the Greenbelt; (i) it has managed the
process of decentralization into specific physical forms. (ii) it has contained patterns of
new development in the interests of economy and access to existing services. (iii) it has

maintained separation between towns. (iv) it has retained valuable agricultural land and

 

13
other space-extensive uses. (v) it has retained accessible land in pleasant surroundings
nearer to people in inner cities than would otherwise have been the case. (vi) it can be
used to assist urban regeneration.

Korean housing market has been known for its unique tenure system. Most
housing market studies were concentrated on demand side analysis and detennination of
tenure system. Follain et a1. (1980, 1982), Lim et al. (1980, 1984), and Renaud (1988,
1989) reported the situations of Korean housing markets and explained the Chonsei
system as an efficient response to the financial depression. Also Kim (1990) argued that
the inadequate mortgage financing system in Korea leads to the market inefficiency. Due
to long standing policies of exports it is widely known that the housing sector has been
equipped with less than Optimal level of capital. Kim and Suh (1991) tried to answer
whether the investment in the housing sector has been suboptimal. They found the
allocation of capital between the housing and non-housing sector is not optimal by using
1970-1986 data.

Most studies about the Greenbelt restriction in Seoul concentrate on discussing
the welfare loss because it has a pervasive effect on residential land and housing supply --
it physically restricts the residential land development and prevents constructing a new
structure inside the Greenbelt area. However, if the Greenbelt has an amenity effect on
the adjacent areas, the welfare loss could be exaggerated because the amenity effect
improves the environmental surroundings in the adjacent areas and this improvement will
be capitalized into the land value and housing price.

Amenity effects will be capitalized in the long run because people tend to put
more weight on environmental quality. In a typical urbanization process, population is
concentrated in the central area at earlier stages and dispersed outward and concentrated
in suburbs later. Population concentration will induce more demand for land and housing

so that it increases the land and housing prices. Population dispersion can be accelerated

 

14
by the amenity effect of the Greenbelt because people will demand a better environment
after enjoying higher incomes. Therefore, the Greenbelt increases the land and housing
prices by both the physical restriction and the amenity effect but not by the physical
restriction alone as assumed in most studies.

Suh (1987) theoretically showed that the Greenbelt induces population
concentration around the Greenbelt if the land demand is close to a linear. In the long run
more people live near the Greenbelt, and total population in urban area increases. This is
quite opposite effect of the Greenbelt because it is designed to check the population
growth. Suh concluded that the Greenbelt is not proper to check the urban population in
the long run if the demand for land is almost linear. Kim (1987) considered the social
gain from releasing the Greenbelt regulation based on the proposition that the physical
restriction affects the housing and land prices in Seoul, but he excluded the possibility of
the amenity effect. The physical restriction and amenity effect work in an opposite
direction on the welfare consequences of the Greenbelt. Choi (1993) estimated the land
rent gradient in the metropolitan Seoul area by using simple semi-log functional form.
He concluded that the simple descriptive model of rent gradient estimation is inferior to
the behavioral model with time analysis.

Most amenity studies have dealt with crime, air pollution, school expenditure,
neighborhood zoning and for the US, non-white population. For air pollution, specific
variables are used for estimating the marginal benefit from the amenity effect. Harrison
and Rubinfeld (1978) used NO2 (nitrogen dioxides) and particles. A new concept of
amenity value measurement was developed by Smith (1978), an amenity premium.

There were several papers in which general variables were used for amenity
estimation. Correll et a1. (1978) and Nelson (1988) used general variables to estimate the
amenity effect. The former analyzed the Greenbelt effect on residential property in

Boulder, Colorado. They found that the property value decreases by $4.2 per foot for

 

15
every foot one moves away from the Greenbelt. Nelson analyzed the amenity influence
on land value in Portland, Oregon. By using 1983-1986 data, he found there were 4%
($7300 per acre) decreases in land value when one moves away from the Growth
boundary by 100 feet.
We will use similar general variables for estimating the amenity effect of the
Greenbelt in Seoul. When one moves away from the Greenbelt, the land rent will

decrease because one enjoys less amenity.

 

Chapter II

ll. Theoretical Analysis of the Effect of the Greenbelt

We look at the basic urban economic theory and adjust it to the case with the
Greenbelt to investigate the effects of Greenbelt. Thanks to the works of Alonso (1964),
Mills (1967) and Muth (1969), urban economics has a strong theoretical foundation.
While Alonso assumed individuals consume land directly, Mills and Muth used a
different presumption that land is only an intermediate input in the production of housing,
and an individual consumes housing services as the final consumption good instead of
components like land directly. Considering the differences in both traditions, we will use
Alonso's model to explain the relationship between land price (or rent) and the amenity-
related variables in the land market while we use the Mills-Muth model to analyze the

amenity effect in the housing market.

1. Land Market

l-l . Model without Amenity

Our simple model is based on a monocentric city. Every household chooses its
own residential location by maximizing the same utility function with the same income
level since all households in urban area are homogeneous. They consume x of composite
good and z of land. Also they commute to work to the central business district (CBD)

and pay tflc) of transportation cost. The price of a composite good is a numeraire and the

16

17
price of land, r(k), varies with the distance, k, from the CBD, that is located at the center
of urban area.

The household's problem of choosing a residential location can be expressed,

(1) Max U= U(x, z)

x, z, k

S.t. y = x + r(k)z + t(k).

From the first order condition, we can get the well-known results,

(2-1) U/U, = 1/r(k)

(2-2) rkz = - t‘,r

Condition (2-1) illustrates the marginal rate of substitution between x and z is equal to the
relative prices. Condition (2-2) shows that when a household moves farther to the CBD,
it pays less rent (rk<0) and more transportation cost (tk> 0). When a household moves
farther from the CBD, it faces a trade-off between the transportation cost and the rental
payment since it must satisfy the budget constraint. This is called as Muth's condition
that the marginal transportation cost is equal to the marginal land cost saving. Therefore
we have a downward SIOping equilibrium rent schedule with respect to the distance from
the CBD which is shown as R 1 and R2 in <Figure 3-(b)>. Two points need to be
discussed in detail; (i) the convexity of the rent schedule and (ii) the relationship between
the market rent schedule r(k) and the household bid rent schedule R ,(k).

The equilibrium rent schedule or bid rent curve need not always be convex as
depicted in the figure. Convexity depends on the shape of transportation cost firnction,

t(k). We may use the indirect utility function of

l8

(2') V(r. y-t(k))=max{ U(x, Z)|1=y-t(k)}

x,z
to find conditions for the convex rent schedule. Define the bid rent function of a

householdi as R, =R,(k,U") or more formally,

(2'? R,- = max { (Vi-t(k)-X)/Z | U(-)=U’}-

Z

Then we haveazR,(lc, Ui)/6k2 = -[tk,/Z,(k, U,)]+[t/Z,~(k, Ui)2]c[6Z,-(k, Ui)/dk] where Z,-(k, U,)
is defined as a bid—max lot size. This bid-max lot size is related to the bid rent, R, at
equilibrium point of U=U’. Tangency of utility and budget constraint at equilibrium
implies that -6x(z, U‘)/az = {y-t(k)-x(z, U‘)}/z. Solving this with respect to 2 gives us
bid-max lot size Z,, and -6x(z, U’)/dz = Ri(k, U‘). The bid rent is the maximum rent that
the household can pay for residing at distance k and enjoy a fixed utility U‘ while the bid-
max lot size is the land demand corresponding to the bid rent. From expenditure
minimization problem the bid-max lot size is equal to the Hicksian demand for land
zci(R,.(k, U‘), U'). Now we know that tk > 0, and az,(k, Ui)/6k > 0 since the following
holds;

62,.(k, U,)/ak = [azci(Ri(k, U‘), U‘)/aR,.] [aR,.(k, U‘)/ak]
= -[azC.-<R.(k, U‘), U’VaRillti/Zflc (1‘)] > 0.

Hence if tkk S 0, then dle-(k, Ui)/0k2 > 0. A linear or concave transportation cost function
means the marginal transportation cost is nonincreasing; it is commonly observed case
(see Fujita, 1989, p.22). The convexity of rent gradient needs a linear or concave

transportation cost function.

 

 

19

In <Figure 3-(a)> k*,. is the optimal location that gives the household 1' the
maximum utility U'. If the household i has a higher bid rent than the market rent, it can
increase its utility level by paying less for rent and purchasing more composite good x (in
case of U1). If the household i has a lower bid rent than the market rent, its utility level is
less than optimum due to more rent payment and less consumption of the composite good
x (in case of U2). Hence in equilibrium the household bid rent R,(k) must be equal to the
market rent r(k). At optimal location of k‘,, U’ = v(R,-(k‘,.),y-t(k‘,.)), r(k‘i)=R,.(k‘,.) and U’ 2
v(R,.(k),y-t(k)) V k¢k‘,. . Because the indirect utility function decreases in r and R,, and
increases in y-t(k), r(k)2R,.(k) V k. If the convexity of bid rent and market rent does not
hold, we have a comer solution rather than tangent solution.

The rent gradient in <Figure 3-(a)> can be interpreted as a market equilibrium rent
curve. Each point corresponds to the chosen equilibrium location of a household and this
household can't get the same utility at other locations since it enjoys the highest utility
level at equilibrium. For the optimal location of k‘, we find that r(k) = R,(k', U‘), r(k) >
R,(k, U‘) V k¢k*. For Muth's condition, we have rk. = Rk. = - tk./z at the optimal location.
If y, < y,, the net income of household 1, y,-t(k) is smaller than that of household 2, y;-
t(k) and R , and R2 intersect as shown in <Figure 3-(b)>. If land is a normal good, then the
following relation holds at an intersected location, k' where R ,=R2=R ’, that is,
Z,(k',U,)=z(R’,y,-t(k')) < z(RCyz-t(k'))=Z2(k’,U2) where z(.) is ordinary demand for land.

When we apply the envelope theorem to the definition of R,(k, U *), we can have,
(3) -6R ,(k', U ,)/0k = tk(k')/Z ,(k', U ,) > tk(k')/Z2(k', U) = -6R2(k', U2)/ak.
This illustrates a comparative static analysis of the effect of the income level on

household location. Higher income households can pay more for both transportation and

land, but lower income households cannot afford to pay more. Therefore, higher income

 

20

Figure 3. Rent Gradients
r(k)

r(0) ..
(a) Simple Rent Gradient

  
  

‘ x \ Ri(k,U*)
r(k)

  

 

 

 

 

 

Ta 2 ‘ ‘
no}, U2)
0
k; k*
r ( ’0
34k)

(b) Location Choices of Different Classes

  
   

H2 r( k)

 

 

3‘
’E
5‘

 

21
household has a flatter bid rent curve and locates farther from the CBD while the opposite

is applied for lower income household.

1-2. Model with Amenity

The Greenbelt will confine the expansion of an urban area and consequently the
residential land supply. Urban sprawl is easily seen in many large cities in the world
including Seoul. As shown in < Figure 4-(a)>, suppose that the Greenbelt restriction is
imposed with a width of g. A circular area with a width of g is not available for
residential development. Physical shortage of urban land raises rent at every location
except in the Greenbelt area that is assumed to receive an agricultural rent. Land
conversion outside the outer boundary of the Greenbelt deepens the discontinuous
development. Inside the inner boundary of the Greenbelt, more intensive development
prevails due to the economizing of land use. This will be a short run adjustment of the
rent gradient.

However, in the long run, urbanization proceeds with economic growth. With
population increases, disamenities such as congestion, bad air, severe noise will prevail
even when the urban area expands. Now the government sets a limiting boundary around
the urban area to prevent further urban expansion. If the limiting boundary is the
Greenbelt, then it may be attractive to some people who appreciate the amenity of better
environment. The Greenbelt is not developed as parks so that people cannot directly
enjoy them. Rather, the Greenbelt amenity can be identified as fresh air, quiet
surroundings, scenic view, or even direct enjoyment for excursion or strolling. As seen in
the simple model, high income classes prefer to live farther from the CBD while low
income classes prefer to live closer to the CBD. Since the Greenbelt is usually imposed

at the city boundary, most of the benefits from the amenity go to high income families

22

Figure 4. Rent Gradient with Greenbelt

‘

(a) Without Amenity Effect

 

 

 

 

 

 

K
r a '
0 ki-g k, kn
(b) With Amenity Effect

'9

J
\-

f .

I &_

 

fa

 

 

 

 

 

 

0 kA *"g kn ken

23

rather than being distributed equally between high and low income classes. If the urban
economy grows at a steady rate, rising income would make people put more weight on
amenity and it will not be a luxury good but a normal good. Demand for amenity
increases steadily in the long run and the rent gradient moves upward at the adjacent
area to the Greenbelt as shown in <Figure 4-(b)> because the amenity is capitalized into
the rental value of land in that area. Therefore, in the short run, the Greenbelt affects
the physical supply of urban land and raises rents equally at every location while it raises
the rent of the adjacent area relatively higher to the other area in the long run if the
amenity effect exists.

Benefits of the amenity effect from the Greenbelt are not distributed equally.
Without the amenity effect, landlords inside the inner boundary of the Greenbelt may
neither win nor lose since they receive higher rent and pay more development costs
because high density development induces higher average costs of building per area.
With the amenity effect, only landlords in the adjacent area of the Greenbelt may enjoy
more benefit. If a rental payment is defined as a monthly payment of tenants to landlords,
tenants neither lose nor win since their rental payments now increase by the amenity
benefit which they enjoy. Higher rent comes from higher land value and higher building
costs.

At locations too far from the Greenbelt the amenity effect is close to zero. Land
located far inside the inner boundary of the Greenbelt receives a usual urban rent. Land
far outside of the Greenbelt outer boundary receives a mere agricultural rent. At locations
with a positive amenity effect outside the Greenbelt outer boundary it may receive higher
rent than the agricultural rent as urban development begins. Considering the dynamic
nature of urban expansion, rent begins with the sum of the agricultural rent, the amenity
benefit and the land conversion costs to urban use. As the urban area expands in the long

run, the peripheral agricultural land is developed and converted into urban use. At

24
locations close to the Greenbelt outer boundary such a development cost is embodied into
the land rent. What has been ignored is landlords inside the Greenbelt, and they are
major losers under the Greenbelt restriction because they receive only agricultural rent
even though the amenity effect is higher than in any other areas.

An amenity may be defined as a location-specific good. This definition implies
that there is no usual market for the amenities. Consumption of amenities varies only
through relocation. The right to live in an area with more amenities must be purchased in
order to increase the consumption level of the amenities. Therefore, the property market
is linked with amenity consumption. In other words, locational amenities affect such
major determinants of household well-being as personal security and health, leisure time,
housing quality, quality education and the opportunity set faced by the household for
market consumption activities.

We can use a simple land market model and introduce some new variables. Let
I(k) be net income that is defined as y - t(k) and let A(k) be an amenity. The household

will choose a residential location by following,

(4-1) Max U(x, z, A(k)) s.t. I(k) = x + r(k)z.

x, z, k

And the first order condition gives,

(4-2) U/U. = r(k),
(4-3) U/U, = {r'(k)z—I'(k)}/A '(k).

The equation (4-3) implies that a household will be in equilibrium only when the
marginal value of the amenity equals the net increment of the two factors divided by the

marginal change in amenity. Rearranging the equilibrium condition (4-3), we get,

25

(4-4) r'(k) = (U A/Ux)A ’(k) + I'(k).

As a household moves away from the CBD, commuting cost increases and income net of
transportation cost decreases, I'<0. If the amenity is negligible at locations near the
CBD, and the marginal utility of the amenity is negligible, the rent gradient is negative as
in the simple model without amenity since the first term in the right hand side is
negligible. Let kA be a location which has a non-negligible amenity effect (see <Figure 4-
(b)>). r’(k) at kaA can be positive depending on the relative magnitude of two terms in
the right hand side of equilibrium condition. As one moves away from the CBD up to kA,
there is no amenity effect. If one resides at the locations of kaA, one can experience a
positive amenity effect. The rent gradient is positive as the marginal increase of amenity
is larger than the marginal decrease of net income. This could happen at the locations
near the Greenbelt.

It brings a question about the shape of the A(k) function. It might be a m-shape
but not symmetric. <Figure 4-(b)> illustrates a possible shape of A(k) function. After k A,
the slope of rent gradient is positive as one moves closer to the Greenbelt. We cannot say

the exact shape of A(k) because it is an empirical question.

2. Housing Market

Let us formalize the amenity effect in an urban system, following the Mills-Muth
tradition for analyzing the housing market. Our system is a typical urban economy that
contains the housing supply and demand in a closed city. A closed city model is based on
the assumption that population size is fixed so that there is neither migration nor
immigration -- in this sense, our model is a short run model. The basic model is

expressed from (5) to (12) below.

26
(5) 110(k) = B-(y-tk)"p(k)€A(k)"
(6) hD(k){dp(k)/dk} = -t
(7) h,(k) = C-L(k)°'K(k)"°'
(8) ap(k)hs(k)/L(k) = r(k)
(9) (1-a)p(k)hs(k)/K(k) =i
(10) n(k)hp(k) = 113(k)
(11) r(k) = (bk ,- 0 s¢s 2n

k‘

(12) l n(k)dk = M.

Housing demand is defined as (5). It depends on income (net-of-transportation-
cost income and the transportation cost is assumed to be linear in k), price and amenity.
This setting of housing demand can be treated as an effective demand for housing.

Housing demand (5) can be rewritten as follows,

(5-1) h“306): B'OHk)"p(k)E-J‘(A(k))-

The last term, f(A(k)) converts the usual housing demand to effective demand by
normalizing the housing demand to be 1. Equilibrium must satisfy Muth's condition of
(6). The supply function is represented as a Cobb-Douglas technology and depends on
two input factors of land and capital as shown in (7). We assume that there is only one
supplier in a circular area at each k km from the CBD and each supplier competes with
other neighboring suppliers. Each supplier must satisfy the zero profit and cost
minimization conditions that are explained by (8) and (9). r(k) and i are prices of land

and capital and are assumed to be given exogenously to the suppliers. Housing demand

   

27
of each household in the housing market determines equilibrium rent gradient, r(k) in the
land market.

In equilibrium, the total housing supply must be equal to the total housing
demand. In each circular area, we have n(k) households and (10) shows the housing
market clearing condition. In each circular area in a city, the amount of land for housing
is given as (11). Total population is fixed as explained above and shown in (12). We
assume that a household is composed of one man and the number of households is equal
to the population in a city.

From (8) and (9), we have the usual result of a constant returns technology as

follows,

(13) p(k)hs(k) = r(k)L(k) + iK(k).
Arranging (8) and putting the result into (9), we can get,

(14) K(k)/L(k) = (1-a)r(k)/ai.
In equilibrium suppliers employ two factors until the marginal product of each input
equals to its price. Equation (14) is the optimal ratio of two factors employed.
Substituting (14) and (7) into (13) and arranging the result, we have the following
equilibrium housing price expressed by factor prices,

(15) p(k) = D-r(k)°'i"°' where D = {C-(I-a)"°‘a°‘}".

Differentiating this with respect to k,

 

 

 

28

(16) dp(k)/dk = aD-{r(k)/i}°' "{dr(k)/dk}.

Substituting (15) into (5) and putting this result and (16) into (6), we have,

(17) Eo(y-tk)’lr(k)B-1A(k)"{dr(k)/dk} +1: 0

where E = orB-D€+’i("°‘)(8+’) and [3 = 0t(e+1).

It is another version of Muth's condition, that is, with given transportation cost and
housing price each household decides where to live by satisfying Muth's condition. The

solution of the differential equation (1 7) is given by,

(18) r(k) = [F+{tBE-(V-tk)""A(k)"p}/ {(1 -p)(y-tk)-t(1 -n)A(k)}]’43
r(0) = {F/(I-p)y}/43 ifA(0) =0.

where F is an integral constant.
This is an equilibrium rent schedule in the land market after satisfying the household's
locational choice problem and suppliers' cost minimization problem. From (8), (11) and
(15) we have,
(19) hs(k) = (¢ia-1/aD)-kr(k)1-a.

Substituting (5), (15) and (19) into (10), we can get

(20) n(k) = G(y-tk)-flA(k)-pkr(k)l-B

where G = ¢B-1[C(I_a)l-aa{(B-1)/(l+8)}]]+8.i(a-I)(l+€).

 

 

29
From the population size condition of (12), we can obtain the numerical solution of F by
using the values of t, E, or, (i), n for given value of k’. Finally, the solution of p(k), by

substituting (18) into (15), can be given as the following,

(21) p(k) = D-[F+{tBE-(y—tk)"“A(k)1'P}/
{(1 -p)(v-tk)-t(1-n)A(k)}lwmmi’“-

From (18) and (21), we see that the amenity effect, A(k), is embodied into the land rent of
r(k) and the housing price of p(k). Note that the slopes of land rent and housing price are
not guaranteed to be negative everywhere any more because they depend on the signs and
magnitudes of parameters such as e, 11 and p.

If the housing demand is unitary elastic with respect to its price, that is, a = -1, we

may have a simpler solution. The differential equation of (l 7) is changed to be

(1 7 ') orB(y-tk)TIA(k)P-[dr(k)/dk]/r(k) +1: 0.

The corresponding land rent function which is the solution of (17-1), can be expressed as,

(189 r00 = Y'eXPl{t(y-tk)""A(k)"p}/{aB(1-P)(V-tk)-t(1-n)A(k)}l-

We may have new n(k) = (¢/ozB)(y—tk)-‘1A(k)'9~kr(k) and the population size condition is

rewritten as,

(20) l [(i/aB)(y-tk)°"A(k)‘P-kr(k)]dk = M.

30

As shown in (18) and (18'), the land demand function is derived from the housing
demand (Muth-Mills' assumption). Strictly speaking, the simple land market model in
section 1 has a different demand for land from the above two demand functions because
the land demand in section 1 is assumed to be directly related with the consumers' utility
(Alonso's assumption). Usually a parcel of land is consumed jointly with housing. In the
line of empirical implications and consumers' behavior in the real world, it is plausible to
say that a consumer demands housing services and the land demand is deduced from the
housing services demand.

We have developed a simple model for explaining the amenity effect in the urban
area. In Alonso's framework the amenity is introduced as an argument in the utility
function. The slope of the rent gradient is not always negative when there is an amenity
effect. After passing the point of k , the rent gradient might increase with the distance
from the CBD. Whether it is negative or positive depends on the relative strength of the
marginal amenity benefit and the marginal transportation cost. We can say that the
amenity effect is capitalized into the land rent and prices, and if the amenity effect is
strong, the SIOpe of the rent gradient is positive near the Greenbelt. The Muth-Mill's
framework shows a similar result. If the demand for the housing services is defined by
three elements of the income, the housing price and the amenity, the amenity is shown to
be capitalized into the housing prices and land rent. Both are based on the assumption of
a single CBD. Whether following the Alonso's or Muth-Mill's line, the amenity effect of
the Greenbelt truly affects housing consumption behavior by raising the land rent and

housing prices up.

Chapter III

lll. Empirical Analysis of the Amenity Effect

We now estimate the equilibrium rent schedule in (18). It contains a full
information of the suppliers' and households' behavior as seen in the last chapter. It is
shown to depend on the distance from the CBD and other parameters. For all the
empirical estimation, we use distances from the central business district and the
Greenbelt. The distance from the Greenbelt is used for measuring the amenity effect.

Land value and land rent are closely related to each other. Land rent is the price
of the services yielded by land during a specific period while land value is the present
value or discounted value of the rent. Therefore if a parcel of land yields a rent of r per

year in perpetuity, the price of the land parcel, PV, can be expressed as following,

(22) PV = r/i.

Note that i is an appropriate interest rate used in discounting. When there are changes in
land rent, they affect land value or land price.
Traditionally, land rent is a function of the distance from the CBD. So the general

form of rent gradient fimction can be written as following,

(23) r =f(k).

As denoted before, k is the distance from the CBD. For estimating the rent gradient, the

negative exponential form or semi-log form is widely used and its basic form is,

31

 

32

(24) = r0 e'qk or [n(r) = ln(r0) - qk.

Spatial variations in land rents can be traced by the two statistics of r0 and q. r0 is the
land rent at the center, k=0 while q shows the gradient or slope coefficient. In empirical
work, the negative exponential form is popular since it is easy to interpret r0 and q. Since
we want to see the amenity effect of the Greenbelt, we include the distance from the
Greenbelt boundary. Let k, and k2 be the distances from the CBD and the Greenbelt

respectively. The above equation can be rewritten as,

(25) r = new? or mm = ln(ro) -(q1k1 + q2k2).

This will be the basic equation to be estimated in our analysis of amenity effect in land
market. Equation (24) and (25) are treated as a simple version of equilibrium rent
gradient (18). Net-of-transportation-cost income, y-tk is replaced by k, while k2 is used

for the amenity effect, A(k).

1. Data

The Korean government has a long tradition of collecting data on land values.
Since the land price has been soaring up, it has made a strenuous effort to monitor land
value. It is easy to get data but they are less than ideal; as mentioned earlier, several data
systems are used by different institutions. We will use data sets released from the Korea
Appraisal Board (KAB). They have been used for previous land value studies; Mills and
Song (1979) and Kim (1987).

The land value data of the KAB are appraised primarily for the finance and

accounting purposes in the private sector. Appraisals are done with the market

 

33

comparison method. There is no systematic evidence on how closely these appraised
land values approximate market values, but they are closer to sale prices than rental
values. The KAB seems to underestimate market values to provide a buffer for financial
institutions to offset the risk of loan default. It is generally believed that this buffer is
around 30%, and that the appraised values are about 70% of the market values on
average. Such an underestimation affects our welfare calculation because estimated
welfare benefit may be less than the true benefit. Our estimation might be biased upward
and exaggerate the true relationships if the market comparison method is based on
comparing each parcel according to the distance to the CBD and the Greenbelt.

Data are composed of each dong and category. A dong is the smallest unit for
legal and administrative purposes, and the categories contain 12 different values
according to the land use and quality. There are about 500 administrative dongs in Seoul,
and the average area of a dong is 1.2 kmz. We will use the residential use category in the
selected years of 1975, 1980, 1984 and 1989. In each year we have three classes of
quality, and they are residential-high quality, residential-medium quality and residential-
low quality. It is not clear what systematic criteria the KAB has used for quality

differences. Descriptive statistics of data are reported in <1" able 2>.

 

34

4 able 2> Descriptive Statistics of Data

 

 

 

 

 

 

 

 

 

Variables DISGB DISCBD V75RH V75RM V75RL
N 426 426 390 351 318
Minimum 0.000 0.010 10.000 7.000 5.000
Maximum 6.400 17.600 350.000 250.000 200.000
Mean 3.231 5.547 131.077 88.598 44,337
Variance 3.101 20.164 6349.351 3143 .618 1384.717
Median 3.700 4.200 110.000 70.000 30.000
Standard

Deviation 1.761 4.490 79.683 56.068 37.212
Variables V8ORH VSORM V8ORL V84RH V84RM
N 376 312 269 354 272
Minimum 70.000 30.000 15.000 60.000 30.000
Maximum 800.000 700.000 450.000 480.000 390.000
Mean 511.609 353.654 219.647 275.475 197.415
Variance 36263.471 17697.217 8249.035 7177.950 2985.498
Median 500.000 350.000 250.000 270.000 197.000
Standard

Deviation 190.430 133 .031 90. 824 84 , 723 54 .540
Variables V84RL V89RH V89RM V89RL
N 240 331 236 189
Minimum 11.000 242.000 151.000 151.000
Maximum 300.000 1050.000 756.000 605.000
Mean 148.300 546.810 430.441 333.217
Variance 2080.805 19123.900 8971.677 6521.022
Median 150.000 514.000 423.000 302.000
Standard

Deviation 45.616 138.289 94.719 80.753

Note ; DISGB -- distance from the Greenbelt (km)

DISCBD -- distance from the CBD (km)
RH -- residential high quality ('000 won)
RM -- residential medium quality (’000 won)
RL -- residential low quality (’000 won)
* Land value in 1975 and 1980 is per pyong and in 1984 and 1989 is per m2.

 

 

 

35

2. Empirical Model

We used a linear spline function because there is no prior information about the
functional form of rent gradient. Spline functions are a device for approximating the
shape of a curvilinear stochastic function without the necessity of pre-specifying the
mathematical form of the function. If the scatter of observations shows that a linear
estimation would be a poor fit, and it is uncertain that any polynomials would improve
the fit, then one can apply a series of linear regressions to each segment. Let the desired

relationship of a piecewise regression be as,

(26) r = [a,+b,(x-x0)]d, + [a2+b2(x-x,)]d2 + [a3+b3(x-x2)]d3 + u

where u is an error term and d,- = I if x,_, S x < x,- , = 0 otherwise.

Scatter of observations are approximated by three linear regressions over three intervals
which are divided by x , and x2. These intervals are called as knots. The regression needs

restrictions to avoid the discontinuity at x 1 and x2. Required restrictions are as follows,

(27) a2 = a, + b,(x,-x0)

a3 = “2 + b2(x2-x,).

Inserting (27) into (26), the piecewise linear regression of (26) can be rewritten as

follows,

(28) r = a, + b,[(x-x0)d,+(x,-x0)d2+(x2—x,)d3]
+ b2[(x-x,)d2+(x2-x,)d3] + b3[(x-x2)d3] + u.

 

36
The above linear spline is our basic funtion for estimating the rent gradient. Piecewise
linear approximation of (26) is converted into a multiple regression of (28).

The linear spline function is not free from shortcomings. The estimated function
is continuous at knots because some restrictions are imposed on the functional form. But
its derivatives are not continuous. This might be a serious disadvantage in many
economic applications where the result would be expressed as elasticities and marginals.
Also the knots which give intervals in estimation are arbitrarily chosen. These
disadvantages are overcome by a cubic spline fiinction, but it is not easy to interpret the
estimated results because it is cubic. The estimated results of linear spline function is
easily interpreted. Furthermore, it may give a robust estimation.

We use the distances from the CBD and the Greenbelt as independent variables,
and they are denoted as x and y respectively in the estimation. Each estimation needs
transformed composite independent variables which are found in bracket of (28). These
transformed composite variables are denoted by subscript i, and i is a knot to decide the

intervals in each estimation.

< Table 3 >
Definition of Variables used in Spline Estimation

 

 

 

 

Variables used in Spline Description of Variables Corresponding
Estimation coefficients
x distance from the CBD [5,
x5 transformed x at x=5 [32
x10 transformed x at x=10 [33
y distance from the Greenbelt [34
y 1 transformed y at y=1 [35
y2 transformed y at y=2 B6
y3_5 transformed y at y=3.5 [37

 

 

 

37

3. Rent Gradient Estimation

If we can identify a proper interest rate, we can calculate the land rent by using the
equation (22) -- P V = r/i. As noted above, the formal financial market has worked for
the export or export-related sectors, and for the land and housing market the informal
financial market had to substitute for a repressed and controlled formal financial market.
Many studies on the Korean housing market used the curb market rate for a proper
interest rate or discount rate since it is widely agreed that it represents the opportunity
cost of capital in the housing market.

We use the corporate bond yield rate, however, as a proper interest rate in the land
market. Even though land is consumed jointly with a housing unit, it is different from
housing. It is not only one of several inputs to housing production but also an investment
good: Land is one of the most popular investment goods such as equity and corporate
bonds in Korea. In this sense, the corporate bond yield rate is proper as an opportunity
cost of capital in the land market. The nominal corporate bond yield rate is 20.1%,
30.1%, 14.1% and 15.2% in 1975, 1980, 1984 and 1989. Actually these numbers are not
much different from the curb market rates in the corresponding years. Also, we implicitly
assume that the land value is the present value of land rent over infinite time period.

Linear spline estimation is done with different settings of knots. First, we use 5,
10 km knots for the distance from the CBD and 1, 2, 3.5 km from the Greenbelt.
Estimated results are reported in <1“ able 4-(a), (b), (c) >.

Residential high quality shows the highest fit among three of the estimated
categories, and R2 decreases for all residential qualities. For residential high quality it
decreases from 0.843 in 1975 to 0.116 in 1989. Decreasing R2 over the estimated period
might be due to (i) emergence of the secondary urban centers in Seoul, (ii) enhanced

public transport system and increasing car ownership, or (iii) techniques of collecting and

 

38
generating data have improved, and results of R2 over the estimated period show this
improvement of random response of the data.

Estimated coefficients show that the rent gradient has been flatter over the
estimated period except for the residential low quality. For residential high quality,
coefficients of the distance from the CBD change from -0.24, 0.166, -0.116 in 1975 to -
0.051, 0.066, -0.041 in 1989. Those of the distance from the Greenbelt show a similar
trend over the estimated period to the distance from the CBD. Most coefficients of the
CBD distance variables are significant while those of the Greenbelt distance variables are
not significant. It is due to land price hikes and severe speculation in Seoul area.
Dramatic land price increases happened roughly once in 10 years and were higher than
inflation rate.

Estimated slope of the rent gradient of residential high quality increases near the
Greenbelt boundary and decreases at location of 1 or 2 km from the Greenbelt; in 1975
and 1989 the Greenbelt distance variables are shown in <1“ able 4> to be -0.368 and -
0.213 respectively while -0.239 and -0.092 in 1980 and 1984. This result says that the
maximum rent location moved from 1 km to 2 km in 1980 and returned to 1 km in 1989.
In case of residential low quality the maximum rent location was 2 km during 1975-1984
and 1 km in 1989. It was 1 km in 1975, 1980, 2 km in 1984 and 1 km in 1989 for

residential medium quality.

39

< Table 4 > Linear Spline Estimation I of Rent Gradient ; using all knots

(a) Residential High Quality

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dependent Natural Log of High Quality Land Rent
Variable
1975 1980 1984 1989
constant 3934* 5334* 4.492’“ 4.975“
x —0.24* -0.116* -0.110* -0.051*
(47.092) (-923) (-8.69) (.3.91)
x5 0.166* 0.078* 0.127* 0.066*
(6.714) (3.683) (6.055) (3.202)
x10 -O.116* -0.075* 0091* -0.041**
(-4.642) (-3.671) (-4490) (-212)
y 0318* 0.117 0.051 0.175“
(3 .259) (1.423) (0.639) (2.257)
y] -0.368** 0.090 0.038 -0.213
(-2131) (0.622) (0.269) (-1.588)
yz 0.033 -0.239* -0.092 0.043
(0.301) (-2.609) (-1037) (0.513)
y3. 5 -0.016 -0.030** -0.033** -0.008
(-0.936) (-2.033) (-2.343) (-O.56)
adjusted R2 0.843 0.713 0.435 0.116
N 390 376 354 331
Note ; 1) ()is t-value.
2) * is significant at 99%, and ** is significant at 95%.
0 Hypothesis Test Results ; F-statistics
Hypothesis 1975 1980 1984 1989
E=B3=0 22.57a 7.931a 18.413a 5.132a
85:86:11,:0 6.967al 17.746a 7.548a 2.306
BZ=B3=B5=B6=137=0 15.463a 16.818a 13.055a 3.881a

 

 

 

 

 

 

 

Note : a denotes that a null hypothesis is rejected at 99%, while b indicates that a null
hypothesis is rejected at 95%.

 

40

(b) Residential Medium Quality

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dependent Natural Log of Medium Quality Land Rent
Variable
1975 1980 1984 1989
constant 3.583“ 4.827 * 3.911* 4.486*
x -0.230* -0.097* -0.057* -0.002
(13.455) (4.616) (2.959) (-0.109)
x5 0.140* 0.069** 0085* 0.030
(4.773) (2.117) (3.046) (1.223)
x10 -0.105* -0.101* -0.119* -0.043**
(3.447) (3.518) (5.182) (2.141)
y 0.174 0.214 0.042 0.136
(1.456) (1.845) (0.457) (1.525)
y 1 -0.115 -0.038 0.179 -0. 124
(0.563) (-0.188) (1.101) (0.824)
yz -0.078 -0175 -0.258** 0.012
(0.613) (1.353) (2.444) (0.128)
y3.5 -0.021 -0.033 0.002 -0.007
(1.035) (1.518) (0.13) (0.491)
adjusted R2 0.803 0.595 0.345 0.032
N 351 312 272 236
Note ; 1) () is t-value.
2) * is significant at 99%, and ** is significant at 95%.
o Hypothesis Test Results ; F -statistics
Hypothesis 1975 1980 1984 1989
BZ=B3=0 11.398a 6.266a 13.506a 2.297
B1=B6=B7=0 4.131a 8.482a 5.164al 1.113
BZ=B3=BS=B6=B7=0 8.135:11 10.6923 11.3738 2.116

 

 

 

 

 

 

Note : a denotes that a null hypothesis is rejected at 99%, while b indicates that a null

hypothesis is rejected at 95%.

 

41

(0) Residential Low Quality

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dependent Natural Log of Low Quality Land Rent
Variable
1975 1980 1984 1989
constant 3096* 4248* 3.727* 4.055*
x -0.259* -0.055 -0.089* -0.024
(10.834) (1.855) (3.757) (1.356)
x5 0.149* -0.014 0.114* 0.077*
(3.885) (0.297) (3.058) (2.889)
x10 -0.109* -0.066 -0.148* -0.065*
(3.129) (1.535) (3.989) (2.593)
y -0.010 0.182 0.005 0294*
(0.069) (1.092) (0.034) (2.806)
y 1 0.105 0.044 0.278 -0.227
(0.436) (0.155) (1.13) (1.329)
yZ -0.005 -0.233 -0.331** -0.015
(0.032) (1.295) (2.154) (0.147)
y 3. 5 -0.048 -0.034 0.003 -0.029
(1.783) (1.121) (0.118) (1.761)
adjusted R2 0.811 0.510 0.291 0.163
N 318 269 240 189
Note ; l) ()is t-value.
2) * is significant at 99%, and ** is significant at 95%.
o Hypothesis Test Results ; F-statistics
Hypothesis 1975 1980 1984 1989
Bz=l33=0 7.7188 2.791 8.1738 4.6848
B5=B6=137=0 1.602 4.9338 3.451b 6.858
BZ=B3=B5=B6=137=0 4.2298 6.3618 6.8648 6.9618

 

 

 

 

 

 

 

Note : a denotes that a null hypothesis is rejected at 99%, while b indicates that a null
hypothesis is rejected at 95%.

 

42

In each table we provide results of hypothesis test about the spline specification.
All results say that the spline specification is proper for estimating the rent gradient.
These are reported in <T able 4> and 4‘ able 5>. In most cases the null hypothesis is
rejected at 99%.

Leaving the set of the CBD knots, for rent gradient 11 in <1" able 5> we change the
set of the Greenbelt knot to 1, 3.5 km in 1975 and 2, 3.5 km in 1980-1989. These
estimated results are reported in <T able 5-(a),(b),(c) >. More of the Greenbelt distance
variables are shown to be significant than those in previous estimation. R2 shows a
slight improvement. R2 decreases over the estimated period; it falls from 0.844 in 1975
to 0.112 in 1989 for the residential high quality (same trend is found in other two quality
categories).

Most estimated coefficients of the CBD and Greenbelt distance variables show
patterns similar to those in the previous estimation. They have fallen over the estimated
period. Coefficients of the CBD distance variables decrease fiom -0.24, 0.166, -0.116 in
1975 to -0.051, 0.069, -0.045 in 1989. Those of the Greenbelt distance variables fall; y
and y3.5 decrease from 0.301, —0.014 in 1975 to 0.061, -0.002 in 1989, and y2 decreases
from -0.l91 in 1980 to -0.069 in 1989. The slope of rent gradient has been flat for the
same reasons mentioned earlier. The rent gradient decreases around 2 km from the
Greenbelt in 1975 and between 3 and 4 km from the Greenbelt in 1980-1989. Because
the distance from the Greenbelt is assumed to measure the amenity effect, the estimated
coefficients of the Greenbelt distance variables indirectly illustrate the existence of the

amenity effect.

43

< Table 5 > Linear Spline Estimation II of Rent Gradient ; dropping some knots

(a) Residential High Quality

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dependent Natural Log of High Quality Land Rent
Variable
1975 1980 1984 1989
constant 3.937 * 5320* 4.479* 5.011*
x -0.240* -0. 166* -0.110* -0.051*
(17.162) (9.232) (8.705) (3.899)
x5 0.166* 0.077* 0.126* 0069*
(6.752) (3.647) (6.058) (3.303)
x10 -0.116* -0.074* -0.090* -0.045**
(4.646) (3.622) (4.494) (2.322)
y 0301* 0.164* 0.071** 0.061 **
(3.820) (5.134) (2.300) (2.037)
y 1 -0.324*
(3.489)
y2 -0.191* -0.072 -0.069
(3.891) (1.511) (1.504)
y 3_ 5 -0.014 -0.032** -0.034** -0.002
(0.921) (2.258) (2.491) (0.165)
adjusted R2 0.844 0.714 0.436 0.112
N 390 376 354 331
Note ; 1) ()is t-value.
2) * is significant at 99%, and ** is significant at 95%.
- Hypothesis Test Results ; F-statistics
Hypothesis 1975 1980 1984 1989
E=B3=0 22.838a 7.759a 18.436a 5.46a
85:13,:0 (1975) or
E=B7=0 (1980-1989) 10.433 26.473 11.3152‘ 2.188
BZ=B3=B5=B7=0 (1975) or
BZ=B3=BEB7=0 (1980-1989) 19.3523 20.9613 16.3443 4.2a

 

 

 

 

 

 

 

Note : 3 denotes that a null hypothesis is rejected at 99%, while b indicates that a null

hypothesis is rejected at 95%.

 

 

 

44

(b) Residential Medium Quality

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dependent Natural Log of Medium Quality Land Rent
Variable
1975 1980 1984 1989
constant 3574* 4833* 3882* 4513*
x -0.229* -0.097* -0.057* -0.002
(13.453) (4.623) (2.951 ) (0.1 12)
X5 0139* 0.070** 0.083* 0.030
(4.758) (2.137) (3.003) (1.258)
x10 -0.106* -0.102* -0.117* -0.043**
(3.481) (3.592) (5.117) (2.16)
y 0.218" 0.194* 0.135* 0.067"
(2.249) (4.285) (3.819) (2.165)
y 1 -0.220**
(1.956)
yz -0.195* -0.l60* -0.052
(2.809) (2.842) (1.055)
y3'5 -0.028 —0.032 -0.003 -0.004
(1.633) (1.521) (0.156) (0.297)
adjusted R2 0.803 0.596 0.345 0.034
N 351 312 272 236
Note ; 1) ()is t-value.
2) * is significant at 99%, and ** is significant at 95%.
- Hypothesis Test Results ; F-statistics
Hypothesis 1975 1980 1984 1989
BZ=BL=0 11.334a 6.546a 13.166a 2.336
B5=137=0 (1975) or
B6=By=0 (1980-1989) 6.028 12.7468 7.1348 1.331
BZ=B3=B5=B7=0 (1975) or
B2=1§3=B6=By=0 (1980-1989) 10.0938 13.3998 13.9028 2.4798

 

 

 

 

 

 

 

Note : 3 denotes that a null hypothesis is rejected at 99%, while b indicates that a null

hypothesis is rejected at 95%.

 

 

(c) Residential Low Quality

45

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dependent Natural Log of Low Quality Land Rent
Variable
1975 1980 1984 1989
constant 3095* 4.239* 3.681* 4.116*
x -0.259* -0.055 -0.089* -0.025
(10.852) (1.854) (3.744) (1.361)
x5 0.149* -0.015 0.110* 0.078*
(3.892) (0.321) (2.963) (2.915)
x10 -0.109* -0.064 -O.l43* -0.065**
(3.138) (1.541) (3.876) (2.57)
y -0.007 0.206* 0.155* 0.165*
(0.062) (3.187) (2.765) (4.254)
y , 0.098
(0.75)
y2 -0.210** -0.187** -0.127**
(2.066) (2.183) (2.13)
y3_5 -0.048** -0.036 -0004 -0023
(2.181) (1.192) (0.175) (1.45)
adjusted R2 0.812 0.512 0.290 0.160
N 318 269 240 189
Note ; 1) () is t-value.
2) * is significant at 99%, and ** is significant at 95%.
o Hypothesis Test Results ; F-statistics
Hypothesis 1975 1980 1984 1989
B =B3=0 7.473 2.815 7.7193 4.7088
B5=B7=0 (1975) or
B =87=o (1980-1989) 2.41 7.4158 4.5331) 9.3538
BZ=B3=B5=B7=0 (1975) or
B =B3=B6=B7=0(1980-1989) 5.303a 7.975a 8.251a 8.225a

 

 

 

 

 

 

 

Note : a denotes that a null hypothesis is rejected at 99%, while b indicates that a null
hypothesis is rejected at 95%.

 

 

 

46

Besides the amenity effect of the Greenbelt, increasing car ownership makes
possible for people to choose to live away from the CBD. Even though their marginal
transportation cost increases as one moves away from the CBD, the total transportation
cost does not increase dramatically due to decrease in travel time to work place. Also the
public transport system such as subways makes commuting more convenient. These
provide people for an opportunity to move away from the CBD without incurring much
cost. As seen in <Figure 2-(b)>, population density in 1988 shows that the area between
13 km and 14 km from the CBD has the highest density. In the following section we
estimate the population gradient.

We plot the estimated value of imputed rent over the distance from the CBD. It is
shown in <Figure 2-(d)>. The Greenbelt starts at 10 - 18 km from the CBD. The
estimated imputed rent in all years shows that it decreases as one moves away from the
Greenbelt. This result partly comes from the knots we have chosen for linear spline

estimation, and note that the knots chosen gave the best results.

 

 

47

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48

4. Population Gradient

Population concentrates and disperses itself in urban areas during the process of
urbanization. In urban economics, demographic studies have been carried out along with
land and housing studies since the conditions in the land and housing markets are closely
related to those demographic changes. Here, we apply the semi-log model to estimate the
population gradient in Seoul. We use the population census data in 1975, 1980, 1985 and
1990. In each year, the population data are available in 225 dongs.

Estimated results are reported in <T able 6>. Overall fit is far from being
significant, but coefficients are found to support the previous findings in rent gradient
estimation. We carry out two different estimations; (i) includes the distances from both
the CBD and the Greenbelt. (ii) includes only the distance from the Greenbelt.

Even though the overall fit is improved in the estimated period, R2 is very low.
Considering that it is a cross-sectional estimation, and that our prior concern is on the rent
gradient, it is useful to explain the amenity effect and rent gradient. In case of (i), the
distance from the CBD is more proper than the distance from the Greenbelt in explaining
the population gradient. In case of (ii) the distance from the Greenbelt shows a poor fit
but its coefficients are rather noticeable. It shows that the further from the Greenbelt, the
less dense is the population. This might be expected partially because the amenity is not
a critical factor for industrial locations. Industrial uses don't compete to locate close to
the Greenbelt but rather they prefer to locate close to the CBD or other secondary centers.
We have to be careful in conclusion because the residential area also decreases with the
distance from the Greenbelt and the population density would give more precise insight

for the population concentration.

 

 

49

< Table 6 > Population Gradient Estimation

 

Dependent Variable ; Natural Log of Population

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Constant x y adjusted R2 N

(i) 1975 9742* 0.036 0.037 0.01 198
(1.867) (0.825)

1980 9544* 0.075* 0.040 0.092 219
(4.006) (0.919)

1985 9497* 0.099* 0.024 0.186 223
(5.402) (0.569)

1990 9283* 0134* 0.024 0.286 224
(6.987) (0.543)

(ii) 1975 10.172* -0.024 0.000 198
(0.759)

1980 10.443* -0.085* 0.029 219
g (2.740)

1985 10.704* -0. 144* 0.082 223
(4.556)

1990 10.897* -0.200* 0.132 224
(5.901)

 

 

Note ; 1) () is t—value.
2) * is significant at 99% and ** is significant at 95%.

Population increases along with the distance from the CBD in estimation (i).
Degree of increasing population rises in the estimated period; from 0.036 in 1975 to
0.134 in 1989. Also population is found to increase with the distance from the Greenbelt,
but its coefficients have been flat in the same peirod; 0.037 in 1975 to 0.024 in 1989. It
means that p0pulation grows faster near the Greenbelt. Next, we drop the distance from
the CBD. In estimation (ii) coefficients of the distance from the Greenbelt are found to

increase in absolute terms; its absolute value increases from 0.024 in 1975 to 0.200 in

 

 

 

50
1989. It indicates that the slope of the population gradient near the Greenbelt is steeper in
the estimated period.

We can build a possible scenario to explain changes in population and rent
gradient in the estimated period. Economic growth puts more in everyone's pocket.
Income increases enough to pay off increasing commuting cost as one lives away from
the CBD, and/or people put more weight on the amenity since they prefer to live a better
life in a descent environment. More people live near the Greenbelt than before, and the
population density increases in this area. Increasing demand for land pushes land prices
and rents up. Along with the amenity effect, the population pressure works in the same
direction on land rent. The coincidence of the estimated results of population and land

rent gradients might be closely related to the amenity effect of the Greenbelt.

Chapter IV

 

IV. Welfare Analysis of Releasing the Greenbelt Restriction

If there exists an amenity effect of the Greenbelt, then releasing the Greenbelt
restriction does not necessarily increase everyone's welfare because some residents are
worse off than before the land release due to lost amenity. We will calculate the social
gain from the land release. If the lost amenity is higher than the gain from low rent at the
one extreme, the social gain might be negative. We find that the amenity effect exists in
the land market. Without considering the amenity effect, the social gain from the land

release might be exaggerated.
1. Releasing Land from the Greenbelt

If a part or all of the total land in the Greenbelt is released from the restriction,
land rent and housing prices will fall. Suppose that the government releases a 8 km wide
of land from the Greenbelt inner boundary. Now the city expands from k‘ to k’+5 while
it must accomodate the same size of population, M as before. The total supply of urban

land increases by
k‘+5

(29) 1 (0k) dk = ¢8(2k*+8)/2 where 0 s03 Zn.

The land supply increases by 4) in each circular area at k km from the CBD where 4)
denotes the proportion of residential area in the total circular land area. Therefore the

total land available for residential uses in each circular area is 0k. The land rent will shift

51

 

52
everywhere since the intercept alone is affected while the other parameters are determined
by preferences and technology (see <Figure 5-(a)>).

In a traditional theory of firms, a reduction of an input price lowers marginal cost
and output increases by using the relatively cheaper input more intensively. In our
model, total land supply is fixed in each location and the housing producer in each
location k with k < k" will combine the same amount of land with a smaller amount of
capital to produce less housing because the price of capital is expensive relatively to the
price of land. The number of households, M, then adjusts spending to equate the total
demand with the reduced supply in these locations and additional output of housing
comes from the production on the released land with k‘ < k < k”+6.

The social gain, W, from the land release is composed of two parts. The first part
is the value of the released land since the released land receives the urban land rent. If we

assume that the released land has received zero land rent before the land release, we have,

k*+5
(30) W,=I okrN(k)dk
kt

where rN(k) is a new land rent schedule after the land release, rN(k) =
[F '+{t BEG-tk)’ ’“A(k)’ 'p}/ {(1 -p)(V-tk)-t(1 -71)A(k)}l”B (F ' is a new
intercept) and r(k) > rN(k).

The second part is the money value of the utility gain from the housing price reduction
and utility gain or loss from the amenity changes. This can be calculated by using the

equivalent variation of each household at each location k. We have,

k.

(31) W2 =1 n(k)0)(k)EV(k) dk

where E V(k) is an equivalent variation at k.

53

Figure 5. Change of Rent Gradient
- 8 km width of land is released from the Greenbelt -

(a) Rent Gradient before and after the Land Release

r(k)

611(k)

 

 

 

 

0 k* k*+8

 

rent

bl

 

[CASE 1]

 

54

(b) Welfare Changes due to Lost Amenity

00

m

 

 

 

 

 

 

 

re
0 k1 k2 * \\\ k*+g distance
[(+5 from the CBD
rent 22332555233
[CASE 2] 5' > 5 Greenbelt Area before Land Release
8! nbelt Area alter Land Release
3'
Released Area

 

 

 

 

fa

 

 

 

 

 

 

 

 

k1 k2 k3 k' k*+8' k‘+g distance
from the CBD

 

 

 

55

(c) Circular Area of Lost Amenity Benefit

Greenbelt Area
/

/ Amenity Benefit

D Lost Amenity
kt

k*+5

 

k"+g

   

 

A : total circular area of bcji
D : total circular area of jdef

 

 

 

(d) Amenity Effect Benefit

[CASE 1] [CASE 2]

 

 

 

/
1 D \“~\
1 < °'
1 \,

k1 k2 k” k*+8 k1 k3 k' ”+5.

 

 

 

/

 

 

56

Thus the social gain from the land release, considering the amentiy effect, is W =
W1+W2. Utility gain or loss from the amenity changes needs more explanation.
Suppose that the amenity effect is good to the location of u km from the Greenbelt inner
boundary. If u _>. 8, the households at the location of (k‘-p.) S k S (k'-u+5) may not enjoy
the same amount of amenity from the Greenbelt any more because they are located too far
away from the Greenbelt. (See <Figure 6-(a)> where we denote the amenity area width as
u). If (K 5, the households at the location of (k'-u) S k s k" may lose the amenity
advantage. These can be either positive or negative depending on how far the amenity
effect of the Greenbelt is applied and how wide the land is released. Whether it can be
negative or not, it is capitalized into the land rent and housing price through (18) and
(19).

Let e(p,A, u) be an expenditure function for a housing price and amenity with a
given level of utility, u and v(p,I,A) be the corresponding indirect utility function (I = y-

tk). By Roy's identity, we can have,

(32) -(av/ap)/(av/81) = hD(p,I,A) = 8.1818218 .

Note that the amenity effect is now capitalized into the housing price. The corresponding

indirect utility function and the expenditure function are,

(33) V*(p,]) = 11* = _B.(1+8)-lpl+eAp+(1_n)-1II-n
(34) e(1484*) = 1 = [(I-n){u*+B-(1+g)-Ip1+eAp}]I/(1-ru

where u* = v*(p,l).

Therefore, if u** = v**(pN,I) represents the new utility level under the land release, the

equivalent variation for a household at k will be given as following,

 

 

57
(35) E V(k) = e(P(k),V**) - e(P(k),V*) = e(P(k),V**) - 1
=[(1-n)(1+8)”B-A"{p(k)’+8-p~(k)’+8} +11-81W-8 - I
=[<1-n)(1+e)-’{B-A8p(k)'+8-B-A8pN(k>1+9 +I'81W-8 - I
=[(1-n)(1+8)" {p(k)-B-A"p(k)8-pN(k)-B-APPM/08} +11 “'1]”("'V- I
=[(1-11)(1+8)"1"‘ {17(k)hD(p’1)'pN(k)hD(pN’1)} +1’ '“I’ /(1 "V - 1 -

where
Pn(k) = DIF'+{tBE-1""A(k)’-P}/{(1-p)I-t(1-n)A(k)}]{1/(1+8)}. iI-a
(F ' is a new intercept, and I = y-tk) and p(k) > p Mk)-

Now once we choose 00(k), we can calculate the social gain/loss. If all the
households have identical preference and income, (n(k) is one for every household and the
aggregate EV will be ME V, which is W2. Also if all the land before the land release is
owned by the urban residents, the consumers' gain from the lower housing price is
canceled out by their loss from the rental income reduction. Therefore, W2 is equal to
foregone amenity benefit of the residents who live in the amenity area before the land
release.

This is illustrated in <Figure 5-(b),(c),(d)>. For convenience of analysis the rent
gradient is drawn as linear in <Figure 5-(b)>. After the land release, the rent gradient will
shift down everywhere, but the amenity effect area shifts outward because the Greenbelt
boundary moves out from k" to k‘+5. W 2 is equal to the shaded area of A in the figure.
This shaded area is missing in cost/benefit analyses of releasing the Greenbelt in the
previous studies. This foregone amenity is generated partly because the Greenbelt is
farther by 5 km than before and partly because the Greenbelt is thinner by 5 km than
before. We can say that the amenity effect is smaller when the Greenbelt is thinner.

Aamh, Acef, Anpu and Aqst denote the amenity effect areas near the Greenbelt. If
5 km wide of the Greenbelt is released from the restriction, then the rent gradient will

shift down everywhere, and its intercept moves from a’ to b'. Because the Greenbelt

 

 

 

58
boundary is farther by 5 km from the CBD after the land release, the amenity area now
moves from klk’ to k2(k’+5), and the amenity effect area of Aamh is the same as Acef
after the land release. At locations between k’ and (k"+5) land rent rises from the
agricultural rent, ra to the urban land rent plus the amenity effect, jk’ or f(k*+5). Benefits
from releasing land at locations between k’ and (k*+5) will be the area of dk*(k’+5)e plus
the area of jdef, and is defined as W1.

W2 is equal to the lost amenity of the area A because saving from lower rent
payment is cancelled out by lost income from lower rent payment in the urban area. Net
social gain of releasing land from the Greenbelt would be smaller with the amenity effect
than without the amenity effect by A. When we look at [case 1] in <Figure 5-(d)>, we
know that the total amenity area is same before and after the land release, that is A = D.
Therefore for society as a whole, A is lost but D is gained for amenity, and there might be
no changes in the total amenity. But looked in at an other way, this might not be ture.
Even though Aamh = Acef, the amenity benefit differes before and after the land release.
The circular area of Aamh is smaller than that of Acef since the farther from the CBD, the
larger the diameter is. Aamh = Acef may lead to conclusion of "area of bcji = area of
jdef", but it is not correct when we look at these from three dimensional view in <Figure
5-(c)>. Even though we have Aamh = Acef, A < D holds, and the amenity benefit is
larger with the land release.

We implicitly assume that the amenity effect does not depend on the thickness of
the Greenbelt area. This is illustrated in [case 2] of <Figure 5—(b),(d)>, and 5’ > 5.
Therefore, we have a thinner Greenbelt area in [case 2] than in [case 1]. If the amenity
benefit area is affected by the width of the Greenbelt, then the amenity benefit declines
after the land release because the width of the Greenbelt shrinks by 5’ km. Now Aamh is
larger than Ac'e'f, and Anpu is larger than Aqst. The lost amenity benefit, A ', will be

larger than A in the previous [case 1] of Aamh = Acef, and the net social gain of releasing

 

59

land shrinks further if Aamh > Ac'e'f leads to A > D in <Figure 5-(c)>. It illustrates a
possibility of shrinkage of the amenity benefit due to interactions of the thickness of the
Greenbelt and the three dimensional effect. If the thinner the Greenbelt is, the less the
amenity effect is, then the zero amenity location of k3 is closer enough to the Greenbelt
boundary that the total circular volume of Ac'e'f (D) is smaller than the total circular
volume of Aamh (A). Which effect out weighs the other is an empirical question.

Therefore, we may conclude that the amenity benefit depends on three things: (i)
it depends on how large the circumference of the Greenbelt is since more contact gives
more amenity, and this is illustrated in <Figure 5-(c)> (ii) it also depends on how far
locations are from the Greenbelt and (iii) it depends on how thick a Greenbelt is. The
possible importance of thickness is illustrated as a steeper slope of CT (in comparison
with the slope of cf) with a closer zero amenity location of k3 in [case 2] of <Figure 5-
(b)> and is shown by the areas of triangles, (C + D) and (C' + D') in <Figure 5-(d)>.
When we release the Greenbelt, the resulting amenity benefit depends on the relative
strength of three factors. The amenity benefit (D) of Acef decreases through (i) steeper
slope, (ii) zero amenity location closer to the Greenbelt as the Greenbelt is thinner, while
the total circular area (D) of Acef increases in a three dimensional view as the Greenbelt
is released. Therefore, we have a trade-off between decreasing D and increasing D, and
there must be an optimal width of 5* depending on the relative strength of decreasing D

and increasing D.

2. Social Gain from Releasing Land

To calculate the welfare changes from the land release, we need to simplify the

land rent function. First, let the land rent be expressed as following,

 

 

60
(36) r(k) = exp[b+b 1k+b2(k’-k)] = y-exp[b,k+b2(k‘-k)].
where k is the distance from the CBD, k‘ is the distance of the Greenbelt

boundary or urban boundary and k’-k is the distance from the Greenbelt.

Note that we use k and (k‘-k) for the distances from the CBD and Greenbelt respectively
while spline estimation of rent gradient includes two more variables for each distance
variable. We use only two variables in (36) for making our demonstration simple. When
we calculate the welfare gain, the estimated rent gradient will be used. Now the new rent

gradient after the land release has to satisfy the following population condition,

k‘ k8+5

(3 7) l n(k)dk = M =1 nN(k)dk.
0 0

Since the total population is same before and after the land release, only the intercept of
the land rent gradient changes while the slope of the rent gradient remains same if other
parameters remain same (see <Figure 5-(a)>.). If we assume that the price elasticity of
housing demand is unity, and the net income and effective demand for amenity are same
before and after the land release, then the population condition is simplified as follows,

k" k‘+5
(3 7.1) l r(k)dk 5 I rN(k)dk.
0 0

The changes in rent gradient are expressed as changes of intercept. Putting equation (3 6)
into (37-1) and rearranging, we can get a rough approximation of intercept ratio as

following,

YN [{exp(b1k‘)}/b1k'] - [{eXP(b2k’)}/b2k’]

Y [{eXP(b1(k’+5))}/b1(k'+5)l - [{eXP(b2(k’+5))}/b2(k‘+5)]

 

 

 

61
and we have estimated values of 7, b1 and b2. Note that we transform the distance from
the Greenbelt into the distance from the CBD by using k=k"-y. Ratio of yN/y gives the
corresponding value of 7N.

If government releases the 1 km wide of land from the Greenbelt, 5=1. The
distance from the CBD to the Greenbelt boundary is about 15 km on average in Seoul.
Coefficients of all variables are reported in <T able 5-(a)>. In our estimation of the rent
gradient we use dummy variables in each interval which is set up by knots. <T able 7>

reports the results of 71,, in 1975, 1980, 1984 and 1989.

< Table 7 > Rent Gradient Intercepts before and after the Land Release

 

 

 

 

 

 

 

 

year y yN yN/y (ratio) rate of change (%)
1975 3.937 3.707 0.942 -7.84
1980 5.32 5.259 0.989 -1.14
1984 4.479 4.343 0.970 -3.03
1989 5.011 4.8025 0.958 -4.16

 

Kim (1987) calculated the rent change from the land release and he got 7.7% decrease of
the intercept by using 1976 housing survey data. Similar results are found fiom the KAB
data. Change of the gradient intercept ranges from -1.l4% to -7.84%. Note that Kim's
finding might overestimate the true change in intercept because he did neither consider
the amenity effect nor his rent gradient was estimated as a simple linear function.

If the amenity effect exists, the releasing land from the Greenbelt will lead to less
social gain than when the amenity effect is ignored because there might be a lost amenity,
W2. We calculate the social gain of the released land from the Greenbelt by using the

equation (30). For simplifying the social gain, we integrate the new rent gradient

 

 

62
between 15 and 16 km, and the integrated rent is multiplied by the average area of

residential land.

16
l rN(k) dk= 1,804.49 won/pyong in 1975
15

16,662.20 won/pyong in 1980
28,393.97 won/pyong in 1984

80,288.36 won/pyong in 1989.

Average residential area between 10 and 18 km in Seoul is used as a proxy to calculate
the social gain from rent decreases (actual social gain includes the term of (1)). The
average ratio of residential area to the total developed area in Seoul is a little higher than
0.4 in 1988, and we use 0.4 because this ratio in 1975, 1980 and 1984 would be lower
than the average residential area ratio of 0.45 in 1988. We assume that the same amount
of land in the released area will be developed as residential use. Average residential area
is 11.8 million pyong. W, is 21.3 billion won in 1975, 196.6 billion won in 1980, 335.05
billion won in 1984 and 947.4 billion won in 1989 respectively.

Now to get the net social gain from the land release we calculate the welfare loss
of the lost amenity. The shaded area of A in <Figure 5—(b)> can be divided into a triangle
between k, and k2, and a parallelogram between k‘ and k'+5. We assume that the amenity
is zero at k,. Average distance from the CBD with zero amenity, k, is 3.35 km, and k2 is
4.35 km. The area of A is 16,981.08 won/pyong (in 1975), 9,094.77 won/pyong (in
1980), 4,980.85 won/pyong (in 1984) and 1,805.70 won/pyong (in 1989) respectively.
With the amenity effect of the Greenbelt the net social gain from the land release is less
than that without considering the amenity effect. <T able 7-l> reports the social gain of

the land release.

 

 

63

< Table 7—1 > Net Social Gains (won/pyong)

 

 

 

 

 

 

 

year W, W2 W(= W1 - W2)
1975 1,804.49 16,981.08 -15,176.59
1980 16,662.20 9,094.77 16,652.25
1984 28,393.97 4,980.85 23,413.12
1989 80,288.36 1,805.70 78,482.66

 

The results of <T able 7-1> show an interesting finding that W,, social gain of
lower land rent, is found to have increased over the estimated period, while W2, social
cost of lost amenity, decreases. This indicates that the Greenbelt constrains the urban
land supply so effectively that the social gain increases during the period of 1975—1989.
A growing pressure of population on land prices in the demand side has been stronger

than the amenity effect.

3. Social Gain in case of No Amenity Effect

We estimated the rent gradient by using the same spline specification, but we
assume that there is no amenity effect this time. Estimated results are reported in <T able
8>. We use the high residential quality only because the high quality is used for
calculating the social gains with the amenity effect of the Greenbelt.

Estimated results in <Table 8> are very similar to those in <Table 5-(a)>.
Coefficients and their significance give the same numbers and signs as found in the
estimation with the amenity effect except for the fit; values of R2 without the amenity

effect is less than those in estimation with the amenity effect. Also the test hypothesis of

 

 

spline estimation is rejected at 99% significance level. Overall estimation shows similar

64

results found in the previous estimation with the amenity effect.

< Table 8 > Linear Spline Estimation of Rent Gradient : No Amenity Eflect

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dependent Natural Log of High Quality Land Rent
Variable
1975 1980 1984 1989
constant 4.145* 5555* 526* 5.793*
x -0.243* -0.123* -0.115* -0.053*
(17.445) (9.395) (8.929) (4.123)
x5 0.180* 0.090* 0.137* 0.069*
(7.397) (4.1 19) (6.506) (3.349)
x10 -0.153* -0.110* -0.111* -0.054*
(6.372) (5.338) (5.591) (2.903)
adjusted R2 0.837 0.675 0.402 0.106
N 390 376 354 331
Note ; l) ()is t-value.
2) * is significant at 99%, and ** is significant at 95%.
o Hypothesis Test Results ; F-statistics
Hypothesis 1975 1980 1984 1989
8, = 133 = 0 28.4468 14.3458 22.2358 5.9478

 

 

 

 

 

 

 

Note : a denotes that a null hypothesis is rejected at 99%.

< Table 8—1 > Change in Intercepts and Net Social Gains : No Amenity Eflect

 

 

 

 

 

 

 

year yN/y (ratio) rate of change (%) W, (won/pyong)
1975 0.9913 -0.87 4,026.6
1980 0.9749 -2.51 13,4058
1984 0.9605 -3.95 59,662.]
1989 0.9538 -4.62 1692652

 

 

 

65

Based on the results in <Table 8>, we can calculate the social gain of releasing
land from the Greenbelt in case of no amenity effect. They are reported in <T able 8-1>
and show a pattern similar to that in <Table 7-1> ; social gain is increasing during the
period of 1975-1989. The second column in <Table 7-1> and the last column in <T able
8-1> show the same net social gain from the land release. The net social gain is larger
with assumption of no amenity effect than with the amenity effect because the lost
amenity benefit is ignored and excluded from calculations. If we let the proportion of the
residential area to the total area be 40% as assumed in the previous calculation of social
gain, then the total social gains from releasing the land are estimated to be 47.51 billion
won in 1975, 158.188 billion won in 1980, 703.54 billion won in 1980, and 1,997.33
billion won in 1989. These numbers are larger than the results with the amenity effect.
Therefore, if there exists an amenity effect of the Greenbelt, and the net social gain is
calculated without considering the amenity effect, then the resulting social gain is apt to

exaggerate the true social gain.

Chapter V

 

V. Green Disks for an Alternative to the Greenbelt

The analysis in the land market shows that the amenity of the Greenbelt exists and
the net social gain of releasing land from the restriction is smaller than expected or
known. In this chapter we propose an alternative system to the Greenbelt.

One of the Greenbelt's goals is to restrict population growth and urban expansion
(Hwang, 1976). If one of the Greenbelt's functions is to check urban expansion, then it is
related to restricting population growth since the urban area is already checked into a
smaller area than without the Greenbelt. Note that construction of new building is
restricted inside the Greenbelt. To restrict population growth is not equal to restricting
immigration from the rural area, but rather it means that as urbanization goes on,
population grows, but there would be a maximum population in the restricted urban area.
Additional people must settle outside of the Greenbelt. It brings urban sprawl or leap
frog development.

However, the Greenbelt in Seoul seems to fail to achieve this goal -- we cannot
calculate the maximum population size of Seoul. Seoul is known to be one of the largest
and most crowded cities in the world, crowded over her maximum capacity. The
Greenbelt raises urban land price by restricting land supply, on the one hand, and
increasing demand through the amenity effect on the other hand. It can be easily seen
that the Greenbelt is ineffective in restricting population growth and urban expansion,
which lead to urban sprawl, since there exists a suburban area or exurban area beyond the

boundary of the Greenbelt in most metropolitan regions, notably Seoul.

66

67
If we accept this proposition, we can conclude that it is not easy to restrict the
natural expansion of growing cities by a contrived physical restriction, especially in the
long run. Let's put aside the effective growth controls and focus on other sides of the
Greenbelt problem —- shortage of urban land supply and the amenity effect of the

Greenbelt.

1. Greenbelt and Green Disks

The Greenbelt is generally a ring shape as its name shows but some forms other
than a ring shape were proposed in the past, one of which is a wedge shape inserted from
city boundary to the CBD. It was proposed in 1968 since the Greenbelt systems in small
urban areas in England had failed to work as intended. For the purpose of checking urban
expansion, a ring shape of the Greenbelt is better than the wedge shape since the ring
shape more effectively restricts the urban area physically. We will look at the ring shape
of the Greenbelt since Seoul's Greenbelt is close to a ring shape as shown in <Figure 1-
1>, and it fits with our simple analysis of theoretical monocentric city.

<Figure 6—(a)> illustrates a typical example of monocentric city with a Greenbelt.
Greenbelt area, A, is m km wide and located between x km and y km from the CBD. City
size is determined by 2 km distance from the CBD where rent gradient equals to
agricultural rent. Areas next to the Greenbelt, B, are amenity effect areas. We assume
that area of 11 km from the Greenbelt boundary capitalizes the amenity effect so that it has
higher rent. In <Figure 6-(b)>, we illustrate an alternative, Green Disks, to the Greenbelt.
Green Disks, C, are scattered in the urban area with diameter of m km which is the same
as the width of the Greenbelt and the areas of the amenity effect, D, have the same
width of 11 km as in the Greenbelt. While the traditional design of the Greenbelt is

concentrated in a circular ring, small Green Disks are scattered.

68

Figure 6. Greenbelt and Green Disks

 

amenity areas ‘7‘».-- _____ __-———
. urban bounda
restricted areas .—--""“~-~~. / ry

—
a”
’

 

 

/.

 

(b) Green Disks

~ —
.~ -—
~-—.-____—————

s-
‘s

 

69

(c) Comparison of Simple Forms of Greenbelt and Green Disks

Greenbelt Green Disks

 

amenity areas

restricted areas

 
 
   

 

70

We want to examine the differences in the two designs. Which one is more land
saving? Which one is more effective in generating amenity effect? How does the
transportation cost vary in different designs? Are rent gradients different? If so, how can
we explain the difference? At a single glance, there must be physical differences since
two designs are different in shape and dispersion. Physical differences will incur changes
in economic valuations since individual locational choice changes.

First, we calculate the areas of A, B, C, and D for the Greenbelt and the Green
Disks and results are shown in <Table 9-(a)>. Note that u is set to be one for
convenience of calculation and g refers to the number of the Green Disks needed under
different settings. If the total area of the Green Disks is equal to that of the Greenbelt
(A=C), then corresponding results are shown in the second row. With the same area as
with the Greenbelt we can have larger amenity effect area in the Green Disks than in the
Greenbelt. This means that the amenity effect is larger and distributed more equally in
the Green Disks than in the Greenbelt. The third row shows a possibly more useful
application. If we keep the areas of the amenity effect same, we need a smaller area to be
restricted for the Green Disks than for the Greenbelt. The Green Disks are land-saving
since they restrict less land with the same size of amenity effect as in the Greenbelt.
While the Greenbelt decreases the urban land supply, we may increase the land supply

when we choose the Green Disks; and the amenity effect areas in both cases are same.

 

71

< Table 9 > Greenbelt and Green Disks

(a) Comparisons of Restricted Area and Amenity Area

; same

g= ; same

    
    

: area
varies with conditions of each city. Others are total areas.

0 Calculations of Areas

(1) Greenbelt
restricted area ; 7ty2-1rx2 = n(yz-xz) = n(y+x)(y-x) = nm(y+x) since m = y-x.
amenity area ; n(y+l)2-1ty2+1tX2-1t(X-l)2 = n(2y+l+2x-l) = 2n(x+y).
(ii) Green Disks
restricted area ; 1t(m/2)2 = m21t/4.
amenity area ; n(l+(m/2))2-1r(m/2)2 = n(l+m).
# of Green Disks for same restricted area ; g = 4nm(y+x)/m21r = 4(y+x)/m.
# of Green Disks for same amenity area ; g = 2n(x+y)/(m+l)1t = 2(x+y)/(m+1).

(b) Numerical examples for comparing the total restricted areas and amenity areas

(ii) same amenity area

use g =
be expressed as a simple integer. 2) We set u=l for simplifying the calculation.

 

72

Numerical examples illustrate the above implications more clearly. We have two
cases of (x,y,m) = (1020,10), (15,20,5). For the number of Green Disks, g, we use the
closest integer solution for the same amenity area (the last row in <1" able 9—(b)>).
However, the critical implication is unchanged. In <Table 9-(b)>, we have two different
cases; the cases of the same restricted area and the same amenity areas. These results are
not surprising because in the Green Disks the amenity effect areas per restricted area are
larger than those in the Greenbelt. All areas around the Green Disks are amenity effect
areas while only two sides of areas are amenity areas in the Greenbelt as shown in
<Figure 6-(c)>.

For the same restricted area, both examples of (x.y.m) show more widespread
amenity effect under the Green Disks and the amenity effect areas increase more than
twice; by 120% and 140% respectively each case. For the same amenity effect areas,
both Show a huge land-saving under the Green Disks. In the first example we need only
half of the land while we need less than half in the second. This indicates that the rent
gradient could shift downward at every location and the urban land price would fall under
the Green Disks systems.

From the above examples, we show that under the Green Disks, we may restrict
less land physically with the same amenity effect areas. Land-saving and bigger amenity
effect areas are not enough to conclude that Green Disks are superior to a Greenbelt. We
have to look at utility changes in both individual and social levels. In urban economics,
transportation cost is critical to determine residential location and the marginal increase
of transportation cost must be equal the marginal saving of rent payment at equilibrium.
With the changes of the amenity effect and the transportation costs, the rent gradient
might be higher than with the Greenbelt and urban residents might lose some utility under

the Green Disks.

 

73
The simple version of equilibrium condition of locational choice (equation 4-1)
may be expressed in an indirect utility functional form. We get the following after totally

differentiating the indirect utility function, V= V(r,t,A),

(39) dV= V,dr- V,dt+ VAdA.

Note that the above indirect utility function is different from that in equation (39). In the
short run, population size is fixed. So when there are changes in variables, dV is not
equal to zero since population size no longer changes to restore the utility equalization
condition at equilibrium. Then utility level is endogenous as in a closed city model.
Replacing the Greenbelt by the Green Disks will decrease rent everywhere and changes

the transportation cost and amenity effect without causing relocation.

2. Changes of Welfare and Rent Gradients under the Green Disks

<Figure 7> is useful to explain these utility changes. In all three panels, the
central point of urban area, 0, is located in the CBD and that of the Green Disks is A.
For simplicity, let the Green Disks be located in the Greenbelt area and two locations at P
and Q have the same distance from the CBD. Panel (a) shows the case where both P and
Q lie outside of the outer boundary of the Greenbelt while in panel (b), they lie inside the
inner boundary. In panel (c), both lie between the inner and outer boundary of the

Greenbelt.

74

Figure 7. Amenity Effect of Green Disks
- along the distance from the CBD -

CBD

 

 

(a) o \

./fl\

 

 

 

 

 

//
Q)
\/

 

 

 

 

 

(C) o

1\\ U
i
l
\
K \\ \
33;.
/

(

0L (73>
\

 

 

 

 

75

In panel (a), P and Q lie outside the Greenbelt outer boundary. If dc is the nearest
door to get into the CBD through the Greenbelt, total commuting distance is PcO at P and
Q0 at Q under the Greenbelt. Under the Green Disks, PfeO is the shortest commuting
distance for P that is much shorter than PcO while there is no change in commuting
distance at Q. The distance from the outer or inner boundary of the Greenbelt indicates
how much a location has an amenity effect, that is, the closer to the boundary it is, the
larger the effect is. While P has same amount of amenity in both systems, Q will
experience a longer distance and less amenity effect. All locations between P and Q have
less amenity effect and more saving in commuting cost since they are located farther to
the boundary. If it is close to Q, the amenity loss is greater than the transportation cost
saving. If close to P, the amenity loss is smaller than the transportation cost saving. Both
P and Q will benefit under the Green Disks if the amenity effect loss is smaller than the
sum of rent and the transportation cost saving effect on utility. For locations inside the
inner boundary, the amenity effect loss is dominant while there is neither gain nor loss in
commuting distance as shown in panel (b). Again, if the rent saving effect is stronger,
then the amenity effect loss could be fully compensated so that the utility may rise. In
panel (c), P and Q, between the inner and outer boundary of the Greenbelt, benefit from
transportation cost saving but they have to pay higher rents after their locations are
released from the Greenbelt. In the aggregate, they might lose if the amenity effect loss is
greater.

On a social level we cannot say which system gives more utility without
constructing the social welfare function. Furthermore, the assumption that the amenity
effect loss is smaller than the sum of the rent and transportation saving effect needs more
verification. Its validity depends on the form of the utility function one chooses and the
relative weights on three different effects. In the long run, the urban area expands with

growing population size, but these are fixed in the short run. Suppose that the Greenbelt

76

is established for containing future urban expansion. The Greenbelt might not be binding
when first established. When the urban area is growing outward in the long run, the
Greenbelt shall be binding at last. Weight on the amenity effect would be lower and
might be negligible at the beginning stage of urban growth since there might be not only
less congestion and environmental problems, but the urban area is rather small. However,
in the long run, shortage of land might be the more serious problem than the amenity loss
since it affects more urban residents in the low and middle income classes--in the panel
(a) and (b), notably as in Seoul. If each individual has the same preference, the total
amenity loss is smaller than the total gain of rent saving and transportation cost saving
since the rent saving is applied to all residents and more residents may give less weight
on the amenity loss.

In the aggregate we cannot conclude whether it is loss or gain without defining the
social welfare function. As in the basic model for the housing market, we can assume
that each member has equal weight in the social welfare function. Under equal weight of
each member, we can say that the social welfare will increase under the Green Disks. For
members in the panel (a) and (b), there is welfare gain while a loss exists for members in
the panel (c). Note that this conclusion is valid only when there is no movement among
members after displacing the Greenbelt by the Green Disks.

As shown above, the Green Disks are land saving and supply more land for urban
uses. This increase in the land supply shifts the rent gradient downward at every location
except for the area released from the Greenbelt restriction. <Figure 8> shows the induced
shifts of the rent gradient. We can have several different rent gradients under the Green
Disks as shown in panel (a) since the restricted area is not a ring shaped.

In the panel (b), more land available for urban uses will shift down the rent
gradient in the range of O-Ol except for the restricted area of (x-y) where one receives

agricultural rent. This shift in the rent gradient from rg to rga will shrink the urban area

 

 

77

Figure 8. Rent Gradients in case of the Green Disks

(a) Green Disks

\
fl"
\ ""

 

 
 

 

 

 

 

 

 

l

I

I

I

I

i 01
I
I

I

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I

I

I

’I
I
II [I
I, ’
I
’ I
’ I
’ I
’ I
a ” 1’
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I
r (b) Rent Gradient of 0-01
’9
[ya \
h
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kga k"

 

78

(c) Rent Gradient 0f a-a

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r
W v 1v V
['3 l'a
0 360
(d) Rent Gradient of 0-02
I'a
k
0 x+(m/2) ka
r (e) Rent Gradient of 0-03
r a J-
k

 

 

 

kg

 

79
from k" to kga. Urban sprawl is less severe in the Green Disks system than in the
Greenbelt system. The Green Disks are neither a belt nor concentrated. So rent varies
even in the same radial circle as shown in the panel (c). As in the panel (b), the
closer to the Green Disks a location is, the higher a rent is due to larger amenity effect.
When we rotate O-O1 closer to O-O3, x and y will move toward each other and the rent
gradient will move along rs, in the panel (c). Rotating more to O-OZ, x meets y at
x+(m/2) where rent gradient shows a hump as in the panel (d). At last, we have a

smoothly downward sloping rent gradient but its slope is flatter for O-O3 as in the panel

(e).

3. Urban Disks : Seoul and Satellite Cities

The Green Disks are preferable to the Greenbelt because they guarantee more
equitable distribution of the amenity effect and more land supply. As seen in <Figure 1-
1>, the actual Greenbelt in the capital region resembles the Urban Disks in <Figure 9-
(a)>. The Greenbelt starts around the urban boundary of Seoul and the satellite cities are
surrounded by the Greenbelt. This simplified form of the Greenbelt approaches to the
Urban Disks somewhat.

Let the distance from the CBD to the Greenbelt be x and s respectively for Seoul
and the satellite cities, and the distance from the CBD to the outer boundary of the
Greenbelt be y, and m denote the thickness of the Greenbelt, n denote the amenity area.
Total restricted area under the Greenbelt is rtm(x+y)-1Ins2 if the number of the satellite
cities is n and the corresponding amenity area is nu{(28-u)n+(2x-u)}. The amenity area
concentrates around the boundaries of Seoul and the satellite cities.

In the long run the urban areas expand outward. Growing satellite cities expand

more than Seoul; because Seoul is already crowded, the satellite cities are more attractive

80

to live in with transport development. A small part of the Greenbelt around the urban
areas has to be released in the long run in order to meet the increasing demand for urban
land because of demand pressure. This shrinks the total Greenbelt area and may affect
the amenity effect due to less green areas. The Greenbelt may be demolished totally after
the satellite cities expand further. One of the Greenbelt's merit is its amenity effect and
the urban residents near the Greenbelt enjoy it. If the Greenbelt shrinks too much to have
zero amenity effect or close to zero amenity effect, then there will be a social loss since
the residents cannot enjoy the amenity benefit any more.

It is illustrated in <Figure 9-(b)>. The diagram implicitly assumes that the area
beyond y km from the CBD of Seoul will not generate amenity effect. But different
assumptions are possible. If the urban areas expand, Seoul and the satellite cities are not
separated by the Greenbelt any more because some part of the Greenbelt is released to
urban uses. If we assume that the urban areas expand by u, then the resulting amenity
area in Seoul disappear while that in the satellite cities shrinks. From <Figure 9-(b)> the
amenity area in the satellite cities may increase if the Greenbelt is thick enough to
surround all the satellite cities. But the Greenbelt area decreases due to the urban
expansion and its erosion. The amenity area decreases roughly by two thirds of that
before expansion. Total restricted area decreases to rt{(y+x)m-2u(y-m ')—n(s+u)-’} where
m’=(y-x-u). Roughly the amenity area shrinks to (2/3)[7ru{(2x+p.)+n(23+u)}]. The
amenity area concentrates around some areas of the boundaries of the urban areas. The
amenity benefit decreases to incur a social loss due to shrinkage of the amenity area.

However, with the Green Disks we may avoid such a social loss. If properly
designed and enforced, the Green Disks can remain effective in generating the amenity
even in the long run. As shown in one stylized possibility of <Figure 9-(c)>, the Green
Disks remain untouched after the urban areas expand. More residents may enjoy the

amenity as the urban boundaries are close to the Green Disks. Total restricted area under

 

81
the Green Disks is ng(m/2)2 and the amenity area after expansion is nug(m+u) where g
denotes the number of the Green Disks. The merits of the Green Disks are already noted;
(i) they can provide more urban land than the Greenbelt can. (ii) amenity benefits are
more equally distributed. We add one more merit to these; it is consistent with the urban

expansions of the satellite cities in the long run.

82

Figure 9. Seoul and Satellite Cities

(a) Before Expansion of Cities

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

"-'-:-:;:;:;:;:;:;:;:;:;:;:;:;:;:;.;.;2:2:1:3:1215:3235:1'3' """" I Satellite City

 

. CBD - Boundaries before expansion

[mm] Amenity Area

 

 

 

---
-— -

83

(b) After Expansion of Cities

 

SEOUL

   

 

 

Q CBD

Urban Boundaries
after expansron

 

vv 7 v
ooooooooo
IIIIIIIII
IIIIIIIII
lllllllll

 

 

 

 

 

 

 

 

 

 

 

Greenbelt Area

.22.... after expansion

Amenity Area

 

 

~ ’
‘~----’

 

-_—-_
—
I’ ‘~

(0) Urban Expansion and the Green Disks

-————
,— ‘.~

I
.—
”’—_— _.‘~ f
I
,’ ‘sl
l
I

x x

I
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_——‘T

 

SEOUL

._-——...~

 

 

 

 

 

 

 

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“-—--- a
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I \
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I \ \
I \s | 1’
I a
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§
‘ ‘ ~
N
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~~

 

 

‘\
‘ \
\
‘1
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a \' " l
,r P- s‘ p, I
\ x l
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’1 \-_____—4
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/ Satellite City

f
a
“~___——"

 

— Urban Boundary before Expansion
---' Urban Boundary after Expansion
—> Urban Expansion

 

[In] Potential Amenity Area

0 CBD
Green Disks

 

 

 

a
~ 4
‘~—__——’

‘\

Chapter VI

 

Vl. Conclusions

In Korea a deregulation movement has begun to flourish. One of the criticized
policy measures is the Greenbelt restriction because it limits the urban land supply in
Seoul and other major cities. The model used to provide the analytical basis of criticism
does not count on the amenity effect of the Greenbelt. In this paper we analyze the
amenity effect of the Greenbelt and reconsider the validity of the deregulation movement
for the Greenbelt.

The simple models of land and housing markets are amended to include the
amenity attributes. Our models developed here are designed not only to have as much
analytical power as the simple monocentric model but to explain the heterogeneity of
housing services in the real world. If an amenity from the Greenbelt varies with the
distance to the Greenbelt, housing on different parcels will provide different degrees of
amenity. If the Greenbelt is a circular ring around the urban areas, the monocentric
model should keep its full analytical power in explaining the amenity effect. The amenity
effect is capitalized into the land rent and value, and the house value and rent vary as the
amenity variable enters the utility function or housing demand function.

Based on the theoretical findings, empirical analyses were carried out for the land
market. Empirical results show that an amenity effect exists in the land market. In the
land market analysis, we estimate the rent gradient by using a linear spline functional
form. Even though the overall fit decreases during the estimated period, most
coefficients are significant. Considering the trend of the coefficients, the rent gradients

have been flatter during the estimated period. Oddly enough the highest rents are not at

85

 

86
the immediate boundary of the Greenbelt but 1 or 2 km inward. This distance rose until
1980, then stabilized. Some tentative reasons for this pattern were explored in chapter
III, but further study would clearly be helpful.

For population gradients we found that population is shown to decrease with the
distance from the Greenbelt while it increases with the distance from the CBD.
Estimated coefficients suggest that such relationships are stronger over the estimated
period. It means that population is relatively concentrated near the Greenbelt. However,
we cannot conclude that the amenity of the Greenbelt has a pulling effect on the
population because (i) it may be coincidential that the high population density areas are
close to the Greenbelt. (ii) increasing income, car ownerships and the public transport
system allow people to live in locations far from the CBD without incurring high cost.

If the amenity effect exists, then releasing land from the Greenbelt restriction
might decrease the social gain due to loss of the amenity benefit. It may be that the
changing the width of the Greenbelt, not just its distance from residences, has important
implications abut the amenity effect. We found the trade-off between decreasing amenity
benefit from the thinner Greenbelt and increasing amenity area from more contact in
circular areas. With the special assumptions outlined in chapter IV, we calculated the
social gain of the land release. Our calculation is -15,176 won/pyong(1975), 16,652
won/pyong(1980), 23,413 won/pyong(l984), and 78,482 won/pyong(l989) respectively
as the 1 km wide of land is released from the Greenbelt. Net social gain from releasing
the land are 4,026 won/pyong in 1975, 13,405 won/pyong in 1980, 59,662 won/pyong in
1984, and 109,265 won/pyong in 1989. In this sense the Kim's finding overevaluate the
net social gain. Our data is known to represent only 70% of the real market value of land.
After adjusting this underestimation, we have -21,680 won/pyong, 23,789 won/pyong,
33,447 won/pyong, and 112,117 won/pyong in the same years.

 

87

If 40% of the total area is developed as residential use, then we can get 11.8
million pyong of newly developed residential area and 47.6 million pyong of the amenity
benefit area. Taking these numbers into account, we can have the results of net social
gains reported in <T able 10>. Generally the net social gain of releasing land from the
Greenbelt restriction is overevaluated if the amenity effect is not considered properly.
The degree of overevaluation has increased over the estimated period of 1975-1989.
Comparing them with the GNP (current prices) of the corresponding years, the ratios of
W in the fourth column in <T able 10> are -7.76% in 1975, -0.64% in 1980, 0.14% in
1984, and 0.61% in 1989 respectively, while those of W, in the fifth column in <Table
10> are 0.47% in 1975, 0.43% in 1980, 1.0% in 1984, and 1.42% in 1989.

< Table 10 > Social Gains of Releasing Land, and Amenity Effect (billion won/month)

 

 
   

(a) With Amenity Effect (b) Without Overevaluation
Amenity ; (b) - (a)

Effect

 

......................................

......................................

............................................................................
......................................

  

 

 

 

 

 

 

 

 

 

year W. W. Wee-1.; """ ._

1975 21.3 808.3 V787* * 47.5% ' i 834.5 ’
1980 196.6 432.9 V236.3*“ 1582 ' 394.5 *
1984 335.05 237.1 97.95 . x 703.5 - 805.55 x
1989 947.4 86.0 861.4 ’ 1,997.3 . . 3 1,115.9

 

 

 

Note : V represents negative numbers, and they indicate the social loss.

Our analysis is not problem free. First, our simple model is far from perfect
because it does not consider the secondary urban centers and commuting time. This lack
might be critical in urban analysis because modern urban life is very sophisticated.
Second, our calculation of net social gain might be different from the true social gain
because we assume unitary price elasticity of housing demand. Also it is assumed that

the net income and amenity demand remain unchanged before and after the land release.

88

To sum up, if the Greenbelt has a pervasive effect on the urban land supply,
eliminating the Greenbelt restriction is an alternative. However, the Greenbelt is found to
be effective in generating an amenity effect. Nowadays the environmental problem is one
of the major issues in the world and is also critical enough to have the attention of
scholars. With respect to long run perspectives of the environment as well as simple
benefit cost analysis, we have to reconsider the deregulation of the Greenbelt.

We propose the Green Disks or scattered reserves, which will help with both the
land supply shortage and the amenity in Seoul. With the Green Disks, we need less land
for the same amenity effect. Above all, we can utilize the land released from the
Greenbelt for other urban uses. It will increase the urban land supply, which will lower
the rent gradient at every location. Total urban utility may rise with a more equally
distributed amenity effect.

<Figure 10> shows that the Greenbelt is displaced by the scattered reserve areas
as an alternative. The scattered reserve areas are drawn according to various principles,
as follows: First, they must resemble the Green Disks in form. Second, they should
approximate the Greenbelt to minimize the changes. Third, they circumscribe other
satellite cities to maximize the amenity effect areas. Compared with the Greenbelt in
<Figure 1-l>, the scattered reserve areas are smaller than the Greenbelt areas. Note that
we do not consider the political and administrative feasibility of the Green Disks or
scattered reserve areas. In order to implement the idea of Green Disks, the political and
administrative feasibility have to be considered.

The simple model with amenity attributes seems to be valid to analyze the
Greenbelt. Existence of the amenity effect of the Greenbelt leads to the conclusion that
the social gain from land release might not be as large as perceived. It seems desirable to
adjust the form of the Greenbelt rather than just to discard the whole idea. The Green

Disks or scattered reserve areas may be proper for replacing the Greenbelt.

 

Figure 10. Examplary Scattered Reserve Areas in Seoul
as an Alternative to the Greenbelt

 

Boundary of Seoul

Satellite Cities ———1
1 Eujeongbu 7 An an ‘ '
l _ V 9 I Green Disks or
‘ 2 Gun 8 Gunpo ( Reserve Areas
! 3 Migum 9 Euwang ‘ ...-...-
4 Hannam 10 Kwangmyung ‘ Major
5 Sungnam 11 Siheung Transportation
6 Kwaehon 12 Buchon '

Route

 

 

 

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