RURAL AMENITY VALUES AND LENGTH

Transcription

1 RURAL AMENITY VALUES AND LENGTH OF RESIDENCY ROBERT J. JOHNSTON,STEPHEN K. SWALLOW, TIMOTHY J. TYRRELL, ANDDANA MARIE BAUER New residents of rural communities are often assumed to have preferences for development and conservation that differ from those of longer-term residents. However, the literature offers little to quantify presumed preference heterogeneity. This article assesses whether stated preferences differ according to length of residency. Results are based on a conjoint (choice experiment) survey of Rhode Island rural residents. Heterogeneity according to length of town residency is modeled using dummy variables, multiplicative interactions, and Lagrangian interpolation polynomials. Results are compared across the three models, and identify a range of attributes for which willingness to pay depends on length of residency. Key words: contingent valuation, Lagrangian interpolation polynomial, length of residency, rural amenity values. New residents of rural communities are often assumed to have preferences for the development and conservation of rural lands that differ from those of longer-term residents (Kelsey, Spain, Myers). Newer residents are often assumed to have relatively stronger preferences for aesthetic and recreational attributes, and to be more willing to accept associated development restrictions (Dubbink, Healy and Short, Spain). Newer residents may also be willing to incur greater costs of living in return for expanded community services, and may be more (or less) willing to accept wildlife nuisance associated with rural lands (Kelsey, Spain, Zin and Aldelt). Despite the ubiquity of assumptions regarding preference heterogeneity and residence duration, the literature offers little to quantify presumed preference shifts. While the literature addresses heterogeneity in stated preferences for resource policies (e.g., Swallow Robert J. Johnston is associate director of Connecticut Sea Grant and assistant professor, Department of Agricultural and Resource Economics, University of Connecticut; Stephen K. Swallow is professor, Department of Environmental and Natural Resource Economics, University of Rhode Island; Timothy J. Tyrrell is professor, Department of Environmental and Natural Resource Economics, University of Rhode Island; and Dana Marie Bauer is graduate research assistant, Department of Environmental and Natural Resource Economics, University of Rhode Island. This research was funded by the USDA Fund for Rural America No and the Rhode Island Agricultural Experiment Station No Opinions belong solely to the authors and do not imply endorsement by the funding agencies. et al., Loomis) typically as related to demographic indicators few works address preference heterogeneity related to length of residency. Those few works that include residence duration as a determinant of rural preferences (e.g., McLeod, Woirhaye, and Menkhaus; Inman, McLeod, and Menkhaus) focus on broad aspects of rural policy, rather than on detailed land use or amenity trade-offs. While geography, rural sociology, and planning research addresses differences between new and more established residents, these works focus primarily on qualitative findings (Salamon and Tornatore, Dubbink), or on general attitudes toward development and conservation (Spain, Theodori and Luloff, Pendall). Quantification of potential preference heterogeneity associated with length of rural residency may improve understanding of the ways in which development and conservation trade-offs influence the welfare of different groups. To this end, this article examines whether stated preferences for development and conservation differ according to length of residency in selected Rhode Island rural communities. Results are based on preferences estimated from a conjoint survey of rural residents, addressing alternative proposals to develop rural lands for residential purposes. Preference heterogeneity is incorporated using three approaches that allow regression coefficients to shift as a function of length of residency. The first approach uses dummy Amer. J. Agr. Econ. 85(4) (November 2003): Copyright 2003 American Agricultural Economics Association

2 Johnston et al. Rural Amenity Values 1001 variables to allow systematic, discrete shifts in slope and intercept coefficients, based on discrete residence time categories. The second approach appends multiplicative interaction terms to the preference function, modeling the influence of model attributes as a linear function of residence duration. The third approach applies Lagrangian interpolation polynomials (LIPs) to model the influence of model attributes as a higher-order polynomial function of residence time (Tyrrell). 1 The Contingent Choice Model A Random Utility Model with Homogeneous Preferences We begin with a random utility model of rural development and conservation trade-offs, in which preferences are assumed to be homogeneous. To model a respondent s choice, we define a utility function that includes attributes of a rural development or conservation plan and the net cost of the plan to the respondent (Hanemann, McConnell): (1) U( ) = U(X c, Y F c ) = v(x c, Y F c ) + ε c where X c is a vector of variables describing attributes of development or conservation plan c; Y is disposable income of the respondent; F c is the change in mandatory taxes paid by the respondent under plan c; v( ) is a function representing the empirically measurable component of utility; ε c is econometric error. If one compares Plan A (c = A) to Plan B(c = B), the change in utility (du) may be modeled as (2) du = U(X A, Y F A ) U(X B, Y F B ) = [v(x A, Y F A ) v(x B, Y F B )] [ε B ε A ] = dv. The model assumes a respondent assesses the difference between utility under the two plans and indicates the sign of du by either choosing Plan A (du > 0) or Plan B (du < 0). Although the literature offers no firm guidance regarding the choice of specific functional 1 Another approach to modeling heterogeneous preferences is the mixed logit or random parameters model (Train). forms for dv, in practice linear forms are often used. Hence, (3) dv = v(x A, F A ) v(x B, F B ) = x (X A X B ) + f (F B F A ) where x is a conforming vector of coefficients associated with the vector of attribute differences (X A X B ) and f as a scalar coefficient associated with the tax difference (F B F A ). The parameter vector x may be interpreted as the marginal utility of various development or conservation attributes of a development plan, while f represents the marginal utility of income. 2 Alternative Approaches to Modeling Preference Heterogeneity A heterogeneous preferences model allows parameters (marginal utility) to vary across groups or individuals (Swallow et al.). The socioeconomic attribute for which preference heterogeneity is modeled is length of residency in a rural community. Although we discuss heterogeneity solely in terms of this variable, identical models apply to any demographic attribute that may be characterized as a continuous variable (e.g., age). The Dummy Variable Approach Perhaps the most common approach to modeling preference heterogeneity is to allow systematic but discrete variations in slope and intercept coefficients using dummy variables. One might, for example, define a dummy variable to distinguish those with less than ten years of town residency from longer-term residents. This would allow different slope and intercept parameters for the two groups, but would impose constant preferences within each group. Formally, this approach redefines dv in (3) to provide a separate utility estimate for each respondent group. In the simplest two-category case, we define a dummy variable D t to equal one for respondents whose residency is t years or more, and to equal zero otherwise. Accordingly, 2 The absence of income (Y) from (3) reflects the fact that disposable income is assumed unaffected by rural development, aside from direct deductions associated with the cost of each plan, and hence subtracts out of the linear model for dv.

3 1002 November 2003 Amer. J. Agr. Econ. (4) dv = t x (1 D t )(X A X B ) + t f (1 D t )(F B F A ) + >t x D t (X A X B ) + >t f D t (F B F A ) where ( t x, t f ) represents marginal utility parameters for respondents whose residence time is less than or equal to t, and ( >t x, >t f ) represents these marginal utilities for respondents with residence times greater than t. The Multiplicative Interaction Approach This approach appends the linear specification of dv (3) with a vector of multiplicative interactions such that (5) dv = x (X A X B ) + f (F B F A ) + x (X A X B )t + f (F B F A )t where t is the length of residency of the respondent. Here, x and f represent adjustments to the marginal utilities x and f, respectively, associated with the length of residency. The interaction model eliminates the discrete preference shifts characteristic of dummy variable models. While (5) allows marginal utility to vary as a continuous function of t, the effect is linear. The Lagrangian Interpolation Polynomial Approach To relax the linear relationship between the marginal utility of plan attributes and residence duration, one may specify the marginal effect of each attribute as a polynomial or otherwise nonlinear function of residence time. A common means to accomplish this is to append the multiplicative interaction model (5) with higher-order interactions. For example, one might specify an interaction model in which attributes interact with both t and t 2, (6) dv = x (X A X B ) + f (F B F A ) + x (X A X B )t + f (F B F A )t + xx (X A X B )t 2 + ff (F B F A )t 2. Here, xx and ff represent adjustments to the marginal utility associated with t 2. A potential disadvantage of this approach is that model output may be somewhat cumbersome in terms of interpretation and hypothesis testing. For example, marginal utilities are not directly illustrated by estimated parameters; additional calculations are required. Tyrrell suggests an alternative approach, which, while statistically equivalent to (6), offers practical advantages. This approach uses Lagrangian interpolation polynomials (LIPs) to shift regression coefficients. Unlike (6), estimated LIP model results directly reveal the value of parameter estimates for individuals at length of residency reference points chosen by the researcher. This can facilitate both model interpretation and statistical tests designed to assess differences in parameter estimates across reference points; equivalent tests using (6) would generate identical results but would be more cumbersome. In addition, direct access to the value of the polynomial at any reference point allows one to more easily constrain the polynomial function. To illustrate the LIP approach, we first specify the effect of independent variable g as a polynomial function of residence duration, (7) P g (t) = g0+ g1 t + g2 t gn t n where g indexes an independent variable corresponding to one of the columns of matrix (X A X B, F B F A ), P g (t) is the value of the polynomial corresponding to variable g, and n represents the degree of the polynomial chosen by the researcher. The gi are unknown parameters determining the value of the polynomial corresponding to attribute g. We use the polynomials in (7) to estimate an empirical version of model (3) that smoothly modifies the basic utility function for individuals whose residence time is t. Thus, the polynomial-based model causes the analyst to index dv by t, such that (8) dv t = P (t)(x A X B ) + P f (t)(f B F A ) where (t) is a row vector whose elements are defined P by (7), conforming to matrix (X A X B ). In comparing this with the systematically varying slopes approach represented by (4), one sees that model (4) is a special case of model (8) where the polynomial parameters are replaced by constant parameters such that (9) [P (t), P f (t)] [ t x [ >t x, t ] f for t t ] for t > t., >t f If residence time is used to define more than two residency groups in the systematically

4 Johnston et al. Rural Amenity Values 1003 varying slopes model, then (4) (9) would be modified accordingly. The function P g (t) takes values gi at n + 1 unique reference points r i, where i (0, 1, 2,..., n) identifies these reference points. The degree of the estimable polynomial, n, depends on the number of reference points (n + 1) chosen by the researcher. These reference points r i represent residence times t = r i at which coefficients gi will be estimated. That is, P g (r i ) = gi. Reference residence times are chosen to aid in policy analysis or assessment of model implications. It is important to note that once the number of reference points is chosen, the choice of particular reference residence points is a matter of convenience; it does not affect the statistical fit or performance of the model. The choice of reference points simply influences the particular points along the length of residency continuum at which the model will provide coefficient estimates. While the underlying polynomial function is influenced by the number of anchor points chosen by the researcher, it is not altered by the choice of particular reference points. This framework implies a system of equations (10) R n+1 g = g where n+1 is a square (n + 1, n + 1) matrix with rows R [1, r i, r 2 i,..., rn i ] corresponding to the n + 1 reference points; g is a column vector [ g0, g1, g2,..., gn ] ; and g is a column vector consisting of elements { gi } for all i {0, 1, 2,..., n}. Combining (7) and (10) allows a restatement of unknown parameters g (Tyrrell, Shchigolev): (11) g = R 1 n+1 g. By defining T(t) as the vector [1, t, t 2,..., t n ], the polynomial functions then become: (12) P g (t) = T(t) g = T(t) R = L(t) g 1 n+1 g where row vector L(t) contains n + 1 elements based on each of the reference residence times incorporated in R n+1. Equation (12) defines the marginal utility represented by P g (t), for attribute g, at residence time t, as an interpolation of its values at the reference points established in g. This interpolation uses Lagrangian interpolation polynomials (LIPs) as given by Tyrrell: (13) L i (t) = k i (t r k ) (r i r k ) for i = (0, 1, 2,...,n) which defines the n + 1 elements of L(t).The LIPs in (12) take on known values at each of the reference points, or residence times r i.in particular, LIP L j (t) = 1 when t equals reference point r j, while L j (t) = 0 when t equals some other reference point r i, for i j. Fort falling between any two reference points, the LIPs will take on interpolated values, yielding an estimated marginal utility for the attribute through equation (12). Equation (13) also implies that i L i(t) = 1. For example, assume that the parameters fi (i = 0,...,n) represent the marginal utility of income at each r i reference point. The model estimates the value of fi at reference points 0, 1,..., n, generating estimates f 0, f 1,..., fn. 3 These estimates represent the marginal utility of income for residents whose length of residency corresponds exactly to the associated reference point, because L i (t) = 1 when t = r i. For residents whose length of residency does not correspond exactly to one of the reference points, the interpolated coefficient value (i.e., marginal utility of income) is equal to f 0 (L 0 (t)) + f 1 (L 1 (t)) + + fn (L n (t)). The Survey The Rhode Island Rural Land Use survey was designed to assess rural residents tradeoffs among attributes of residential development and conservation (Johnston, Swallow, and Bauer). Respondents from four Rhode Island rural communities (Burrillville, Exeter, West Greenwich, and Coventry) were asked to consider alternative development options for hypothetical tracts of forested land located in their local town. Respondents were provided with two development options, a current development plan and an alternate development plan, where each plan could differ across a set of spatial and nonspatial attributes. These attributes characterized 3 In this case, parameters ( gi ) are estimated using maximum likelihood, more specifically a binary logit model incorporating random effects.

5 1004 November 2003 Amer. J. Agr. Econ. land use features and amenities identified by focus groups and interviews with growth management practitioners. Survey development required approximately eighteen months, and involved background research, and interviews with policy makers and focus groups. Individual and group pretests ensured that survey language and format could be easily understood by respondents, and that respondents shared consistent interpretations of survey scenarios (cf. Johnston et al.). Attributes distinguishing management plans were chosen based on focus groups and interviews, and characterized protected open space (acreage, location, access), residential development (housing density, acreage, location, shape), unprotected undeveloped land, scenic views, wildlife habitat, recreational facilities, traffic, and taxes. Table 1 characterizes attributes distinguishing hypothetical management plans. Prior to presenting respondents with development choices, the survey provided background information on community land use and trade-offs implicit in development choices. Contingent choice instructions and questions were then presented. Each respondent considered three potential pairs of current and alternate plans for the same 400-acre undeveloped site. Respondents were instructed to consider each pair independent of previous choices, and to assume that all choices applied to the same parcel. Respondents were told that if you do not vote for either plan, development will automatically occur as shown by the current development plan, thereby specifying the status quo that would occur if no choice were made (Adamowicz et al.). This framework was chosen to mimic actual community considerations of development proposals, wherein a landowner possesses the property rights necessary to permit development. However, officials may seek to influence the configuration of the development, delaying permits unless changes are made. As a result, officials may exert control over the ultimate form of development. A fractional factorial design was used to construct survey questions with an orthogonal array of attribute levels. 4 All attributes were free to vary over their full range for both the current and alternate plans, with no imposed ordering of attribute levels between the two 4 The statistical design was conducted by Don Anderson of STATdesign, Evergreen CO. plans. This resulted in 128 unique contingent choice questions divided among forty-three different survey booklets (three questions per booklet). Surveys were mailed to 4000 randomly selected residents of the four Rhode Island towns, following the total survey design method (Dillman). Of 3702 deliverable surveys, 2157 were returned, providing 6062 (94% of the potential 6471) complete and usable responses to dichotomous choice questions. Of these, 5774 observations included information regarding length of residency. Resident groups were defined based on responses to the survey question: How long you have lived in your current town? The question was open-ended, and specified that the response be given in years. Approximately 41% of all usable observations indicated ten or fewer years of residency, 35% indicated between eleven and thirty years of residency, and 17% indicated more than thirty years of residency. The Econometric Model Based in part on results of focus groups, reference points for length-of-residency were set at 0, 10, and 30 years. This results in three LIPs, implying a quadratic polynomial function. Based on (12), the three LIPs are given by (14) L 0 (t) = L 1 (t) = L 2 (t) = (t 10)(t 30) (0 10)(0 30) (t 0)(t 30) (10 0)(10 30) (t 0)(t 10) (30 0)(30 10), where t represents the length of residency for each observation. Combined with (13), the terms in (14) provide the basis for empirical estimation of the LIP model. As noted above, these reference points are chosen for convenience of interpretation only; statistical properties of the model are identical regardless of the particular anchor points chosen. Corresponding with the cut-points selected for the LIP model, three length-of-residency categories were selected for the dummy variable (or systematically varying slopes) model. These distinguished residents with (a) less than 10 years of residency; (b) between 10 and 29 years of residency, inclusive; and (c)30 or more years of residency. Following (4), the

6 Johnston et al. Rural Amenity Values 1005 Table 1. Model Variables: Definitions and Summary Statistics Units and Mean Variable Name Description Measurement (Std. Dev.) Adj open Iso open Size dif Dense dif Lg mammal Sm mammal Com bird Uncom bird Wet sp Traf light Taxdif Lowvis Edgearea Develop2 The difference between acres of open space adjacent to developments and roads in the CDP and ADP. The difference between acres of open space not adjacent to developments and roads in the CDP and ADP. The difference between acres of residential development in the CDP and ADP. The difference in housing density in the CDP and ADP. Difference between habitat quality for large mammals in the CDP and ADP. Difference between habitat quality for small mammals in the CDP and ADP. Difference between habitat quality for common birds in the CDP and ADP. Difference between habitat quality for uncommon birds in the CDP and ADP. Difference between habitat quality for wetland species in the CDP and ADP. Difference between dummy variables indicating the presence of a traffic light on the main road, in the CDP and ADP. Difference in additional annual taxes and fees between the CDP and ADP (resulting from management plan). Difference between dummy variables indicating the presence of development either highly screened or not visible from the main road in the CDP and ADP. Survey versions included eight different photographs characterizing different development visibility levels; four of these photographs are characterized as low visibility development. The difference between the edge-area ratio of residential development shown in the CDP and that in ADP. Ratios are calculated as the sum of the perimeter(s) divided by the sum of the area(s) of land highlighted for residential development. Difference between dummy variables indicating the presence of a two-section, fragmented development in the CDP and ADP. In all cases, development sections are rectangular. Acres in CDP minus acres in ADP. (Range: 200 to 200) Acres in CDP minus acres in ADP. (Range: 200 to 200) Acres in CDP minus acres in ADP. (Range: 200 to 200) Houses/acre in CDP minus houses/acre in ADP. (Range: 2 to2) Difference in wildlife habitat quality scale (1 = worst; 5 = best). Difference in wildlife habitat quality scale (1 = worst; 5 = best). Difference in wildlife habitat quality scale (1 = worst; 5 = best). Difference in wildlife habitat quality scale (1 = worst; 5 = best). Difference in wildlife habitat quality scale (1 = worst; 5 = best). Difference between dummy variables for CDP and ADP. Dollars in CDP minus dollars in ADP. (Range: $325 to $325) Difference between dummy variables for CDP and ADP Calculated at a scale of 1 unit = ft. (e.g., a 1 unit 1 unit square is equivalent to 20 acres or 871,180 square feet, with an edge-area ratio of 4). (Range: to 8.5) Difference between dummy variables for CDP and ADP ( ) ( ) ( ) (0.9821) (1.2311) (1.2444) (1.7470) (1.7316) (1.7348) (0.7059) ( ) (0.7004) (3.7059) (0.4273)

7 1006 November 2003 Amer. J. Agr. Econ. Table 1. Continued Units and Mean Variable Name Description Measurement (Std. Dev.) Develop4 Develop road Lo inc Age Hi edu Difference between dummy variables indicating the presence of a four- or five-section, fragmented development in the CDP and ADP. In all cases, development sections are rectangular. Difference between dummy variables indicating the presence of developments located adjacent to main roads, in the CDP and ADP. Dummy variable identifying those respondents with reported household income below $40,000 per year. Reported age of survey respondent, in years. Dummy variable identifying those respondents with at least a four-year college education. Note: CDP = Current Development Plan; ADP = Alternate Development Plan. model estimates unique slope and intercept parameters for each of the three categories. The interaction model (5) does not require specification of anchor points or a priori categories. As the final data comprise three responses per respondent, there is a possibility of correlated errors across responses (Alberini, Kanninen, and Carson; Poe, Welsh, and Champ). One common approach to modeling such potential correlation is to split in (2) into two components: that is i.i.d. across all respondents and for each individual respondent, and a random effect h that represents systematic variation related to unobserved characteristics of respondent h (Alberini, Kanninen, and Carson; Hsiao), such that (15) du h = dv h ( + h ) Difference between dummy variables for CDP and ADP. Difference between dummy variables for CDP and ADP (0.6041) (0.7199) Dummy variable (0,1) (0.4045) Years ( ) Dummy variable (0,1) (0.4707) where the subscript h indexes individual respondents. If the h are assumed normally distributed across respondents, and we assume a logistic distribution of, the model is estimated as a random effects logit model (Pendergast et al.). Preliminary random-effects LIP models were estimated to assess whether (13) should be amended to incorporate quadratic interactions with demographic attributes such as age, education, and income. Likelihood ratio tests assessing the joint significance of these appended interactions fail to reject the null hypothesis of zero joint influence for interactions including a respondent s age ( 2 = 50.6, df = 51; p = 0.49) and a dummy variable indicating respondents with at least a four-year college education ( 2 = 54.5, df = 51; p = 0.34). Likelihood ratio tests reject the null hypothesis of zero joint influence for interactions involving a dummy variable identifying respondents with income below $40 k ( 2 = 77.81, df = 51; p = 0.01). However, analogous tests fail to reject the null hypothesis of zero joint influence for interactions between the low-income dummy variable and all model attributes except the payment vehicle ( 2 = 48.42, df = 48; p = 0.46). Based on these results, the final models include quadratic interactions between the low-income dummy and the tax change (i.e., the payment vehicle), but exclude other demographic interactions. Empirical Findings Table 2 illustrates the results for the LIP and dummy variable models; table 3 illustrates the results for the interaction model. For the LIP model, parameter estimates prefixed with L 0, L 1, and L 2 correspond to estimated parameter values at the reference points of 0, 10, and 30 years of residency, respectively. For the dummy variable model, the same prefixes correspond to parameter values for those with 0 9 years, years, and >30 years of residency, respectively.

8 Johnston et al. Rural Amenity Values 1007 Table 2. Results for Lagrangian Interpolation Polynomial and Dummy Variable Models Lagrangian Interpolation Polynomial Model Dummy Variable Model Variable Reference Parameter Std. Reference Parameter Std. Name Point Estimate Error Point Estimate Error Intercept L 0 (0 yrs.) L 0 (0 9 yrs.) Intercept L 1 (10 yrs.) L 1 (10 29 yrs.) Intercept L 2 (30 yrs.) L 2 (>30 yrs.) Edgearea L L Edgearea L L Edgearea L L Develop2 L L Develop2 L L Develop2 L L Develop4 L L Develop4 L L Develop4 L L Iso open L L Iso open L L Iso open L L Adj open L L Adj open L L Adj open L L Develop road L L Develop road L L Develop road L L Lg mammal L L Lg mammal L L Lg mammal L L Sm mammal L L Sm mammal L L Sm mammal L L Com bird L L Com bird L L Com bird L L Uncom bird L L Uncom bird L L Uncom bird L L Wet sp L L Wet sp L L Wet sp L L Dense dif L L Dense dif L L Dense dif L L Size dif L L Size dif L L Size dif L L Traf light L L Traf light L L Traf light L L Lowvis L L Lowvis L L Lowvis L L Taxdif L L Taxdif L L Taxdif L L Taxdif lo inc L L Taxdif lo inc L L Taxdif lo inc L L ln( ) ln( ) Log Likelihood (Likelihood Ratio Test) p < 0.10; p < 0.05; p < 0.01.

9 1008 November 2003 Amer. J. Agr. Econ. All models are statistically significant at p < 0.01, based on likelihood ratio tests at the appropriate degrees of freedom (tables 2, 3). Likelihood ratio tests (of the three unrestricted models versus a restricted model in which homogeneous preferences are imposed) reveal that restrictions imposing homogeneous preferences have a statistically significant impact at p < 0.01 for the LIP model ( 2 = 61.02, df = 36) and at p < 0.05 for the interaction model ( 2 = 29.98, df = 17). However, for the dummy variable model we cannot reject homogeneity in preferences at p < 0.10 ( 2 = 41.59, df = 36, p < 0.25). That is, where both the LIP and interaction models are able to detect joint, statistically significant preference heterogeneity, this heterogeneity cannot be established by the dummy variable model. Given the inability of the dummy variable model to identify statistically significant heterogeneity in preferences, subsequent discussions are based primarily on the results of the LIP and interaction models. Although likelihood ratio tests indicate that length of residency has a significant effect on both the LIP and interaction models, results for individual attributes may vary. Hence, for each individual model attribute, we test for statistically significant differences in parameter estimates between the reference points of 0 and 10 years, 10 and 30 years, and 0 and 30 years. The results are shown in table 4. To reduce table size, the test results are shown only for variables for which homogeneity in preferences can be rejected at p < 0.10, based on asymptotic Wald tests (Judge et al.). The results for other attributes are suppressed. Wald tests reject the null hypothesis of preference homogeneity for seven of sixteen attributes (table 4). These results indicate that residence duration may or may not influence the marginal utility of rural development or conservation outcomes, depending on the particular attributes involved. While the magnitude and sign of the estimated parameter shifts are often similar across the interaction and LIP models, the attributes and reference points over which the null hypothesis is rejected are not identical. For example, change in the parameter estimate associated with adj open (open space adjacent to developments) is similar in both models. However, while the interaction model rejects the null hypothesis of preference homogeneity between the reference points of 0 and 10 years, 10 and 30 years, and 0 and 30 years, the LIP model only rejects the null hypothesis between 10 and 30 years. Table 3. Results for the Interaction Model Parameter Std. Variable Name Estimate Error Intercept Intercept years Edgearea Edgearea years Develop Develop2 years Develop Develop4 years Iso open Iso open years Adj open Adj open years Develop road Develop road years Lg mammal Lg mammal years Sm mammal Sm mammal years Com bird Com bird years Uncom bird Uncom bird years Wet sp Wet sp years Dense dif Dense dif years Size dif Size dif years Traf light Traf light years Lowvis Lowvis years Taxdif Taxdif years Taxdif lo inc Taxdif lo inc years ln( ) Log Likelihood (Likelihood Ratio Test) p < 0.10; p < 0.05; p < Identical results would be generated were one to compare the (first-order) interaction model with an analogous model that also incorporated quadratic interactions (i.e., (6)), given the statistical equivalence of a secondorder LIP and quadratic interaction model. Hence, the comparison between interaction and LIP model results may also be interpreted as illustrating the implications of modeling marginal utilities as a higher-order

10 Johnston et al. Rural Amenity Values 1009 Table 4. Model Attributes With Significant Differences in Estimated Coefficients Estimated at 0, 10 and 30 Years of Residency (Wald Test Results) Lagrangian Interpolation Polynomial Model Interaction Model Parameter Estimated 2 for Null Estimated 2 for Null Estimates Coefficient Hypothesis Coefficient Hypothesis Attributes Compared Difference (Diff. = 0) Difference (Diff. = 0) Develop Develop road Sm mammal Traf-light Adj open Dense dif Taxdif Lo inc p < 0.10; p < 0.05; p < polynomial function of residence duration. In this case, the introduction of nonlinearity into the relationship between length of residency and marginal utility allows the model to identify additional attributes for which length of residency may influence marginal preferences (e.g., devroad, taxdif lo inc). However, for other attributes (e.g., develop2, dense dif ) a statistically significant length-of-residency effect is found in the simpler interaction model but disappears when one models marginal utilities as a higher-order polynomial function of residence duration. Length of Residency and Rural Amenity Preferences Effects related to length of residency notwithstanding, the signs of parameter estimates correspond with prior expectations derived from focus groups, where prior expectations exist. For example, respondents preferred development plans characterized by: (a) larger areas of preserved open space, both isolated from and adjacent to roads and developments (iso open; adj open); (b) smaller areas of developed land (size dif ); (c) lower housing densities (dense dif ); (d) improved habitat for large mammals (lg mammal), birds (com bird; uncom bird), and wetland species (wet sp); (e) low visibility development (lowvis); and (f ) lower taxes (taxdif ). As shown in table 4, the attributes for which homogeneity in preferences may be rejected by either the LIP or interaction models include develop2 (indicating developments in two-part clusters); develop road (indicating developments adjacent to main roads); sm mammal (habitat quality for small mammals); traf light (indicating the presence of traffic lights); adj open (acres of open space adjacent to developments and roads); dense dif (number of houses per acre in developed areas); and taxdif lo inc (interaction between the payment vehicle and a dummy variable identifying households with annual income <$40,000). Implications for each attribute are summarized below, along with the models in which significant heterogeneity is identified.

11 1010 November 2003 Amer. J. Agr. Econ. 1. Develop road (LIP model): Residents prefer developments to be isolated from main roads. This effect diminishes as length of residency increases 5 ; the placement of developments adjacent to main roads has a more negative marginal utility for new residents. 2. Develop2 (interaction model): Respondents with five or fewer years of residency have a positive marginal utility associated with the division of developments into two distinct subclusters. As length of residency increases marginal utility declines, such that respondents with six or more years of residency have a negative marginal utility for this attribute. 3. Sm mammal (LIP and interaction models): A positive marginal utility for improvements in small mammal habitat at zero years of residency declines with increases in residence time. Marginal utility for this attribute becomes negative at approximately ten years of residency. 4. Traf light (LIP and interaction models): All groups have positive preferences for the presence of traffic lights. As length of residency increases, positive marginal utility increases. 5. Adj open (LIP and interaction models): All groups have positive marginal utility associated with open space preserved adjacent to residential developments or roads; marginal utility declines as length of residency increases. 6. Dense dif (interaction model): Respondents have a negative marginal utility for housing density that increases in magnitude with length of residency. 7. Taxdif (LIP model): All groups have negative preferences for tax increases, and the coefficient estimate associated with linear (i.e., not interacted with income) tax increases cannot be shown to differ as a function of length of residency. However, the effect of low income (i.e., those with incomes less than $40 k; table 1) on the marginal utility of taxes differs as a function of length of residency. Tax changes have a greater impact on utility for lowincome individuals as length of residency increases. Welfare Implications While the valuation literature places a dominant concern on estimating WTP and welfare changes, we caution that the policy relevance of preference differences may hinge directly on marginal utilities. In some contexts, such as voting on growth control policies or voicing concerns in public hearings, it may be differences in marginal utilities that drive the dynamics of public input. Moreover, differences in marginal utilities may imply that differences in WTP are relevant, even if WTP differences fail to meet preset criteria for statistical significance. Despite these potential caveats, estimated changes in marginal WTP remain an important means of policy assessment. Accordingly, marginal WTP estimates are calculated for all model attributes over the reference points of 0, 10, and 30 years of residency; the resulting differences are tested for statistical significance. For the LIP model, WTP is calculated following Hanemann; mean WTP for a marginal change in the gth attribute is equal to g / f, where g is the parameter estimate corresponding to the gth attribute, and f is the parameter estimate corresponding to cost (taxdif ). This approach is extended to incorporate the interaction between taxdif and the low-income indicator variable (lo inc), such that WTP differences between length-ofresidency reference points for the gth attribute are given by (16) g,li f,li + ( f lo inc,li lo inc) g,lj f,lj + ( f lo inc,lj lo inc) for i j. Here, i,j = (0, 1, 2) correspond to the three length-of-residency reference points, f lo inc represents the parameter associated with taxdif lo inc, and WTP is calculated based on the sample mean value for lo inc (table 1). For the interaction model, WTP at any particular length-of-residency reference point, for the gth attribute is calculated 5 The LIP model indicates that the parameter estimate for develop road is negative over the entire range of length of residency. The interaction model indicates a negative parameter estimate for all residents with less than 65 years of residency. (17) ( g + ( g t t)) ( f + ( f t t)) + ( f lo inc + ( f lo inc t t))

12 Johnston et al. Rural Amenity Values 1011 Table 5. Differences in Estimated WTP at 0, 10 and 30 Years of Residency Lagrangian Interpolation Polynomial Model Interaction Model t-statistic t-statistic Estimated for Null Estimated for Null WTP WTP Hypothesis Coefficient Hypothesis Attributes Comparison at: a Difference (Diff. = 0) Difference (Diff. = 0) Develop2 0 vs. 10 yrs vs. 30 yrs vs. 30 yrs Develop road 0 vs. 10 yrs vs. 30 yrs vs. 30 yrs Sm mammal 0 vs. 10 yrs vs. 30 yrs vs. 30 yrs Traf light 0 vs. 10 yrs vs. 30 yrs vs. 30 yrs Adj open 0 vs. 10 yrs vs. 30 yrs vs. 30 yrs a WTP differences are calculated by subtracting WTP at the second reference point from WTP at the first reference point. p < 0.10; p < 0.05; p <0.01. where t represents length of residency, g t represents the parameter estimate associated with the quadratic interaction of the gth attribute and t, and f t represents the parameter estimate associated with the quadratic interaction of taxdif and t. The results are shown in table 5; only those attributes supporting at least one significant WTP difference are shown. Standard errors for estimated WTP are generated following Park, Loomis, and Creel, and Krinsky and Robb. Significant (p < 0.10) WTP differences are found for five attributes in the LIP model, and for three attributes in the interaction model. Despite differences in statistical significance, the relationship between WTP and length of residency is similar across both models (table 5). 6 Compared to new residents, longer-term residents are willing to pay (a) less to prevent the placement of developments adjacent to main roads; (b) more for the addition of traffic signals; and (c) less for open space adjacent to developments and roads. Longerterm residents have a negative WTP for small mammal habitat quality; WTP is positive for new residents. 6 The one notable exception is the attribute develop2, which manifests different WTP patterns across the two models (table 5). In addition to the results shown in table 5, both the LIP and interaction models allow calculation of estimated marginal WTP for the full range of residency durations. These results are illustrated graphically for sm mammal and adj open, two attributes for which both the LIP and interaction models indicate statistically significant changes in WTP associated with residence duration (figures 1 and 2). WTP change is also illustrated for develop road, an attribute for which the LIP model indicates a statistically significant change in WTP associated with residence duration, but for which the interaction model does not indicate a statistically significant WTP difference (figure 3). All figures illustrate estimated WTP, as estimated by both models, over the range of zero to forty years. As shown in figures 1 3, changes predicted by the LIP and interaction models are similar, even for the case in which only one model predicts a statistically significant change in WTP (i.e., develop road in figure 3). In the case of adj open, the two models predict virtually identical changes in WTP. Similar results hold for a wide range of model attributes; despite differences in functional form and the resulting statistical significance of WTP differences (table 5), point estimates of WTP as influenced by length of residency are similar across both models.

13 1012 November 2003 Amer. J. Agr. Econ. $20.00 Marginal WTP: sm_mammal... $15.00 $10.00 $5.00 $0.00 -$5.00 -$ $ $ Years of Residency LIP Interact Figure 1. Marginal willingness to pay for habitat improvements for small mammals (sm mammal; 5-point habitat index) Discussion For attributes whose parameter estimates reveal statistically significant changes associated with residence duration, WTP changes match those suggested by prior research. For example, the negative influence of residence time on WTP for small mammal habitat suggests that certain species may be increasingly viewed as nuisance species as residence time in rural communities increases. This matches similar findings from the wildlife management literature, which suggests that negative reactions to certain small mammals may increase with long-term proximity (Zin and Andelt). The results suggest that preferences for scenic and related attributes of residential developments differ according to length of residency, again supporting common intuition (Spain). According to survey results (table 5, figure 3) newer residents have a higher WTP to prevent the location of new developments in a more visible location adjacent to main roads. 7 Similarly, compared to longer-term residents, newer residents have a higher marginal WTP for open space located adjacent to roads and developments (table 5, figure 2). Despite these findings, preferences for low-visibility development (lowvis) do not differ across groups. Hence, although results reveal evidence of differences in preferences for scenic attributes, these findings are not universal. Model results also indicate that longer-term residents are less willing to support develop- 7 Estimated WTP for develop road is negative; hence respondents are willing to pay to prevent the presence of developments adjacent to main roads. ments characterized by multiple clusters of developed land; this again corresponds with prior evidence in the literature. Both models indicate a generally negative effect of length of residency on WTP to split residential developments into two equal parts (develop2), compared to development of equal area in a single contiguous unit. 8 This corresponds with prior findings of McLeod, Woirhaye, and Menkhaus, who find a negative influence of residence duration (in Sublette County, Wyoming) on the probability of endorsing cluster development. Preferences for traffic control reveal a significant and intuitive increase in WTP among those with longer residency. This may indicate that new residents have moved to rural communities in part to escape traffic congestion that they associate with traffic controls, and hence maintain a lower WTP for such attributes. The results may also indicate a relatively stronger preference for more rapid travel with fewer traffic controls among newer residents. The latter explanation would fit the common characterization of new rural residents as commuters who rely on rapid automobile transportation to reach places of employment in central cities or suburbs (Dubbink). Finally, while neither model predicts welfare changes that are contrary to intuition, preferences for many attributes addressed by the survey cannot be shown to differ according to 8 In the LIP model, WTP is negative, with the magnitude of negative WTP increasing with the length of residency. In the interaction model, WTP is positive at zero years of residency, declining with length of residency to become negative at approximately six years of residency.

14 Johnston et al. Rural Amenity Values 1013 $1.40 Marginal WTP: adj_open... $1.20 $1.00 $0.80 $0.60 $0.40 $0.20 LIP Interact $ Years of Residency Figure 2. Marginal willingness to pay for preserved open space adjacent to roads or developments (adj open; dollars per acre) length of residency. These include attributes characterizing both residential development and open space (e.g., size dif, iso open; table 1). Other attributes, such as dense dif (housing density), reveal statistically significant changes in parameter estimates that do not translate into significant changes in WTP. Hence, while results suggest statistically significant differences in development and conservation preferences between newer and more established rural residents, for many attributes the null hypothesis of preference homogeneity is not rejected. Conclusion This article explores whether stated preferences for development and conservation Marginal WTP: develop_road $0.00 -$ $ $ $ $ $60.00 trade-offs differ according to length of residency. We find that residence duration is associated with statistically significant changes in marginal WTP for attributes of residential developments, preserved open space, traffic infrastructure, and wildlife habitat. Where statistically significant welfare effects are found, changes in WTP match common intuition. However, as might be expected, statistically significant changes in marginal WTP only apply to a subset of land use attributes included in the survey. Analysis of the change in marginal WTP for rural amenities reveals that the LIP and interaction models provide similar forecasts, despite differences in the models ability to identify statistically significant changes in WTP across length-of-residency reference points. These findings suggest that results indicating LIP Interact Figure 3. -$ Years of Residency Marginal willingness to pay to locate development on main roads (develop road)