prospects for the use of choice modelling for benefit transfer

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ava i l ab l e a t www.sc i enced i rec t . com

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Prospects for the use of choice modelling for benefit transfer

Mark Morrison a,*, Olvar Bergland b

a School of Marketing and Management, Charles Sturt University, Australiab Department of Economics and Resource Management, Norwegian University of Life Sciences, Norway

A R T I C L E I N F O

⁎ Corresponding author. Tel.: +61 2 6338 4253E-mail address: [email protected] (M

0921-8009/$ - see front matter © 2006 Elsevdoi:10.1016/j.ecolecon.2006.06.014

A B S T R A C T

Article history:Received 4 November 2005Received in revised form22 June 2006Accepted 22 June 2006Available online 30 August 2006

Many of the earliest studies that sought to test the validity of benefit transfer, whichtypically involved the use of contingent valuation or travel cost applications, producednegative findings. One of the recommendations from this early testing was to trialalternative methods to produce source studies for benefit transfer, includingmulti-attributetechniques. Subsequently, there have been a number of studies conducted that have soughtto test the validity of benefit transfer using choice modelling. The purpose of this paper is toreview these studies, and to assess the current state of knowledge regarding the validity ofusing choicemodelling for the purpose of benefit transfer.We also describe and consider themerits of an alternative approach for extending the use of choice modelling in benefittransfer, Bayesian benefit transfer.

© 2006 Elsevier B.V. All rights reserved.

1. Introduction

Most testing of the validity of benefit transfer has involvedtesting of the equivalence of either model parameters or valueestimates. In the case of thepassiveuse or non-use values,manytests of this type have been conducted using the contingentvaluationmethod (e.g. Bergland et al., 1995; Kirchhoff et al., 1997;Brouwer and Spaninks, 1999). In the majority of the studies, theevidence is not supportive of the validity of using contingentvaluation for benefit transfer. There are several possible reasonswhy these contingent valuation estimates were not found to beequivalent in these tests. It could be due to differences in whatwas valued — the base level of environmental quality or theextent of the improvement may have been different. Or thedivergence could be due to different preferences respondentshave for the sites, or becauseof differences between respondentsin each of the valuation exercises, or both.

Multi-attribute techniques, such as choice modelling, havebeen used in a number of benefit transfer tests because of theircapacity to produce estimates of marginal changes in environ-mental quality. Theyare therefore potentially able to dealwith atleast one of the reasons why value estimates in contingentvaluation benefit transfer tests were found to be different. By

.. Morrison).

ier B.V. All rights reserve

producingmarginal value estimates, differences in the extent ofenvironmental improvements at two different sites will poten-tially not be a cause of divergences between value estimates.However, theoretically, the extent to which this will be anadvantage of choice modelling will depend on whether thebaseline level of environmental quality is similar at both sites. Ifthe baseline level of quality is the same at both study and policysites it is more likely that values estimates will be similar. Yet ifthe baseline level of environmental quality is different, thesimilarity of value estimates will depend on whether themarginal utility of changes in environmental quality is constant.

The evidence from the thirteen studies reviewed in thispaper, as will be explored in Section 3, suggests that there ismuch greater convergence between value estimates generatedusing multi-attribute techniques when the sites being valuedand the populations sampled are similar. However, there arecases, even when multi-attribute approaches are used, wherevalue estimates have been found to be different (e.g. Morrisonand Bennett, 2004; Van Bueren and Bennett, 2004; Hanley et al.2006a). This may be due to the extent of the differencesbetween policy and study sites. Or it may be because thepopulations where the samples are drawn are quite distinct.While it is usually possible to allow for differences in

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sociodemographic characteristics, as noted by Morrison andBennett (2004) differences in populations may not be com-pletely accounted for by the standard sociodemographicvariables that are included in demand functions (e.g. income,age, education, gender,work status). Differences in valuesmaybemore closely related to factors such aswhether a populationis urban or rural, or lives in proximity or remote to the site ofinterest.

Consequently, several approaches have been developedthat can be used to produce value estimates when substantialdifferences between sites or in preferences are anticipated.These include the use of pooled models, meta-analysis1 andBayesian benefit transfer. We consider the potential use ofone of these approaches — Bayesian Benefit Transfer — inSection 4 of this paper.

Fig. 1 –Types of benefit transfer tests.

2. Types of benefit transfer

Before discussing the results from the existing choice modellingstudies that have tested benefit transfer, it is useful to considerthe types of benefit transfer tests that have previously beenconducted. Broadly, four kinds of tests can be identified, asshown in Fig. 1. The simplest form of testing is where you haveone study site and you compare the value estimates held bydifferent populations (Type 1). This could involve comparison ofthe values held by respondents who reside near or within thestudy area,with thosewho live outside of the study area or somedistance away. Or it could involve comparison of the values ofthose who reside in a rural township, a regional centre or a statecapital. Thesecond formof testing (Type2) involves comparisonsbetween the values heldby a single population formultiple sites.This testing asks, for example, whether the population for acapital city has similar values for two different rivers. In the thirdtest, the values held by different but equivalent populations fordifferent sites are compared (Type 3). Typically this involvescomparing the values that respondents have for a naturalresource within their region to the values that another group ofrespondents who reside in a different region have for a similarresource in their region. The final type of transfer seeks to ask thequestion of whether transfer of values is appropriate acrossdifferent geographic scales (Type 4). That is, whether implicitprice generated, say, at a catchment level are equivalent toimplicit prices at a regional or national level. Next we synthesisethe results within the literature from the testing of these fourdifferent types of benefit transfer.

3. Empirical evidence about the validity ofbenefit transfer using choice modelling

Before summarising the results of the thirteen choice model-ling studies we have identified that have tested the validity ofbenefit transfer, a brief comment is needed on methodology.This is needed as the studies do differ methodologically intheir testing, which does complicate the synthesising of re-

1 The use of meta-analysis for benefit transfer is covered by theBergstrom and Taylor (2006-this issue).

sults. Broadly, three main approaches have been used to testequality of the results from different valuation studies. Thefirst of these is to compare the equality of parameter esti-mates, which has been argued to be the most robust methodof testing (Cameron et al., 2002). This usually involveslikelihood ratio tests2, and also adjustment for differences inscale parameters. Second, is the comparison of implicit prices.This is perhaps the most common form of testing, althoughstudies vary in the way that they do this testing. The majorityof studies have estimated p-values for the differences betweendistributions, as recommended by Poe et al. (1997, 2004).However, other studies have relied only on overlapping con-fidence intervals for testing differences (e.g. Van Bueren andBennett, 2004), which has been demonstrated to overstate theequality of value estimates (Poe et al., 1997, 2004). Finally, asmall number of studies have compared surplus estimates.The latter is the most appropriate measure of value for use incost–benefit analysis, however as Morrison et al. (2002) havenoted, it is possible to derive a nearly infinite set of surplusestimates for testing which makes this form of testing some-what arbitrary.

In the discussion that follows, we report the results of allthree forms of testing. However, as the majority of studieshave only reported tests of the equality of implicit prices this iswhere we focus our efforts at synthesis.

3.1. Type 1: across population transfers

Eight studies have examined transfers across populations,with all of these studies apart from three (Hanley et al., 2001;Yoshida, 2002; Kerr and Sharp, 2006) having been conducted inAustralia. Four of the studies have focused on improved rive-rine health or wetland quality, two on land and water degra-dation, one on biodiversity and one on hedgerows. Four maintypes of population transfer tests can be identified withinthese eight studies. First, several studies have compared thevalues held by residents in regional centres with those in statecapitals (e.g. Morrison et al., 2002; Van Bueren and Bennett,

2 Bergland, Magnussen and Navrud (1995) argued that the score(Lagrange multiplier) test is more appropriate in benefit transfertesting as the study site has precedence over the policy site.

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2004; Rolfe et al., 2006). Secondly, several studies have com-pared values for populations that have a similar relationshipto the case study site. For example, Hanley et al. (2001) com-pared the values of respondents in Cambridgeshire, Devonand Shropshire (three regional areas) for hedgerow improve-ment in the UK, Yoshida (2002) compared the implicit prices ofresidents in four Japanese cities for improved land and watermanagement in Japan, while Kerr and Sharp (2006) comparedimplicit prices for riverine mitigation held by residents inSouth and North Auckland, New Zealand. Third, one study byHatton-MacDonald and Morrison (2005) compared implicitprices of residents in the state capital to those held by resi-dents of all other areas in the state. Finally, several studieshave compared implicit prices for those living within thestudy area to those held by residents who live away from thestudy area. For instance, Morrison and Bennett (2004) com-pared implicit prices of within catchment and out-of-catch-ment samples (which was effectively the rest of the state) andRolfe et al. (2006) compared implicit prices in a nearby ruraltown, a regional centre and a state capital, while Hatton-Mac-Donald and Morrison (2005) compared implicit prices fromrespondents who resided within the study area, within thestate capital, and within other areas of the state.

In terms of results, as shown in Table 1, the evidence ismostly supportive of the validity of transferring implicit pricesbetween the regional centre closest to the study site and statecapitals. Morrison et al. (2002) and Van Bueren and Bennett(2004) found that the majority or all of the implicit pricestested were equivalent in their comparisons. However, in onestudy by Rolfe et al. (2006), only two out of four implicit priceswere found to be equivalent. Nonetheless the weight of evi-dence suggests that in transfers between state capitals andmajor regional centres the implicit prices are likely to beequivalent.

For the second type of population transfer — where studieshave compared values held by populations that have a similarrelationship to thecase study site— the implicit priceshavealsoconsistently been found to be equivalent. For instance, Yoshida(2002) compared implicit prices for water pollution, landconservation and conservation of rural amenities derived fromseparate surveys in four Japanese cities, and found all of theimplicitprices tobe equivalent.While similar resultswere foundin the other two studies by Hanley et al. (2001) and Kerr andSharp (2006), theauthors of bothstudiesnote that resultsappearto be due to small sample sizes and wide confidence intervals.

For the third type of population transfer — between statecapitals and other areas within the state — the results arealso supportive of the validity of benefit transfer, althoughonly one study of this type has been conducted. Hatton-MacDonald and Morrison (2005) found that the implicit pricesfor biodiversity for residents in Adelaide were similar tothose held by residents in the rest of the state (apart from thestudy area).

However, there is less support for the appropriateness oftransfers between those living within the study area withthose who live away from the study area. Morrison and Ben-nett (2004) found that three-fifths of implicit prices in withincatchment and out-of-catchment comparisons were not equi-valent. Hatton-MacDonald and Morrison (2005) found thatresidents within the study area had completely different pre-

ferences to those living either in the state capital or elsewherein the state. Finally, Rolfe et al. (2006) compared implicit pricesof residents from the rural town closest to their study areawith the regional centre and the state capital. They foundgreater comparability between the implicit prices of residentsin the rural town and the regional centre, than between resi-dents of the rural town and the state capital. Thus overall, theevidence is less supportive of the equality of transfers bet-ween people who live within the study area and outside of thestudy area.

3.2. Type 2: transfers across sites

Only two studies have examined the validity of transfers ac-ross sites. Morrison et al. (2002), in a study valuing improve-ments in wetland health, found that three out of four implicitprices were equivalent. Parameter vectors were found to bemarginally different. They also compared surplus estimates,which were found to be equivalent in only two out of eightcases, although they had greater similarity than with thetransfers across populations. In the second study, Rolfe et al.(2006) had the same findings in relation to the parametervectors and implicit prices. They found that the parametervectors were different, and that three out of four implicitprices were equivalent. However, they found that all nineof the surplus estimates that they tested were equivalent.In summary, the evidence is supportive of this form of bene-fit transfer for implicit prices, and more supportive of thetransfer of surplus estimates than with transfers acrosspopulations.

3.3. Type3: transfers across sites and equivalent populations

Seven studies of this type have been conducted by Van Buerenand Bennett (2004), Christie et al. (2004), Morrison and Bennett(2004), Colombo et al. (2005), Yiang et al. (2005), Hanley, WrightandAlvarez-Farizo (2006), andHanley, Colombo, BlackandTinch(2006). Across the seven studies quite different results have beenfound. In the study by Colombo et al. (2005) there is substantialconvergence betweenvalue estimates across regional centres. Inthat study, surplus estimates were found to be equal in three-quarters of comparisons, while almost all implicit prices werefound to be equivalent. Similarly, Yiang et al. (2005) comparedfive implicit prices for coastal landmanagement inRhode Islandand Massachusetts and found that confidence intervals over-lapped for each comparison. However, their results appear to bedriven by particularly wide confidence intervals for their Massa-chusetts model. When surplus estimates were compared, themean estimate across 128 alternatives was found to be $38 forMassachusetts and $15 for Rhode Island, and statistically dif-ferent. Hanley et al. (2006b) sought to compare implicit pricesfor improved riverine health in two small catchments inEastern Scotland using random parameters logit models withboth correlated and uncorrelated attributes. They found thattwo out of four implicit prices were different using each modeltype. Nonetheless, surplus estimates were found to beequivalent, and the authors suggested that transfer errorstended to be fairly small in this study of relatively similar riverand populations. Van Bueren and Bennett (2004) derivedsimilar results for their comparison of implicit prices across

Table 1 – Type 1 — transfers across populations only

Study Type of transfer What was valued Population Results

Hanley,Oglethorpe,Wilson, andMcVittie(2001)

Same good, differentregional populations(A1 vs A2 vs A3)

Hedgerows in the UK Cambridgeshire A1 •Implicit prices all equivalentShropshire A2 •Parameter vectors different for

attributes only models in two out of threepairwise comparisons (scale test notincluded); parameter vectors different inall comparisons when sociodemographicvariables included in models

Devon A3

Morrison,Bennett,Blamey, andLouviere(2002)

Same wetland,different populations(regional centre vs statecapital) (B1 vs B2)

Wetland quality atGwydir Wetlands, NSW

Sydney, AU (state capital) B1 •Parameter vectors different.Moree, NSW (regional centre) B2 •Implicit prices different in only one out

of four comparisons.•Surplus estimates all different.

Yoshida(2002)

Same good, differenturban populations(C1 vs C2 vs C3 vs C4)

Water pollution,national landconservation,conservation of ruralamenities

Kamogawa C1 •Parameter vectors different in only twoout of six comparisonsKoshoku C2

Himi C3 •Across the six comparisons, all implicitprices were equivalentHorai C4

Van Buerenand Bennett(2004)

National context,different populations(national and regionalcentres D1 vs D2 vs D3)

Land and Waterdegradation:

National D1 Albany, WesternAustralia (regional centre) D2Rockhampton, Queensland(regional centre) D3

•Implicit prices for the same good in anational context differ across nationaland regional populations for someattributes

(1) Nationally

Regional context,different populations(regional centres vsstate capitals D4 vs D5,D6 vs D7)

(2)Great SouthernRegion, WesternAustralia

Perth, Western Australia (statecapital) D4Albany, Western Australia D5

•Implicit prices for the same good in aregional context are equivalent inregional centres and state capitals

(3) Fitzroy Basin Region,Queensland

Brisbane, Queensland (statecapital) D6Rockhampton, Queensland D7

Morrisonand Bennett(2004)

Same rivers, comparisonof values of withincatchment and out-of-catchment populations(E1 vs E2 and E3 vs E4)

Improved riverinehealth (all in NSWAustralia)

Within catchment E1 out-of-catchment (rest of state) E2

•For both the Murrumbidgee and GwydirRivers, three out of five implicit prices arenot equal

(1) Gwydir River Within catchment E3 out-of-catchment (rest of state) E4(2) Murrumbidgee River

Hatton-MacDonaldandMorrison(2005)

Same good, differentpopulations(F1 vs F2 vs F3)

Biodiversity in UpperSouth East of SouthAustralia

(1) Upper South East F1 •Implicit prices equivalent in Adelaideand other areas of State, but implicitprices in Upper South East different toboth other areas.

(2) Adelaide (state capital) F2(3) All other areas in the state F3

Rolfe, Lochand Bennett(2006)

Same river, differentpopulations

Improved riverinehealth in the Comet/Nogoa/Mackenzie andDawson catchments

Emerald (regional town) G1Rockhampton (regional centre)G2 Brisbane (state capital) G3

•Model parameters different only forRockhampton vs Brisbane comparison.

(G1 vs G2 vs G3) •Two out of four implicit prices differentin Rockhampton vs Brisbane comparison,and one out of four in Emerald vsBrisbane comparison. All implicit pricesare equal in the Emerald vs Rockhamptoncomparison.•All surplus estimates equivalent acrossthe three samples

Kerr andSharp (2006)

Mitigation with samerivers, differentpopulations withinthe same city

Riverine mitigation (1) South Auckland H1 •Implicit prices all equivalent in elevencomparisons

(H1 vs H2)

(2) North Shore H2 •Parameter vectors different (scale testincluded)


state capitals — implicit prices were equivalent in three out offour comparisons. But for equivalent regional centres, VanBueren and Bennett found that implicit prices were equal inonly two out of four cases.

The remaining three studies, however, found less evi-dence of convergence between value estimates. Christie etal. (2004) found that implicit prices were different in themajority of their comparisons — in only two out of six

Table 2 – Type 2 — transfers across sites only


Morrison, Bennett,Blamey, andLouviere (2002)

Different wetlands,same population(state capital) (B1 vs B3)

Wetland quality at: •Parameter vectors different.(1) Gwydir Wetlands, NSW Sydney, AU

(state capital) B1•Implicit prices different in onlyone out of four comparisons.

(2) Macquarie Marshes, NSW Sydney, AU(state capital) B3

•Surplus estimates are differentin six out of eight cases.

Rolfe, Loch,and Bennett (2006)

Different rivers, samepopulation (state capital)(G4 vs G5)

Improved riverine health: Brisbane(State capital) G4

•Model parameters are different,implicit prices are equivalent inthree out of four cases

(1) Comet/Nogoa/Mackenziecatchments

Brisbane(State capital) G5

•Surplus estimates equivalent innine out of nine cases

(2) Dawson catchment


comparisons were implicit prices found to be equal. In theirstudy they compared biodiversity values for populations inNorthumberland and Cambridgeshire in the UK, which arefairly different in terms of populations, with the latter beingmore university oriented. While in the largest study of thistype, byMorrison andBennett (2004) in a study valuing riverinehealth, itwas found that implicit priceswereequivalent in onlyabout half of the implicit prices tested. For some comparisonswhere the rivers were more similar (e.g. Gwydir vs Murrum-bidgee) all of the implicit prices were equivalent, while inother comparisons all of the implicit prices were different. Itshould be noted that in their selection of studies,Morrison andBennett (2004) deliberately chose source studies that would berepresentative of their region within NSW, and not necessarilysimilar to each other. Therefore it would be expected thatdifferent rivers would be valued differently by equivalent po-pulations, if the rivers were essentially different. A final studyby Hanley et al. (2006a) compared implicit prices and choicemodels for river ecology in the UK and Scotland using bothconditional logit and random parameters logit models. Thecompared implicit prices of people living near the River Wear(Durham, England) with those of people living near the RiverClyde (Central Scotland). They found that all three implicitprices were substantially different, with respondents near theRiver Wear being willing to pay only a third of the amount ofrespondents in the River Clyde. Hanley et al. (2006a) notedtheir surprise at this finding given the larger income level ofrespondents near the River Wear, and suggest that it might bebecause of differences in riverine characteristics, availablesubstitutes or tastes. Thus in summary, there is evidence inthe literature that transfers across sites and equivalent popu-lations are likely to be valid, except when the natural resourcebeing valued is quite different or the populations sampled aredifferent.

3.4. Type 4: transfers across geographic scale

The final type of testing has only been conducted by VanBueren and Bennett (2004). They sought to test the validity oftransferring implicit prices generated at a national context to aregional context. They found that all of the implicit pricesgenerated at a regional context exceeded those generated at anational context. This means that respondents were willing topay more for an improvement to occur in their own regionrather than nationally. As the attributes represented fixedamounts of environmental quality (e.g. hectares restored), this

result would be expected. However, the results indicate thatthis sort of benefit transfer is not appropriate.

3.5. Summary

The findings from this review suggest that implicit pricesgenerated using choice modelling are likely to be equivalentwhen (1) the populations surveyed are relatively similar and (2)when the sites that are valued are either the same or aresimilar. However, if the populations that are surveyed aredifferent the implicit prices are more likely to be different. Forexample, differences are more likely to be found between thepreferences of those living within a study area or catchmentand those who do not. Changes in the nature of the site that isvalued are also likely to affect value estimates. The evidencefrom studies such as Morrison and Bennett (2004) and Hanleyet al. (2006a) also indicate that as environmental goods becomemore different, they are valued differently. The resultsgenerated by Van Bueren and Bennett (2004) furthermoreindicate that context matters: valuing a good at a nationalcontext rather than a regional context can be expected toinfluence the equality of implicit prices. Overall this is sup-portive of the validity of non-market valuation: if non-marketvaluation is valid it would be anticipated that as the nature ofthe good valued changes, and the type of people surveyedbecome more different, then value estimates ought to change(Tables 2, 3 and 4).

4. A Bayesian approach to benefit transferusing choice modelling

The empirical evidence from the use of choice modelling forbenefit transfer suggests that if the context of the valuationexercise changes (either due to site or population differences),then simple transfer of implicit prices is likely to be subject togreater error. Arguably other and more sophisticated forms ofbenefit transfer are required in order to handle context effects.

Agee and Crocker (2004) argued that the least restrictivestatistical foundation for benefit transfer is the Bayesianconcept of exchangeability (De Finetti, 1974). The Bayesianapproach to benefit transfer dates back to a (largely ignored)paper by Atkinson et al. (1992). Under the assumption ofexchangeability, there exists a grand model and the coeffi-cients pertinent to a study are random realizations of thiscommon structure. Bayesian statistical methods are used to

Table 3 – Type 3 — transfers across sites and equivalent populations


Van Bueren andBennett (2004)

Regional context, differentregional populations(regional centres only)(D5 vs D7) and differentstate capitals (D4 vs D6)

Land and waterdegradation

Perth, WesternAustralia (state capital)D4

Implicit prices differ across regionalcentres for two out of four attributes,and for state capitals for one out offour attributes(1) Great Southern

Region, WesternAustralia

Albany, WesternAustralia D5Brisbane, Queensland(state capital) D6

(2) Fitzroy BasinRegion, Queensland

Rockhampton,Queensland D7

Christie et al.(2004)

Regional context, differentregional populations (I1 vs I2)

Biodiversity Implicit prices differ in four out of sixcomparisons. Likelihood ratio testindicates that parameter vectorsare different.

(1) Northumberland Northumberland (I1)(2) Cambridgeshire Cambridgeshire (I2)

Morrison andBennett (2004)

Different rivers, values held bywithin catchment populations(E1 vs E2, E1 vs E3, E1 vs E4, E1vs E6, E2 vs E3, E2 vs E4, E2 vsE6, E3 vs E4, E3 vs E6, E4 vs E6)

Improved riverinehealth (all in NSWAustralia)

Implicit prices different in about halfof the comparisons of within catchmentpopulations (28 out of 50 comparisons,at 5% level). Value estimates were moresimilar for some rivers than others.

(3) Georges River Within catchment E1(4) Clarence River Within catchment E2

Different rivers, comparisonof values from out-of-catchment populations(E5 vs E7)

(5) Bega River Within catchment E3 Implicit prices for out-of-catchmentpopulations all equivalent(6) Gwydir River Within catchment E4

Out-of-catchment (restof state) E5

(7) MurrumbidgeeRiver

Within catchment E6Out-of-catchment (restof state) E7

Colombo, Hanley,and Calatrava-Requena (2005)

Different rivers, valuesheld by within catchmentpopulations (J1 vs J2)

Soil erosion Parameter vectors were different(1) Genil

Catchment, SpainWithin catchment J1Within catchment J2 Implicit prices equal in 15 out of 16

comparisons (across two differentmodels).

(2) GuadajozCatchment, Spain

Yiang, Swallow,and McGonagle(2005)

Different coastal areas,values held by withinarea populations(K1 vs K2)

Coastal areaimprovements

Parameter vectors only found to beequivalent in model with choiceattributes included; different inpreferred model.

(1) Rhode Island Within area K1(2) Massachusetts Within area K2

Implicit prices equivalent for allcomparisons, but very wide confidenceintervals in Massachusetts model.Surplus estimates found to bestatistically different betweentwo samples.

Hanley, Wright,and Alvarez-Farizo(2006) Hanley,Colombo, Black,and Tinch (2006)

Different rivers, valuesheld by within catchmentpopulations (L1 vs L2)

Riverine health Parameter vectors were found to bedifferent (scale differences not tested)

Different rivers in smallercatchments, values held bywithin catchmentpopulations (M1 vs M2)

(1) River Wear Within catchment L1(2) River Clyde Within catchment L2 Implicit prices different for all

comparisons Parameter vectorswere equivalent

Riverine health

(1) MotrayCatchment

Within catchment M1 Two out of four implicit prices werefound to be different

(2) BrothrockCatchment

Within catchment M2 Compensating surplus estimateswere equivalent for three policyrelevant alternatives.


draw systematic inferences about coefficients in a new con-text from previous studies. If exchangeability is absent, eachstudy has its own structure and no valid inference aboutother studies can be drawn. Both traditional meta-analysis(see for example Johnston et al., 2005) and Bayesian meta-analysis (Brundson and Willis, 2002; Moeltner et al., 2006), as

well as pooled models (Morrison and Bennett, 2004), takeexchangeability as a maintained hypothesis without treatingit as a testable hypothesis.

Bayesian statistical inference is based on combining priorinformation about the model parameters with the likelihoodof the data to form the posterior distribution of the

Table 4 – Type 4 — transfers across geographical scale


Van Buerenand Bennett(2004)

National vs regionalcontext (same population)(D2 vs D5, D3 vs D7)

Land and water degradation Albany, Western AustraliaD2 Rockhampton, Queensland(both regional centres) D3

Implicit prices in a regionalcontext exceed implicit pricesin a national context (sameregional population)

(3) Nationally

(4) Great Southern Region,Western Australia

Albany, Western Australia D5

(5) Fitzroy Basin Region,Queensland

Rockhampton, Queensland D7


parameters3. Let the model parameters be θ, the likelihoodfunction l(x|θ) where x is the data, and then let π0(θ) be theprior, then the posterior distribution is given by:

ppðhjxÞ~lðxjhÞp0ðhÞ

The Bayesian approach to benefit transfer proposed byLeón et al. (2002) involves the elicitation of a prior distributionand then estimation based upon data from one or more sites.The resulting posterior distribution of the parameters servesas the prior for a new context and represents the Bayesiantransfer to this new context. The tests reported by León et al.(2002) and Lehr (2005) showed clearly that the Bayesian benefittransfer outperforms conventional benefit transfer. For exam-ple, Lehr (2005) showed that combining a prior with a smallsample at the study site results in a very precise benefittransfer. Thus the use of priors and Bayesian methods offersits own variant of inexpensive valuation where only a smalloriginal valuation study is conducted in the new context.

León et al. (2003) formation from experts and utilizing thisinformation by itself, or in combination with past study data,to form a prediction in the form of a new prior. In theexperiment conducted by León et al. (2003) individual expertpredictions did not accurately reflect the posterior distribution.However, averaging across experts resulted in predictionsmuch more consistent with the empirical results.

Bergland (2006) takes issue with the use of posterior distri-butions of the model parameters as the foundation for benefittransfer as this ignores the variability between studies. In-stead, the exchangeability of studies is explicitly modelled byconsidering a hierarchical model (Lindley and Smith, 1972;Berger, 1985); that is the above model can be rewritten as

ppðhjxÞ~lðxjhÞp0ðhjkÞp1ðkÞ

where λ is a vector of hyper parameters with prior π1(λ) andwhere the prior on θ has been made conditional λ. The inter-pretation of this model is that the hyper parameters λ governthe distribution of the parameters θ. At any study context theparameter θ will be given and the valuation sample is drawn

3 Difficulties in the calculation of the posterior distribution havetraditionally been a major obstacle in Bayesian statistics. However,recent developments in computer based simulation methods havemade Bayesianmodeling feasible and accessible. See Chib (2001) fora general review in econometrics, Koop (2003) for a textbooktreatment, and several papers in Scarpa and Alberini (2005) forapplications in environmental economics. Estimation of contingentvaluation models is discussed by Fernández et al. (2004).

conditional upon θ. The posterior distribution of θ is condi-tionalupon thedataobtainedat a particular site and is relevantfor the analysis of that site. The posterior distribution for thehyper parameters, πp(λ), represents the unconditional beliefsabout the distributions of values across all possible sites. Berg-land (2006) proposed to use a predictive distribution obtainedfrom the posterior πp(λ) as the (unconditional) benefit transferto a new context. In a benefit transfer exercise using contin-gent valuation data for water quality improvements, Bergland(2006) obtained rather wide benefit transfer values reflectingthe range of values covered by the available studies and theunconditional character of the benefit transfer.

So far the Bayesian benefit transfer has not utilized choicemodelling data. Yet there are now available Bayesian modelsthat are applicable to choicemodelling data such as themixedlogit model by Train (2003) and the multinomial probit modelby Imai and van Dyk (2005). Either of these models could formthe statistical basis for a Bayesian model and benefit transferof the type proposed by León et al. (2002) and/or Bergland(2006). The relative merit of such models compared toconventional benefit transfer discussed in previous sectionsof this paper and Bayesian meta-analysis (Moeltner et al.,2006) is unknown and should be explored in future researchinto benefit transfer.

5. Discussion

Multi-attribute techniques suchas choicemodellinghave beenproposed for use in benefit transfer because of their ability tovalue marginal changes in environmental attributes. The em-pirical evidence reviewed in this paper provides some supportfor this proposition. When sites and populations are similar,value estimates at policy and study sites have shown to bestatistically equivalent. However, as the policy and study sitesbecome more different, or the populations sampled becomemore different, the value estimates generally diverge. This sug-gests that thereare limits towhere choicemodellingbasedvalueestimates can validly be transferred, and that practitioners ofbenefit transfer need to be cognisant of any differences thatmight be present and their likely effect on value estimates.Overall, this finding is encouraging — this sensitivity of valueestimates to population and site differences is an indication ofconstruct validity.

These results do have implications for the use of benefittransfer when populations and sites are likely to be different.More sophisticated methods of benefit transfer are likely to beneeded in these cases, however these approaches are onlybeginning to be developed. Meta-analysis has been widely


used in the literature to capture context effects, particularlywhere source studies are available that have used the hedonicpricing, contingent valuation and travel cost methods (e.g.Bergstrom and Taylor, 2006-this issue). However, the use ofmeta-analysis depends on the availability of a large stock ofsource studies that is currently not available for choicemodels. Only pooled models have been used so far to allowfor context effects in a study by Morrison and Bennett (2004).Thesemodels have lesser data requirements, so they are likelyto be used more frequently than meta-analytic models.However, pooled models have their own limitations: theremust be access to original data sets and consistency inattribute and level selection. A third alternative we discussfor evaluating context effects is Bayesian benefit transfer. Webelieve this to be a promising future direction for benefittransfer using choice modelling. Bayesian benefit transfertheoretically has the potential to produce for practitioners adistribution of benefit estimates for different environmentalattributes, thus clarifying the influence of site and populationdifferences on value estimates. This may provide benefittransfer practitioners with amethod for further improving theaccuracy of benefit transfer in situations where contextdifferences occur, however further research is needed toexplore the potential of this approach.

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prospects for the use of choice modelling for benefit transfer

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