Full text of DOI:10.1111/0002-9092.00141

The Joint Influence of Agricultural and
Nonfarm Factors on Real Estate Values:
An Application to the Mid-Atlantic Region
Ian W.Hardie, Tulika A.Narayan, and Bruce L.Gardner
County level farmland and residential housing values are estimated for the Mid-Atlantic region
as a function of farm returns, developed land values, household incomes, population densities, and
location. Results are based on the hypothesis that farmland owners anticipate land development and
that nonfarm factors are important determinants of farmland prices. Response of farmland prices
to change in farm returns is found to be inelastic and relatively uniform in rural and urban counties.
Response to nonfarm factors is found to be more elastic and substantially greater in rural counties.
Key words: farmland values, land prices, Mid-Atlantic region, rural development, spatial econometric
model.
Most studies of agricultural land values in often exceed the reasonably expected future
the last thirty years have explained prices returns from farming, even in the absence of
in terms of the discounted expected future a speculative agricultural land boom.
returns from farming the land, with elabora-
tion concerning expected interest rates, infla-
tion, and speculative bubbles. For a brief
review and assessment of such studies, see
Just and Miranowski or Falk and Lee. The
main observation that sparked these stud-
ies was the boom in land prices of the
1970s followed by the subsequent bust in the
1980s: macroeconomic factors were brought
in to explain prices that could not be readily
explained in terms of observed or reason-
ably expected returns to farming. An alter-
nate approach to assessing agricultural land
values that has received increasing attention
in recent years focuses on potential non-
farm uses of agricultural land, particularly
the value of a real estate parcel when con-
verted to suburban residential or other non-
farm use. Shi, Phipps, and Colyer survey
a number of studies that incorporate both
agricultural returns and conversion to nona-
gricultural uses, and provide an application
to West Virginia. The main observation that
underlies this body of work is that land prices
The purpose of this paper is to explain
farm real estate values in terms of both
agricultural returns and potential nonfarm
value. We extend the existing models in
three ways. First, we introduce the geograph-
ical/locational element of real estate value
more explicitly following models of urban
growth pioneered by Alonso, Mills, and Muth.
Second, since these models indicate that the
market valuation of farmland and residen-
tial housing is jointly determined, we develop
a simultaneous equation model of farm and
house prices. Third, we use recent develop-
ments in spatial econometrics to test and
correct for possible spatial autocorrelation
between land values in neighboring counties.
Our empirical model provides estimates of
the effects of both farming and residential-
use factors in determining the value of farm
real estate, and provides information on
which of these factors are most important in
explaining farmland prices.
The Model
Ian W. Hardie, Tulika A. Narayan, and Bruce L. Gardner are
professor, graduate research assistant, and professor, respectively,
Agricultural and Resource Economics, University of Maryland,
College Park.
Urban economists (e.g.,Anderson, Brueckner,
Capozza and Helsley) model the value of
farmland as the discounted present value of
future rents from a combined stream of agri-
culture and nonfarm uses. Land is used in
Research was funded from
a competitive grant from the
Maryland Agricultural Experiment Station, College of Agricul-
ture and Natural Resources, University of Maryland, College
Park.
Amer. J. Agr. Econ. 83(1) (February 2001): 120–132
Copyright 2001 American Agricultural Economics Association

Hardie, Narayan, and Gardner
Influences on Real Estate Values
121
agriculture until a conversion date, t∗, after as the equilibrium price of residential land
which the land is used for a nonfarm use. If and
the nonfarm use is residential, the value of
(4)
P a(t0ꢀ z)
agricultural land at location z at time t0 is
ꢀ
ꢁ
ꢂ
Rꢀ(tꢀ z)e−r(t−t ) dt
∞
∗
ꢀ
t0
1
r
t
0
(At − Gta)e−r(t−t ) dt
=
A +
0
(1) P(t0ꢀ z) =
t0
z > zb
ꢀ
∞
(Rt − Gtu)e−r(t−t ) dt
0
+
t∗
as the equilibrium price of undeveloped
farmland. In these equations, N represents
population, D(Nꢀ z) represents the value of
accessibility of the urban center to residen-
tial households, Rꢀ(= dR/dt) represents the
marginal change in urban rents due to growth
over time in population, and zb represents
the radial distance from the urban center to
the rural–urban fringe. Location parameter z
is the radial distance from the city center to
whatever parcel is under consideration.
This model simplifies land development by
placing all new housing construction at the
rural–urban fringe, where land is being con-
verted from rural to urban use. The value of
accessibility, D(Nꢀ z), declines with (zb − z)
and becomes zero when z = zb.3 Note that
equation (3) applies only to sites within the
rural–urban boundary and equation (4) only
to sites outside of it, but that when taken
together, the two equations define a continu-
ous price surface for all locations. This model
feature depends on P d and P a being simul-
taneously determined. The marginal rent
change Rꢀ occurs because population growth
increases the distance of the new housing at
the rural–urban fringe from the urban cen-
ter. Faced with higher costs of commuting this
greater distance, housing consumers become
willing to pay more for a site that is closer to
the urban center. Because the value of agri-
cultural land depends on future urban rents
(equation (1)), this marginal increase in loca-
tion rent also increases the market price of
agricultural land.
∗
0
− Ct∗
e
−r(t −t )ꢀ
where At is the rental value of parcel z when
used in agriculture, Rt is the rental value of
the parcel in residential use, C is the cost of
converting land from agricultural to residen-
tial use, t is time, t0 the time at which the
valuation is made (the present), t∗ is the time
of conversion, r is the discount rate, and Ga
and Gu are property taxes on agricultural and
residential land, respectively. The conversion
date t∗ that maximizes P(t0ꢀ z) is the date
when the residential rental value becomes
equal to the sum of the agricultural rental
value and the interest from the conversion
cost:1
(2) Rt∗ − Gtu∗ = At∗ − Gta∗ + rCt∗
ꢁ
Note that if C is sufficiently high or R suffi-
ciently low, tꢀ will be far enough in the future
that for practical purposes the value of land
will be determined by its discounted future
rental value in agriculture, as in the tradi-
tional farmland valuation model.
Equilibrium prices can be derived for farm-
land and for developed land in residential
use by incorporating this type of land value
capitalization into the monocentric open city
model used to analyze urban growth.2 The
simplest formulation (Capozza and Helsley)
yields
ꢁ
1
(3) P d(t0ꢀ z) = C +
A + D(Nꢀ z)
r
∞
ꢀ
ꢂ
0
+
Rꢀ(tꢀ z)e−r(t−t ) dt
Although quite simplified, the urban
growth model retains many key features
observed in reality, notably that conversion of
land from farming to residential use occurs
mostly at a fringe zone that evolves outward
from an urban center over time. These mod-
els also explain the discrete drop-off of land
values that can be observed as one moves
t0
z ≤ zb
1 Brueckner and Capozza and Helsley assume that A and C are
constant over time. This assumption is stronger than needed. It is
sufficient that changes over time in Rꢀ Aꢀ Ga, and Gu, together
with the cost of back-conversion from housing to farming, never
make it profitable to convert land from residential back to agri-
cultural use.
2 Equilibrium refers here to prices that ensure that all house-
holds are housed. These prices are conditional on population,
income, transport cost, and, in this model, average lot size. Lot
size has been made endogenous in more complex formulations
of the monocentric open city model; see, for example, Fajita or
Wheaton.
3 D(Nꢀ z) replaces the term (T /rL)(zb − z) in the Capozza–
Helsley paper, where T is a constant per unit transport cost, and
L is the average housing lot size. We use the model’s equilibrium
condition ϕzb(t)2 = LN (t) to substitute zb out of this expression,
so that the unobservable distance is replaced by population.

122
February 2001
Amer. J. Agr. Econ.
beyond the fringe area, and the rise in farm (Capozza and Helsley, p. 300, equation (18)),
prices that occurs in anticipation of devel- D(Nꢀ z) is omitted from equation (6). But
opment. But agricultural rent A is assumed
to be constant across space and over time
in the Capozza–Helsley model, while in actu-
ality, farmland parcels at different locations
will have different agricultural rental values
because of differences in soil productivity
and suitability for crops that differ in mar-
ket value. Agricultural land values also will
vary across space when location creates dif-
ferences in the costs of access to input supply
and farm product markets. This key element
is omitted from the urban growth models, but
will be included in our empirical implemen-
tation by including variables that influence
farmland prices at a given site, notably eco-
nomic returns in cropping.
The empirical model also will relax the
homogeneity of housing assumption of the
Capozza–Helsley model by including vari-
ables that indicate the heterogeneity of exist-
ing housing. This extension will introduce the
possibility that parcels differ in residential
value because of soil characteristics (e.g., per-
meability), landscape features, infrastructure
availability, and age of house. The introduc-
tion of variable farmland rents and hous-
ing heterogeneity puts us in a position to
estimate the effects of both farming and
residential-use factors in determining the
value of farm real estate, and to provide
information on which of these factors are
most important in explaining farmland prices.
The Capozza–Helsey model implies that
farmland and residential land prices are
simultaneously determined. Our empirical
implementation of this model is a simulta-
neous equation land price model with two
equations:
this accessibility value will enter implicitly
through P h(tꢀ z) because of the simultaneity
hypothesis.
Xd and Xa are vectors of exogenous vari-
ables introduced to allow for our depar-
tures from the simplifying assumptions of the
urban growth model. In addition to including
agricultural rental variables and housing het-
erogeneity measures, we also include house-
hold income to relax the identical income
assumption of the urban growth model. We
replace its simple distance measure with a
version of the gravity measure of accessibil-
ity developed by Shi, Phipps, and Colyer, and
we introduce variables representing differ-
ent climates and topographies. These changes
convert the representative city model into
a regional model with multiple metropolitan
areas and also assist in econometric identi-
fication of the price equations. Conversion
into a regional model is necessary because we
use county data, with each county containing
both residential and agricultural land.
Shi, Phipps, and Colyer carried out the
empirical investigation that comes closest to
implementing the ideas embodied in our
econometric model. They consider counties
in West Virginia, estimating a single equation
model for farmland that includes locational
as well as economic variables. Besides con-
sidering additional features of the real estate
market, we generalize their approach in two
main ways. First, we estimate the value of
farmland as simultaneously determined with
residential real estate values. Second, we uti-
lize spatial econometric methods to correct
for spatial autocorrelation in unexplained
deviations of real estate values in counties
that are adjacent to each other. Simultaneous
estimation could be important in identifying
the spatial economic forces that determine
farmland values. The effect of residential real
estate value on farmland value in a county is
likely to be a locational effect in part, in that
high real estate values indicate high values
of farmland upon conversion, and real estate
values will be higher in favorably located
counties. But location also may matter for
farm value over and above the conversion
prospects, for reasons of marketing costs as
spelled out in von Thunen models.
(5) P h(tꢀ z) = Fd(P a(tꢀ z)ꢀ D(Nꢀ z)ꢀ Xd)
and
(6) P a(tꢀ z) = Fa(P h(tꢀ z)ꢀ Xa)ꢁ
Costs of development implicitly enter
equation (5) because P h(tꢀ z) is defined as
a housing price instead of as a developed
land price. Costs of buildings, streets, and
other infrastructure associated with devel-
oping a parcel of land will be included
in this price if the developed land market
is in equilibrium and, at the rural–urban
Equation (1) assumes perfect foresight of
fringe, P a(tꢀ z)
=
P h(tꢀ z) − C. Follow- future rental values, taxes, and conversion
ing the open city equilibrium price model costs. This assumption is of course false. Our

Hardie, Narayan, and Gardner
Influences on Real Estate Values
123
empirical implementation uses current val- consists of two equations that simultaneously
ues of economic variables, which implicitly explain residential and farm real estate prices.
The equation for the residential real estate
price is
assumes na¨ıve expectations of agricultural
rental values, that is, that current values are
used in agents’ valuation of farmland. As
the analysis in Just and Miranowski indi-
cates, this assumption makes the model quite
unpromising for explaining variations in land
prices over time. It does not allow for ratio-
nal dynamic adjustments in expectations or
for speculative price bubbles as analyzed,
for example, in Feldstein, Featherstone and
Baker, or Falk and Lee. Thus we will not
attempt to explain changes in land prices
over time.4
(7) Ph(iꢀ t) = a0 + a1Pa(iꢀ t) + a2Y(iꢀ t)
+ a3Z(iꢀ t) + a4(Y • Z)1/2
+ a5DS(iꢀ t) + a6A(iꢀ t)
+ a7SD(iꢀ t) + a8DD(iꢀ t)
+ eh(iꢀ t)ꢀ
where Ph(iꢀ t) is the median value of sin-
gle family housing in county i in year t (in
thousand dollar units), Pa(iꢀ t) is the mean
value of farmland and buildings (in thou-
sand dollars per acre), Y is median household
income (in thousand dollars), Z is population
density (persons per square mile), DS is the
index of accessibility of the county to rele-
vant urban centers, A is an index of the aver-
age age of houses in the county, and SD is an
approximate measure of the standard devia-
tion of house values within the county. Both
A and SD are introduced to allow for hetero-
geneity in housing quality. DD is a vector of
dummy variables, a0 to a8 are parameters to
be estimated, and eh is a random error term
that follows a spatial autoregressive process
while being correlated with ea, the error in
equation (8).
Since residential land rents are condi-
tional on income and population, household
income and population density are included
as primary housing demand factors in the
econometric model. Income per household is
expected to increase the demand for housing
and hence real estate values for a given land
area. Population in a given area also increases
demand and is expressed as population per
square mile in order to adjust for differences
in the size of counties in our sample. Note
that population density indicates more peo-
ple per acre of residential land, i.e., smaller
lots, so that density may increase the value
of real estate per acre while nonetheless
decreasing the value of the median house.5
Indicators of housing quality are included
because the characteristics of the existing
housing stock are likely to be important and
Data and Econometric Analysis
The data used for both agricultural and res-
idential real estate values are for 230 coun-
ties in six Mid-Atlantic states: Delaware,
Maryland, New Jersey, Pennsylvania, Virginia,
and West Virginia. Specific land parcels would
provide a larger and more varied database,
but we lack data for key variables for such
parcels, notably farm return data and the
value of land in alternative residential use.
We have three cross-sections of observa-
tions, for 1982, 1987, and 1992. These are
pooled in the econometric analysis, with a
dummy variable giving a different intercept
for each year (fixed-effects approach). This
allows land price to change between these
years, without specifying whether differences
between years are due to commodity prices,
general inflation, interest rates, or other vari-
ables that had common changes between
years across all our observations.
The data are from the Census of Agricul-
ture, the National Resource Inventory, and
the Census of Population and Housing. Cen-
sus data for counties has often been used
in the empirical literature explaining land
use and real estate values (see Miller and
Plantinga and references therein). Following
equations (5) and (6), our econometric model
4 In their review of evidence and prior studies finding incon-
sistency between the time series nature of U.S. average rental
value of farmland and farm real estate prices, Clark, Fulton, and
Scott note that the results suggest that land markets in differ-
ent regions of the country may be quite different. They state: “A
cross-sectional comparison of land markets might be useful in
shedding light on which of the factors discussed above are impor-
tant in generating differences in the time series of land prices
and land rents within a particular market.” (p. 154). This is a fur-
ther justification for our analysis.
5 We tried to account for the variation in lot size by adding
a measure of the acreage of urban land per person, but found
that it added nothing to the explanation of the variation in the
median residential house price across counties. We do not know
whether this happens because of offsetting effects, a poor mea-
sure of lot size, or correlation between the population density
and the lot size proxy variable.

124
February 2001
Amer. J. Agr. Econ.
may vary substantially across our sample of income is higher (and that increased den-
counties. We do not have data on measures sity could even reduce the value of hous-
ing if income is low). The square root of the
cross product (the geometric mean) is used
as a simple (generalized Leontief) extension
of the linear model.
of square footage or number of rooms on a
consistent basis for our sample, but we do
have data on the age and value distributions
of houses in each county. Housing age is used
as an indicator of quality on the assumption
that newer houses will have depreciated less.
The Censuses of Population and Housing in
1980 and 1990 asked whether the residence
was less than one year old, less than three
years old, less than ten years old, and other
age increments up to forty. We estimated a
mean age for each county’s housing stock by
using midpoints of each age range, and an age
of seventy-five for the open-ended class of
houses over forty years old. Linear interpo-
lation and extrapolation was used to project
the 1980 and 1990 mean ages to 1982, 1987,
and 1992.
A similar procedure was used to approx-
imate the standard deviation of housing
value in each county. The 1980 and 1990
housing censuses estimated the number of
houses worth less than $20,000, the num-
ber in $10,000 intervals between $20,000 and
$49,999, and the number in $50,000 inter-
vals between $50,000 and $199,999. We used
a midpoint of $350,000 for the open-ended
interval of $200,000 and over, and computed
an approximate standard deviation of this
frequency distribution of housing values for
each county.
The vector of dummy variables is a set of
instruments for variables that are expected
to influence real estate values but for which
we do not have quantified measures. Omit-
ting them would risk correlation between
included variables and the error term. The
vector DD includes year dummies to allow
a different intercept for 1982, 1987, and
1992 (as discussed earlier), and state dum-
mies to reflect differences between states
in infrastructure or policies (tax rates, land-
use restrictions) that may affect property
values. It also includes dummies for fifteen
“major land resource areas” as delineated by
the USDA Soil Conservation Service.6 These
areas differ in ways that may affect con-
struction costs or amenities that influence the
value of residential real estate.
The second equation of our econometric
model explains the mean value of farm real
estate in the sample counties. This equation is
(8) Pa(iꢀ t) = b0 + b1V (iꢀ t) + b2W(iꢀ t)
+ b3K(iꢀ t) + b4Ph(iꢀ t)
+ b5Z(iꢀ t) + b6DS(iꢀ t)
+ b7DD(iꢀ t) + ea(iꢀ t)ꢀ
The distance measure, DS, is the sum
of two components. We use the formula
where Pa is the estimated value of farm land
and buildings in county i and year tꢀ V is the
per-acre market value of agricultural prod-
ucts, W is farm production expenses per acre,7
K is the per-acre value of machinery reported
in the Census of Agriculture (a measure of
non-land capital), Ph is the median price of
residential real estate in the county, and DS
and DD are the same distance index and
dummy variables used in equation (7).
DSi
=
N0/z20 + Nj /z2j to calculate the
population-weighted distance measure, with
the subscript 0 indicating population (N0) and
distance (z0) from the county i to New York
City and j indicating the nearest central
city to the ith county. The predominance of
New York City is observable in our data.
Simple correlation coefficients indicate signif-
icantly declining real estate values through-
out the Mid-Atlantic area for both house
and farm as distance from New York City
increases. The whole structure of real estate
prices is lower in counties further west or
south of New York City, irrespective of local
price gradients associated with Pittsburgh,
Philadelphia, Washington DC, Norfolk, or
other city centers.
6 The land resource areas are primarily agriculturally based.
Our data includes the following areas, with their NRI identifying
numbers: Erie fruit and truck area (100), Cumberland Plateau
and Mountains (125), Central Allegheny Plateau (126), Eastern
Allegheny Plateau and Mountains (127), Southern Appalachian
Ridges and Valleys (128), Blue Ridge (130), Southern Coastal
Plain (133A), Southern Piedmont (136), Glaciated Allegheny
Plateau and Catskill Mountains (140), New England and Eastern
New York Upland (144A), Northern Appalachian Ridges and
Valleys (147), Northern Piedmont (148), Northern Coastal Plain
(149A), Atlantic Coast Flatlands (153A), Tidewater (153B), and
Mid-Atlantic Coastal Plain (153C).
Equation (7) is linear in variables except
for the cross-product term (Y ∗ Z)1/2. This
term is introduced with the expectation that
the positive effect of population density on
7 Different sets of expenditure items were reported in the Cen-
suses of 1982, 1987, and 1992. We use expenditures from the list
the price of housing will be larger when of 1982 items, which are reported in all three Censuses.

Hardie, Narayan, and Gardner
Influences on Real Estate Values
125
V ꢀ W , and K are the main economic vari-
Spatial autocorrelation is an econometric
ables in equation (8). V − W provides an issue that has received attention in recent
estimate of net cash value of farm out- statistical analysis of geographical cross-
sectional data. Measurement errors can arise
if spatial effects on land prices do not cor-
respond to counties as units of observa-
tion. For example the flue-cured tobacco belt
of Virginia extends across a set of con-
tiguous counties. If the tobacco program
affects land values in those counties over and
above effects of the cost and return variables
because of the role of the tobacco quota,
and we have no variable to measure this
effect, we would expect correlated errors in
this set of counties. Of course, if we have
data on such a variable, it should be included.
But there are many reasons why neighbor-
ing counties may be similar, in respects for
which no data are available, and there is a
real possibility that any model using county
data may have correlated errors among geo-
graphically adjacent observations. Depending
on whether the correlation is positive or neg-
ative, the estimated variances of the uncor-
rected model would be too small or too large.
Anselin spells out different methods to
deal with spatial autocorrelation, and the
econometric literature shows that a maxi-
mum likelihood estimator can achieve the
desirable properties of unbiased parameter
estimates, consistency, asymptotic efficiency,
and asymptotic normality (Andrews). Follow-
ing Benirschka and Binkley, we assume that
the errors for each equation in our simultane-
ous system follow a first order Markovpro-
cess: ej = λj Wej + ujꢀ j = aꢀ h, where, since
our model is a panel for three years, the spa-
tial weight matrix W is defined as
put per acre. Our reason for disaggregating
is that the two components, in the cross-
sectional data we have, may incorporate dif-
ferent kinds of information. For example, the
market value of output is likely to have a
larger transitory component than does input
expenditures, because random variation in
output prices is greater than in input prices.8
Therefore a $1 increase in V in a particular
year will have a smaller effect on farmland
price than a $1 increase in W , because V is
a less reliable source of information about
persistent economic changes that influence
asset prices. The econometric result would be
b1 < b2 in absolute value.
A theoretical justification for a (capital-
ized) farmland rent model, based on maxi-
mizing quasi-rents to a fixed land factor, can
be found in Palmquist. In our model K is
included along with V and W because the
returns to land given by V − W incorpo-
rate returns to all fixed factors, not just land.
The availability of more capital per acre will
increase V by the marginal product of capital,
but that effect should already be measured
in V . For a given level of V and W , meaning
a given level of measured current net cash
flow per acre, more capital per acre may be
an indicator of larger permanent net returns
per acre, and hence increased farmland value
per acre.
The theoretical model justifies inclusion
of the value of residential housing. A full
analysis also should incorporate the value
of land in alternative commercial uses, for
example, retail businesses or manufacturing
facilities. We lack data on county-level real
estate values of land for these purposes. Our
assumption is that equilibrium in the nona-
gricultural land market roughly equates the
marginal value of land in all urban uses, so
that those counties that have a high value of
residential housing also have similar values
of commercial real estate. But if there are
important exogenous variables that influence
the value of commercial real estate and that
are not captured by our population, income,
and locational variables, then their influence
will be omitted.



W1
0
0
0

(9) W = 0 W2
0
0 W3
The contiguity matrix for each year, Wt, can
differ across years in the number of observed
counties. These matrices summarize all of the
information about spatial dependence in the
model. W is constructed so that the (iꢀ k)
element of Wt is 1 if a county is contigu-
ous and zero if it is not. The lambdas are the
spatial autoregressive coefficients that mea-
sure the correlation between county i error
and composites of the errors of its contiguous
counties.
GLS estimates are obtained by transform-
ing the stacked data:
8 For the 1910–1997 period, the standard deviation of annual
changes in the log of USDA’s index of prices received by farmers
is 0.128, while the analogous standard deviation in the prices paid
index is 0.082.
(10) [I−(λ⊗W)]Y=[I−(λ⊗W)]Xb+uꢀ

126
February 2001
Amer. J. Agr. Econ.
where u ∼ N(0ꢀ σ2I)ꢀ Y contains the price is thousands of dollars per acre while value
variables Pa(iꢀ t) and Ph(iꢀ t), X contains of production is measured as dollars per acre.
the explanatory variables in equations (7) Thus, the coefficient of 0.00295 for V means
and (8), b contains the stacked parameters of that a $1 increase in output value per acre
the two equations, and λ is a 2 by 2 diago- generates a $2.95 increase in the price of
nal matrix containing λj . Parameter estimates farmland, other things equal. The coefficient
for, λb, and σ2 are obtained for the system for W similarly implies a $4.82 decline in the
by maximizing the corresponding likelihood price of farmland for every $1 increase in
function.
production expenses. An increase in receipts
or reduction in costs of $1 per acre would
be expected to generate a higher multiple
of asset value if they were expected to be
permanent. But in our county cross-sectional
data for single years, the differences between
counties may have a substantial transitory
component and/or measurement error, which
would bias the coefficients of both V and
W toward zero.10 Note that the absolute
value of the expense coefficient is larger than
the receipt coefficient, as hypothesized ear-
lier. The coefficient of the non-land capital
variable, K, also is significant, and means a
$2.95 land price increase for a $1 increase in
machinery value per acre.11
A principal motivation for our study is to
investigate the effects of non-land opportu-
nities for farmland in determining the mar-
ket value of land that remains in farming.
The variable that most directly measures this
effect is Ph, the median price of residential
houses in the county. The coefficient of Ph is
significantly positive, and has a higher t statis-
tic than any of the farm economic variables.
The coefficient of 0.0272 means that a $1,000
increase in the value of the median house
increases the value of farmland by $27.20
per acre.
Estimation Results
Table 1 gives the coefficients and standard
errors of the equation used to predict
farmland prices after correction for spatial
autocorrelation (equation (8)). The spatial
autocorrelation coefficient λa is 0.353, signif-
icantly different from zero at the 5% level.
This indicates that neighboring counties have
farmland values that are positively corre-
lated for reasons that are not captured by
the set of explanatory variables used in the
model. In the unadjusted equation, however,
93% of the variation in farmland price is
explained. This is large compared to most
results with cross-sectional data, and suggests
that omitted variables cannot add a lot to the
explanation of county farmland prices in the
Mid-Atlantic region. As is the case with auto-
correlation in time series analysis, we do not
expect correction to change the magnitude of
coefficients by correcting for bias, but rather
we hope to find improvements in efficiency.
In fact, using either a 1% or 5% two-tailed
significance test, only one variable (an area
dummy) that was insignificant in the uncor-
rected model became significant as a result
of the spatial autocorrelation correction, and
no variable that was significant in the uncor-
rected model became insignificant after cor-
rection. Coefficients were observed to change
only slightly. Thus, although we do find spa-
tial clustering of the residuals from the fitted
equation (8), correcting for this turns out to
have no important consequences for statisti-
cal inference about the determinants of farm-
land prices.9
The distance variable DS is a varia-
tion of the Shi–Phipps–Colyer population-
weighted measure, the calculation of which
was described earlier. Ideally, the effects of
location on capitalized income from agri-
culture would be captured by our cost and
return measures. But transportation and mar-
ket access costs are not included in the
10 As noted earlier, we included only expenses in the categories
that were common to all three Census years in the variable W .
Thus this measure of expenditure data is incomplete. Another
measurement problem is that the receipts include livestock sales,
which are less directly related to land returns in many farming
Table 1 shows the economic variables to
be significant and to have the expected signs.
The unit of measurement for farmland price operations. Both errors-in-variables problems will tend to bias
the coefficients toward zero.
11 One of the reviewers of the paper states that “I think you
could go further in your discussion of the impact of more capi-
9 This is qualitatively similar to the findings of Benirschka and
Binkley. The effects might have been stronger in magnitude if we
were using individual farm data instead of county level aggre-
gates, as it is possible that contiguous farms would be more
strongly spatially correlated.
tal per acre. More capital per acre probably increases net returns
per acre because it reduces the amount of labor input required
per acre. Labor cost per acre is not included in W , yet it is cer-
tainly an important determinant of net returns per acre.” This is
plausible, since only the cost of hired labor is included in W .

Hardie, Narayan, and Gardner
Influences on Real Estate Values
127
Table 1. Parameter Estimates for the Farmland Price Equation—Dependent Variable: Value
ofFarmland and Buildings ($1,000/Acre)
Parameter
Estimate
Variable
t-Statistic
Variable Description
−1ꢁ308
0ꢁ388
−5ꢁ86
3ꢁ60
Intercept
DD1
DD2
V
W
K
Ph
DS
DD3
DD4
DD5
DD6
DD7
λa
Dummy for 1982
−0ꢁ0018
0ꢁ00295
−0ꢁ00482
0ꢁ00294
0ꢁ0272
0ꢁ0264
−0ꢁ090
0ꢁ919
−0ꢁ01
Dummy for 1992
4ꢁ39
Market value of farm production ($/acre)
Farm production expenditures, 1982 items ($/acre)
Farmer-owned farm machinery ($/acre)
County median house price (1,000 $)
Distance index (see text)
−3ꢁ65
4ꢁ51
21ꢁ57
12ꢁ27
−0ꢁ321
4ꢁ16
Dummy for Delaware
Dummy for New Jersey
0ꢁ386
2ꢁ00
Dummy for Virginia
0ꢁ031
0ꢁ17
Dummy for Pennsylvania
0ꢁ394
2ꢁ06
Dummy for West Virginia
0ꢁ353
5ꢁ85
Spatial autoregressive coefficient
farm cost data collected in the Census of are even less affected by correcting for spa-
tial autocorrelation than was the case for the
farmland price equation.
Agriculture. The estimated coefficient is sig-
nificantly positive, indicating that greater
nearness (which gives larger values of DS
since distances appear in the denominators)
is associated with higher farmland values. An
increase in the index of 10% of its mean
value (5.45) is estimated to increase the value
of farmland by $14 per acre.
The coefficients of the fifteen land resource
area dummies included in the equation are
not shown in table 1. Using an F test on
exclusion of the whole set of land resource
dummies, we cannot reject the hypothesis at
the 90% confidence level that all of these
coefficients are zero. Coefficients on the state
The main economic variables in the
house value equation are median household
income, population density, and the interac-
tion between them. As discussed earlier, the
reason for including the interaction term is
to allow population density to have different
effects in high-income and low-income areas.
Using the notation of equation (7), the par-
tial derivative of Ph with respect to income,
Y , is
∂Ph
∂Z
0ꢁ5a4Z0ꢁ5
(11)
= a2 +
Y 0ꢁ5
dummies, which are jointly significant, indi- and the partial derivative of Ph with respect
to population density, Z, is
cate that it is worth $910 an acre to be in
the state of New Jersey, $368 an acre to be
in Virginia, and $394 to be in West Virginia,
as compared to Maryland, Pennsylvania, and
Delaware, which are all insignificantly dif-
ferent from one another. The year dummies
indicate a significantly higher price of farm-
land in 1982 than in 1992 or 1987 (the inter-
cept), with prices all measured in 1987 dollars
using the Consumer Price Index as defla-
tor. This result is not unexpected as national
farmland prices fell more than in proportion
to net farm income in the early 1980s.
∂Ph
∂Z
0ꢁ5a4Y 0ꢁ5
(12)
= a3 +
ꢁ
Z0ꢁ5
Using the coefficients of table 2 and mean
values of Y and Z, the partial effect of Y on
Ph is 0.626, meaning that a $1,000 increase
in median household income increases the
median value of the county’s houses by $626.
The partial effect of Z on Ph is 0.0277, mean-
ing that an increase of 100 people per square
mile would increase the median house value
by $2,770. The cross-product term (coeffi-
cient of (Y ∗ Z)1/2) being positive while that
for Z is negative means that lower county
income levels, as expected, decrease the pos-
itive effect of population density on housing
prices. The partial effect of 0.0277 is calcu-
The estimated coefficients for the
equation explaining the median house price
(equation (7)) are shown in table 2. The spa-
tial autocorrelation coefficient, λh, is 0.146,
significantly different from zero, but it is
small in magnitude and the parameter values lated at the mean sample income value of

128
February 2001
Amer. J. Agr. Econ.
Table 2. Parameter Estimates for the House Price Equation—Dependent Variable: Median
House Value ($1,000)
Parameter
Estimate
Variable
t-Statistic
Variable Description
−8ꢁ174
3ꢁ092
−1ꢁ73
2ꢁ77
−5ꢁ44
17ꢁ04
−4ꢁ86
6ꢁ16
Intercept
DD1
DD2
Y
Dummy for 1982
−6ꢁ29
Dummy for 1992
2ꢁ054
County median income (1,000 $)
Population per square mile
Square root of income times population density
Average age of houses
Z
−0ꢁ0164
0ꢁ1508
−0ꢁ672
0ꢁ542
(YZ)1/2
A
−3ꢁ99
16ꢁ18
0ꢁ34
STD
DS
Pa
DD3
DD4
DD5
DD6
DD7
λa
Standard deviation of house values
Distance index (see text)
0ꢁ0133
1ꢁ069
0ꢁ94
Value of farmland and buildings ($1,000/acre)
Dummy for Delaware
−3ꢁ21
−1ꢁ01
7ꢁ14
2ꢁ70
Dummy for New Jersey
−1ꢁ82
−4ꢁ17
3ꢁ13
−0ꢁ98
−2ꢁ23
1ꢁ60
Dummy for Virginia
Dummy for Pennsylvania
Dummy for West Virginia
Spatial autoregressive coefficient
0ꢁ146
2ꢁ46
$27,150. At the income level of the county
In contrast with the farmland value
with the lowest median income in our sam- equation, an F test indicates that exclusion
of the group of land resource area dummies
has a significant effect on the house value
equation.Again, to conserve space, their coef-
ficients are not shown in table 2. House
values are significantly lower, holding other
variables constant, in areas 126, 133a, 136,
144a, 149a, and 153b (see footnote 6 for loca-
tions). The state and year dummy coefficients
are shown. New Jersey median house values
are $7,140 higher and Pennsylvania $4,170
lower compared to Maryland (the state in the
intercept), holding other variables constant.
With respect to the year dummies, 1992 is
$6,290 lower than the intercept year (1987),
and 1982 is $3,090 higher. This indicates a
declining trend in real (1987 dollars) hous-
ing prices since 1982, reflecting the general
decline in housing prices that occurred in the
Eastern U.S. during this period.
ple, $10,200, the partial effect of density is
reduced to 0.0164. Thus, even when qual-
ity of housing is held constant, the posi-
tive demand effect of increasing population
density on house values is attenuated when
median income is lower.12
Our indicator of housing quality, the aver-
age age of houses as reported in the 1990
Census of Population and Housing, has a sig-
nificantly negative effect on residential real
estate values. The coefficient indicates that
each additional year of average age of houses
reduces the average value by $672. We also
included in the house value equation an indi-
cator of the heterogeneity of housing value,
the standard deviation of house values as
explained earlier. This variable is highly sig-
nificant in explaining the house values, its
positive sign meaning that greater variation
in housing values in a county is associated
with higher average values. However, neither
farmland value nor closeness to urban cen-
ters, as indicated by our distance index, has
a significant effect on house values given the
county’s housing quality, income, and popula-
tion density.
How Urbanization Affects Farmland Prices
Table 3 presents some results from an anal-
ysis of how farmland prices respond to
changes in land value determinants in coun-
ties with different population densities.13 Val-
ues in this table are computed by sorting the
12 It could be argued that population density is properly an
endogenous variable, because low housing values attract more
people. If true, the mis-specification in our model would mean
our estimated positive effect of density is biased toward zero
(because it is contaminated by the negative causality running
from housing value to density). Therefore our estimated positive
effect should be viewed as a lower bound on the true effect.
13 The results in table 3 are for 1992. We also computed these
values for 1987 and 1982. Results are similar for the three years
and our interpretations apply to all three time periods. Numerical
results are presented only for 1992 to simplify explanation and
to save space.

Hardie, Narayan, and Gardner
Influences on Real Estate Values
129
Table 3. Relationships between Farmland Value and Selected Land Value Determinants, by
County Population Density Quintile Grouping, 1992
Population Density Quintile Grouping
Item
1st
2nd
3rd
4th
5th
Population per square mile
Farmland value ($/acre)
25ꢁ7
52ꢁ3
85ꢁ2
199ꢁ3
1537ꢁ4
7ꢀ892
1ꢀ173
1ꢀ473
217ꢁ83
0ꢁ437
68ꢀ273
1ꢁ262
30ꢀ449
1ꢀ952
2ꢀ719
Farm revenues ($/acre)
Mean revenue elasticity
182ꢁ79
0ꢁ460
399ꢁ86
0ꢁ605
373ꢁ06
0ꢁ405
1ꢀ234ꢁ19
0ꢁ462
Median house value ($)
Median house value elasticity
59ꢀ461
1ꢁ381
83ꢀ156
1ꢁ161
34ꢀ286
101ꢀ351
1ꢁ016
40ꢀ277
149ꢀ668
0ꢁ517
Median household income ($) 28ꢀ211
Mean income elasticity
49ꢀ827
1ꢁ396
1ꢁ217
1ꢁ405
0ꢁ902
0ꢁ432
Mean population elasticity
0ꢁ042
0ꢁ045
0ꢁ043
0ꢁ043
−0ꢁ004
county observations by population density, per acre, farms also are increasingly pur-
finding quintile values, and then calculating chased for purposes other than income gen-
mean values for farmland prices, farm rev- eration. Table 3 shows that average revenue
enues, house prices, household incomes, per acre increases substantially with popu-
and population densities for the counties
within each quintile grouping. Partial elastici-
ties then are computed using estimated coef-
ficients from tables 1 and 2 and the means
for each quintile grouping. These elasticities
show the percentage response in estimated
farmland prices to small percentage changes
in farm revenues per acre, county median
house prices, median household incomes, and
population,14 other land value determinants
held constant. They can be compared across
quintile groups to see the potential effect
of urbanization on the response of farmland
prices to changes in other economic factors.
The comparison indicates that policies or
events that affect revenues, house prices,
incomes, and population size can affect farm-
land prices differently in rural and urban
counties. For some policies, these effects will
vary substantially, and a uniformly applied
policy will create quite different farmland
price responses. For others, population den-
sity will not matter and responses will be rel-
atively uniform across counties.
lation density across the quintile groupings.
Despite this increase in absolute value, farm-
land prices respond similarly to changes in
farm revenue in rural and urban counties. As
a rule of thumb, the table indicates that each
permanent 1% change in farm revenue trans-
lates into an approximate change in farmland
price of 0.4 to 0.6%. Although not shown in
the table, a similar pattern can be observed
for farm expenditures. Each permanent 1%
change in farm expenditure translates into an
inverse 0.2–0.5% change in farmland values,
with the largest response of −0ꢁ5 occurring
in the counties in the third quintile group-
ing and the smallest response of −0ꢁ2 occur-
ring in the urban counties in the fifth quintile
grouping.
More distinct differences between rural
and urban counties are observed in farm-
land prices when median house values and
non-farm household incomes are considered.
Farm prices tend to increase systematically
relative to house values as counties become
more populous, and the elasticity of response
of farmland price to house price diminishes
as a result. The elastic response of farmland
prices to changes in house values observed in
rural counties becomes an inelastic response
when urban counties are considered. From a
policy perspective, a change in inflation, taxes,
or other factors that uniformly change house
values will alter the structure of farmland
prices across counties.
Gardner and Heimlich and Barnard have
noted that the character of farming changes
as areas become more urban and farming
practices alter to reflect more expensive land
and greater access to markets. While com-
mercial farmers seek to increase net revenues
14 Since total county land area drops out of the elasticity com-
putation, these partial elasticity estimates may be interpreted as
the response to a change in either total county population or in
the number of people per square mile within the county.
Why farmland prices rise more rapidly than
house prices as counties become more urban

130
February 2001
Amer. J. Agr. Econ.
Figure 1. Elasticity offarmland prices with respect to median household income, 1992
remains an open question. One reviewer of Mid-Atlantic region. Counties represented by
this paper points to changes in the ratio of
value of the structure to the lot: bigger houses
on smaller lots and more houses per acre
increase the value of an acre of developable
land in urban areas relative to rural areas.
But other factors also may come into play.
“Gentlemen farmers”seeking country estates
may, for example, demand more farmland in
urban counties where access to urban centers
is high. It is interesting to note that capitaliza-
tion of farm revenues into land values does
not seem to change with urbanization, since
there is no systematic pattern in the ratio of
farmland values to farm revenues across the
quintile groupings.
Elasticities for household income show a
similar pattern to those for house prices, in
part because the effect of income on farm-
land price occurs through change in house
prices in the model. This response conse-
quently involves both price equations. The
numbers in the table indicate that a uni-
form change in household income, such as
might occur from changing a standard income
tax exemption, will act through house val-
ues to alter the structure of farmland prices
across counties. Prices in rural counties will
increase significantly more than prices in
urban counties if income increases. But if
income decreases, prices in rural counties
will decrease significantly more than prices in
urban counties.15
the lightest shade in the figure have inelastic
price responses. Rural counties represented
by the darkest shade have elasticities that are
greater than 1.25. As the figure shows, inelas-
tic responses are mostly restricted to areas
around major urban centers.
Computation of the elasticity of farmland
price to change in county populations also
involves both equations of the model, as pop-
ulation is postulated to be a fundamental
determinant of both farmland and housing
prices. Interestingly, the response of farm-
land prices to change in population density
turns out to be very stable across all but
the fifth quintile grouping of counties. Farm-
land prices increase about 0.04 to 0.05% for
every 1% increase in population. In the fifth
quintile grouping, the elasticity turns nega-
tive due to a negative relationship between
median house value and population den-
sity. Although signs change when counties
become urban in nature, all of the elasticities
of farmland price with respect to population
are close to zero. Thus farmland prices are
found to respond to changes in income, house
prices, farm revenues, and expenditures, but
to be very inelastic with respect to popula-
tion change when these other effects are held
constant. Most of the effect of population
change on farmland prices appears to operate
through the markets for products obtained
from land, rather than directly on farm real
estate values.
Figure
1
shows how these different
responses are distributed throughout the
15 This result is possibly related to the distance-to-market expla-
nation of farmland price volatility investigated by Benirschka
and Binkley.

Hardie, Narayan, and Gardner
Influences on Real Estate Values
131
Conclusions
house prices than by policies that specifi-
cally change farm returns. Furthermore, these
effects, whether for better or worse, will be
greater in rural counties where population
density is lower and development is less. As
an example, an income tax policy change that
affects all residents of a rural county would
have a greater effect on farmland prices than
a policy that directly changes farm prod-
uct prices or costs. Incidence of these effects
also will be different, with small differences
between rural and urban counties in the case
of farm income policies and substantial differ-
ences in the case of nonfarm income changes.
These conclusions are specific to the Mid-
Atlantic region and we do not know if
they extend to the rest of the nation. They
do suggest, however, that policies developed
for broader purposes may have as much or
more effect on farmland prices as policies
targeted directly at improving agricultural
returns. Also, our findings suggest that events
that change the potential gains from devel-
oping farmland may play a greater role in
explaining the volatility of farmland prices
than has been recognized in previous studies.
As noted at the outset, the analysis in this
paper was carried out primarily to learn more
about how non-farm factors might affect
farmland prices.The model requires that farm
owners be aware of land development oppor-
tunities. It depends on the hypothesis that the
effect of these opportunities can be captured
in an equilibrium farmland price model by
including residential real estate house prices
and factors such as population density as
explanatory variables. Urban growth theory
indicates, in turn, that developed land val-
ues depend on farmland values. Thus we esti-
mate a model that simultaneously determines
housing and farmland prices.
Results indicate that farm earnings and
non-farm factors both play significant roles
in determining farmland prices. When non-
farm factors are controlled, An increase of
$1.00 per acre in farm revenues is estimated
to change the value of farmland by $2.95. A
change of $1.00 per acre in farm expenditures
is estimated to change farmland value in the
opposite direction by $4.82. The larger mag-
nitude of the expenditure effect is explained
as a consequence of permanent and tempo-
rary value change; change in farm expendi-
tures, as observed in any given year, has a
smaller transitory component than change in
farm revenues.
[Received August 1999;
accepted February 2000.]
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