WPTC 0505
I 'ional Agricultural Trade and Policy Center
URBAN SPRAWL AND FARMLAND PRICES
By
Grigorios Livanis, Charles B. Moss, Vincent E. Breneman, & Richard F.
Nehring
WPTC 0505 June 2005
WORKING PAPER SERIES
'V
i~fr
UNIVERSITY OF
FLORIDA
Institute of Food and Agricultural Sciences
INTERNATIONAL AGRICULTURAL TRADE AND POLICY CENTER
THE INTERNATIONAL AGRICULTURAL TRADE AND POLICY CENTER
(IATPC)
The International Agricultural Trade and Policy Center (IATPC) was established in 1990
in the Institute of Food and Agriculture Sciences (IFAS) at the University of Florida
(UF). The mission of the Center is to conduct a multidisciplinary research, education and
outreach program with a major focus on issues that influence competitiveness of specialty
crop agriculture in support of consumers, industry, resource owners and policy makers.
The Center facilitates collaborative research, education and outreach programs across
colleges of the university, with other universities and with state, national and
international organizations. The Center's objectives are to:
* Serve as the Universitywide focal point for research on international trade,
domestic and foreign legal and policy issues influencing specialty crop agriculture.
* Support initiatives that enable a better understanding of state, U.S. and international
policy issues impacting the competitiveness of specialty crops locally, nationally,
and internationally.
* Serve as a nationwide resource for research on public policy issues concerning
specialty crops.
* Disseminate research results to, and interact with, policymakers; research, business,
industry, and resource groups; and state, federal, and international agencies to
facilitate the policy debate on specialty crop issues.
Urban Sprawl and Farmland Prices
By
Grigorios Livanis,
Charles B. Moss,
Vincent E. Breneman,
And
Richard F. Nehringt
May 23, 2005
T Grigorios Livanis is a postdoctoral research associate in IATPC and Charles B. Moss is a professor in
the department of Food and Resource Economics, both at the University of Florida. Vince Breneman and
Richard Nehring are economists with the Economic Research Service of the United States Department of
Agriculture. The views presented in this manuscript represent those of the authors and do not necessarily
correspond with those of the USDA. The authors thank the editor and two anonymous referees of this
journal for their comments on previous drafts of this study. All remaining errors are the authors.
Florida Agricultural Experiment Station Journal Series No. XXXX.
Abstract
Urban Sprawl and Farmland Prices
A theoretical model of farmland valuation is developed that allows urban sprawl to affect
farmland values through the conversion of farmland to urban uses, shifts in production to higher
valued crops, and the speculative effect of urban pressure on farmland values. This model is
estimated using county level data in the continental United States. Evidence is found for all three
effects of urban sprawl on farmland values, with a significant contribution of urban pressure on
net agricultural returns around major urban centers. Ancillary evidence supports that the latter
effect is attributable to shifts to highvalued crops.
Keywords: hedonic determinants, land prices, spatial productivity, urban sprawl.
JEL Classification: R14, Q15, D24, C33.
Urban Sprawl and Farmland Prices
Urban sprawl and land use has become a major policy issue since the 1980s. The expansion of
urban areas has led to a reduction in the amount of farmland around many major metropolitan
areas along with a reduction in prime farmland, and rangeland (Imhoff et al.; Greene and Stager).
This increased farmland demand for urban uses has led to higher farmland values over time,
particularly in areas of rapid urban growth (Shi, Phipps and Colyer). This paper investigates
whether urban sprawl has also affected the productivity of farmland close to urban centers by
increasing the share of highvalued crops resulting in higher farmland prices.
The effect of urban sprawl (e.g., population, income) on farmland prices have been
investigated by several studies (i.e., Chicoine; Shonkwiler and Reynolds; Mendelsohn, Nordhaus
and Shaw; Shi, Phipps and Colyer). Recently, several studies have used the urban growth model
of Capozza and Helsley (1989) to examine the effect of urbanization on farmland values at the
parcel (Cavailhes and Wavresky) and county level (Plantinga and Miller; Hardie, Narayan, and
Gardner; Plantinga, Lubowski, and Stavins). Hardie, Narayan, and Gardner applied the model at
the county level to six MidAtlantic States. Their results indicate that the response of farmland
values to changes in development is more elastic and greater in rural counties, while response to
changes in farm returns is inelastic and relatively uniform for rural and urban counties. Plantinga,
Lubowski, and Stavins use the stochastic version of the model (Capozza and Helsley 1990) to
decompose farmland values into rents from agricultural production and future land development
at the county level of the United States. Their results suggest that option value associated with
irreversible and uncertain land development is capitalized into current farmland values.
The idea behind the urban growth model of Capozza and Helsley (1989) as well as other
models of urban sprawl (i.e., Arnott and Lewis; Wheaton; Brueckner) is that current farmland
values represent the present value of future agricultural and potential development rents. This
formulation assumes that the return to agricultural production initially exceeds the return to
urbanization for a period of time until the value of urban use increases enough to trigger
conversion. As a result, land far enough from a city sells for its discounted rents from
agriculture, while farmland close to the urbanrural boundary sells for a premium that is equal to
the present value of anticipated increases in rent after the land is converted to urban use.
Proximity of farmland to urban centers may not only affect the development component
of farmland values but may also increase the productivity of farmland by reallocating production
from commodityoriented agriculture to highervalued alternatives. That is, urbangrowth could
increase the share of areaspecific, highvalued crops, such as fruits, vegetables, and horticultural
crops, and reduce land in commodities such as corn, wheat, and soybeans. This phenomenon is
apparent in Table 1, which presents the share of highvalued crops for groups of counties ranked
by their 1997 accessibility index. The accessibility index is a measure of urban pressure that
increases as the population weighted distance to urban centers decreases.1 From this table it is
apparent that counties that are more accessible have a larger share of highvalued crops.
The shift to highvalued crops increases the profitability of agriculture, which in turn
accentuates the increase in farmland values from urban pressure. Thus, urban pressure also
affects the anticipated rents from agricultural production. Differences between the two effects
have implications for the farm sector. Increased farmland values that result from increased
opportunity for conversion implicitly increase the opportunity cost of farmland. This increased
opportunity cost could then result in reduced competitiveness and productivity for agriculture
adjacent to urban areas. However, increased farmland values resulting from changes in the crop
portfolio towards highervalued crops represent increased productivity for farms close to urban
areas. The novelty of this paper is the examination of the effect of urban sprawl on agricultural
returns and, in turn, the isolation of this effect in determining farmland values.
This paper investigates the effect of urban sprawl on farmland values in the United
States, explicitly accounting for the effect of urbanization on farmland productivity and the rents
from future farmland development. In the next section we develop a theoretical approach for this
decomposition. We assume that at each point of time, farmland may be converted into urban use
or remain in agriculture. Each event is modeled as a Poisson probability that depends on
population and on the distance from the urban center. Following the insights of von Thunen we
develop a theoretical formulation showing that higher farmland values close to urban centers
may be related to shifts in production to highervalued crops. We then rely on Brueckner to
model the effect of urbanization on the development component of farmland. Unlike the
formulations of previous studies, our formulation includes three relationships: one for farmland
pricing, one for returns to agriculture, and one for development rents. This specification isolates
the relative contribution of urban pressure to returns to agriculture and the contribution of urban
pressures through the conversion of farmland to urban uses. We then apply our model to county
data of the contiguous United States. The results are presented in the following two sections.
Finally, we discuss the results and implications of our estimates.
Modeling Conversion of Farmland and Productivity
Let T be a stochastic variable that denotes the moment of farmland conversion to residential
land. In all moments after T land remains in residential use. Following the formulation in urban
growth models (Capozza and Helsley 1989), farmland value at time t and location 3 reflects
both the discounted economic rents from farming plus the discounted rents from urbanized
farmland if urbanization occurs:
T
VA )=E, fersRR(s,3)ds+ fesR,(s,,)ds (1)
It T
where RG (s, 8) is the net return to farmland in period s at location 5, 5 is a vector of spatial
coordinates, R (s, 3) is the net return to urbanization in period s at location 3 (including the
cost of conversion), r is the discount rate, and E, [.] is the expectation operator conditional on
information available at time t.
Suppose that farmland will be converted with probability Ads in the interval ds. If
A = 0 conversion will never occur, while if A > o0 conversion occurs instantly (A can take any
nonnegative value). Using the Poisson distribution the probability of farmland remaining in
agriculture at a given moment s (i.e., implying that the conversion did not happen until that
moment) is e ". The probability that farmland converts into residential uses in moment s, is
given by Ae s. Since we are interested in crosssectional changes in farmland values (as in
Plantinga, Lubowski, and Stavins) we assume for the moment that net agricultural rents are
constant over time (RAG(s,8) = RAG(8) for all s). We also assume that returns to urbanization
are constant over time (R (3)).2 Solving for the value function of the second term in Equation 1
the farmland value at time t and location 3 can be written as
V,(t,) e= sRAG)eds + R (3)Ae "ds (2)
t t r
Next, we assume that the arrival rate A of the Poisson process depends on a parameter 0
related to agglomeration (i.e., population) and on the distance 3 of the parcel of farmland to the
central business district (CBD) of the urban place (A = A(0, )). An increase in population is
expected to have a positive effect on the probability of urbanization, while an increase in the
distance to the CBD is expected to have a negative effect on the probability of urbanization.3
Since rents per unit of land decline at a decreasing rate with distance 3 from the CBD of
the urban place (Muth), we assume that a similar specification holds for the probability of
urbanization per unit of time. O'Kelly and Homer use a similar specification to measure
accessibility or the relative potential of a given location. Hence, we adopt the following
specification for the arrival rate
A(O,8) =0 (3)
The expected value of the Poisson process is given by (1/A) and defines the expected time of
urbanization for a specific parcel of land. The expected time to urbanization decreases as
distance to the CBD decreases or as population increases. Taking into account the above
specification for the arrival rate, Equation 2 becomes
et(r+e(,s)) /(, ) e t(r+( ,se))
V (t, 8)= R4RAG ()+ Ru (.R8) (4)
r + A(6, 6) r(r +A(0, ))
Evaluating this expression at t = 0 yields
V (0,3 )= RAG(g)+ RA,(0,) () (5)
r + lA(0,5 ) r (r + A (0, 3))
The intuition behind Equation 5 is consistent with economic theory. The first part of the
equation represents the discounted value of net agricultural returns. As in the standard farmland
pricing formula, the value of farmland is an increasing function of the net return to agriculture
and a decreasing function of the discount rate. The second term in the righthand side of
Equation 5 is the discounted expected returns to development, which have a positive effect on
the farmland value. Moreover, both terms depend on the speculative component of farmland
values as captured by the probability of conversion A(O, 8). Comparative statics on Equation 5
lead to the following proposition:
Proposition 1. If 8b defines the distance from the CBD to the boundary of urban place, then
farmland values in equilibrium are characterized by the following properties.
(a) If > 0 or 3 > +* then A > 0, which implies that lim V, (0,,) = RAG ()/r, V > b.
(b) If 0 +o or > 0+ then A > +oc, which implies that lim V,(0, 3) = R( ()/r, V5 < b.
(c) Ceteris paribus, an increase in the instantaneous probability of conversion results in a
smaller percent offarmland value contributed by net returns to agriculture and to a larger
percent contributed by the net returns to urbanization, since V5 > 8b we have that
(o0, ) (R, (3) (3)) .
OA (r +A)
The proof of the proposition is straightforward with the exception of Proposition 1.b where we
have applied L' Hospital's rule and in Proposition L.c where we assume that net returns to
urbanization are always positive, for every 3. Proposition 1.a indicates that in locations with
low population density or that are far from the CBD, the probability of conversion is zero and so
the value of farmland should only be reflected by the discounted net returns to agriculture. If the
land is located within the CBD (3 <3b ) then it has been converted into urban uses and its value
is reflected by the discounted net returns to urbanization (1.b). Given that the probability of
conversion A has also been defined as the accessibility of a given location to the CBD, then
from Proposition 1.c we have that the effect of accessibility to the value of farmland depends on
the relationship between net returns to agriculture and urbanization. Specifically, if net returns to
agriculture are negative or if the net returns to urbanization are greater than the net returns to
agriculture, then an increase in the accessibility (3 4 or 0 T) of farmland will lead to an increase
in its value. However, for farmland at a given location > 8b, where the net returns to
agriculture are greater than net returns to urbanization, an increase in accessibility will result in
lower farmland values. 4
Equation 5 allows for a crosssectional decomposition of the current farmland value into
agricultural and development components. Following the insights of von Thunen and Ricardo,
farmland at different locations will have different net returns to agriculture because of
differences in soil characteristics, suitability for crops with different market values, and
proximity to urban centers. The latter implies that net returns to agriculture are endogenously
determined in Equation 5.
Effect of Urban Pressure on the Return to Farmland
To model the effect of urban pressure on the agricultural component of farmland values, we
construct a profit function formulation consistent with the von Thunen effect of distance from a
central place that explicitly accounts for heterogeneity in soil characteristics of different parcels
of land and climate. Under the von Thunen formulation, highervalued crops with relatively high
transportation costs are grown in proximity to urban areas. As the distance to the central place
increases agriculture becomes increasingly commodity focused.
Profit at the farm level, accounting for the spatial variation in farmland prices and
differences in soil quality, is given by
max (pr(3))'yw'xrDeRu
y,x,A,K,D
st f(y, x, A, K, S) = 0 (6)
(K K)+(A A)V = DD
where p is a vector of output prices, y is a vector of outputs, w is a vector of input prices, x is
a vector of inputs, r is the interest rate on farm debt, D is the level of farm debt, f(.) is a
multiproduct production function, A is the acres of farmland, K is the level of intermediate
assets, S denotes soil characteristics, VA is the value of farmland, r(3) is the transportation cost
associated with each commodity, 3 is the distance from the parcel of farmland to the CBD and
the subscript zeros denote initial levels. As the multiproduct production function is written in an
implicit form, we assume that f, < 0, f, < 0, fK < 0, f, < 0 and f, > 0, where the subscripts
denote partial derivatives.
From this formulation, we develop the marginal value of each unit of output given the
transportation cost and the marginal value of farmland. The marginal value of each output is
L ( ,f(y,x, A,K,S)0 (7)
= (ap, ,()) =0 (7)
where /u, is the shadow value on the production constraint (the Lagrange multiplier for the first
constraint in Equation 6). Equation 7 yields the standard relationship that the marginal rate of
transformation between two products equals the inverse of their price ratios. Note that increases
in the transportation cost for each commodity implies a relative reduction in the output of that
commodity. Equating the shadow value of production across all outputs yields
.... (8)
/1 f(y,x,A,K,S) Of(y,x,A,K,S)
,1 Yn
Differentiating the shadow value with respect to distance then yields
aT,(s)
1 < 0 (9)
8Of(y,x,A,K,S)
ay,
as long as the transportation cost is an increasing function of distance.
Turning to the value of farmland, the firstorder condition with respect to debt implies
that p2 = r (where /p is the Lagrange multiplier for the second constraint in Equation 6).
Substituting this result into the firstorder condition with respect to land values yields the
standard Ricardian equation for farmland values
f (y,x, A,K, S)
VA = A (10)
r
Since the partial of the multiproduct production function with respect to land is negative,
Equation 10 is the same value as found in Equation 5, if conversion to urban use never occurs. In
particular, we are interested in specifying the net return to agricultural activities in Equation 1 as
f (y,x, A, K, S)
RAG() = /  (11)
OA
Merging the results of Equations 8 and 11, we have
(p, r, (3)) Of (y,x, A,K, S) dy,
R4(G ^^) ( 30 ) _^)) (12)
Af(y,x,A,K,S) OA dA
where the last derivative is evaluated at the optimal point of production.
Given the results from Equation 9 we conclude that the net return to farmland is a
decreasing function of the transportation cost and distance to the market. In addition, the value of
farmland is an increasing function of the relative productivity of farmland. Specifically,
f (y,x, A, K, S)
dy. A (13)
dA Of(y,x,A,K,S)
ay,
The solution in Equation 13 assumes that all agricultural products are produced continuously
throughout the region. The formulation in Equation 6 could be changed to guarantee that only
nonnegative quantities of crops could be chosen. This would transform the problem into a
KuhnTucker optimization problem. The point is that not all crops would meet the marginal
value condition in Equation 8. Hence, lowvalued crops would not be grown close to urban
places. This an important finding since it implies that higher values of farmland close to urban
places are not entirely explained by agglomeration but instead may also be related to increased
productivity as farmers shift their production to highvalued crops suitable for the specific area.
While the intuition of the von Thunen formulation appears sound, our formulation
explicitly recognizes two caveats. Highvalued crops are assumed to have the highest
transportation costs. Undoubtedly this assumption would be justified by the value of freshness in
delivering produce. However, improvements in transportation technology and infrastructure have
flattened the von Thunen plane. In addition, differences in soil quality, climate, or economies of
scale may be sufficient to offset transportation cost advantages.
Determinants of the Development Component ofFarmland Values andAggregate Model
We impose additional structure on the farmland valuation model by specifying the determinants
of the net return to urbanization. Following, the opencity model of Brueckner, we assume that
the preferences of urban residents can be represented by the utility function U(C, C,,, P), where
C, is consumption of land, C,, is consumption of a numeraire nonland good and P is urban
population. Assuming that individual land consumption is fixed at one unit per person the budget
constraint becomes R + C,, + k= M, where M denotes income, R, is urban land rent, and
k is the commuting cost from a residence to the CBD of the city, with 3 < 8b denoting this
distance. Solving for this utility maximization problem, the returns to urbanization should satisfy
R, = R, (, P) (14)
where urban land rent is a decreasing function of distance to the CBD. The effect of population
on urban rent can be either negative or positive depending on whether the disamenity effect
(Brueckner) is greater or lower than the positive effect induced by increased demand for land.
Consequently, Equations 5, 12 and 14 specify a recursive system of equations that form
our empirical model of farmland valuation across space. This farmland valuation model is at the
parcel level of analysis, where farmland is located around a monocentric city and farmers
commute their products to the CBD of the city. Further, we have assumed that distance to the
CBD, net returns to agriculture, and development are constant over time. Since our empirical
analysis is based on two years of county data with each county containing both residential and
agricultural land, we convert this model into a county model where multiple cities may be
observed and allow rents and distance to change over time. Therefore, we consider the following
farmland valuation model at time t and location 3
VA(t, 5) = F, (R, ((t), S(t)), R, (t), P(t, M(t)), A (0(t), (t))) (15)
RAG (t,) = F2 (3(t), S(t)) (16)
R, (t, 3) = F3 ((t),P(t), M(t)) (17)
Following Plantinga, Lubowski, and Stavins we define RAG(t, ) as the average (per acre) net
return to agriculture in the vicinity of 3. Thus, RAG (t, ) is countyspecific. Similarly, VA (t, )
and R, (t, 8) are defined as the average farmland value (per acre) and net return to development,
respectively. The probability of conversion A(0, 3) has been defined as a function of population
and distance to a CBD. We replace the simple distance measure 3 with an accessibility measure
that accounts for the average distance of any given location in a county to multiple cities and is
weighted by the population of each city.5 A similar measure is used by O'Kelly and Horner. In
Equation 16, S(t) denotes the average soil characteristics in the county, while in the net returns
to development, Equation 17, we include residential income (M(t)) as an exogenous variable to
relax the homogeneous income assumption.
Empirical Analysis
The theoretical model developed above is the basis for our econometric model, which we apply
to county data for the contiguous United States. We employ two crosssections of observations
for the Agricultural Census years 1992 and 1997. To control for differences between these years
due to changes in interest rates or other variables that have a common effect in all observations,
we use a timespecific fixedeffects approach. That is, we include a year dummy variable that
allows for a different intercept for each year of the sample. To correct for inflation we converted
all the economic variables to real 2000 dollars using the personal consumption expenditures
component of the implicit GDP deflator. The data were collected from the Census of Agriculture,
the Census of Population and Housing, the Economic Research Service of the United States
Department of Agriculture, the National Climatic Data Center, and the Bureau of Economic
Analysis. Details for the source and nature of the data are provided in the Appendix.
Since we lack data on key variables such as net returns to agriculture or development and
farmland value at the parcel level for counties in the United States, we estimate the model
outlined above using county level data for the 1992 and 1997 agricultural census years.
However, we recognize that a parcel level analysis would provide more variation, since
aggregate county level data may not be representative of the soil characteristics, land values and
returns to agriculture, especially for very large counties.6 Yet, we support our specification with
results of Clark, Fulton, and Scott who suggest that land markets in different regions of the
country may be quite different implying that a crosssectional comparison should be performed.
Thus, results of studies at the parcel level of analysis for a specific region cannot be generalized
over all the counties in the United States.
The first equation of our econometric model is based on Equation 15 and decomposes the
farmland value for county i in year t into agricultural and development components
VA (i, t) = a + aRAG(i, t) + a2H(i, t) + a3AC(i, t) + a4N(t) + u (i, t) (18)
where VA(i, t) is the average market value of farmland and buildings in county i in year t (in
dollars per acre); RAG (i,t) is the average net returns from agriculture including government
payments (in dollars per acre); H(i,t) is the median value of singlefamily houses (in dollars);
AC(i, t) is the index of accessibility of any given location within the county to the nearest urban
centers (within 50 miles); N(t) is a dummy variable which takes the value 1 for the year 1997
and 0 for 1992; and uA (i, t) is a random error term that follows a spatial autoregressive process.
Given the implicit nonlinearity of Equation 5, all variables in Equation 18 are transformed in
logarithmic form except for the year dummy and the net returns to agriculture (RAG). The latter
variable was specified as linear, given the existence of negative net returns to agriculture for
many counties for both years in the sample. Further, this specification allows for separability
between the agricultural and development components of farmland values.
Since demand for housing is the most important use of urban land (Brueckner and
Fansler) we used the county median value of singlefamily homes without a business on the
property, as a proxy for the returns to urbanization at the urban fringe.7 By using this variable we
make an implicit assumption that singlefamily homes are constructed at the urban boundary.
This proxy serves also in capturing implicitly the cost of converting farmland to residential use,
since its value reflects both the price of the land and the house.
The probability of conversion measure, AC(i, t), for each county i is a population
weighted sum of inverse distances within 50 miles of any given location in the county. Formally,
we let AC, be the accessibility at location s in county i, 0 the population at area j, and define
8, as a matrix of straightline distances between area centroids. Then the accessibility index of
area s in county i is given by AC, = O6,j To impose a threshold to delimit which areas
may count in the area's accessibility index, we specify a maximum radius of 50 miles (see
O'Kelly and Homer). The county accessibility index AC(i,t) is then an average value for all
locations s in the county.
The second equation of our econometric model relates the average net returns to
agriculture to the full set of productive and locational attributes of the farmland in the county.
This equation is
RAG(i, t) = b + bAC(i, t) + b2S(i) + b3PIr(i, t) + bPDSI(i, t) + bN(t) + u (i, t) (19)
where all variables are specified as linear; RAG(i,t), AC(i, t) and N(t) are the same variables as
in Equation 18 but now AC(i,t) is linear; and S(i) is a vector of soil characteristics8 that
captures effects due to soil properties and quality across counties (see Table 3). To further
control for heterogeneity across counties we included the percent of irrigated acres (PIr(i,t))
that is expected to have a positive effect on RAG(i,t). In addition, climatic differences across
counties are captured by the Palmer Drought Severity Index (PDSI). In particular, for each year
in the analysis we incorporated for each county 3 average values of the PDSI that correspond to
the planting, harvesting and fallow seasons.
The explanatory variable of primary interest in Equation 19 is the distance to the markets
where producers ship their products. If there was a single market, distance could be measured by
actual transport cost or physical distance. However, in a region such as United States it is
generally unknown who supplies whom (Benirska and Binkley). Thus, we use the accessibility
index in each county as a measure of distance. Since this index is a measure of urban pressure
within 50 miles of any given location in the county, it should matter mostly to highvalued crops.
However, a comparison across counties will show how urban pressure affects net returns to
agriculture.
As shown in the previous section, returns to urbanization are conditional on income,
population and distance to the CBD. Thus, based on Equation 17, a loglinear specification for
returns to urbanization is given by:
H(i, t) = co + c,M(i, t) + cAC(i, t) + c,DPD(i, t) + c4N(t) + c5RD(i) + uH (i, t) (20)
where H(i,t), AC(i,t) and N(t) are the same variables as in Equation 18, M(i,t) is the median
household income in county i at time t, and DPD(i,t) is the average residential population
growth rate in county i during the five years preceding 1992 and 1997. To control for
unobserved differences across counties that affect property values, we included a set of nine
regional dummies (RD(i)) which represent the geographical and historical development of the
United States (Theil and Moss). We used the Lower Mississippi region (Alabama, Arkansas,
Kentucky, Louisiana, Mississippi, Missouri and Tennessee) as a base. All the variables were
specified in logarithmic form, except for the residential population growth and regional
dummies, which were specified as linear.
The comparison between the impacts of urban pressure on productivity versus the effect
of urban sprawl is captured by the coefficients on accessibility in Equations 19 and 20. For
instance, if increased accessibility causes a change in the relative crop mix, or in the price for a
particular crop, this effect will be manifested through coefficient b, in Equation 19. However, if
the impact of accessibility comes only through urbanization, it will be captured in the c2
coefficient in Equation 20. Also, the direct effect of accessibility on farmland value is captured
by coefficient a3 in Equation 18, while coefficient a, captures the opportunity cost of farmland.
The system of Equations 1820 is blockrecursive and is estimated with 3010 counties for
each year, resulting in a total of 6020 observations. Writing this system in a compact form
Y= ZB + U, with E[U'U]= Y (21)
where Y contains the variables VA(i,t), RAG(i,t) and H(i,t), Z contains the explanatory
variables in Equations 1820, B the stacked parameters of the three equations, and U the
stacked disturbances.
Tests for diagonal Y such as the likelihoodratio test and BreuschPagan test (Greene, pg.
621) rejected the null hypothesis that Y is diagonal at the 0.01 level of confidence. Since Y
must be estimated, a system estimator such as threestage least squares (3SLS) or an iterated
SUR is more plausible (Lahiri and Schmidt).
Given the crosssectional nature of the data and the results of other spatial studies of
farmland values (Benirschka and Binkley, Hardie, Narayan, and Gardner, and Plantinga,
Lubowski, and Stavins), we allow for spatial autocorrelation of errors. Specifically we assume
that the disturbances are determined by the following firstorder, spatially autoregressive process
U= (p W)U +U or u= pWuk +uk, k= V,R,H (22)
where p is a 3 x 3 diagonal matrix containing the spatial autocorrelation parameters Pk, U is
the spatially autocorrelated matrix of residuals, W is a 2nx2n (where n= 3,010 is the number
of counties in each year) contiguity matrix summarizing all the information about the spatial
structure of the data, and U* is the matrix of uncorrelated residuals. Since our model is a
balanced panel of two years the weight matrix W is defined as
W = 0
0 Wn
W is constructed so that the (i,j) element of W, is one if counties are contiguous and zero if
not. Further, all diagonal elements of W, are set to zero implying that counties are not
contiguous to themselves.
A CochraneOrcutt transformation of Equation 22 yields
[I(pW)]Y =[I(p W)]ZB +U* (23)
where E[U* = 0 and E U*U*' = Y I Parameter estimates can be obtained by maximizing
the likelihood function. However, this estimator is not computationally feasible for large
numbers of observations. To estimate the system we use the stepwise generalized spatial 3SLS
estimator (GS3SLS) developed by Kelejian and Prucha. First, we apply a twostage least squares
(2SLS) to Equation 18. Equations 19 and 20 were estimated by ordinary least squares since there
is no endogeneity problem in these equations. Second, the residuals of each equation are then
used to estimate the spatial autoregressive parameters Pk with a generalized moments procedure.
While the asymptotic distribution of p, is unknown, the spatial autocorrelation coefficients of
Equations 19 and 20 follow an asymptotic normal distribution.9 Third, using the estimate of pk
the system is transformed (Equation 23) and the disturbances of this transformation are used to
estimate i. Fourth, this X matrix is used to estimate the GS3SLS specification.10
Empirical Results
The estimated coefficients for the farmland equation are presented in Table 2. Before correcting
for spatial autocorrelation the adjusted R2 of this equation is 0.75, indicating that this
specification explains most of the variation in farmland values and that the likelihood of omitted
variables is small. However, in the presence of spatial autocorrelation, the adjusted R2 has a
limited interpretation (Anselin). The estimated spatial autocorrelation for Equation 18 is 0.097.11
The estimated parameters for each effect on farmland prices in Equation 18 are
statistically significant at the 0.01 level of confidence and have the anticipated signs. Farmland
values increase in response to an increase in the net return to agriculture, the median house value,
and the accessibility index. The dummy variable for 1997 is negative indicating that farmland
values declined from 1992 to 1997 after all other factors are taken into account. However, since
the estimated parameter is not statistically significant at any conventional confidence level, we
conclude that farmland values at the two census years remained constant after adjusting for
external effects, such as differences in net returns to agriculture and urban pressure.
Taking into account the semilogarithmic form of Equation 18, the interpretation of the
magnitude of the estimated parameters differs. Since farmland values, median singlefamily
house values, and accessibility in Equation 18 are specified in natural logarithms, the respective
parameters presented in Table 2 denote elasticities. However, given that the return to agricultural
assets is specified as a linear variable in Equation 18, its coefficient is dependent on the scale of
the endogenous variables. Hence, the estimated coefficient on the net return to farmland implies
that a $1 increase in the net return on farmland will cause farmland values to increase by
$5.81/acre given a sample average price of farmland of $1,572/acre. This estimate is similar to
the results of Plantinga, Lubowski, and Stavins who find that on average, a $1 increase in net
agricultural returns causes farmland values to increase by $5/acre.
The direct effect of development opportunities in farmland values is captured by R,
which denotes the median value of a singlefamily home in the county. Its coefficient indicates
that a one percent increase in the median house value results in a 0.40 percent increase in
farmland values. Thus, at the sample average, a $1,000 increase in the median house value
results in a $9.07/acre increase in farmland values.
Further, a one percent increase in the accessibility index results in a 0.22 percent increase
in farmland values (Table 2). Since distance to urban centers appears in the denominator of the
accessibility index, this result implies that farmland values close to urban areas are higher than
farmland values in rural areas, even after differences in the median house values have been taken
into account. This result is also consistent with the findings of Archer and Londsdale who found
that farmland values in metroadjacent (metropolitan) counties were about onethird (three times)
higher than farmland values in rural areas from 1978 through 1992. This persistence, apart from
differences in median house values, may be attributed to the speculative demand for
development (i.e., the differences in the probability of conversion, or 2(0,8) in Equation 5).
Table 3 presents the estimated coefficients for the hedonic specification of the net return
to agriculture specified in Equation 19.12 The R2 of the estimates without correcting for spatial
autocorrelation is 0.28, which is analogous to the R2 found in hedonic studies (0.220.55) using
countylevel data for different States of the U.S. (e.g., Miranowski and Hammes; Palmquist and
Danielson; Roka and Palmquist). The estimated spatial autocorrelation coefficient pR is 0.101
and assuming an approximate standard normal distribution, the z statistic for this coefficient is
36. The latter implies that the null hypothesis of no spatial autocorrelation can be rejected at any
conventional level of confidence.
Urban pressure can affect the value of farmland by affecting the productivity of farmland
(i.e., through changes in the crop portfolio). The results in Table 3 support the significance of
this effect. The estimated parameter for the effect of accessibility on the net return to agriculture
is positive and statistically significant at the 0.01 level of confidence. Numerically a one percent
increase in the accessibility index causes the net return to agriculture to increase by 0.17 percent.
In dollar terms based on an average accessibility index of 163.25, a one percent increase in
accessibility yields a $12.90/acre increase in net returns to agriculture. Linking this result to the
discussion above, a one percent increase in accessibility implies a $74.95/acre (or 4.8 percent)
increase in the value of farmland independent of urban pressure from conversion or the
speculative demand for farmland for eventual conversion.
The soil characteristics and Palmer Drought Severity Index in Equation 19 capture
differences in land quality and weather, respectively. Most of these estimated coefficients are
statistically significant at the 0.01 level of confidence and have the expected sign. Increases in
cationexchange capacity, soil texture, bulk density, permeability, and soil depth are associated
with increased net returns to agriculture. Net returns to agriculture are also an increasing function
of the percent of farmland irrigated at the 0.01 level of confidence. A one percent increase in the
share of farmland irrigated increases the net return to agriculture by $3.74/acre. Finally, the
estimated coefficient for the 1997 dummy variable of $23.00/acre is statistically significant at the
0.01 level of confidence. This estimate indicates that net returns to agriculture were significantly
higher in 1997 than in 1992 even after such factors as increased urban pressures and differences
in weather (through the Palmer Drought Severity Index) are taken into account.
The estimated coefficients for the inverse demand for housing, depicted in Equation 20,
are presented in Table 4. Before adjusting for spatial autocorrelation, the R2 is 0.82 indicating
that the specification explains most of the variation in house prices even with crosssectional
data. After correcting for spatial autocorrelation, the estimated spatial autocorrelation coefficient
pH is 0.102 with a z statistic of 51, and so the null hypothesis of no spatial autocorrelation can
be rejected at any reasonable level of confidence.
All the coefficients presented in Table 4 have the anticipated sign and are statistically
significant at the 0.01 level of confidence. A one percent increase in the median household
income yields a 0.82 percent increase in the median value of a singlefamily house, while a one
percent increase in accessibility increases the median house value by 0.10 percent. In addition, a
one percent increase in residential population growth leads to a 4.12 percent increase in single
family house values.
The results presented in Table 4 also indicate regional differences in the effect of house
values on farmland values. The estimated dummy variable for the Pacific region implies that the
median house values in that region are $41,538 higher than singlefamily house values in the
Lower Mississippi region (the region in the intercept) with all other factors held constant. The
dummy variable for the New England region indicates that median house values are $35,301
higher in New England than in the Lower Mississippi region. Thus, farmland values are higher in
both the Pacific and New England regions than in the Lower Mississippi region due to
differences in the return to urbanization, all other factors held constant.
Finally, the estimated coefficient on the dummy variable for 1997 indicates that house
values were significantly higher in 1997 than in 1992. This effect persists despite accounting for
changes in other factors (i.e., changes in median income and population growth) and inflating
both 1992 and 1997 median singlefamily house values to 2000 dollars.
The Effect of Urbanization on Productivity and Land Values
The model estimated in this study allows for the decomposition of the effect of urban sprawl on
farmland values into three components: the effect of changes in nonfarm opportunities as
captured by the median house value variable in Equation 18, the speculative component of urban
pressure as measured by the probability of conversion (i.e., accessibility coefficient in Equation
18), and the effect of urban pressure on productivity through changes in the crop portfolio (i.e.
accessibility coefficient in Equation 19). In this section we examine the relative magnitude of
each effect on farmland values, as well as the effect of urban sprawl on net returns to agriculture.
To determine the relative contribution of accessibility (i.e., von Thunen effect) compared
with the effect of soil quality attributes in the determination of net returns to agricultural assets
we divide the expected value of Equation 19 into two components
RG (i, t)= RG (i, t)+RG (,t)
RA (i, t) = b + bzS(i) + bPIr(i, t) + b4PSDI + b5N(t) (25)
RAG (i,t) b AC(i,t)
where RAG(i,t) is the net return to agriculture that is explained by soil quality and climatic
information, RAG(i,t) is the net return to agriculture that is explained by the von Thunen or
productivity effect of urban pressure, and R,,(i,t) is the expected return to agricultural assets
from both sources13
Table 5 presents the statelevel netreturn on agricultural assets for each component
ranked by the relative share of the von Thunen effect. These results indicate that the von Thunen
component of net returns to agriculture is generally higher for states in the Northeastern region
of the United States. This result is consistent with the general precepts of our model. Higher
valued agriculture appears more likely in the Northeastern region due to increased access to
several large cities. For example, the estimate for New Jersey indicates that 41.9 percent of net
returns to agriculture are attributable to increased market access. Similar results hold for states
adjacent to the Northeastern region (e.g., Ohio with 23.3 percent, Michigan with 16.9 percent,
Indiana with 15.5 percent, Virginia with 15.7 percent, and Tennessee with 15.5 percent).
South Dakota is an anomaly with 19.2 percent of net returns to agriculture explained by
proximity to urban areas. To explain this anomaly we note that South Dakota has the lowest
expected return to agricultural assets (of $4.8/acre). Thus, even though the effect of proximity to
urban areas is the second lowest in the sample ($0.9/acre), the relative share of value attributed to
the von Thunen effect is large.
The spatial effect of urban pressure on net returns to agriculture at the county level is
depicted in Figure 1. Consistent with the results in Table 5, the urban effect of net returns to
agriculture exceed 30 percent for most counties in the Washington, D.C. to Boston corridor.
Other areas of significant urban pressure on net agricultural returns include the Pittsburgh,
Toledo, Detroit regions of Pennsylvania, Ohio, and Michigan, the area between Chicago and
Milwaukee of Illinois and Wisconsin, and the Dallas, Austin, Houston area in Texas.
Interestingly, urban areas in California, Florida, Oregon, and Washington cast a relatively small
footprint on net returns to agriculture despite the share of high valued crops in each area. In these
cases the presence of highvalued crops are attributable primarily to hedonic characteristics of
the region (i.e., soil and climatic of the region) and not the presence of urban areas.
To examine the relative dollar per acre magnitude of each effect on farmland values we
define four measures. We define the response of farmland values with respect to a one percent
change in, net returns to agriculture (s,), median house values (E2), speculative component of
urban pressure (83), and urban pressure through changes in productivity (84) as:
F1 = alRAG(, t)Ji( (I, t)
83 = a3V, ((i,
84 = abAC(i,t)VA(i,t)
We estimate these elasticities for each county and aggregate the county estimates to the state
level by using the share farmland in each county.
Table 6 presents the results of each component along with the current farmland values
(denominated in real 2000, $s/acre) and ranked by the percentage change in median house
values. As in the rankings of the effect of accessibility on net returns to agriculture, farmland
values in the Northeastern United States are more sensitive to changes in the urban sprawl
components. New Jersey is the most sensitive where a one percent change in accessibility
increases farmland values by $15.46/acre followed closely by Connecticut with an increase of
$13.83/acre, Rhode Island with an increase of $13.75/acre and Maryland with an increase of
$12.14/acre. In addition to their sensitivity to urban sprawl components, farmland values in these
states are also sensitive to changes in net returns to agriculture. For example, a one percent
change in net returns to agriculture causes an increase of $59/acre in farmland values in New
Jersey, a $34/acre increase in farmland values in Connecticut, and a $43/acre increase in
farmland values in Rhode Island.
For many states on the top of the list, a one percent increase in net returns to agriculture
will increase farmland values by more than a one percent increase in median house values. For
instance, in New Jersey a one percent increase in median house values will increase farmland
values by $28/acre, while a one percent increase in the net returns to agriculture will result in a
$59/acre increase in farmland values. However, the pure agricultural (soil quality and climate)
effect is smaller if one accounts for the effect of urban sprawl in farmland productivity and in
turn to farmland values. That is, the response of farmland values to accessibility through net
returns to agriculture is also large, mainly for the Northeastern United States. For instance, a one
percent increase in accessibility is associated with a $28/acre increase in farmland values through
net returns in New Jersey, a $15/acre increase in farmland values in Connecticut, a $16/acre
increase in farmland values in Rhode Island, and a $15/acre increase in farmland values in
Massachusetts. Thus, increases in farmland values from net returns to agriculture are not only
connected with differences in soil productivity but also with urban pressure in the specific area.
Discussion and Implications
This analysis examined the effect of urban pressure on farmland values nationwide, explicitly
accounting for three effects of urban sprawl: changes in nonfarm opportunities, speculative
effect of urban sprawl, and conversion to highvalued agriculture. Traditionally studies of
farmland values have emphasized the role of farmland as a factor of production. Following this
formulation, farmland values have been modeled as the discounted returns to agricultural
production. More recently, several studies have emphasized the effect of urban pressure on
farmland values. These studies typically focus on the impact of converting farmland to urban
uses on farmland valuation. This study blends the two approaches by examining the effect of
urban pressure on the net returns to agriculture as well as through conversion to urban use.
Thus, our study makes two important contributions in the literature. First, we provide a
theoretical justification and empirical evidence on the effect of urban sprawl in net returns to
agriculture. We start from the standard formulation of farmland values in urban growth models,
as the present value of future returns to agriculture and potential development rents. Unlike
previous studies we assume that at each point of time there is a Poisson probability for
conversion of farmland. This probability of conversion depends on population and distance from
urban centers and reflects the speculative component of the effect of urban sprawl. This analysis
provides a model for the value of farmland that depends on three components: net returns to
agriculture, median house values, and probability of conversion. It is apparent from this
formulation that both net returns to agriculture and to future development are endogenous. Thus,
using the concept of von Thunen we show that there is a potential for farmland located close to
urban centers to convert into highervalued crops. That is, the increased market access of these
areas implies not only reductions in transportation costs (which are small) but also to conversion
to highvalue crops. A first indication of this result was given in Table 1, which shows states
with higher values of accessibility have a larger farmland share of highvalued crops. Figure 1
reveals that the urban component of net returns to agriculture has a substantial share in areas
located close to urban centers. For instance, the urban effect on the net agricultural returns
exceeds 30 percent for most counties in the Washington, D.C. to Boston corridor. Other areas of
significant urban pressure on net agricultural returns include counties around major urban centers
in Pennsylvania, Ohio, Michigan, Illinois and Texas.
The possible differences in urban effects on farmland values (e.g., the effect of increased
farmland values due to conversion rather than increased returns) raise several issues. For
example, urban effects manifested only in the conversion of farmland into urban uses increase
the wealth of farmers without increasing their income stream. The only way for farmers to access
this increased wealth is either through selling farmland or by borrowing against the increased
asset values. However, increases in farmland values that result from changes in the crop portfolio
accrue through increased net returns to agriculture. In the first scenario, an increase in farmland
values from increased demand for farmland in urban use implies an increase in the opportunity
cost of production agriculture. In the second scenario urban pressure results in increased returns,
which enhances the farmer's profitability and productivity.
The second contribution of this study is the decomposition of these effects in determining
farmland values along with the effect of the speculative component of urban sprawl and the
effect of net returns to agriculture. We found that at the sample average, a $1 increase in the net
return on farmland will cause the farmland values to increase by $5.81/acre, while a $1,000
increase in median house values increase farmland values by $9.07/acre. The speculative
component of urban sprawl is also significant, a one percent increase in the accessibility index
results in a $3.45/acre increase in farmland values per acre. Concerning the effect of the
accessibility index on net returns to agriculture, a one percent increase causes the net return to
agriculture to increase by 0.17 percent. In dollar terms, a one percent increase in accessibility
yields a $12.90/acre increase in net returns to agriculture and a $74.95 /acre increase in the value
of farmland independent of direct urban pressure for conversion or the speculative demand for
farmland for eventual conversion. The latter effect is mostly evident in the Northeastern United
States where farmland values are more sensitive to changes in the urban sprawl components. In
those States, an increase in farmland values from net returns to agriculture is not only connected
with differences in soil productivity but also with urban pressure in the specific area.
While our analysis provides a new method to decompose the effects of urban sprawl in
farmland values, it is still based on a static, crosssectional framework. A topic for future
research would be the inclusion of the present model in a dynamic framework. Further, we have
shown that it is possible for an increase in the probability of conversion to lead to a decrease in
farmland values. It was justified by a potential negative externality effect, such as competition
over natural resources or pollution through increased population. Although, our data do not
support this effect at the county level of the United States, it may be evident in a parcel of land
level of analysis.
References
Archer, C.J. and R.E. Lonsdale. "Geographical Aspects of US Farmland Values and Changes
During the 19781992 Period." Journal of Rural Studies 13(1997):399413.
Arnott, R. and F. Lewis. "The Transition of Land to Urban Use." Journal of Political Economy
87(11)(1979):161169.
Benirschka, M. and J.K. Binkley. "Land Price Volatility in a Geographically Dispersed Market."
American Journal ofAgricultural Economics 76(2)(1994): 185195.
Breneman, V.E., "Population Accessibility". Analysis of US Bureau of Census 1990 block group
levelpopulation data USDAEconomic Research Service, 1997.
Brueckner, J.K. "Growth Controls and Land Values in an Open City." Land Economics
66(3)(1990):237248.
Brueckner, J.K. and D.A. Fansler. "The Economics of Urban Sprawl: Theory and Evidence on
the Spatial Sizes of Cities." The Review of Economics and Statistics 65(1983):479482.
Capozza, D.R. and R.W. Helsley. "The Fundamentals of Land Prices and Urban Growth."
Journal of Urban Economics 26(1989):295306.
Capozza, D.R. and R.W. Helsley. "The Stochastic City." Journal of Urban Economics
28(1990):187203.
Cavailhes, J. and P. Wavresky. "Urban Influences on Periurban Farmland Prices." European
Review ofAgricultural Economics 30(3)(2003): 333357.
Chicoine, D.L. "Farmland Values at the Urban Fringe: An Analysis of Sales Prices." Land
Economics 57(1981): 353362.
Clark, J.S., M. Fulton, and J.T. Scott, Jr. "The Inconsistency of Land Values, Land Rents, and
Capitalization Formulas." American Journal of Agricultural Economics 75(1)(Feb.
1993): 14755.
Greene, R.P. and J. Stager. "Rangeland to Cropland Conversions as Replacement Land for Prime
Farmland Lost to Urban Development." The Social Science Journal 38(2001):543555.
Greene, W.H. Econometric Analysis, Fourth Edition, PrenticeHall, Inc., 2000.
Hardie, I.W., T.A. Narayan, and B.L. Gardner. "The Joint Influence of Agricultural and Nonfarm
Factors on Real Estate Values: An Application to the MidAtlantic Region." American
Journal ofAgricultural Economics 83(2001):120132.
Imhoff, M.L., W.T. Lawrence, D. Stutzer, and C. Elvidge. "Assessing the Impact of Urban
Sprawl on Soil Resources in the United States Using Nighttime "City Lights" Satellite
Images and Digital Soils Maps." In "Perspectives on the land use history of North
America: a contextfor understanding our changing environment", edited by Sisk, T.D.
U.S. Geological Survey, Biological Resources Division, Biological Science Report
USGS/BRD/BSR19980003, 1999.
Kelejian, H.H. and I.R. Prucha. "Estimation of Simultaneous Systems of Spatially Interrelated
Cross Sectional Equations." Journal ofEconometrics 118(2004):2750.
Lahiri, K. and P. Schmidt. "On the Estimation of Triangular Structural Systems." Econometrica,
46(1978): 12171221.
Mendelsohn, R., W.D. Nordhaus and D. Shaw. "The Impact of Global Warming on Agriculture:
A Ricardian Analysis." American Economic Review 84(1994): 753771.
Miranowski, J. A. and Hames, B. D., "Implicit Prices of Soil Characteristics for Farmland in
Iowa", American Journal ofAgricultural Economics, (1984), 7459.
Muth, R.F. "Economic Change and RuralUrban Land Conversions." Econometrica 29(1961): 1
23.
O'Kelly, M.E. and M.W. Horner. "Aggregate Accessilibity to Population at the County Level:
U.S. 19402000." Journal of Geographical Systems 5(2003):523.
Palmquist, R.B. and L.E. Danielson, "A Hedonic Study of the Effects of Erosion Control and
Drainage on Farmland Values", American Journal ofAgricultural Economics, 71 (1989):
5562
Plantinga, A.J. and D.J. Miller. "Agricultural Land Values and the Value of Right to Future Land
Development." Land Economics 77(2001):5677.
Plantinga, A.J., R.N. Lubowski, and R.N. Stavins "The Effects of Potential Land Development
on Agricultural Land Prices." Journal of Urban Economics 52(2002): 56181.
Ricardo, D. Principles of Political Economy and Taxation Amherst, New York: Prometheus
Books, 1996.
Roka, F.M. and R.B. Palmquist. "Examining the Use of National Databases in a Hedonic
Analysis of Regional Farmland Values." American Journal of Agricultural Economics
79(5)(1997):16511656.
Shi, Y.J., T.T. Phipps, and D. Colyer. "Agricultural Land Values under Urbanizing Influences."
Land Economics 73(1997): 90100.
Shonkwiler, J.S. and J.E. Reynolds. "A Note on the Use of Hedonic Price Models in the Analysis
of Land Prices at the Urban Fringe." Land Economics 62(1986): 5861.
Theil, H. and C.B. Moss. "A Proposed Set of Nine Regions for the United States." Empirical
Economics 25(4)(2000): 7159.
U.S. Department of Commerce, Census of Agriculture 1997: Geographic Area Series 1B; US
Summary and County Level Data on CDROM. Bureau of the Census, Washington, DC,
1999.
U.S. Department of Commerce, County and City Data Book on CDROM. Bureau of the Census,
Washington, DC, (1998).
Von Thunen., H. J. von Thunen's isolated state. Trans. by C. M. WartenBerg, Ed. By P. Hall.
New York: Pergamon Press, 1966.
Wheaton, W.C. "Urban Residential Growth under Perfect Foresight." Journal of Urban
Economics 12(1982):121.
Endnotes
1 A formal definition is provided in the Empirical Analysis section of the present paper.
2 Although returns to development are expected to be increasing over time, alternative
specifications allowing for linear rate of changes in returns to urbanization or as a composite
term consisting of a spatial and a temporal component that follows a Brownian motion (Capozza
and Helsley 1990) led to an intractable model. In the econometric specification of the model the
assumptions of constant returns to agriculture and urbanization will be relaxed.
3 Since we focus on changes in the value of parcels of farmland in different locations we assume
that distance 8 is exogenous with respect to time. An endogenous formulation of the distance
(i.e., 8(t)) would be more plausible but it would unnecessarily complicate the analysis.
4 In this formulation it is possible to get a negative effect on farmland values when RAG > R,. A
possible justification is negative externalities, since an increase in the probability of conversion
could also imply increased pollution and competition over natural resources. This is an
interesting topic but beyond the scope of this paper, and so it is left for future research.
5 This accessibility index has been developed by Breneman at the USDA using Geographical
Information Systems (GIS) county data.
6 We would like to thank one of the reviewers of this paper for this comment.
7 While a peracre median house value would be more plausible for the model, we lack data on
the mean lot size and the value that this lot represents in the median house value. Such data are
reported only for the four main census regions of US. Thus, as in Hardie, Narayan, and Gardner,
we used median house values.
8 The same data set of soil characteristics was utilized for both years in the sample.
9 See Kelejian and Prucha: http://www.econ.umd.edu/prucha/STATPROG/OLS/desols.pdf.
10 The procedures were written in Gauss and are available by the authors upon request.
11 To test for the fragility of the estimated parameters, we estimated the system of equations
including dummy variables for each of the ten USDA/ERS production regions in the farmland
value equation. Neither the estimated coefficients from Equation 18 nor the estimated spatial
autocorrelation coefficient change significantly with this respecification. Thus, the estimated
coefficients presented in Table 2 are robust with respect to regional specifications.
12 Again, to test for the fragility of the estimated accessibility coefficient, which is the main
variable of interest, we estimated the system of equations including dummy variables for each of
the ten USDA/ERS production regions in the net returns to agriculture equation. The estimated
coefficient did not change significantly with this respecification.
13 We include the intercept and yeardummy terms in the effect of soil characteristics, since any
other specification would yield implausibly large von Thunen components for many rural and
greatly agricultural counties. For a similar justification see Plantinga, Lubowski, and Stavins.
Table 1. Share of HighValued Crops, Ranked by Accessibility Index
1997 1992
Number of Accessibility Average share of Average share of Accessibility
Counties range highvalued crops highvalued crops Change
84 7492.8 1005.7 0.202 0.185 0.101
122 996.2 500.5 0.124 0.115 0.150
384 493.6 200.6 0.092 0.085 0.146
572 199.5 100.0 0.050 0.043 0.124
815 99.945.0 0.035 0.030 0.104
940 44.9 0.47 0.016 0.015 0.070
Note: Quintile grouping of the counties does not alter the qualitative results.
Table 2 Generalized Spatial 3SLS Estimates for the Farmland Value Equation
Coefficient
Variable Description estimate Standard error
Dependent variable: Logarithm of farmland value VA(i,t), ($/acre)
Intercept 1.4021a 0.2228
RAG (i,t) Net returns to agriculture ($/acre) 0.0037a 0.0001
ln(H(i,t)) Median singlefamily house value ($) 0.4021a 0.0216
ln(AC(i, t)) Accessibility index (see text) 0.2223a 0.0067
Year Year dummy, 1997=1 0.0118 0.0205
Pv Spatial autocorrelation coefficient 0.0972
denotes statistical significant estimate at the 0.01 level of confidence.
Table 3 Generalized Spatial 3SLS Estimates for the Net Agricultural Returns Equation
Coefficient
Variable Description estimate Standard error
Dependent variable: Net Returns to Agriculture RG (i,t) ($/acre)
Intercept 48.1907a 14.4112
AC Accessibility index (see text) 0.0789a 0.0035
text Soil texture (index) 3.6493a 1.3312
catex Cation exchange capacity (meg/100g) 0.4066c 0.2660
ph Soil reaction (pH) 13.8290a 1.7549
om Organic matter (%) 1.1201 0.8674
tfact Tfactor erosion tolerance (index) 0.1689 1.2197
calcarb Calcium carbonate (%) 0.2435 0.4875
wattabd Water table depth (inches) 9.5319a 1.3591
bulkd Bulk density (grams/ccm) 41.5655a 8.4489
perm Permeability(inches) 4.5167a 0.8364
slinity Salinity (mmhos/cm) 5.3150a 1.7122
drainage Drainage (index) 0.0331 1.1777
soild Soil depth (inches) 0.7751a 0.2172
rock3 Threeinch rocks (%) 0.1199 0.3961
PIr Irrigated acres (%) 3.7443a 0.1387
PSDI1 Palmer index Planting season 3.6486b 1.5812
PSDI2 Palmer index Harvesting season 0.9827 1.1719
PSDI3 Palmer index Fallow season 1.1570 1.7241
Year Year dummy, 1997=1 23.0089a 5.5553
PR Spatial autoregressive coefficient 0.1007
ab and c denote statistical significance at the 0.01, 0.05, and 0.10 level of confidence,
respectively.
Table 4 Generalized Spatial 3SLS Estimates for the House Value Equation
Coefficient
Variable Description estimate Standard error
Dependent variable: Logarithm of Median House Value H(i,t) ($)
Intercept 1.8576a 0.1554
ln(M(i,t)) Median household income ($) 0.8271a 0.0155
ln(AC(i, t)) Accessibility (index) 0.1000a 0.0031
DPD(i, t) Residential population growth 4.1281a 0.1885
NEN Dummy for New England region 0.5066a 0.0287
MAT Dummy for Middle Atlantic region 0.2115a 0.0223
SAT Dummy for South Atlantic region 0.1825a 0.0165
GLA Dummy for Great Lakes region 0.1219a 0.0155
NCE Dummy for North Central region 0.0944a 0.0171
SCE Dummy for South Central region 0.0770a 0.0175
MOU Dummy for Mountain region 0.4520a 0.0182
PAC Dummy for Pacific region 0.5961a 0.0230
Year Year dummy, 1997=1 0.0218b 0.0098
PH Spatial autoregressive coefficient 0.1021
a and b denote statistical significant estimate at the 0.01 and 0.05 level of confidence,
respectively.
Table 5 The Contribution of Soil Productivity/Quality and Von Thunen Components to the
1997 Values of US Net Agricultural Returns, by State (in Real 2000, Dollars per
Acre)
State
New Jersey
Connecticut
Rhode Island
Massachusetts
Maryland
Pennsylvania
Ohio
South Dakota
New York
Michigan
Virginia
Indiana
Tennessee
Arizona
Delaware
New Hampshire
Kentucky
South Carolina
North Carolina
Illinois
West Virginia
Alabama
Texas
Oklahoma
Wisconsin
California
Florida
Vermont
Georgia
Missouri
Soil productivity/quality
component
($/acre)
125.6
80.0
115.8
110.0
97.1
76.4
69.8
3.9
80.3
95.5
70.0
89.7
67.5
21.0
157.5
102.1
65.0
81.5
106.8
85.1
58.0
68.8
44.9
36.7
87.9
161.2
182.3
59.4
98.2
78.6
von Thunen
component
($/acre)
90.4
54.7
66.2
58.2
41.5
27.2
21.2
0.9
16.7
19.4
13.1
16.5
12.4
3.8
26.4
17.1
10.6
12.7
16.3
12.9
7.9
8.9
5.7
4.7
10.9
18.8
20.5
6.7
9.9
6.4
von Thunen share of net
returns to agriculture
(percent)
0.419
0.406
0.364
0.346
0.299
0.262
0.233
0.192
0.172
0.169
0.157
0.155
0.155
0.154
0.144
0.143
0.140
0.134
0.132
0.131
0.120
0.114
0.113
0.113
0.110
0.104
0.101
0.101
0.091
0.076
Table 5 The Contribution of Soil Productivity/Quality and Von Thunen Components to the
1997 Values of US Net Agricultural Returns, by State (in Real 2000, Dollars per
Acre) (continued)
Soil productivity/quality von Thunen von Thunen share of net
component component returns to agriculture
State ($/acre) ($/acre) (percent)
Iowa 69.8 5.4 0.072
Minnesota 74.0 5.7 0.071
New Mexico 21.5 1.5 0.066
Washington 59.1 4.2 0.066
Colorado 57.4 4.0 0.065
Louisiana 125.4 8.1 0.061
Utah 50.6 3.0 0.056
Maine 99.3 5.3 0.051
Mississippi 117.4 6.2 0.050
Oregon 61.9 2.9 0.044
Kansas 68.4 3.0 0.043
Arkansas 174.6 5.7 0.032
Montana 16.9 0.6 0.032
North Dakota 32.9 0.9 0.028
Wyoming 26.0 0.6 0.024
Idaho 125.0 2.8 0.022
Nebraska 90.0 2.0 0.022
Nevada 66.7 1.1 0.017
Table 6 The Contribution of Urban and Agricultural Components to the 1997 U.S. Farmland
Values, by State (in Real 2000, Dollars per Acre)
Value of Change in Farmland Value ($/ac
State name Farmland RA Ru
($/acre) ($/acre) ($/acre)
New Jersey
Connecticut
Rhode Island
Massachusetts
Maryland
Delaware
California
Pennsylvania
New Hampshire
Florida
Illinois
North Carolina
Indiana
Ohio
Virginia
Tennessee
Iowa
Michigan
Vermont
Georgia
South Carolina
Kentucky
Alabama
New York
Wisconsin
Washington
Louisiana
Maine
Minnesota
Arkansas
West Virginia
Missouri
6,956
6,221
6,186
5,462
3,316
2,784
2,768
2,501
2,385
2,372
2,235
2,186
2,172
2,150
2,027
1,901
1,786
1,756
1,595
1,575
1,572
1,525
1,513
1,350
1,309
1,271
1,268
1,257
1,225
1,216
1,150
1,125
58.99
34.47
43.09
38.31
17.94
19.26
21.40
10.63
11.49
20.09
8.47
10.11
8.83
7.74
6.52
5.72
5.06
7.93
3.95
6.46
5.45
4.51
4.46
5.72
4.98
3.89
6.16
5.00
3.82
7.99
2.90
3.83
27.97
25.02
24.88
21.97
13.34
11.20
11.13
10.06
9.59
9.54
8.99
8.79
8.74
8.65
8.15
7.64
7.18
7.06
6.41
6.33
6.32
6.13
6.09
5.43
5.26
5.11
5.10
5.06
4.93
4.89
4.62
4.52
re) in 2000 from 1% Change in
Speculative
Urban pressure
($/acre)
15.46
13.83
13.75
12.14
7.37
6.19
6.15
5.56
5.30
5.27
4.97
4.86
4.83
4.78
4.51
4.22
3.97
3.90
3.54
3.50
3.50
3.39
3.36
3.00
2.91
2.82
2.82
2.79
2.72
2.70
2.56
2.50
von Thunen
($/acre)
27.98
14.97
15.79
15.00
6.45
3.18
2.59
3.59
2.03
2.34
1.36
1.57
1.49
2.02
1.26
1.12
0.39
1.67
0.43
0.86
0.89
0.79
0.60
1.46
0.69
0.41
0.47
0.36
0.39
0.29
0.41
0.37
Table 6 The Contribution of Urban and Agricultural Components to the 1997 U.S. Farmland
Values, by State (in Real 2000, Dollars per Acre) (continued)
Value of Change in Farmland Value ($/acre) in 2000 from 1% Change in
State name Farmland RG Speculative von Thunen
($/acre) Urban pressure (/ac
S ($/acre) ($/acre) ($/acre) $/acre)
Mississippi 1,105 5.06 4.44 2.46 0.28
Idaho 1,070 5.97 4.30 2.38 0.16
Oregon 1,009 3.40 4.06 2.24 0.42
Nebraska 683 3.20 2.75 1.52 0.10
Colorado 648 1.81 2.61 1.44 0.15
Oklahoma 641 1.10 2.58 1.42 0.16
Texas 628 1.35 2.53 1.40 0.29
Kansas 608 1.69 2.44 1.35 0.12
Utah 607 1.82 2.44 1.35 0.20
Arizona 469 1.61 1.89 1.04 0.18
North Dakota 422 0.55 1.70 0.94 0.02
Nevada 413 1.71 1.66 0.92 0.04
South Dakota 366 0.18 1.47 0.81 0.02
Montana 309 0.32 1.24 0.69 0.01
Wyoming 234 0.36 0.94 0.52 0.01
New Mexico 208 0.24 0.84 0.46 0.02
515
1530
> 30
Note: Counties with white color indicate missing observations, and the label defines the urban share of net returns to agriculture.
Figure 1 Estimated Share of Urban Influence on Net Returns to Agriculture
Appendix: Data Sources and Variables Definition
VA (i, t) is the average market value (dollars) of farmland (all land in farms) and buildings in
county i per unit of land (acres) in 1992 and 1997. These data are reported in the Census of
Agriculture 1997 as a county average (dollars per acre). VA(i,t), as all the economic variables
were converted to real 2000 dollars using the personal consumption expenditures index (PCE).
H(i,t) is the median value (dollars) for specified owneroccupied housing units in
county i in 1992 and 1997. It consists of the owneroccupied singlefamily homes on less than
10 acres without a business or medical office on the property. These data were taken from the
decennial Census of Population and Housing (Summary Tape File 3), which are reported in 1990
and 2000 at the county level (http://factfinder.census.gov). We used the House Price Index
(HPI) provided by the Office of Federal Housing Enterprise Oversight (OFHEO) and linear
extrapolation and interpolation to project the 1990 and 2000 values to 1992 and 1997. This index
is reported quarterly at the state level (http://www.ofheo.gov/) and tracks changes in the price of
singlefamily homes. A median lot size for singlefamily homes is not available at the county
level but only at the four regions of U.S. and so any attempt to project these lot sizes in order to
get the median house value per acre would add considerable measurement error.
RAG(i,t)is the average net return (dollars per acre) to agriculture in county i in 1992 and
1997. The data were taken from the Agricultural Census and RAG(i) at time t is computed as
(TR TC, G) / A, where TR, is the dollar value of all agricultural products sold, TC, is the
total farm production expenses, GIP are the total government payments received by farmers and
A is the approximate land in farms (acres).
S(i) is a vector of soil characteristics in county i and is the same for both years in the
sample. It was obtained from ERS and a formal definition of each variable can be found at the
website of the National Resources and Conservation Service (http://soils.usda.gov/) of the
USDA. PIr is the percent of irrigated acres in each county as reported in the Agricultural
Census.
PDSI is the palmer severity drought index, for county i, where we have estimated 3
average values for each county at a given year corresponding to the planting (AprilJuly),
harvesting (AugustNovember) and fallow season (DecemberMarch). This is a water balance
index that considers water supply (precipitation), demand evapotranspirationn) and loss (runoff)
for each county. It was obtained from the NCDC at ftp://ftp.ncdc.noaa.gov/pub/data/cirs/ and is
reported by climatic divisions of each state.
M(i,t) is the median household income in county i in 1992 and 1997 (in dollars). These
data were taken from the decennial Census of 1990 and 2000, where are reported in 1989 dollars
for the year 1990 and in 1999 dollars for the year 2000. To find the corresponding 1992 and
1997 median household incomes we used as an index the per capital personal income (PCI) in
each county of the US for all the years in the period 19892000. These data were available online
at the Bureau of Economic analysis website, through the Regional economic information system
(REIS) cdrom (http://www.bea.gov). We followed a similar interpolation as in the case of
median house values.
DPD(i, t) is the average residential population growth rate in county i during the five
years preceding 1992 and 1997 and it was normalized in people per 1000 acres in each county.
Data on county residential population were taken from the Census cdrom (USA Counties 1998)
for the period 19871997. Then for each county we divided total county population by the total
land area (in 1000 acres) available for the Agricultural Census. To estimate the growth rate of
residential population in 1992 and 1997, we used the arithmetic mean of the growth rate for five
years before the years in question.
RD is a set of regional dummies as were classified in Theil and Moss (2000).
Specifically, it consists from the following regions: New England (Connecticut, Maine,
Massachusetts, New Hampshire, Rhode Island, Vermont), Middle Atlantic (Delaware, Maryland,
New Jersey, New York, Pennsylvania), South Atlantic (Florida, Georgia, North and South
Carolina, Virginia, West Virginia), Great Lakes (Illinois, Indiana, Michigan, Ohio, Wisconsin),
North Central (Iowa, Minnesota, Nebraska, North and South Dakota), South Central (Kansas,
Oklahoma, Texas), Mountain (Arizona, Colorado, Idaho, Montana, Nevada, New Mexico, Utah,
Wyoming), Pacific (California, Oregon, Washington) and the lower Mississippi region that was
dropped as a base.
