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A SPATIAL ANALYSIS OF LAND VALUESAT THE RURAL URBAN FRINGE

Lonnie R. Vandeveer1, Steven A. Henning1, Huizhen Niu1, and Gary A. Kennedy2

1Department of Agricultural Economics and Agribusiness, Louisiana State University2Department of Agricultural Sciences, Louisiana Tech University

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A Spatial Analysis of Land Values at the Rural Urban Fringe

Introduction

Location has long been recognized as an important factor in explaining rural land values.

This factor has become increasingly important because of the expansion of urban areas and the

resulting increase in the demand for rural land. Chicoine noted that soil productivity’s influence

on farmland prices at the urban fringe market appears to be overshadowed by the locational at-

tributes of parcels. Clonts, in an analysis of land values at the urban periphery, estimated that

urban development explained 30 percent of the variation in the value of land and improvements.

Other studies have found location to have a significant influence in explaining the varia-

tion in per acre land values in rural land markets. In an Oklahoma study, Kletke and Williams

concluded that location within the state was likely to be as important as any other factor in de-

termining value. Adrian and Cannon found that land values in the urban fringe of Dothan, Ala-

bama were almost three times the values in the rural segment. Shonkwiler and Reynolds con-

cluded that in studies without variables to reflect the effect of non-agricultural use potential, dis-

tance variables must be recognized as measuring a set of the non-agricultural effects.

More recent literature has emphasized the need to consider spatial characteristics in con-

ducting economic research (Krugman). Anselin notes that computer technology capable of pro-

viding spatial analysis has developed at a rapid rate. Consistent with this observation, Vandeveer

et al. used Geographical information systems (GIS) to review spatial characteristics of a rural

land sales database. These procedures, along with spatial statistics, indicated spatial autocorre-

lation in Louisiana rural land submarkets. Dubin indicates that modeling real estate markets in

the presence of spatial autocorrelation using traditional OLS procedures may result in models

with less than desirable statistical characteristics. Similarly Pace et al. indicates that real estate

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and spatial statistics complement each other, and employing spatial estimators provides benefits

over ignoring dependencies in the data. The benefits include improved prediction, better statisti-

cal inference through unbiased standard errors, and better estimates because of the way that lo-

cation is handled within the modeling procedure.

This research reviews procedures for estimating rural land values at the rural-urban

fringe. Spatial econometric procedures are used because of the importance of location in these

areas and because of the potential statistical problems noted above. In following sections, rural

land value modeling procedures and rural land value data from an area in northwest Louisiana

are presented and discussed. Both simple statistics and multiple regression diagnostic tests are

used to test data for spatial autocorrelation. Hedonic modeling procedures and diagnostic tests

for spatial autocorrelation are presented and discussed in following sections. A spatial error

model is used to develop predicted rural land values from location and economic development

variables. These predictions are then used to estimate rural land value contours, which provide a

visual representation of rural land values at the rural-urban fringe.

Model

An empirical procedure that has been used to analyze rural land markets includes the he-

donic pricing model. Rosen (1974) defined hedonic prices as implicit prices of attributes and

notes that they are revealed to economic agents from observed prices of differentiated products

and the specific amounts of characteristics associated with them. Prices of these characteristics

are implicit because there is no direct market for them. In 1984, Palmquist provided a discussion

of the theoretical basis for using hedonic analysis in rural land value studies and Danielson, in

the same year, used the procedure to empirically analyze the rural land market in North Carolina.

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This study follows the approach used by Danielson. Value in a rural land submarket is

specified by the following transcendental function:

m nPrice = β0 Z1

β1 exp [ ∑ αi Xi + ∑ γj Dj + ε ], (1) i=1 j=1

where Price is the per acre price of land, Z1 is the size of tract in acres, m is the number of addi-

tional continuous variables (Xi), n is the number of discrete (dummy) variables (Dj), and ε is a

random disturbance term. Taking the natural logarithm of both sides of equation (1) gives:

m nln Price = ln β0 + β1 ln Z1 + ∑ αi Xi + ∑ γj Dj + ε. (2)

i=1 j=1

Because the price of land is hypothesized to decline as the size of tract (Z1) increases, but at a

decreasing rate, nonlinearities were incorporated for Z1. Therefore, β1 is hypothesized to be

negative.

The implicit marginal price of each characteristic is an estimate of the amount by which

the per acre land price changes, given a unit change in the characteristic. For all except the dis-

crete variables in equation (2), the implicit marginal prices (i.e., the partial derivatives) are given

by the following:

∂Pricet / ∂Z1,t = IMPSIZE1,t = [ β1 / Z1,t ] x Pricet

∂Pricet / ∂Xi = IMPXi,t = αi x Pricet. (3)

The subscript, t, implies there are implicit marginal prices associated with each land transaction.

An estimate of the implicit marginal price at the mean price and mean level of characteristic over

all observations is obtained by substituting mean values of each variable in equation (3).

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The derivation of implicit marginal prices for discrete variables (Dj) in semilogarithmic

equations is not as straightforward. Kennedy (1981) suggests the following estimation procedure

where the variance of the coefficient of the discrete variable is taken into account:

IMPDj = (exp [ cj – 1/2 V(cj) ] - 1) x Mean Price, (4)

where IMPDj is the implicit marginal price of the discrete variable, cj is the estimated coefficient

of the discrete variable parameter, Dj; V(cj) is the variance of the estimated coefficient, cj; and

Mean Price is the mean price per acre over all observations used in the model. Taking V(cj) into

account can lead to less bias in the estimate when the variance of cj is substantial.

Estimation

When spatial autocorrelation is expected to exist within data, special econometric proce-

dures are necessary. In this case, hedonic model estimation using standard econometric proce-

dures can result in estimates that are not efficient. Inefficient estimates may result in misleading

inferences from the model. Following Anselin (1995), spatial autocorrelation is the situation

where the dependent variable or error term at each location is correlated with observations for

the dependent variable or error term at other locations. This means that for neighboring locations

i and j:

E(yiyj) ≠ 0 (5)

or

E(εiεj) ≠ 0 (6)

where (5) is defined as a spatial lag situation (Anselin). The spatial lag situation is specified by

the following model:

y = ρWy + Xβ + ε (7)

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where:

y = vector dependent observations, ρ = spatial autoregressive coefficient, Wy = spatially lagged dependent variable, X = matrix of explanatory variables, β = vector of regression coefficients, and ε = vector of error terms.

W is a spatial weights matrix that takes into consideration the spatial arrangement of observa-

tions. In this spatial autoregressive model, if ρ is not equal to zero, then ordinary least square

estimates will be biased and inefficient. Intuitively, the spatial lag model is consistent with the

real estate appraisal process of using comparable sales in valuation, in that nearby rural land

sales are used to explain per acre rural land prices in the spatial lag model.

When spatial dependence occurs in the error, as defined in (6), a regression specification

with a spatial autoregressive error term is used to develop model estimates. The spatial error

model is:

y = Xβ + ε (8)

ε = λWε + ξ (9)

where:

y = vector of dependent observations, X = matrix of explanatory variables, β = vector of regression coefficients, ε = vector of error terms, Wε= spatial lag for error terms, λ = autoregressive coefficient, and ξ = error term with mean 0 and variance matrix σ2I.

Again, W is a spatial weights matrix that takes into consideration the spatial arrangement of ob-

servations. This matrix is based on distances between observations. The logic of this model is

that it is generally difficult to develop variables that explain all dimensions of the rural land mar-

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ket. With this situation, the spatial error model makes adjustments for spatial interaction in the

error term.

Diagnostic statistical tests are used to test for spatial dependence and to identify the cor-

rect model (i.e., spatial lag or spatial error) for estimation (Anselin). For this analysis, Lagrange

Multiplier tests are used to test for spatial dependence. The joint use of the Lagrange Multiplier

error and Lagrange Multiplier lag tests are used to determine which spatial model is appropriate.

When both Lagrange Multiplier tests have high values and are statistically significant, the one

with the highest value will tend to indicate the appropriate model (Anselin).

Data

Data for this study are based on rural land market sales from the Red River area of Lou-

isiana that were collected using mail survey techniques. Data for this study area is a subset of a

larger data base collected for the state for the period January 1993 through June 1998. The rural

land market survey was mailed to state certified appraisers, officers in commercial banks, Farm

Service Agency, Federal Land Bank personnel, Production Credit personnel, members of the

Louisiana Chapter of the American Society of Farm Managers and Rural Appraisers, and mem-

bers of the Louisiana Realtors Land Institute. Each respondent was asked to provide rural land

sales of ten acres or more including attachments to the surface such as buildings and other im-

provements and sales outside the boundaries of towns and cities .

The Red River area as defined by Kennedy et al. is illustrated in Figure 1. The area in-

cludes six parishes in northwest Louisiana that border the Red River. The soils of the area are

primarily Recent Alluvium and Coastal Plain. Primary agricultural enterprises include cotton,

soybeans, pasture, pine timber, and hardwood timber. The area includes metropolitan statistical

areas of Shreveport and Alexandria. In Figure 1, each symbol represents a GIS plot of the loca-

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tion of each of the 254 rural land sales included in this study. The plot generally shows that sales

are well distributed throughout the study area with sales of relatively larger per acre values being

located near to the metropolitan areas of Alexandria and Shreveport.

Variables hypothesized to influence per acre rural land values are defined in Table 1.

PRICE in Table 1 is the dependent variable used in the hedonic model and represents the average

per acre selling price for each tract of rural land and improvements. Continuous variables ex-

pected to have an inverse relationship with per acre selling price include size of tract (SIZE) and

distance to nearest city (DNC). There is generally a negative relationship between size of tract

and per acre selling price because fewer buyers compete in markets for larger tracts; whereas,

many buyers compete in markets for smaller tracts. The distance variable is expected to be

negative because location theory generally suggests an inverse relationship between distance to

markets and per acre selling prices. Continuous variables expected to positively influence rural

land values include the percent of cropland (PERCROP), percent of pastureland (PERPAST),

the value of improvements made on or to the tract (VALUE), and the time of sale (TIME). Crop

and pasture lands represent open land that is expected to contribute to income earning capacity or

other uses, which is expected to have positive influences on value. As shown in Table 1, im-

provements are expected to have a positive influence on value, and because land values have

been trending upward during the study time period, time is also expected to have a positive in-

fluence on per acre value.

Each of the three discrete variables shown in Table 1 are expected to have a positive in-

fluence on per acre value. Paved road access (RT) is expected to reflect development potential

and accessibility. Similarly, commercial influence (COMINF) and residential influence

(RESINF) are expected to have a positive effect on the demand for a tract of land.

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Prior to developing hedonic models of the rural land market, data in each of the study ar-

eas are tested for spatial autocorrelation. Spatial autocorrelation occurs if a variable (i.e., rural

land values) is correlated with itself over space (Barber). Knowledge of spatial autocorrelation is

of concern because its presence means there is interdependence in the data, whereas most statis-

tical methods assume independence in the data. As previously discussed, ignoring spatial auto-

correlation in a hedonic analysis of real estate values may result in inefficient and biased

econometric results.

The presence of spatial autocorrelation was tested using the SpaceStat algorithm (An-

selin). A G statistic developed by Getis and Ord was used to measure and test for spatial asso-

ciation of per acre land values. Specifically, the G statistic was used to measure overall spatial

association in the data. The G statistic was computed for all observations in the Red River area

and the results are presented in Table 2. Estimates in Table 2 indicate that z values (corre-

sponding to the normal distribution) are statistically significant at the 5% level for distances from

5 to 30 miles. A positive and statistically significant z value suggests positive spatial autocorre-

lation in the rural land value data. This suggests that observations with relatively large per acre

sale values group together and affect each other.

OLS Model Results

The first stage hedonic model estimates using OLS procedures are presented in Table 3.

Results indicate that hypothesized variables explain 49 percent of the variation in per acre rural

land values. With the exception of distance to nearest city (DNC), all variables are statistically

significant the five percent level of significance or greater and exhibit the expected sign. Size of

tract (SIZE) and distance to nearest city (DNC) are estimated to have a negative influence on per

acre value, while other variables are estimated to have a positive influence on per acre value.

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Diagnostic results for the hedonic OLS model are presented in Table 4. The multi-

collinearity condition number (13.51) is under 20 suggesting that multicollinearity is not a prob-

lem in the rural land value model. Similarly, the Keifer-Salmon test does not indicate a rejection

of the hypothesis that error terms are normally distributed at the ten percent level. The Breusch-

Pagan test is not highly significant suggesting that heteroskedasticity is not a problem in the

analysis.

Spatial dependence diagnostic tests for the OLS model (Table 4) suggest the presence of

spatial autocorrelation in the model. Following procedures outlined in Haining, a row stan-

dardized spatial weights matrix (W) of 30 miles was found to provide the best fit in the data and

was used to conduct the tests. As shown in Table 4, both the Lagrange Multiplier, and the Ro-

bust Lagrange Multiplier error tests are highly statistically significant. This suggests the pres-

ence of spatial autocorrelation in the data and that a spatial error model should be used to adjust

for spatial autocorrelation.

Maximum Likelihood Spatial Error Model

The ML spatial error model is estimated to address the problem of spatial autocorrelation

indicated in the OLS model. The ML spatial error model results are also presented in Table 3.

All model coefficients are statistically significant at the ten percent level or greater. In evaluat-

ing measures of fit between models, the traditional R2 measure of fit with the OLS estimation

procedure is not directly comparable to the R2 of the ML estimation procedure. However, the

maximized log likelihood (LIK), Akaike information criterion (AIC), and Schwartz criterion

(SC) measures of fit are directly comparable across the two different estimation procedures. The

maximized log likelihood (LIK) estimates suggest that ML spatial error model better fits the data

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because -175.092>-179.045. Similarly, smaller measures of both the AIC and SC estimates for

the ML spatial error model suggest that this model better fits the data.

Specification diagnostic tests for the ML spatial error model presented in Table 5 do not

suggest any heteroskedasticity or spatial autocorrelation problems. The Likelihood Ratio test on

the spatial autoregressive coefficient λ is highly statistically significant in the analysis. Values

for the Likelihood Ratio test and the Wald test are not highly statistically significant suggesting

that the ML spatial error model successfully adjusted for spatial autocorrelation. In addition, the

Wald statistic is greater than the Likelihood Ratio test, which provides additional validity to the

test (16.09 > 9.22). The last Lagrange Multiplier test presented in Table 5 indicates that spatial

lag dependence is not statistically significant in the model.

Marginal implicit prices presented in Table 3 are used to observe the magnitude and di-

rection of influence of various model factors on per acre land values. For convenience, marginal

implicit prices are evaluated at mean values of per acre price and of the characteristic. A positive

marginal implicit price suggests that an increase in that characteristic results in an increase in the

per acre price of rural land, other things constant. Conversely, a negative marginal implicit price

resulting from a negative coefficient has a depressing effect on per acre real estate prices. Mar-

ginal implicit prices are estimated from means of variables using equations 3 and 4.

Comparison of marginal implicit prices between models (Table 3) does not indicate large

differences between model estimates of implicit prices for most of the continuous variables. The

marginal implicit price for the OLS model suggests that an increase of improvements by $1,000

will increase per acre land value by $8.17, while this same value for the ML spatial error model

suggests that if value of improvements increase by $1,000 then per acre value increases by$7.87.

For the ML Model in Table 3, the marginal implicit price for size of tract at the mean size and

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price is estimated to be $-1.32. This means that land price declines by $-1.32 per acre with a one

acre increase in size at the mean.

Relatively larger differences for marginal implicit prices between models (Table 3) are

shown for discrete variables included in the analysis. The residential influence variable is esti-

mated to have $824.33 positive influence on per acre value for the OLS model, whereas it is es-

timated to have a $740.26 influence for the ML spatial error model. With exception of percent

pasture variable, marginal implicit prices for all variables at mean levels are less for the ML spa-

tial error model than for the OLS model. In general, marginal implicit prices seem to suggest

that results from the OLS model overestimate the effect of location and economic development

on per acre rural land values in the study area.

Land Value Contours

Rural land value estimates from spatial econometric models, along with GIS, are used to

estimate rural land value contours. Rural land value contours are estimated to provide a visual

representation of the relationship between location and economic development and per acre rural

land value. Specifically, spatial econometric models are used to predict values based on location

and economic development, and these predictions are used to estimate rural land value contours

with GIS procedures. A rural land value contour is an iso-price line that represents areas which

have approximately equal prices. The method used to estimate land value contours is the Trian-

gulated Irregular Network (TIN) available within the ARC/INFO data model. The TIN proce-

dure provides an efficient means for estimating detailed contours without requiring a huge

amount of data.

Rural land value contours from predictions of the ML spatial lag model for the Red River

area of Louisiana area are presented in Figure 2. Tract size (SIZE), percent cropland (PER-

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CROP), percent pasture (PERPAST), improvement value (VALUE), time of sale (TIME) vari-

ables were held constant in developing land value predictions, while distance to nearest city

(DNC), road type (RT), commercial influence (COMINF), and residential influence (RESINF

variables were allowed to vary across observations. Similar to topographic maps that show equal

elevation above sea level, the Louisiana land value contour map presented in Figure 2 depicts

areas with approximately equal per acre land values. Each contour line is drawn as a continuous

line identifying land values at $200 price intervals. Isolines located close together indicate steep

price gradients in short distances, and isolines located further apart indicate much smaller price

gradients.

Results presented in Figure 2 generally illustrate the effects of Alexandria and Pineville

on rural land values in this area. Rural land values range from $800 to $1800 per acre depending

on the proximity to Alexandria. In the Shreveport area, contour analysis does not provide strong

visual evidence of the effects of location and economic development on per acre rural land val-

ues. Additional rural land sales data in the immediate vicinity of both Alexandria and Shreveport

are needed to improve the visual results of this study.

Summary and Conclusions

The general objective of this discussion was to use spatial econometric procedures to

model rural land values at the urban fringe. Spatial statistics (G statistics), along with GIS pro-

cedures, were used to test for spatial autocorrelation within the rural land market in Red River

area of Louisiana. Simple spatial statistics suggested the presence of spatial autocorrelation

within rural land sales data. Based on these tests, an OLS model was estimated and further di-

agnostic tests were conducted for the presence of spatial autocorrelation in the model. Diagnos-

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tic tests indicated the presence of spatial autocorrelation and results of these tests suggested the

use of a ML spatial error model.

Statistical measures of fit generally indicated improved results for the ML spatial error

model over the model estimated using OLS procedures. Comparison of measures of fit (LIK,

AIC, SC) indicated that the ML spatial error model better fit the data than the OLS model.

Specification diagnostic tests also suggested that the ML spatial error model adequately adjusted

for spatial autocorrelation.

Marginal implicit prices for each model were estimated from first stage hedonic results.

Although there were not large differences between marginal implicit price estimates of the OLS

and ML spatial error models, eight of nine marginal implicit price estimates were smaller for the

ML spatial error model than for the OLS model. Moreover, the greatest differences were for the

tract accessability and non-agricultural influence variables. These factors along with theoretical

statistical considerations suggest that marginal implicit price estimates from the ML spatial error

model are superior to those from the OLS model.

Most rural land value modeling studies have not dealt with the problem of spatial auto-

correlation in the data. This research illustrates that spatial autocorrelation can occur and that

spatial econometric and GIS procedures are effective ways of developing improved rural land

value models. Further research should continue to test for spatial autocorrelation in data bases, to

explore alternative functional forms, and to develop better measures of the effects of location and

economic development in rural land markets.

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References

Adrian, John L. and M. Darren Cannon. “Market for Agricultural Land in the Rural-UrbanFringe of Dothan Alabama.” Bulletin 613. Agr. Exp. Sta., Auburn University, 1992.

Anselin, Luc. “Exploratory Spatial Data Analysis and Geographic Information Systems.” Re-print 94/18, Regional Research Institute, West Virginia University, 1994.

Anselin, Luc. SpaceStat Version 1.80 User’s Guide. Regional Research Institute, West VirginiaState University, 1995.

Barber, G.M. Elementary Statistics for Geographers, New York: Guilford Press, 1988.

Chicoine, David L. “Farmland Values at the Urban Fringe: An Analysis of Sale Prices.” LandEconomics, 57(August 1981): 353-362.

Clonts, Howard A., Jr. “Influence of Urbanization on Land Values at the Urban Periphery.” LandEconomics, 46(1970): 489-487.

Danielson, Leon E. "Using Hedonic Pricing to Explain Farmland Prices." The Farm Real EstateMarket, Proceedings of a Regional Workshop, Southern Natural Resource EconomicCommittee, p. 57-74, 1984.

Dubin, Robin A. “Estimation of Regression Coefficients in the Presence of Spatially Autocorre-lated Error Terms.” Review of Economics and Statistics, 70(August 1988): 466-474.

Getis, Arthur and J.K. Ord. “The Analysis of Spatial Association by Use of Distance Statistics,” Geographical Analysis, 24(July 1992): 189-206.

Haining, Robert. Spatial Data Analysis in the Social and Environmental Sciences, Cambridge:Cambridge University Press, 1990.

Krugman, Paul. Development, Geography, and Economic Theory. Cambridge, Massachusetts:The MIT Press, 1995.

Kennedy, Gary A., Steven A. Henning, Lonnie R. Vandeveer, and Ming Dai. “Multivariate Pro-cedures for Identifying Rural Land Submarkets,” Journal of Agricultural and AppliedEconomics, 29,2(December 1997):373-383.

Kennedy, Peter E. "Estimation with Correctly Interpreted Dummy Variables inSemilogarithmic Equations." American Economic Review, 1981 v.71 p. 801.

Kletke, Darrel D. and Clark A. Williams. “Location and Size Impacts on Rural Land Values,”Current Farm Economics, 65(March 1992): 43-61, Department of Agricultural Econom-ics, Oklahoma State University.

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Pace, R. Kelley, Ronald Barry, and C. F. Sirmans. “Spatial Statistics and Real Estate,” Journal ofReal Estate Finance and Economics, Vol. 17:1, 5-13 (1998).

Palmquist, Raymond B. "Heterogeneous Commodities, Hedonic Regressions, and the Demandfor Characteristics." The Farm Real Estate Market. Proceedings of a Regional Work-shop, Southern Natural Resource Economics Committee, 1984:45-56.

Rosen, Sherwin M. "Hedonic Prices and Implicit Markets: Product Differentiation in Pure Com-petition," Journal of Political Economy, 82(1974): 34-55.

Shonkwiler, J.S. and J.E. Reynolds. “A Note on the Use of Hedonic Price Models in the Analysisof Land Prices at the Urban Fringe,” Land Economics, 62(February 1986): 58-63.

Vandeveer, Lonnie R., Gary A. Kennedy, Steven A. Henning, Chunxiao Li, and Ming Dai. “GISProcedures for Conducting Rural Land Market Research,” Review of Agricultural Eco-nomics, 20:2(Fall/Winter 1998): 448-461.

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Table 1. Variables used in hedonic model estimation, Red River area, Louisiana rural land market survey,1993-1998.

Symbol Variable Expected Sign

Continuous Variables PRICE Per acre price of land ($) SIZE Size of tract (acres) (-) PERCROP Percent of cropland in tract (+) PERPAST Percent of pasture in tract (+) VALUE Value of improvements ($) (+) DNC Distance to nearest city (mile) (-) TIME Month of sale (+)Discrete Variables (1,0) RT Paved access road (+) COMINF Commercial influence (+) RESINF Residential influence (+)

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Table 2. Spatial association among per acre values, Red River area, Louisiana rural land market survey, 1993-1998.

Distance in miles G-statistica z-valueb Probability

5 0.00055 2.1563 0.0311

10 0.00106 2.8855 0.0039

15 0.00162 3.1051 0.0019

20 0.00230 2.4605 0.0139

25 0.00269 2.5981 0.0094

30 0.00320 2.1581 0.0309

35 0.00362 1.8198 0.0688

40 0.00436 1.4671 0.1424

45 0.00488 1.2313 0.2182 a Developed by Getis and Ord to test for spatial autocorrelation. b Estimated for the normal distribution.

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Table 3. Estimated first stage OLS and ML models and marginal implicit prices, Red River area, Louisiana, 1993-98.

OLS model ML spatial error model

ItemEstimated

coefficientsa

Marginalimplicitpricesb

Estimatedcoefficientsc

Marginalimplicitpricesb

Variable SIZE -0.294595 -1.34028 -0.291190 -1.32479

(-9.457)*** (-9.501)***

PERCROP 0.003651 3.20071 0.003796 2.96304(3.771)*** (3.917)***

PERPAST 0.002009 1.76129 0.002198 1.92682(2.012)** (2.239)**

VALUE 0.000009 0.00817 0.000009 0.00787(-9.168)*** (9.135)***

TIME 0.010061 8.82124 0.008656 7.58946(4.984)*** (4.442)***

DNC -0.004100 -4.38293 -0.004479 -3.92703(1.913)* (-1.717)*

RT 0.344003 357.14588 0.335105 346.30893(5.080)*** (5.033)***

COMINF 0.683095 786.57568 0.651835 741.67956(2.336)** (2.339)**

RESINF 0.672322 824.32564 0.621072 740.25878(4.871)*** (4.639)***

Intercept 7.273720 --- 7.274820(49.757)*** (49.836)***

Measures of fit Maximized log likelihood (LIK) -179.045 -175.092 Akaike information criterion (AIC) 378.090 370.184 Schwartz criterion (SC) 413.464 405.558 R2 .4949 .4565Number of observations 254.00000 254.00000

a Student t-ratios are in parentheses, *** denotes statistical significance at the .01 level, ** denotes statistical signifi-cance at the .05 level, and * denotes statistical significance at the 0.10 level.

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b Estimated in dollars at the mean value for each variable.c Standard normal z-values are in parentheses, *** denotes statistical significance at the .01 level, ** denotes statisticalsignificance at the .05 level, and * denotes statistical significance at the 0.10 level.

Table 4. OLS regression and spatial dependence diagnostics, Red River area, Louisiana rural land market survey, 1993-1998.

Test Value Probability

Regression diagnostics

Multicollinearity condition number 13.50575 ---

Keifer-Salmon (normality of errors) 4.46517 0.10725

Breusch-Pagan (heteroskedasticity) 9.18145 0.42070

Diagnostics for spatial dependence

Moran=s I (error) 2.72847 0.00636

Lagrange Multiplier (error) 6.63613 0.00999

Robust Lagrange Multiplier (error) 5.77602 0.01625

Lagrange Multiplier (lag) 2.37321 0.12343

Robust Lagrange Multiplier (lag) 1.51310 0.21867

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Table 5. Maximum likelihood spatial error model regression diagnostics, Louisiana land market survey, 1993-1998.

Test Value Probability

Diagnostics for heteroskedasticity

Spatial Breush-Pagan test 9.57273 0.386168

Diagnostics for spatial dependence

Likelihood Ratio test for spatial error dependence 7.90622 0.004926

Likelihood Ratio test for common factor hypothesis 9.22034 0.417188

Wald test for common factor hypothesis 16.08822 0.065062

Lagrange Multiplier test of spatial lag dependence 1.05578 0.304178

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