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Modeling Distance Decay Within Valuation Meta-Analysis

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Abstract

Environmental benefit transfers increasingly rely on welfare estimates generated using meta-regression models (MRMs) of non-market willingness to pay (WTP). Theory and intuition suggest that these estimates should generally be sensitive to spatial dimensions. A common spatial pattern found in primary valuation studies is distance decay, in which WTP for environmental improvements diminishes as a function of distance to affected areas. Despite the potential importance of distance decay for benefit transfer accuracy, no valuation MRM in the published literature has developed an explicit mechanism to account for it. This paper outlines an approach to model the systematic effect of distance within valuation MRMs. The approach is illustrated using a meta-analysis of WTP for quality improvements in US water bodies. The metadata are drawn from stated preference studies that estimate per household WTP for water quality changes, and combine primary study information with external geospatial data. Results demonstrate statistically significant and intuitive influences of distance and other spatial factors on WTP. The resulting benefit transfers are more accurate than otherwise identical transfers that cannot account for spatial variations.

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Notes

  1. Comparability of welfare measures is required across multiple dimensions. Commodity consistency requires that the nonmarket commodity being valued is approximately the same across studies included in the metadata. Welfare consistency requires that these welfare measures represent comparable theoretical constructs. Only observations that satisfy a minimum degree of welfare and commodity consistency should be pooled within metadata (Bergstrom and Taylor 2006; Nelson and Kennedy 2009; Smith and Pattanayak 2002), although Moeltner and Rosenberger (2014) and Johnston and Moeltner (2014) show that the empirical relevance of these consistency rules varies.

  2. For example, see Abildtrup et al. (2013), Adamowicz et al. (1997), Bateman and Langford (1997), Bateman et al. (2011a, b), Brouwer et al. (2010), Campbell et al. (2008, 2009), Carson et al. (1994), Colombo and Hanley (2008), Concu (2009), Czajkowski et al. (2016), De Valck et al. (2017), Georgiou et al. (2000), Hanley et al. (2003), Johnston and Duke (2009), Johnston and Ramachandran (2014), Johnston et al. (2015a, 2017a), Jørgensen et al. (2013), León et al. (2016), Lizin et al. (2016), Loomis (2000), Martin-Ortega et al. (2012), Meyerhoff et al. (2014), Moore et al. (2013), Morrison and Bennett (2004), Pate and Loomis (1997), Rolfe and Windle (2012), Schaafsma et al. (2012), Sutherland and Walsh (1985), and Tait et al. (2012), among many others.

  3. MRMs that incorporate spatial variables typically do so using categorical variables identifying features such as whether quality changes affect single or multiple areas, or size categories such as large/medium/small or national versus regional (Brouwer et al. 1999; Johnston et al. 2003, 2005; Lindhjem 2006; Lindhjem and Navrud 2008; Rosenberger and Loomis 2000b; Santos 2007; Van Houtven et al. 2007).

  4. For example, the scope or magnitude of a water quality change can be measured using a standard water quality ladder or index (Johnston et al. 2003, 2005; Van Houtven et al. 2007).

  5. Availability of substitutes reflects the quantity/quality of substitute resources in proximate areas (Brander et al. 2012b; Johnston et al. 2002; Loomis and Rosenberger 2006; Schaafsma 2015; Schaafsma et al. 2012). For example, households’ WTP to improve water quality in a lake might depend on the existence and size of other, nearby lakes.

  6. Theoretical expectations for (and the empirical extent of) distance decay depend on the type of values under consideration (Hanley et al. 2003; Holland and Johnston 2017; Rolfe and Windle 2012).

  7. For example, analysts may arbitrarily truncate the area over which benefits are estimated or assume an ad hoc distance decay factor (e.g., Griffiths et al. 2012; US EPA 2015).

  8. A typical assumption in the valuation literature is that \(d_i \) reflects the distance between the household and the nearest point on an improved water body, although other assumptions are possible.

  9. We assume that the analyst has determined an appropriate measure of distance, for example the geodesic or travel distance between the geocoded household address and the nearest point on the shoreline of the affected water body. Various measures of distance may be applicable, depending on the type of value being considered.

  10. If this is not the case, then reported sample WTP does not represent WTP of the population, and should be used for policy analysis only with considerable caution (Johnston et al. 2017b).

  11. When applied over large or densely populated areas, this direct approach would likely require distances to be calculated over millions of geocodes. Approaches such as this could be increasingly feasible with advances in GIS data access and computational capacity. The accuracy of this direct approach would be subject to potential geocoding errors for households (Bonner et al. 2003).

  12. These distances may be calculated readily for any known geographical region with sufficient GIS data—all that is required is that each primary study identify (a) the region or market area sampled when implementing the stated preference survey, and (b) the regions affected within the stated preference scenarios used to calculate WTP.

  13. The accuracy of this approximation depends on factors including the shape and distribution of resources and households within sub-regions. This is established by the theory of distance in bounded areas (García-Pelayo 2005).

  14. Sources searched included: (1) literature databases and search engines (EBSCO, Google Scholar, Google), (2) online reference and abstract databases (Environmental Valuation Resource Inventory (EVRI), Benefits Use Valuation Database (BUVD), AgEcon Search, RePEc/IDEAs), (3) webpages of authors and programs known to publish stated preference studies or water quality valuation research, (4) web sites of organizations and agencies known to conduct valuation (e.g., Resource for the Future, National Center for Environmental Economics), (5) websites of key resource economics journals for the years 2005–2013 (Land Economics, Environmental and Resource Economics, Marine Resource Economics, Journal of Environmental Economics and Management, Water Resources Research, and Ecological Economics).

  15. WQIs combine information on physical and chemical water quality parameters into a single index linked to the presence of aquatic species and use suitability (Abbasi 2012; Van Houtven et al. 2014). They are among the most common means to measure water quality for valuation and benefit transfer (Griffiths et al. 2012; Walsh and Wheeler 2013). Additional details are provided by McClelland (1974), Mitchell and Carson (1989, p. 342), and Vaughan (1986). The WQI allows the use of objective water quality parameters to characterize ecosystem services or uses provided by a water body. Van Houtven et al. (2007) discuss other means of reconciling water quality measures.

  16. Alternative models were also estimated that measured the spatial scale of water improvements using (1) the surface area of improved water bodies and (2) the area of affected watersheds or catchments as the measure of spatial scale. Model results are robust across models including these alternative measures.

  17. This functional form implies that the partial derivative of linear \(WTP_j \) with respect to distance (\({\bar{s}}_{dj}\)) is given by \({-}\, {\hat{\beta }}_{s_{dj} }( {{WTP_j }\big /{{\bar{s}}_{dj} }})\), and the parallel derivative with respect to \(land\_area_j\) is given by \({\hat{\beta }}_{s_{dj} } ( {{WTP_j }\big /{land\_area_j }})\), where \({\hat{\beta }}_{s_{dj} } \) is the estimated parameter on \(ln\_size\_ratio_j \).

  18. This is defined formally as \({ river\_size\_ratio}=river*( {{ land\_area}/{{\bar{s}}_{dj} }} )\). The associated parameter is only statistically significant in the model when river is interacted with linear size_ratio, as opposed to ln_size_ratio.

  19. Model performance does not improve when including separate proportional variables for rivers, lakes/ponds and estuaries/bays (prop_chg_reach, prop_chg_area, prop_chg_bay); hence the final MRM includes only the composite index variable prop_chg (Table 2).

  20. The influence of prop_chg on WTP may be interpreted from two perspectives (Johnston et al. 2017a). First, it may be viewed as proportional measure of affected resource scale, with an expected positive influence on WTP. Second, it may be viewed as inversely related to substitutes. That is, as the quality improvement affects a larger proportion of regional waters, there are fewer remaining substitutes (i.e., water bodies not improved by the policy). As the relative proportion of these potential substitute waters declines (i.e., as prop_chg increases), we expect WTP to increase.

  21. These variables approximate substitutes and complements across the metadata. The extent to which particular resources serve as substitutes or complements in any particular context is case-specific and depends on numerous factors that are unobservable by the meta-analyst (Ghermandi and Nunes 2013; Loomis and Rosenberger 2006).

  22. Similar results are obtained when using random effects estimation.

  23. Advantages of this functional form include an ability to capture curvature in the valuation function, a multiplicative rather than additive effect of independent variables, and the implied constraints that WTP approaches zero when water quality change, income, and the size/distance index variable (ln_size_ratio) approach zero.

  24. This is not a theoretically necessary result. There may be some cases in which the total WTP of a nonuser sample exceeds the total WTP of an otherwise identical user sample. However, prior meta-analyses have found that WTP of users and general population samples frequently exceeds that of nonuser samples (Johnston et al. 2003).

  25. Ghermandi and Nunes (2013) include the total quantity of wetlands with a fixed 20km buffer of each site as a proxy for substitute wetlands. However, this variable does not quantify affected versus unaffected areas.

  26. The rationale for this result is discussed by Johnston et al. (2017a). For example, compared to non-agricultural rural areas, agricultural areas may not be as heavily used for water-based recreation and may not have the type of nonuse values associated with more pristine areas; this is expected to decrease WTP for improvements in agricultural areas.

  27. An increase from 37,767 to 1,363,262 reflects a percentage change of 3510%. The proportional effect on WTP is calculated \(e^{( {\hbox {ln}( {\frac{( {100+3510} )}{100}} )*0.1373} )}=1.6385\), or a percentage increase of 63.85%

  28. While not a central focus of this analysis, the model suggests additional advantages of the unrestricted model. For example, the negative and significant estimate for mult_bod in the unrestricted model (\(p<0.01\)) implies that for a given geospatial scale, WTP is lower when elicited for multiple rather than single water body types. The same parameter estimate is not significant in the restricted model. The variable lnincome is also significant in the unrestricted model only. Findings such as these suggest that the addition of geospatial variables to MRMs can enable other statistically significant and theoretically intuitive patterns to emerge.

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Authors and Affiliations

  1. George Perkins Marsh Institute and Department of Economics, Clark University, 950 Main St., Worcester, MA, 01610, USA

    Robert J. Johnston

  2. ICF International, 100 Cambridgepark Drive, Suite 501, Cambridge, MA, 02140, USA

    Elena Y. Besedin

  3. Abt Associates Inc., 55 Wheeler Street, Cambridge, MA, 02138, USA

    Benedict M. Holland

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  1. Robert J. Johnston
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  2. Elena Y. Besedin
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Correspondence to Robert J. Johnston.

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Funded by United States Environmental Protection Agency contract No. EP-C-13-039 to Abt Associates Inc. This research has not been subject to the Agency’s review and therefore does not necessarily reflect the views of the Agency. No official endorsement should be inferred.

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Johnston, R.J., Besedin, E.Y. & Holland, B.M. Modeling Distance Decay Within Valuation Meta-Analysis. Environ Resource Econ 72, 657–690 (2019). https://doi.org/10.1007/s10640-018-0218-z

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