Coastal Setback and the Impact of Water Amenities


Smith, B.H.

Geographical Analysis 26(4): 364-369

1994


Bruce
H.
Smith
Coastal
Setback
and
the
Impact
of
Water
Amenities
This
article
analyzes
the
impact
of
a
large
water
body—Lake
Michigan—on
residential
property
values
using
two
models
that
incorporate
a
coastal
"set-
back"
term.
The
econometric
results
in
both
models
strongly
suggest
that
Lake
Michigan
and
the
setback
width
from
the
Lake
significantly
impact
property
values.
Coastal
development
has
been
an
important
public
policy
issue
for
cities
and
states
for
the
last
three
decades.
The
city
of
Milwaukee
has
added
twenty-five
acres
of
park
land
along
Lake
Michigan
since
1981.
Milwaukee
has
improved
pub-
lic
access
to
the
shore
and
improved
the
Summerfest
grounds.
In
the
1980s,
the
city
of
Erie
acquired
Erie
Sand
and
Gravel
and
the
Grain
Dock
for
waterfront
development.
Chicago
has
more
than
twenty-six
miles
of
lakefront
with
2,500
acres
devoted
to
parkland.
Eight
recreational
harbors,
twenty-one
public
beaches,
and
seven
major
museums
are
located
along
Chicago's
"greenbelt."
Of
the
625
public
outdoor
recreation
areas
in
the
Lake
Michigan
basin,
536
involve
the
use
of
water
(U.S.
Dept.
of
the
Interior
1965).
Many
states
have
sought
to
vigorously
protect
unspoiled
coastal
areas.
This
pro-
tection
includes
moratoriums
on
building
within
a
proscribed
distance
from
the
coast,
for
example,
California's
one-mile
ban.
Several
states
restrict
industrial
and
commercial
development
(Hyde
1975).
Some
of
the
toughest
controls
are
New
Jersey's
Coastal
Area
Facility
Review
Act
and
Delaware's
Coastal
Zone
Act.
[Young
and
Haveman
(1985)
present
a
literature
review
of
recreational
demand
for
water.]
The
advantages
of
living
near
a
large
water
body
are
well
known.
Most
water
bodies
are
esthetically
pleasing.
The
breezes
blowing
off
the
ocean
or
lake
make
habitation
desirable.
Ocean
and
lake
breezes
have
been
described
as
"nature's
air
conditioner"
(Neuberger
and
Cahir
1969)
The
city
of
Chicago
has
been
the
backdrop
for
several
interesting
investigations
of
the
value
of
water
amenities.
Pollard
(1980)
found
that
residents
of
a
lakefront
apartment
were
paying
26
percent
of
their
housing
expenditures
for
their
location
privilege.
Grimes
(1982)
concluded
that
land
price
per
square
foot
falls
by
an
average
of
14
percent
for
every
1
percent
rise
in
distance
inland
from
Lake
Michi-
gan
and
the
lake-distance
variable
alone
explained
19
percent
of
the
variation
in
land
price
for
the
sample
as
a
whole.
Diamond
(1980)
found
that
living
within
five
Bruce
H.
Smith
is
director
of
Arizona
Economic
Institute.
Geographical
Analysis,
Vol.
26,
No.
4
(October
1994)
©
1994
Ohio
State
University
Press
Submitted
2/10/92.
Revised
version
accepted
9/21/93.
Bruce
H.
Smith
/
365
miles
of
Lake
Michigan
increased
the
value
of
a
house
in
Chicago
by
$2,219
(1970
dollars).
Smith
(1992)
found
that
a
coastal-distance
population-density
gradient
(equal
to
.08)
exceeded
the
standard
CBD
population-density
gradient
(equal
to
.06).
Brown
and
Pollakowski
(1977)
note
that
"economists
have
not
yet
turned
their
attention
to
the
economic
significance
of
the
existence
and
width
of
the
undevel-
oped
apron
affecting
public
use
and
access
to
bodies
of
water
in
urban
areas."
They
go
on
to
test
the
significance
of
the
width
of
the
"setback"
from
the
water
body
on
property
values
in
the
Seattle
area.
They
hypothesize
that
property
value,
V,
is
related
to
the
perpendicular
distance
to
the
water
body,
y,
and
width
of
the
setback,
y,,
as
follows:
V
=
ln
A
+
b
i
ln
y
+
b
2
ln
y
s
b
1
<
0,
b
2
>
0
(1)
where
A
is
a
collection
of
housing
attributes
and
a
constant
term.
They
found
the
estimated
parameters
for
b
1
and
b
2
to
be
both
the
right
sign
and
statistically
sig-
nificant.
The
width
of
the
setback
had
a
strong
impact
on
housing
values
in
the
locations
they
studied.
Equation
(1)
is
particularly
attractive
because
it
assumes
that
as
the
setback
width
is
increased,
housing
values
increase
but
at
a
decreasing
rate.
What
is
unat-
tractive
about
(1)
is
that
it
omits
the
primary
spatial
variable
in
most
urban
mod-
els—distance
to
work
from
residence.
This
is
approximated
by
simply
adding
a
radial
distance-from-CBD
variable,
u,
to
equation
(1):
V
=
In
A
+
b
l
In
y
+
b
2
In
y
s
+
b
3
In
u
b
1
<
0,
b
2
>
0,
b
3
<
0.
(2)
The
word
"approximated"
is
used
because
the
typical
polynucleated
city
involves
travel
to
work
that
is
not
necessarily
CBD-directed.
Because
the
direction-
and
distance-to-work
travel
is
unknown
and
dependent
on
the
dwelling's
occupant,
CBD
distance
must
be
used
as
a
proxy.
Specification
(2)
is
not
the
typical
nega-
tive-exponential
value
function
that
follows
from
the
standard
urban
model
but
in
a
sense,
all
hedonic
regressions
represent
a
search
for
the
best
statistical
fit
for
a
set
of
equilibrium
prices
for
housing
characteristics
and
is,
thus,
necessarily
ad
hoc.
Smith
(1992)
presents
an
alternative
model
of
coastal
distance
and
setback
width
which
assumes
a
Mills-Muth
model
and,
thus,
does
exhibit
the
familiar
neg-
ative-exponential
rent
function
and
does
contain
the
radial
distance-to-CBD
term.
This
equation
is
as
follows:
ln(V)
=
In
A
+
bou
+
b
2
In
y,
+
bo
y
In
y
s
.
(3)
But
even
this
specification
assumes
an
ad
hoc
form
for
the
behavior
of
the
num-
ber
of
recreational
visits
to
the
amenity-providing
water
body.
Specifically,
it
as-
sumes
that
the
number
of
"trips"
to
the
amenity
is
proportional
to
the
natural
logarithm
of
the
size
of
the
coastal
setback.
Because
the
assumptions
and
deriva-
tions
of
the
Smith
and
Brown-Pollakowski
models
are
different,
it
is
impossible
to
derive
a
functional
form
which
makes
equation
(3)
identical
to
equation
(2).
DATA
Estimation
of
theoretical
relationships
for
equations
(2)
and
(3)
was
undertaken
using
a
sample
of
the
mortgage
files
of
savings
and
loan
associations
in
Chicago.
The
sample
consists
of
all
outstanding
mortgages
issued
on
homes,
apartments,
366
/
Geographical
Analysis
TABLE
1
Regression
Results
for
Brown-Pollakowski
Functional
Form
Dependent
Variable:
Sales
Price
Deflated
to
1982
Explanatory
Variable
Coefficient
t-Value
Constant
55,124
56.31***
Log
of
radial
distance
(in
miles),
u
—8,398
—12.68***
Amenity
Variables
Log
of
distance
to
Lake
Michigan
(feet)
—2,631
—10.90***
1
if
there
is
a
view
of
Lake
Michigan
6,720
13.77***
Setback
Variables
2,064
6.31***
Log
of
width
of
setback
(feet)
1
if
parking
at
the
coast
49.5
1.09
Other
Housing
Attributes
Floor
area
(sq.
ft.)
17.3
4.58***
Age
of
structure
(years)
—620
—1.97**
Number
of
baths
3,027
7.21***
1
if
kitchen
is
complete
440
1.25
1
if
structural
defects
—2,471
—12.13***
1
if
air
conditioned
260
2.53***
Number
of
rooms
(excl.
baths)
327
5.98***
1
if
neighborhood
has
abandoned
buildings
—4,855
—8.92***
1
if
commercial
activity
in
the
neighborhood
—375
—1.76*
R
2
=
.78
d
f
=
532
*p
<
.10,
**
p
.05,
***
p
5
.01
and
condominiums
within
two
miles
of
Lake
Michigan
between
July
1982
and
October
1984.
However,
in
the
sample
attached
dwellings
accounted
for
only
4
percent
of
all
observations.
Rather
than
introduce
a
dummy
variable
for
attached
dwellings,
observations
for
condominiums
and
apartments
were
dropped
from
the
sample.
All
prices
were
deflated
to
1982
dollars
by
the
average
rate
of
change
in
the
CPI
during
this
period.
After
exclusion
for
incomplete
information,
the
data
set
consisted
of
547
observations
located
in
the
range
of
the
Chicago
CBD.
Sites
without
setback
were
eliminated.
The
sample
extended
from
the
southern
edge
of
Waukegan
to
a
point
fifteen
miles
south
of
the
Chicago
CBD
(defined
as
the
intersection
of
Michigan
and
Adams
Avenues).
The
sale
price
of
housing
was
regressed
against
distance
and
amenity
variables
as
well
as
an
assortment
of
available
housing
characteristics.
The
regression
results
are
presented
in
Tables
1
and
2.
Table
1
corresponds
to
equation
(2)
and
Table
2
corresponds
to
equation
(3).
In
both
equations
(2)
and
(3),
A
represents
hedonic
housing
variables
arranged
multiplicatively.
The
coefficients
for
these
log-linear
terms
are
reported
in
the
tables.
Not
all
of
the
dwelling
information
that
was
avail-
able
was
actually
used
in
the
regressions.
Several
structural
variables,
such
as
a
set
of
dummy
variables
indicating
type
of
heating
employed,
made
very
little
explana-
tory
contribution
to
any
of
the
regression
runs
and
was
therefore
dropped.
Since
the
preliminary
regressions
indicated
a
presence
of
heteroskedasticity
in
Table
1,
all
observations
were
weighted
by
the
inverse
of
floor
area.
No
heteroskedasticity
was
detected
in
Table
2.
The
interpretation
of
the
distance
variables
vary
markedly
between
the
two
re-
gressions
because
the
functional
forms
are
significantly
different.
For
example,
the
change
in
value
of
dwelling
for
a
unit
change
in
distance
from
the
CBD
in
the
Smith
model
(Table
2)
is
dV/du
=
b
0
V.
For
a
one-mile
increase
in
radial
distance
and
a
house
value
of
$60,000,
there
is
a
fall
in
house
value
of
$3,840.
In
the
Brown-Pollakowski
model
(Table
1)
the
change
in
value
for
a
unit
change
in
ra-
dial
distance
is
equal
to
dV/du
=
b
3
/u
=
—8,
398/u.
Here,
the
change
in
value
depends
on
distance
and
not
on
value.
At
five
miles
away
from
the
CBD,
a
one-
mile
increase
in
CBD
radial
distance
results
in
a
$1,680
drop
in
house
value.
Bruce
H.
Smith
/
367
TABLE
2
Regression
Results
for
the
Smith
Functional
Form
Dependent
Variable:
Natural
Log
of
Sales
Price
Deflated
to
1982
Explanatory
Variable
Coef
f
icient
t-Value
Constant
11.1
71.3***
Radial
CBD
distance
(in
miles)
—.064
—15.7***
Amenity
Variables
Interaction
term,
y
In
y
s
—.024
—9.3***
1
if
there
is
a
view
of
Lake
Michigan
.105
11.8***
Setback
Variables
Log
of
setback,
In
y
s
.056
14.3***
1
if
parking
at
the
Coast
.0008
1.02
Other
Housing
Attributes
Floor
area
(sq.
ft.)
.0003
3.71***
Age
of
structure
(years)
—.010
—2.77***
Number
of
Baths
.050
4.50***
1
if
kitchen
is
complete
.072
1.81*
1
if
structural
Defects
—.041
—12.78***
1
if
air
conditioned
.004
1.43
Number
of
rooms
(excl.
baths)
.005
4.29***
1
if
neighborhood
has
abandoned
buildings
—.077
—12.99***
1
if
commercial
activity
in
the
neighborhood
—.006
—2.43***
R
z
=
.91
d
f
=
532
*12
.10,
"
p<
.05,
***
p
.01
Similarly,
the
effect
of
moving
away
from
the
Lake
Michigan
coast
is
different
in
interpretation.
Accommodations
located
directly
on
the
coast
in
the
Brown-Polla-
kowski
model
are
valued
at
$24,336
more
than
the
same
accommodations
located
two
miles
from
the
coast—irrespective
of
house
value,
setback
size,
and
CBD
ra-
dial
distance.
In
the
Smith
model,
the
change
in
house
value
resulting
from
a
unit
change
in
distance
from
the
coast
(y)
equals
dV/dy
=
b
4
V
lny
s
.
Thus,
if
setback
width
is
one
hundred
feet
and
house
value
is
$60,000,
a
change
in
location
from
on
the
beach
to
two
miles
inland
results
in
a
fall
in
house
value
by
$13,386
(more
than
$10,000
less
than
the
Brown-Pollakowski
model
predicted).
Both
models
also
permit
an
assessment
of
the
impact
on
housing
values
as
a
result
of
modifying
the
width
of
the
setback.
In
the
Brown-Pollakowski
model,
the
change
in
value
resulting
from
an
incremental
change
in
setback
width
de-
pends
only
on
the
setback
width,
dVIdy
s
=b
2
ly
s
=
2,
064/y
s
.
So,
for
example,
if
the
present
setback
is
one
hundred
feet
and
then
doubled
to
two
hundred
feet,
the
resulting
change
in
dwelling
value
is
$2,064.
The
corresponding
calculation
in
the
Smith
model
yields
a
handy
elasticity
coefficient:
e
s
=
d
In
VI
d
lny,
=
b
2
+
1)
4
y
=
.056
.024y.
For
example,
if
dwelling
value
is
$60,000,
initial
setback
one
hundred
feet,
and
the
dwelling
is
located
one
mile
from
the
shore,
a
doubling
of
setback
width
to
two
hundred
feet
causes
that
domicile
to
increase
in
value
by
$1,938.
Setback
distance
is
not
the
only
measure
of
coastal
accessibility.
Use
of
the
water
amenity
depends
upon
driving
accessibility
as
well
as
walking
accessibility.
Indeed,
some
communities
erect
road
signs,
barricades,
and
inspection
and
en-
forcement
by
town
police
to
ensure
that
beaches
are
accessible
only
to
commun-
ity
residents.
Grimes
(1982)
asserts
that
"the
fact
that
the
slope
of
the
land-
price—distance-inland
function
approaches
zero
at
a
point
1,500
feet
from
Lake
Michigan
strongly
suggests
that
walking
accessibility
is
of
greater
importance."
However,
Grimes
considered
only
rural
properties
of
land
on
Lake
Michigan.
To
test
this,
a
zero-one
variable
indicating
parking
facilities
at
the
coast
was
intro-
duced.
In
both
regressions,
property
values
were
predicted
to
be
higher
if
park-
368
/
Geographical
Analysis
ing
facilities
were
present
at
the
coast,
but,
in
neither
case
were
the
estimates
statistically
significant.
The
amenity
coast
is,
itself,
composed
of
a
number
of
characteristics.
Setback
size
permits
more
activities
to
be
had
at
and
along
the
coast.
Distance
from
the
coast
inhibits
ready
use
of
the
water
resource.
But
esthetic
appreciation
of
the
water
need
not
be
impeded
if
a
view
of
the
amenity
exists.
And
a
view
does
not
necessitate
that
the
coastal
inhabitant
locate
directly
on
the
coast.
To
capture
the
significance
of
building
heights
as
a
way
to
enjoy
the
Lake
Michigan
view
on
prop-
erty
values,
a
dichotomous
variable
was
introduced.
In
both
regressions,
if
a
view
was
present,
it
increased
property
values
by
about
$6,700
(evaluated
at
mean
property
value).
This
variable
was
highly
significant.
CONCLUSION
It
is
important
to
recognize
that
there
is
no
shortage
of
possible
functional
forms
explaining
the
behavior
of
property
values
as
a
function
of
CBD
and
coastal
distance
as
well
as
setback
width.
Only
two
functional
forms
have
been
used
in
this
paper—the
only
two
I
know
of
including
a
setback
term.
In
both
cases,
property
values
fall
with
distance
from
the
water
and
rise
with
setback
size.
The
results
of
the
numbers
in
this
paper
are
pregnant
with
public
policy
signi-
ficance.
The
importance
of
amenity
analysis
to
policy
and
planning
cannot
be
over-
estimated.
Governments
use
amenity
analysis—implicitly
or
explicitly—to
regu-
late
and
zone.
Greater
understanding
of
land
use
is
needed
for
most
planning
purposes.
Since
the
setback
size
and
quality
matter
for
housing
values,
they
also
affect
population
density,
filtering,
and
even
city
size.
Similarly,
the
same
things
that
influence
house
prices
also
determine
location
patterns.
Local
governments
are
confronted
with
changes
in
population
patterns
as
a
result
of
zoning
decisions
(for
example,
lot
size).
This
influences
the
size
and
location
of
city
services
and
infrastructure.
An
analysis
that
focuses
only
on
access
to
amenities
may
inaccur-
ately
reflect
political
and
social
realities.
The
marginal
cost
of
dwellings
sold
in
a
competitive
market
declines
with
coastal
distance.
"Since
the
average
cost
is
greater
than
marginal
cost,
an
entre-
preneur
seeking
an
optimal
amount
of
open
space
cannot
cover
his
costs
if
he
follows
the
competitive
prescription
of
setting
price
equal
to
marginal
cost
of
open
space
for
all
beneficiaries.
Either
the
entrepreneur
must
be
permitted
to
deviate
from
marginal
cost
pricing
or
he
must
receive
a
subsidy"
(Brown
and
Pol-
lakowski,
p.
1).
As
with
other
public
goods,
falling
cost
and
nonexclusion
are
rea-
sons
that
the
determination
of
setback
width
is
a
public
issue.
Possible
public
policy
solutions
include
subsidizing
the
establishment
of
coastal
setbacks
or
re-
quire
it
of
builders—either
by
zoning
or
direct
purchase.
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