Land Supply and Capitalization
by Christian A. Hilber and Christopher J. Mayer
Key Conclusions
1. The theory predicts that the extent of house price capitalization varies substantially depending
on the availability of land (or land supply elasticity respectively).
2. The theoretical predictions are confirmed by the empirical findings: Fiscal variables and
amenities are capitalized to a much greater extent in towns with little available land. These towns
also have a lower elasticity of land supply.
3. It is quite possible that communities with greater capitalization might be more likely to
undertake costly spending programs knowing that their expenditures are more likely to be reflected
in higher house values.
4. The capitalization of net benefits of governmental measures mainly benefits owners of real
estate in urban and suburban areas and, to some degree, farmers in rural areas.
1
LAND SUPPLY AND CAPITALIZATION
by
Christian A. Hilber
and
Christopher J. Mayer∗
Abstract:
Researchers and policy makers typically assume that house prices capitalize amenities and fiscal
variables at a constant rate across locations. In this paper we argue that the extent of house price
capitalization can vary substantially depending on the availability of developable land. In
particular, we expect that the extent of capitalization of fiscal variables and amenities should be
especially high in urban areas where the elasticity of land supply is low and quite low in rural
locations where land is more readily available. We establish this point in a two-community
model (urban/suburban and rural towns) with perfectly mobile households and endogenous
property tax rates. The second part of the paper tests the major theoretical predictions using a
unique data set for Massachusetts that includes a measure of available land by community.
Consistent with the theory, we find that fiscal variables and amenities are capitalized to a much
greater extent in towns with little available land, and confirm that these locations have a lower
elasticity of land supply.
JEL classification: H53, H7, R14
Keywords: Capitalization, land supply, urbanization
∗
Christian Hilber is Visiting Scholar at The Wharton School, University of Pennsylvania. Christopher Mayer is
Associate Professor at The Wharton School, University of Pennsylvania. The authors wish to thank Harold
Elder, Joe Gyourko, Bob Inman, Wallace Oates, and Todd Sinai for helpful comments. Any errors, of course, are
our own. Financial assistance from the Swiss National Science Foundation and the Max Geldner Foundation is
gratefully acknowledged.
2
1
Introduction and Background
Following the publication of Oates’ pioneering paper in 1969, a large theoretical and
empirical literature has addressed house price capitalization in a variety of forms. For the most
part, the literature agrees that long-run house va lues should fully reflect cross-sectional
differences in the present discounted value of future tax burdens or benefits, after controlling for
housing characteristics. Such an approach depends on demand factors alone, and assumes that
the supply of land is inelastic and similar across locations.
A few theoretical papers have argued the opposite point; that the supply of land is perfectly
elastic, and thus the degree of capitalization should be quite limited. For example, Edel and Sclar
(1974) suggest pressure from developers will successfully pressure communities to expand any
type of housing that earns economic rents. Hamilton (1975) shows that under very restrictive
assumptions, including perfectly elastic housing supply, there is no capitalization of local
amenities.
Recent econometric studies (among others Yinger et al. 1988, Stull and Stull 1991, Man
and Bell 1996, Palmon and Smith 1998a and 1998b, Sinai 1998, and Black 1999) strongly
confirm the existence of capitalization, although the literature fails to reach consensus regarding
the extent of capitalization. One exception is MacMillan and Carlson (1977), who use a sample
of small Wisconsin towns and show that amenities are not capitalized in a hedonic regression. 1
In this paper we attempt to reconcile these two alternative literatures on capitalization. We
posit that capitalization of fiscal variables and amenities should vary across communities, with a
greater degree of capitalization in communities with a more inelastic supply of residential land.
This result is quite intuitive. As long as land supply is not perfectly inelastic (or perfectly elastic)
and communities are not perfect substitutes, both price and quantity will adjust in response to
demand shocks. However, price adjustment should be larger (and quantity adjustment smaller) in
places with less available land.
Regional differences in the extent of house price capitalization can have important policy
implications. Consider intergovernmental transfers from federal or state governments to
communities based on the number of poor residents. Such transfers will raise property values in
communities receiving the transfers. Many authors have pointed out that location-based aid (as
1
However, as we argue later, such a regression suffers from a number of possible biases, including measurement
error and aggregation, that make it difficult to interpret their results.
3
opposed to grants to poor individuals) can have adverse consequences since poor residents are
typically renters who will be forced to pay higher rents if the transfers are capitalized into higher
house prices. Our results suggest that such adverse redistributional effects should be
concentrated mainly in urban areas. 2 Also consider the debate over the capitalization of the
mortgage interest deduction and the implications of other types of fundamental tax reform in the
US.3 Our findings imply that subsidies to home ownership are capitalized into higher house
values to a much greater extent in urban areas with little available land.
In the following analysis we argue that the extent of capitalization of fiscal variables and
amenities should be particularly high in densely populated places—typically urban and suburban
communities—where residential land supply is relatively inelastic because (almost) all land is
already zoned for residential purposes. 4 In rural areas, however, residential land supply is
typically quite elastic. When the relative attractiveness of rural communities increases, open
farmland is converted into residential land, leading to relatively minor effects on local residential
land values. Our assumption is founded on the findings of the “endogenous zoning literature”. 5
For example, the empirical estimates of Pogodzinski and Sass (1994) strongly indicate that after
controlling for selection bias, land-use regulations appear to “follow the market”.
To establish the point that the land supply elasticity influences the extent of capitalization,
Section 2 presents a model of two jurisdictions that differ in their land supply elasticity.
Households are assumed to be perfectly mobile and property tax rates are taken as endogenous.
Equilibrium is established when residents are indifferent between the two communities. In this
framework, the extent of capitalization of an exogenous demand shock, such as a change in fiscal
subsidy from the state or federal government, depends negatively upon the land supply elasticity
2
3
4
5
Hamilton (1976) first makes the link between capitalization and inequality. He argues that if differential fiscal
surpluses are fully capitalized into demand curves for property, there can be no inequality in a static world.
Wyckoff (1995) suggests that voter movement will cause equalizing intergovernmental aid (such as state
education aid) to be capitalized into housing prices. Assuming a fixed housing supply, he shows theoretically
that in many cases, intergovernmental grants have no net effect on the welfare of the poor citizens (i.e. the
welfare effect of intergovernmental aid on poor voters is completely offset by higher housing costs), and in a few
cases, the grants may even make them worse off. However, if land supply is not completely inelastic fiscal
differences do not have to be fully capitalized into housing values and therefore the conclusions of Wyckoff need
not hold.
For a discussion of the effect of mortgage interest deductions on housing prices see Capozza, Green, and
Hendershott (1996).
For example Yinger (1982) points out that the finite size of urban areas makes land a scarce resource. Fischel
(1990) points to a number of political factors that explain why commu nities pass restrictive zoning measures that
move beyond just solving demand externalities and effectively limit supply.
For a summary of the “endogenous zoning literature” see Pogodzinski and Sass (1994). The literature on
“economics of zoning” is founded on Mills and Oates (1975). For a general review of the literature see Fischel
(1990) and Pogodzinski and Sass (1991).
4
and can therefore differ from full capitalization. Thus, the model suggests that capitalization
depends crucially on the degree of urbanization of a particular jurisdiction. In fact, our model
describes circumstances in which capitalization rates could even exceed unity in a community
with little available land.
In section 3 we test the theoretical predictions using data for the Commonwealth of
Massachusetts. We build on the empirical framework used in Bradbury, Mayer and Case (1999)
that avoids many of the empirical problems that Palmon and Smith (1998b) argue have plagued
past capitalization studies. 6 This procedure uses exogenous variation from a tax limit,
Proposition 2½, to help predict spending levels across communities and looks at how house
prices respond to variations in spending using instruments drawn from the tax limit. Consistent
with theory, our results suggest that fiscal differentials and amenities are capitalized into house
values to a much greater extent in locations with greater land availability, as measured by the
amount of undeveloped land in each city and town based on aerial photos. Finally, we confirm
that locations with more undeveloped land have a greater land supply elasticity. We conclude in
section 4 with a brief discussion of policy implications.
2
Theoretical Framework
We want to explore how the residential land supply elasticity affects the extent of
capitalization of fiscal variables and amenities into land values. Our initial intuition is that the
extent of capitalization is particularly high in urban and suburban areas where residential land is
not easily expandable. In rural areas, however, exogenous improvements in local attractiveness
should lead to the conversion of open farmland into residential land rather than just an increase
in land values.
6
Virtually all past empirical capitalization studies are based on Lancaster’s (1966) hedonic price index approach
that treats a commodity as a bundle of characteristics. Utilizing the market parallel to Lancaster’s approach, the
price of a house can be described as a function of the valuation of the various characteristics of the house, such as
site, structure, neighborhood, public services and taxes. However, this empirical procedure has a number of
important problems that can lead to significant biases when it is implemented. Palmon and Smith (1998b) place
the empirical problems into five broad categories: (1) underidentification, (2) potential correlation between
included and excluded variables, (3) measurement error in the variables, (4) simultaneity bias, and (5) potential
misspecification.
5
2.1 A Simple Model with a Single Community
To establish this point, we begin by considering a model with a single community where
the number of households is fixed. This simple model distinguishes between two cases: a
urban/suburban community and a rural location. The urban/suburban community has low
commuting costs to the central business district (CBD) and consists of a relatively large number
of households that live in houses on lots of a fixed size. All land in this community is zoned as
residential land, that is, the residential land supply QS is completely inelastic. In the rural
community, the commuting costs to the CBD are high and there are relatively few households.
By assumption, the rural community is the same size as the urban/suburban community,
however, the share, θ, of land that is zoned as residential land is a function of its price: Open
farmland is converted into residential land as the price of residential land increases. 7
Figure 1 compares the effects of an equal-sized demand shock on land prices r in the
urban/suburban and rural communities, assuming a constant elasticity of land supply in the rural
location. Demand for land QD is larger in the urban/suburban community due to its lower
commuting costs. Consequently, the price of residential land is lower in the rural community. 8
7
8
In reality, this political zoning process only works in one direction. It is highly improbable that land that is once
zoned as residential land is reconverted into farmland as residential land prices decrease.
The price elasticity of the demand for residential land is assumed to be –1 in both cases. This result can be
derived from the maximization problem in appendix A. Most recent empirical findings even suggest a higher
elasticity of the demand for residential land. Using a two-stage-least squares specification, Gyourko and Voith
(2000) find that the price elasticity of demand for residential land is fairly high, -1.6. In addition, they report
empirical evidence that OLS estimates of the price elasticity are biased upward substantially as predicted by
Bartik (1987) and Epple (1987).
6
Figure 1: Inelastic versus Elastic Land Supply in a Single Community Model
r
r
QS
r1*
QS
Q1D
r0*
r1*
Q0D
r0*
Q
Q1D
Q0D
Q
Q
urban/suburban community
rural community
Q
In this simple world, the extent of capitalization is negatively affected by the elasticity of
the land supply. In the urban/suburban community, an exogenous demand shock—such as a
ceteris paribus decrease in property taxes—is fully capitalized into land values. In the rural
location, however, an equal-sized demand shock not only changes the price of land (the
capitalization effect), but also changes the per capita consumption of land (the quantity effect).
Therefore, the extent of capitalization per square unit of land is smaller in the rural community
than in the urban/suburban location.
For small changes in property tax rates, the extent of property tax capitalization Cap∆t , ∆r
depends only on the elasticity of the land supply ? where
Cap∆t ,∆r = −
1
.
1 +η
(1)
(See appendix A for a mathematical derivation of this result.) Thus, if the land supply elasticity ?
is 1 in the rural community, changes in the tax rate are capitalized at a 50 percent rate (or -1/2
from the above equation). In the urban/suburban community (completely inelastic land supply ?
of 0), property tax changes are fully capitalized.
7
One problem with this simple setting is that it is explicitly partial-equilibrium and ignores
potential equilibrium responses such as mobility and endogenous changes in local tax rates. In a
more realistic setting, the result is less obvious. In particular, households might move away from
densely populated communities when house prices rise, mitigating the impact of shocks to the
attractiveness of these communities. In the next section, therefore, we consider a model with a
urban/suburban and a rural community where households can costlessly relocate and property
tax rates are endogenous.
2.2 Model with Mobile Households
We consider a two-community model with perfectly mobile households, that is, the
number of residents of a community and its density of development are endogenous. All
households i = 1, …, N work in the CBD and earn the same income yi but live in one of two
purely residential communities k = A, B. 9 The urban/suburban community A is located nearer to
the CBD than the rural community B and therefore has lower commuting costs Ck.
This model has its foundations in Tiebout’s (1956) original vote-with-the- feet model and in
the standard monocentric models of urban land use pioneered by Muth (1961 and 1971) and
Alonso (1964). However, nothing in our model requires a monocentric city. In solving this
model, we assume that the densely populated (urban/suburban) community A with no
undeveloped land has lower commuting costs. This could easily be the case in a city with
suburban sub-centers, so long as the locations with less available land are located closer to the
sub-centers. Furthermore, the presented model has similarities to the framework in Hilber
(1998) and in Hoyt’s (1999) model about capitalization and city size. However, these previous
papers assume that land supply elasticities are constant across jurisdictions.
We make the following assumptions:
1. All households have identical Cobb-Douglas 10 preferences.
9
10
Therefore, we assume that in suburbs and rural communities no land is zoned as industrial land. Of course, land
is used for many purposes other than housing and farming, but the latter two are by far the most important in
suburban and rural areas. The other forms of land use are neglected here for analytic simplicity.
The Cobb-Douglas utility function assumes certain restrictions on preferences. In particular, it assumes that a
constant share of the available income is spent on each good independent of the relative price. Using a more
realistic specification of preferences, a change in land rents is also expected to cause a substitution effect, i.e. the
household expenditures for all other goods (including house construction expenditures) change. However, as
long as land q and the numeraire good z are normal goods, the effect of a demand shock on rental land prices will
still persist, albeit to a reduced degree.
8
2. Household i in community k receives utility from two goods : a numeraire private
good zki and residential land (or housing) 11 qki, available at a (rental) 12 price of rk.
3. All households can relocate between the two communities A and B without cost,
thus ∑ nk = N where nk is the number of households in community k.
k = A, B
4. The rural community B has x times the size (in square units) of the urban/suburban
community A, thus, QB QA = x where Qk is the total amount of available land in
community k and where x can be smaller than, equal, or larger than one.
5. Lot sizes are not fixed in either community. The residential land supply in the
urban/suburban community A is completely inelastic, that is, all land is already
zoned as residential land (θA=1). In the rural community B the share of zoned
residential land θB is not fixed but increases proportional to the relative rental land
price rB / rA , given rB < rA .
The opportunity costs of open land are low as long as community B is relatively
unattractive compared to community A; that is, rB /rA is low. The political pressure to transform
open agricultural land into residential land increases with the opportunity costs of open land.
Thus, the share θB of zoned land in community B increases. If both communities were equally
attractive, that is, rB = rA, all land in community B would be zoned as residential land and the
community would become a urban/suburban community. We do not explicitly model the
political process that leads to this result. However, the assumption that more farmland is
converted to residential use as residential land values increase is consistent with the findings of
the “endogenous zoning literature” (see section 1). We also assume that the urban/suburban
community A is more “attractive” to residents than the rural community B, that is rB < rA .
Fiscal differentials 13 between the two communities are modeled as follows:
6. Each community has exogenous expenditures of gk per capita for local services (that
are private goods). While expenditures gk can differ between the two communities,
local services in both communities are of equal quality.
11
12
13
For analytic simplicity we do not distinguish between residential land and housing (i.e. residential land plus
structure). However, structure still exists in the model as part of the numeraire good z.
The model consists only of one time period what implies that the rental price is equal to the land value.
Fiscal differentials may occur because the two communities differ (1) in their cost-efficiency of providing public
services, (2) in their level of positive or negative spillovers from other communities, or (3) in their level of grants
from the state or federal government.
9
Thus, we neglect the impact of local services on the household utility function and gk can
be interpreted as non-benefit expenditures or as net costs per capita of the local provision of
public services.
7. Expenditures gk are financed with property taxes t k on the value of the land in
community k.
Therefore, the property tax rate t k is endogenous. For analytic simplicity we assume that
this tax is only levied on residential land and not on structure. The tax rate is determined by the
“attractiveness” (level of non-benefit expenditures gk and level of commuting costs Ck) of
community k.
8. There is no pure public good in the model. 14
The maximization problem of household i can be written as
max U ki = α ⋅ ln qki + β ⋅ ln z ki
(2)
qki ,zki , k
s.t.
yi = (1 + t k ) ⋅ rk ⋅ q ki + z ki + Ck
t k ⋅ rk ⋅ qki = g k ,
(2.1)
(2.2)
where
Uki
is the utility of household i in community k.
Equilibrium Conditions
Given the assumptions above, we state two equilibrium conditions:
14
As our model consists of homogenous households and as our goal is not to explain sorting effects between
different income groups or between groups with different preferences, this turns out to be not a very restrictive
assumption. In addition, in reality property tax revenues on the local level are ma inly spent for school
expenditures that have more the economic character of a private than of a pure public good.
10
Condition 1. The utility of household i must be the same in both communities, with all
households having chosen optimal consumption levels given the rental price where * denotes the
equilibrium solution. Assuming that not all individuals live in the same community, this can be
expressed as
*
U *Ai (q*Ai , z*Ai ) = U *Bi (qBi
, z *Bi ) .
(3)
Condition 2. Supply of housing must equa l demand for housing in both communities. This
requires that
and
Q A = n*A (rA* ) ⋅q*Ai (r A* )
(4)
r*
*
* *
*
*
θ B ⋅ QB = B ⋅Q B = nB ( rB ) ⋅ q Bi (rB ) .
*
rA
(5)
Equilibrium Solution
The optimal choice of qki* , zki* can be expressed as
α ⋅( y − C − g α)

i
k
k
(qki* , zki* ) = 
, (1 − α ) ⋅ ( y i − C k )  .


r *k


(6)
The relationship between housing rents in A and B at the optimum is
rA* 
=
rB* 
yi
yi
1−α
− C A − g A / α   yi − C A  α
≡Ψ.
 ⋅

− CB − g B / α   yi − CB 
(7)
The population density in each community k=A,B can be expressed as
n*
d k* = k .
Qk
(8)
11
Using the equations (4) to (8), the relationship between population densities in A and B at
the optimum is
2 − 2α
*




dA
y − CA − g A /α
yi − CA α
ˆ .
= i
≡Ψ
⋅

*
y
−
C
−
g
/
α
y
−
C
dB  i
B
B
  i
B
(9)
Assuming that the urban/suburban community A is more “attractive” than the rural
community B, that is, rB* < rA* (see assumption 5), we conclude that d *A > d *B .
Comparative Statics
Consider a change in per capita expenditures gk in one of the two communities. This
change can be interpreted as a lump sum federal grant or state aid given to one or the other of
these communities. With Cobb-Douglas preferences, the change in per capita expenditures in
each community exactly equals the change in the value of consumed land, or
rk1 ⋅ qk1 − rk 0 ⋅ q k 0
= −1 .
gk1 − gk 0
(10)
For small changes in expenditures, equation (10) can also be written as
∆rk ⋅ qk ∆qk ⋅ rk
+
= −1 .
∆ gk
∆g k
(10.1)
The first term of the expression represents the price effect (extent of capitalization of
expenditures) while the second term represents the quantity effect. Mathematically, the extent of
capitalization of expenditures into land values in community k is expressed as
Cap∆gk , ∆rk =
drk
⋅ qk .
dg k
(11)
12
Using the equations (4) to (9) we can solve for rk as a function of exogenous variables.
Differentiating rk with respect to g k , we can finally express the extent of capitalization
(equation 11) in both communities as
Cap∆g A , ∆rA = −1 −
1
1
, Cap∆gB , ∆rB = −
.
ˆ
x
Ψ
1+
1+
ˆ
Ψ
x
(11.1)
Thus, the relative extent of capitalization can be represented as
R∆g k , ∆ rk =
Cap∆ g A , ∆ rA
Cap∆g B , ∆ rB
=1+
2⋅ x
.
ˆ
Ψ
(12)
Given that x and Ψ̂ are strictly positive, equation (12) shows that R∆g k , ∆rk is always
strictly greater than 1. If both communities are otherwise identical, except for differences in the
elasticity of the land supply, the relation R∆g k , ∆rk = 3. Thus, ceteris paribus, land supply
elasticity negatively affects the extent of capitalization.
Interpretation of the Results
Unlike the simple analysis in section 2.1, in this model a shift in the attractiveness of either
of the two locations causes a quant ity response in both communities. Any exogenous change of
non-benefit expenditures gk in one community always simultaneously affects the demand for land
in the other community as a result of the relocation of the households. If, for example, the
urban/suburban community A receives an additional grant from the federal government, ceteris
paribus, new households are attracted from the rural community B. This causes an additional
increase in demand for residential land in A and a decrease in community B. Thus mobility
reinforces the direct capitalization effect.
Equation (11.1) implies more than full capitalization of expenditures in the urban/suburban
community A. This outcome is the result of two effects:
13
Tax capitalization effect: A federal grant is used to reduce non-benefit expenditures gA
in the beneficiary community A. This exogenous shock allows a decrease of the
property tax rate in community A. Given Cobb-Douglas preferences, each household
always spends the same share of available income for each good. Thus, holding the
number of households in each community constant and assuming completely inelastic
land supply, the decrease in the per capita tax burden exactly equals the additional
expenditures for land. In addition, the average lot size remains constant. An increase in
demand for land leads to an increase in the rental price for residential land (full
capitalization), but does not cause a quantity effect (i.e. change in individual land
consumption).
Migration effect: The tax decrease in community A makes community A relatively
more attractive compared to community B. As a consequence some households move
from B to A until the equilibrium conditions are fulfilled again (i.e. all households are
indifferent between the two communities). Migration to A increases demand for
residential land in A and, as the land supply is inelastic, decreases average lot sizes and
causes an additional increase of the residential land price in community A (additional
capitalization effect). The extent of this “migration based” effect depends on the
relative density of the two communities ( Ψ̂ ) and on the relative community size (x).
(See explanation below.)
On the other hand, the rural community B exhibits less than full capitalization. As
described in section 2.1, an exogenous decrease of non-benefit expenditures gB in the rural
community B leads to a positive land price effect and a positive quantity effect (i.e. the land
consumption increases as land supply is elastic). Thus, the “tax capitalization effect” in the rural
community is smaller than 1. The “migration effect” also consists of a positive price effect but of
a negative quantity effect (i.e. ceteris paribus the individual land consumption decreases as new
residents move to the rural community B). Thus, the extent of capitalization is larger than the
pure “non-migration effect” but always remains <1 as indicated in equation (11.1). The extent of
the migration based change in demand for land also depends on the relative density of the two
communities (i.e. Ψ̂ ) and on the relative community size (i.e. x).
14
Equation (12) implies that the elasticity of the land supply always has a negative effect on
the extent of capitalization. The strength of this nega tive effect, however, depends on two
factors: R∆g k , ∆rk increases with x and decreases with Ψ̂ . The reasoning behind this result is
quite intuitive. First, a shift in the non-benefit expenditures in a community always changes the
relative attractiveness of the two communities. If the affected community is small, the relative
change in demand for land is large and thus the relative price effect is stronger. The smaller the
urban/suburban community compared to the rural community (i.e. the larger x), the larger is the
relative price change in the urban/suburban community compared to the price change in the rural
community. Second, a change in per capita expenditures per square unit of land , the
denominator of equation 11), is much higher in densely populated areas than in non-dense areas.
The model also allows us to analyze the impact of a change in commuting costs, such as
widening access roads or adding a new rail line, on land values. In contrast to a change in percapita expenditures, it is possible to show with simulations that the extent of capitalization of
commuting costs is not necessarily higher in the urban/suburban community where the elasticity
of the land supply is low. (See appendix B for a mathematical derivation of this result).
Finally, we note that the model incorporates a single period, so there is no distinction
between owning and renting. In this case, the price of land is equivalent to its rental value. In
reality, a majority of households in the United States are owner-occupiers. Our model ignores the
possibility that when the rental price of residential land increases, the affected households receive
a capital gain that may offset the increased price. This wealth effect ceteris paribus increases the
available income and thus the demand for land. Unless owners of valuable land mostly live in
rural areas, however, this wealth effect will be stronger in urban/suburban areas than in rural
communities as land values are generally higher in urban/suburban areas. Thus, in a multi period
model with home ownership, the effect of land supply elasticity on the extent of capitalization of
fiscal variables and amenities (see below) should be even stronger than the theoretical model
suggests.
15
3
Empirical Results
The model in the preceding section predicts that land prices, and thus house prices, in areas
with little available land should change more strongly in response to an exogenous demand shock
than house prices in rural areas. To test this hypothesis, we turn to data from Massachusetts and
look at the impact of a popular tax limit measure—Proposition 2½—on property values. In doing
so, we utilize the basic framework in Bradbury, Mayer and Case (1999—referred to as BMC,
below) to explore empirically how capitalization rates vary with the amount of available land in a
community.
BMC examine how Proposition 2½ affected the fiscal behavior of cities and towns in
Massachusetts and the capitalization of that behavior into property values. Proposition 2½ places
important limits on local municipal spending: effective property tax rates are capped at 2.5
percent and nominal annual growth in property tax revenues is limited to 2.5 percent, unless
residents pass a referendum allowing a greater increase. BMC analyze a time period—1990 to
1994—when Massachusetts municipalities faced significant fiscal stress because of a 30 percent
cut in real state aid and a demographically driven increase in school enrollments. These
conditions presented a good setting to explore the impact of spending changes on housing values.
BMC have three principal findings: 1) Proposition 2½ significantly constrained local
spending in some communities, with most of its impact on school spending, 2) constrained
communities realized gains in property values to the degree that they were able to increase school
spending despite the limitation, and 3) changes in non-school spending had little impact on
property values. By constraining school spending, Proposition 2½ may have added a scarcity
premium for housing in localities that were able to increase school spending at a time of great
fiscal stress. The authors interpret their results as indicating that the marginal homebuyer may
place a higher value on school spending than the median voter, possibly because typical
homebuyers may have been more likely to have children in public schools. BMC also show that
communities with higher beginning of period school test scores had higher appreciations rates,
reinforcing the positive correlation between high quality schools and house prices.
We choose the methodology from that paper for a number of reasons. First and foremost,
BMC are able to estimate the impact of government policy on house values using a wellidentified methodology. Identification is quite important given that fiscal variables, such as
government grants and property taxes, are not chosen randomly, and may depend on local
16
conditions, including house prices. Thus it is often difficult to estimate a basic capitalization
equation, even before considering differences in the extent of capitalization across communities.
BMC use community characteristics and measures of Proposition 2½ from the date of its original
passage in 1980 as instruments for spending changes ten years later.
Second, and equally important, we have very detailed data on land availability in
Massachusetts that allows us to directly look at the amount of available land in each community,
rather than using proxies such as density or distance from the city center. After all, the
theoretical model depends on potential new construction to mitigate changes in house prices.
Density can depend on other factors such as the amount of commercial development and local
zoning restrictions that might obscure our ability to link capitalization with land availability.
Similarly, distance from the city center only proxies for land availability in a typical monocentric
city without suburban sub-centers and with equal access to the city center from all directions.
Neither of these assumptions holds for Boston, the major metropolitan area in our sample.
Finally, we focus on changes in spending and house prices, rather than levels of those
variables, which differs from most previous research. Using first differences controls for the
omitted variable problems that can bias cross-sectional regressions. In addition, we address the
possibility that the values of some fixed attributes change over time. Controlling for changes in
the value of attributes such as town location and school quality is important because these
attributes may be correlated with factors related to Proposition 2½.
3.1 Empirical Specification
Specifically, we examine whether the capitalization of changes in local school spending
and school quality are larger in locations with little available land. Following BMC, our basic
estimating equation for house prices is as follows:
∆P = β 0 + β1 (local characteri stics) + β 2 ( ∆spending) + β 3 ( ∆Q) + ε .
(E1)
This equation is derived by differencing a standard hedonic equation. Recognizing the
difficulty in measuring the quality of local services and schools, we include only spending on the
right- hand side of the equation. Following Brueckner (1982), we interpret the coefficient on
17
(change in) school spending as the net impact on house prices of spending another dollar on
schools, holding constant the taxes necessary to pay for the additional spending.
Regressions for house price changes between 1990 and 1994 are estimated using two-stage
least squares 15 and assume that changes in spending and new single- family home permits (∆Q)
are endogenous. Instruments include the amount of developable land in 1984 and lagged permits
as instruments for change in quantity, and additional instruments for spending changes using
variables from the time immediately surrounding 1980 when the tax limit was passed. One group
of such instruments comes directly from Proposition 2½, while a second group of instruments
add resource and cost factors that affect spending changes, including the growth in state aid from
1981 through 1984 to capture the state government’s immediate response to Proposition 2½. As
with BMC, we also report a second set of estimates that utilize additional instruments from the
late 1980s that help identify changes in non-school spending, but are less clearly exogenous. (See
BMC for a more detailed explanation of these instruments and possible issues relating to
exogeneity for all of these regressions.)
The estimating equation also contains a number of levels variables to account for possible
changes over time in the capitalized value of selected town characteristics as a result of aggregate
shocks. 16 For example, the aging of the baby boom and the associated echo baby boom has led to
an increase in public school enrollments in Massachusetts since 1990. The resulting increase in
the number of households with children in public schools has raised the demand for houses in
towns with good quality schools. BMC show that the increase in demand for good schools led to
higher house prices in communities with good test scores over the 1990-94 time period.
In examining differential capitalization, we divide the sample into 2 groups based on a
number of different indicators of land supply elasticity. Our most direct measure is the
percentage of open and public (undeveloped) land in each community. This variable comes from
a University of Massachusetts aerial survey of the entire Commonwealth of Massachusetts in
1984. All land is classified into 21 uses, including open or undeveloped land. We divide the
sample into 2 equal-sized groups and compare the coefficients across these two groups. We also
examine the measure population density, but expect that this measure will perform more poorly
than the amount of undeveloped land.
15
16
We are utilizing White’s (1980) heteroskedasticity-consistent estimator of the variance-covariance matrix and
thus report robust standard errors.
Using a similar data set, but an earlier time period, Case and Mayer (1996) find that the capitalized values of
good schools, of proximity to Boston, and of other town attributes vary significantly over time.
18
The most direct test of our hypothesis suggests that the coefficient on school spending (β 2 )
will be smaller in communities with additional available land. We also expect that school quality
will be capitalized to a greater extent in locations with a smaller elasticity of new supply.
A second test of the model comes when we compare the supply or quantity response across
different types of communities. To do so, we specify a supply equation consistent with the
demand equation (E1):
∆Q = γ 0 + γ 1 ( ∆P) + γ 2 (lagged permits ) + µ .
(E2)
We have a large number of demand instruments from equation (E1), and include all
exogenous demand variables as instruments when we estimate equation (E2). Our model predicts
that locations with more available land will have a greater land supply elasticity (γ1 ) and,
possibly, higher levels of new construction (γ2 ). This second test provides important reinforcing
evidence that the differences in capitalization identified in the price equation are due to
differences in the land supply elasticity as opposed to differences in “unobserved” community
attributes that may be correlated with available land.
In assessing the results, notice that our empirical specification looks at changes in house
prices over a 4-year period and thus is likely capturing short-run price and quantity responses to
changes in policy. To the extent that long-run supply is more elastic than short-run supply, our
empirical work might over-estimate the price effects and underestimate the quantity effects of a
given fiscal change in towns with more available land. This will bias us against finding any
effect of land availability on capitalization and supply elasticities.
3.2 The Data
The analysis below includes a large number of community characteristics, school
indicators, and fiscal variables. These variables are summarized in Table 1. During the 1990-94
period, communities show significant variation in all of these variables. For example, despite an
average increase in school spending of 15 percent, individual towns had large positive and
negative changes over the relatively short four-year time period.
The house price indexes presented in this paper are obtained from Case, Shiller, and Weiss,
Inc. and are estimated using a variation on the weighted repeat sales methodology first presented
19
in Case and Shiller (1987). 17 Because the indexes involve repeat sales of the same property, they
are not affected by the mix of properties sold in a given time period or differences in average
housing quality across communities. We use the same sample as BMC, which includes 208 of
the 351 cities and towns. In general, communities were dropped from the sample because they
had too few sales to generate reliable indexes. As such, this data limitation might lead us to
underestimate the impact of supply elasticity on capitalizatio n. Communities with the fewest
transactions that are dropped from the sample also are likely to have the most available land and
thus exhibit the smallest degree of capitalization.
3.3 Results
To begin, we estimate the same equation as in BMC, but split the sample into two parts
based on the percentage of available developable land. In doing so, we test the basic hypothesis
above, that the extent of capitalization is larger in communities with less available land. The
results—reported in Table 2—are strongly consistent with the model posited above. Our
preferred specification is reported in columns (Ia) and (Ib). In all cases, coefficients in the house
price equation in column Ia—communities with little available developable land—are larger in
absolute value than coefficients in the house price equation in column Ib—locations with more
available land. The variable of greatest interest in BMC—change in school spending—has a
coefficient that is almost three times larger (0.32 versus 0.12) in towns with little available land.
In fact, the coefficient for change in school spending is not statistically different from zero in
column (Ib), but is highly statistically significant in column (Ia). We find smaller, but
qualitatively similar results for the average test score. A test of equality for all of the coefficients
in columns (Ia) and (Ib) rejects the hypothesis with a p- value of 0.06.
The coefficients on other variables are also of interest. For example, price changes with
respect to new supply are muc h larger in developed communities, where there is much less
construction. Good commuting locations appear to matter more in communities with little
available land—communities in the Boston MSA and in the suburban ring—although our
17
The method uses arithmetic weighting described by Shiller (1991) and is based on recorded sales prices of all
properties that pass through the market more than once during the period. The Massachusetts file contains over
135,000 pairs of sales drawn between 1982 and 1995. First, an aggregate index was calculated based on all
recorded sale pairs. Next, indexes were calculated for individual jurisdictions.
20
theoretical model does not make strong predictions about the impact of commuting costs on
capitalization.
Columns (IIa) and (IIb) report the same regressions using a broader set of instruments from
BMC. The results here are quite consistent with those in the first two columns in virtually all
cases, although the difference in coefficients is slightly smaller in a couple of cases.
Table 3 reports the same regressions, except that we split the sample based on population
density instead of available land. In general we would expect that these results would be weaker
than those in Table 2. Cross-sectional differences in commercial development and zoning
policies could weaken the relationship between available supply and population density.
However, population density is reported in 1990, more contemporaneous to our sample period
than land availability, which is only available in 1984. Consistent with our model, in most cases
the primary variables, change in school spending and average test scores, are larger in absolute
value in dense than less dense locations. Nonetheless, as expected, these results are somewhat
weaker than in the previous table.
Finally, we return to the quantity test described above. Here we find evidence in favor of
the hypothesis that locations with more available land have a higher elasticity of land supply.
That is consistent with our theoretical model, as it suggests that shocks to demand lead to greater
new construction in locations with more available land. As we demonstrate above, these
locations also have a lower extent of capitalization of demand shocks.
The number of single- family home permits is the dependent variable in all supply
equations. It is important to keep in mind that these regressions measure short-run changes in
supply over a four year period and thus might significantly understate long-run differences.
Columns (Ia) and (Ib) in Table 4 report land supply elasticities without using lagged supply as
exogenous variable. The two columns show large differences between the two groups. The
coefficient on change in house prices is quite small and not statistically significant in the more
developed locations. The test of equality between the coefficients in columns (Ia) and (Ib) rejects
with a p-value of 0.11. Columns (IIa) and (IIb) in Table 4 include lagged permits to control for
other factors that might lead to new construction. The coefficient on change in house prices is
about one third larger in locations with more available land, and the test of equality between the
coefficients in columns (Ia) and (Ib) rejects with a p-value of 0.13. In addition, the constants
suggest that steady-state construction is one-half as large in relatively developed regions. We
21
would also note, however, that the estimated elasticities are much lower in this paper than other
work that looks at longer time periods. (See Gyourko and Voith 2000, for example.)
4
Conclusion
In this paper we present a model and supporting empirical work that shows that the extent
of capitalization depends critically on the supply elasticity of available land within a metropolitan
area. In particular, we argue that capitalization of fiscal variables and amenities should be
especially high in urban areas where the elasticity of land supply is low and capitalization should
be quite low in rural locations where land is more readily available. We establish this point in a
two-community model (urban/suburban and rural towns) with perfectly mobile households and
endogenous property tax rates. The second part of the paper tests the major theoretical predictions
using a unique data set from Massachusetts that includes a measure of available land for a large
number of communities. Consistent with the theory, we find that fiscal variables and amenities
are capitalized to a much greater extent in towns with little available land, and confirm that these
locations have a lower elasticity of land supply.
We see a number of possible directions for future research. Our model could be expanded
to consider political conflicts between farmers and owners of residential land, and to include
multiple income groups. We could also add homeownership and a pure public good. On the
empirical side, one could gather data on grants across localities to explicitly test the prediction of
more than full capitalization. However, any such project would have to overcome the daunting
problem that redistributive grants are not given exogenously, but instead to communities that
often have fiscal problems that might have an independent effect on house prices. In addition,
one might explore how the political support for public spending differs in communities
depending on the extent to which that spending is capitalized into higher house prices. It is quite
possible that communities with greater capitalization might be more likely to undertake costly
spending programs knowing that their expenditures are more likely to be reflected in higher
housing values.
While our model makes no distinction between renting and owning a home, we can
consider a number of possible redistributional implications of our findings. Free mobility implies
that any governmental measure—such as federal grants or state aid—targeted at one location can
impact house prices across a metropolitan area. In fact, subsidies or taxes to urban locations can
22
result in more than full capitalization, while the same subsidies or taxes in rural locations result in
much less than full capitalization. We can conclude that the capitalization of net benefits of
governmental measures mainly benefits owners of real estate in urban and suburban areas and, to
some degree, farmers in rural areas. To the extent that homeowners are wealthier than renters,
adverse redistribution effects caused by capitalization should be stronger in urban areas than in
rural areas.
23
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26
Appendix
A. Basic Model with Immobile Households and Comparative Statics
We consider a purely residential community with a fixed number of households that all
have identical Cobb-Douglas preferences. All households i = 1,…,N work in the central business
district (CBD), earn the same income yi and have commuting costs of C. Only two goods are of
interest to household i: a numeraire private good zi and residential land qi, available at a rental
price r. The property tax t is assumed to be a pure non-benefit tax and is exogenous. Thus, the
maximization problem of household i can be written as
max U i = α ⋅ ln qi + β ⋅ ln zi
(A.1)
qi ,zi
s.t.
yi = r ⋅ qi + t ⋅ r ⋅ qi + z i + C ,
(A.2)
where
Ui
α, β
is the utility of household i,
are the shares of available income that are spent on residential land and on the numeraire good
(all other goods) where α + β =1 ,
Urban/suburban Case (Inelastic Land Supply)
In equilibrium, demand for residential land must equal supply. Mathematically, this
equilibrium condition can be expressed as
N S ⋅ q *i ( r * ) = Q ,
(A.3)
where Q is the total amount of available land in the community, where N S is the number of
households in the urban/suburban case, and where * denotes the equilibrium solution.
Solving the maximization problem and using equation (A.3), the rental price of residential
land can be written as
*
r =
α ⋅ ( yi − CS ) ⋅ N S
.
(1 + t ) ⋅ Q
(A.4)
27
where C S are the commuting costs in the urban/suburban case.
Rural Case (Elastic Land Supply)
The land market equilibrium can be expressed as
θ ( r * ) ⋅ Q = N R ⋅ qi* ( r * ) ,
where
{
(A.5)
}
θ = min λ ⋅ ( r *)η ,1 ,
(A.6)
with η as the elasticity of the land supply, λ as a constant, and N R as the number of households
in the rural case.
For the elastic part of the supply curve (θ < 1), the equilibrium solution for the price for
residential land can be written as
1
 α ⋅ ( yi − CR ) ⋅ N R 1+η
r * = 

.

(1 + t ) ⋅ λ ⋅ Q
(A.7)

Comparative Statics
We now consider an exogenous demand shock: The federal government gives a grant to the
community that is used to lower taxes. Using the equations (A.4) and (A.7), the residential land
price effects of a change in the property tax rate t can be expressed as
dr
1 α ⋅ ( yi − C S ) ⋅ N S
=−
⋅
dt
(1 + t )
(1 + t) ⋅ Q
(A.8)
for the urban/suburban case and as
1
 α ⋅ ( yi − C R ) ⋅ N R  1+η
dr
1
=−
⋅
dt
(1 + η) ⋅ (1 + t )  (1 + t) ⋅ λ ⋅ Q 
(A.9)
28
for the rural case.
In our simple model with Cobb-Douglas preferences the change in property tax payments
exactly equals the change in the value of consumed land. This can be expressed as
or as
∆r ⋅ q + ∆q ⋅ r
= −1
∆T
(A.10)
∆r ⋅ q
∆q ⋅ r
+
= −1 .
(∆t ⋅ r ⋅ q ) + t ⋅ ( ∆r ⋅ q + ∆q ⋅ r ) (∆t ⋅ r ⋅ q ) + t ⋅ ( ∆r ⋅ q + ∆q ⋅ r )
(A.11)
The first term of equation (A.11) represents the price effect (capitalization effect) while the
second term represents the quantity effect. The extent of tax capitalization can also be expressed
as
Cap∆t , ∆r =
1
1
=
,
 ∆q q  ∆t ⋅ r + t ⋅ (1 + η )
∆t

r⋅
+ t ⋅  1 +
∆r
∆r
∆r r 

(A.12)
where η is the elasticity of the land supply. Equation (A.12) points out that the elasticity of the
land supply negatively affects the extent of tax capitalization. Using the derivations of the
expressions in equation (A.12) and simplifying mathematically, this can also be expressed as
Cap∆t, ∆ r =
dr (1 + t )
⋅
.
dt
r
(A.13)
Inserting the equations (A.4), (A.7), (A.8) and (A.9) into equation (A.13), we finally find
that
Cap∆t , ∆ r = −
1
.
1 +η
(A.14)
Thus, the extent of property tax capitalization only depends on the elasticity of the land
supply.
29
B. Capitalization of Changes in Commuting Costs
The capitalization of a change in commuting costs in community k can be expressed as:
Cap∆Ck , ∆rk =
drk
⋅ qk ,
dCk
(B.1)
where
α+
( yi − C A − g A α ) ⋅ ( 2 − 2α )
yi − C A
ˆ x
1+ Ψ
Cap∆C A , ∆r A = −α −
(B.2)
and
ˆ ⋅ (1 − α ) ⋅ ( yi − C B − g B / α )
−α − 1 − x Ψ
yi − C B
Cap∆C B , ∆rB =
.
ˆ x
1+ Ψ
(
)
(B.3)
The relation of the extents of capitalization can be expressed as
R∆C k , ∆rk =
Cap∆C A , ∆r A
Cap∆C B , ∆rB
2 ⋅ x x  (2 − 2 ⋅ α ) ⋅ ( yi − C A − g A α ) 

+ ⋅ 1 +
ˆ
ˆ 
α ⋅ (yi − C A )
Ψ
Ψ
.
x   (1 − α ) ⋅ ( yi − C B − g A α ) 


1 + 1 −  ⋅  1 +
ˆ  
α ⋅ ( yi − C B )
 Ψ

1+
=
As can be shown with simulations, this expression can be smaller or larger than 1.
(B.4)
30
Table 1
Variable List and Means
N=208
Variable
Standard
Deviation
Minimum
Maximum
-0.077
0.15
0.083
0.046
0.057
0.09
0.158
0.038
-0.208
-0.15
-0.323
0.001
0.071
0.54
0.680
0.230
Fiscal Variables:
Effective property tax rate, FY1980
Dummy, one year of initial levy reductions, FY1982
Dummy, two years of initial levy reductions, FY1982-83
Dummy, three years of initial levy reductions, FY1982-84
Excess capacity as percentage of levy limit, FY1989
Dummy variable, at levy limit and no overrides, FY1989*
Dummy variable, passed override(s) prior to FY1990
Dummy variable, "unconstrained" in FY1989*
Equalized property value per capita, 1980 (000)
Nonresidential share of property value, FY1980
Percentage of revenue from state aid, FY1984
Percentage of revenue from state aid, FY1981
Percentage increase in state aid, FY1981-84
0.031
0.46
0.12
0.034
0.018
0.44
0.11
0.46
16.4
0.19
0.26
0.19
0.43
0.009
0.50
0.32
0.181
0.036
0.50
0.31
0.50
6.2
0.09
0.10
0.08
0.31
0.012
0
0
0
0.000
0
0
0
6.3
0.04
0.05
0.05
-0.44
0.086
1
1
1
0.200
1
1
1
44.1
0.60
0.52
0.43
3.38
Community Characteristics:
School test scores, 1990*
Fraction of 1980 population under age 5
Dummy variable, in Boston metro area (PMSA)
Dummy variable, in Boston suburban ring*
Developable land per housing unit, 1984*
Single family permits per 1990 housing unit, 1989
Enrollment/population ratio, 1981
Median family income, 1980 (000)
Dummy variable, member of regional district
Dummy variable, member of regional high school
Percent of adult residents with college education, 1980
2690
0.062
0.45
0.19
0.66
0.008
0.20
21.0
0.26
0.19
0.20
168
0.013
0.50
0.40
0.41
0.007
0.04
5.6
0.44
0.39
0.12
2160
0.032
0
0
0.04
0.000
0.08
11.5
0
0
0.05
3080
0.112
1
1
2.17
0.038
0.42
47.6
1
1
0.60
Endogenous Variables:
Percent change in house prices, FY1990-94
Percent change in school spending, FY1990-94
Percent change in non-school spending, FY1990-94
Single family permits, 1990-94, per 1990 housing unit
Mean
Notes, marked with asterisks:
"At levy limit" is defined as levy within 0.1 percent of levy limit.
"Unconstrained" communities are not at levy limit in FY1989 and have passed no overrides prior to FY1990.
School test scores is combined math and reading MEAP test score for 8th graders in 1990.
Boston suburban ring is defined as within MSA but outside PMSA.
Developable land is defined as open, non-public acres plus land in residential use.
Sources: Massachusetts Department of Education; Massachusetts Department of Revenue, Division of Local Services,
Municipal Data Bank; U.S. Department of Commerce, Bureau of the Census.
31
Table 2
House Price Regression Results
Dependent Variable: Percent Change in House Prices, Fiscal Years 1990-1994
Sample divided by percentage of open and public (undeveloped) land in each community
Specification
Explanatory Variable
Base set of instruments
(Ia)
developed
(Ib)
undeveloped
Base set of instruments
plus Proposition 2½ variables
from late 1980s
(IIa)
(IIb)
developed
developed
Single family permits, 1990-1994,
per 1990 housing units
-.64 **
(.20)
-.14
(.17)
-.49 **
(.15)
-.087
(.15)
Percent change in school spending,
FY 1990-94
.32 **
(.12)
.12
(.11)
.24 **
(.088)
.13
(.087)
Percent change in non-school spending,
FY 1990-94
Combined math and reading MEAP test
score, 8th grade students, 1990
Dummy variable, in Boston metro area
Dummy variable, in Boston suburban ring
Constant
Number of observations
.064
(.089)
.038
(.061)
.033
(.051)
-.021
(.038)
.00014 **
(.000028)
.00011 **
(.000032)
.00014 **
(.000026)
.00012 **
(.000026)
.097 **
(.013)
.075 **
(.011)
.095 **
(.011)
.076 **
(.011)
.11 **
(.022)
.036 **
(.0094)
.10 **
(.019)
.036 **
(.0089)
-.55 **
(.078)
-.42 **
(.081)
-.54 **
(.069)
-.46 **
(.068)
104
104
104
104
Numbers in parentheses are robust standard errors.
* Significantly different from zero with 90 percent confidence.
** Significantly different from zero with 95 percent confidence.
Notes: Bold variables are endogenous. Instruments in column (Ia) and (Ib) include effective tax rate in 1980,
dummy variables for the number of years required to reduce spending due to Proposition 2½, 1980 levels of
resource variables from Table 1 (equalized property value per capita), non residential share of property value,
median family income, and percentage of adults with a college degree), percentage increase in state aid 1981-84,
percentage of revenue from state aid in 1984, and dummies for regional school district or high school. Instruments
in column (IIa) and (IIb) include those from column (Ia) and (Ib) plus 1989 constraint variables (excess capacity as
a percentage of the levy limit, dummy indicating the community is at its levy limit, and a dummy indicating the
community had previously passed an override) and the increase in education spending from 1993-94 required by
the education reform bill.
32
Table 3
House Price Regression Results
Dependent Variable: Percent Change in House Prices, Fiscal Years 1990-1994
Sample divided by population density in each community
Specification
Base set of instruments
Explanatory Variable
(Ia)
dense
(Ib)
non-dense
Single family permits, 1990-94,
per 1990 housing units
.027
(.25)
-.27
(.18)
Percent change in school spending,
FY 1990-94
.26 *
(.15)
Percent change in non-school spending,
FY 1990-94
Combined math and reading MEAP test
score, 8th grade students, 1990
Dummy variable, in Boston metro area
Dummy variable, in Boston suburban ring
Constant
Number of observations
.14 *
(.083)
Base set of instruments
plus Proposition 2½ variables
from late 1980s
(IIa)
(IIb)
dense
non-dense
.013
(.22)
-.11
(.13)
.12
(.10)
.15**
(.073)
-.076
(.085)
.042
(.054)
.026
(.050)
-.038
(.041)
.00018 **
(.000028)
.000069 **
(.000030)
.00016 **
(.000023)
.000081 **
(.000030)
.10 **
(.014)
.072 **
(.0092)
.086 **
(.011)
.073 **
(.0092)
.059 **
(.012)
.058 **
(.013)
.056 **
(.011)
.057 **
(.011)
-.64 **
(.078)
-.32 **
(.082)
-.57 **
(.060)
-.36 **
(.082)
104
104
104
104
Numbers in parentheses are robust standard errors.
* Significantly different from zero with 90 percent confidence.
** Significantly different from zero with 95 percent confidence.
Notes: Bold variables are endogenous. Instruments in column (Ia) and (Ib) include effective tax rate in 1980,
dummy variables for the number of years required to reduce spending due to Proposition 2½, 1980 levels of
resource variables from Table 1 (equalized property value per capita), non residential share of property value,
median family income, and percentage of adults with a college degree), percentage increase in state aid 1981-84,
percentage of revenue from state aid in 1984, and dummies for regional school district or high school. Instruments
in column (IIa) and (IIb) include those from column (Ia) and (Ib) plus 1989 constraint variables (excess capacity as
a percentage of the levy limit, dummy indicating the community is at its levy limit, and a dummy indicating the
community had previously passed an override) and the increase in education spending from 1993-94 required by
the education reform bill.
33
Table 4
Land Supply Elasticity Regression Results
Dependent Variable: Single family permits, 1990-1994, per 1990 housing units
Sample divided by percentage of open and public (undeveloped) land in each community
Specification
Explanatory Variable
Percentage change in house prices,
1990-1994
Base set of instruments
(without lagged supply as
exogenous variable)
(Ia)
(Ib)
developed
undeveloped
.0070
(.056)
.15
(.080)
*
Single family permits, 1989,
per 1989 housing units
Constant
Number of observations
Base set of instruments
(with lagged supply as
exogenous variable)
(IIa)
(IIb)
developed
undeveloped
.13 **
(.038)
.18 **
(.047)
4.9 **
(.44)
3.6 **
(.43)
.043 **
(.0055)
.064 **
(.0086)
.016 **
(.0049)
.032 **
(.0062)
104
104
104
104
Numbers in parentheses are robust standard errors.
* Significantly different from zero with 90 percent confidence.
** Significantly different from zero with 95 percent confidence.
Notes: Bold variable is endogenous. The instruments are all of the exogenous variables in the demand equation in
table 2 plus the exogenous instruments from the demand equation of columns (Ia) and (Ib) in table 2.