embedding in market demand systems

Ž .JOURNAL OF ENVIRONMENTAL ECONOMICS AND MANAGEMENT 30, 369]380 1996ARTICLE NO. 0025

Embedding in Market Demand Systems

ALAN RANDALL AND JOHN P. HOEHN1

Department of Agricultural Economics, The Ohio State Uni ersity; and Department ofAgricultural Economics, Michigan State Uni ersity

Received November 3, 1993; revised March 3, 1995

Ž .The term embedding has been popularized by Kahneman and Knetsch KK toŽ .describe a phenomenon often observed in contingent valuation CV data sets:

willingness to pay for a particular good may vary ‘‘over a wide range depending onwhether the good is assessed on its own or embedded as part of a more inclusive

w xpackage’’ 7, p. 58 . They argue that embedding is a pathology that may be fatal toCV: ‘‘No measuring instrument can be taken seriously if its permitted range of

Ž .applications yields drastically different measure of the same object’’ p. 60 .KK, apparently, are arguing that observed embedding effects demonstrate that

CV is an unreliable device for measuring economic value. Reliability in measure-ment refers to consistency; for example, repeated measurements of the same objectshould obtain similar results. More precisely, measurement is reliable to the extent

w xthat results are similar every time they should be similar 13, p. 88 . Reliabilityrequires that measurements be invariant to irrelevant side-conditions.

However, stability in the face of changing economic conditions is not a propertythat one would expect of prices and welfare measures. It is a fundamentaleconomic principle that prices and economic values are conditional. They reflectthe preferences, technologies, and scarcity conditions that prevail within an econ-omy. Economists argue that this conditionality is the great virtue of price: pricesadjust rapidly in response to changes in conditions, providing incentives that tendto reallocate resources and to ration consumption so as to restore efficiency.Nevertheless, it creates conceptual difficulties for value measurement: any theoryof measurement for economic values must come to terms with the fundamentalconditionality of price and economic value.

To evaluate the KK criticism, it is necessary to determine whether the level ofembedding is one of the conditions to which economic values should be responsive,or merely in irrelevant side-condition for valuation. To this end, we summarize thestandard economic-theoretic results concerning valuation of complex packages andtheir components goods The phenomena that KK call embedding are not inconsis-tent with these standard results. That is, economic theory predicts that economicvalues are sensitive to the level of embedding. Then, we use an estimated demandsystem for marketed goods to simulate embedding structure for decreases andincreases in the prices of these goods. The kinds of embedding effects observedwith contingent valuation of nonmarket goods are also observed here with market

1 Research was supported by the Ohio Agricultural Research and Development Center and theMichigan Agricultural Experiment Station through regional project W-133, and by the National Oceanicand Atmospheric Administration.

3690095-0696r96 $18.00

Copyright Q 1996 by Academic Press, Inc.All rights of reproduction in any form reserved.

RANDALL AND HOEHN370

demands for private goods. Finally, we recognize that discretionary budgets areoften much less than the present value of lifetime earnings. A common way tointroduce this insight into demand analysis is via multi-stage budgeting. Weintroduce multi-state budgeting into our embedding simulations with market de-mands, and observe that embedding effects are magnified.

We conclude that embedding is an ordinary economic phenomenon. If followsthat welfare measures, whether for private or policy goods and whether obtainedwith stated preference or revealed preference methods, should be sensitive to thelevel of embedding. Furthermore, the benchmarks that market observations mightprovide for CV suggest that rather substantial embedding effects are not inconsis-tent with economic reality. Observed sensitivity of CV results to the level ofembedding is therefore insufficient to establish the invalidity of CV in general or ofany particular application. Nevertheless, the possibility remains that the CVprocess itself andror various imperfections in particular CV applications mayexacerbate embedding effects.

THEORY OF VALUATION FOR COMPLEX PACKAGES OF GOODS

w xRandall et al., 11 were the first to report systematic embedding effects in CV:Ž .willingness to pay WTP for air quality improvements at the Grand Canyon was

smaller when evaluated as the third increment to a larger package of air qualityimprovements than when offered alone. They conjectured that these observedeffects could be explained by standard economic interactions involving substitutionand budget constraints. Subsequently, a general theory of the relationship betweentotal value of a complex package of goods and the values of its various components

w x w x w xhas been articulated by Hoehn and Randall 5 , Hoehn 4 , and Madden 8 . Theimportant findings follow.

Ž1. As the number of prospects whether of goods for acquisition or of policies. Žfor implementation increases, the impacts of scarcity whether of household

.budget or of national resources become more pronounced. It follows that as thenumber of prospects in a package grows, WTP for the package becomes unambigu-ously smaller than the sum of WTPs for its component prospects each evaluatedindependently.

2. Suppose the package is built-up sequentially, by adding component prospectsin order. Then the incremental contribution of a particular component to the totalvalue of the package will be smaller the later its place in the sequence. In otherwords, component values are sequence-dependent.

3. Provided that Hicksian welfare measures are used, the total value of thepackage of prospects is path-independent.

Ž .4. For willingness to accept compensation WTA for prospective reductionsin goods or policies, results 1 and 2 above, hold with the signs reversed. As thenumber of prospects becomes large, WTA for the package becomes unambiguouslylarge than the sum of WTAs for its components evaluated separately, and theincremental contribution of a particular component to total WTA is larger thelater its place in the sequence. To see this intuitively, an example may help.Consider the case of two recreation sites that are perfect substitutes. The house-hold is absolutely indifferent between use of site A or site B and may use eithersite without any loss of well-being due to not using the other site. First, consider

EMBEDDING IN MARKET DEMAND SYSTEMS 371

the household’s WTA to accept the loss of A given that B remains available anduncongested. WTA is zero since the household would simply use site B and sufferno loss utility. Now, consider the household’s WTA to accept the loss of A giventhat B is no longer available. WTA is now positive since the household would haveneither site available and would therefore incur a loss of well-being. WTA for lossof any good increases as substitute goods deteriorate in quality or quantity.

5. Suppose that discretionary budgets are much less than household wealth.Households typically are locked into long-term agreements regarding expendituresfor housing, education, and consumer durables, and must provide for necessitiessuch as food and clothing. They also face cash-flow and liquidity constraints thatprevent them from converting long-term wealth into current expenditures. Acustomary way of analyzing demands under these conditions is via incompletemulti-stage budgeting. When the discretionary budget is small relative to totalwealth, the relationships reported under 1, 2, and 4, above are exacerbated. Forexample, the incremental contribution of a component to total WTP for thepackage declines even more rapidly as the component is placed later in thesequence.

The embedding effects discussed by KK are consistent with this general theoryof value for complex packages of goods and policies. Result 2 predicts what KK call

Ž .an order effect: the value of a second highly perishable ice-cream cone immedi-ately after the first one is consumed is much reduced. Note that this effect ispredicted by economic theory; reliable measurements should exhibit this effect.Thus, it is quite different from the standard order effects}where, e.g., responsesto attitudinal questions might depend on the order in which the questions areasked}that survey researchers test for, but hope not to find. Result 1 predicts the

Žeffect that KK call embedding: WTP for a policy in their case, improve rescue.equipment and personnel was considerably larger when evaluated alone than

when included in a larger set of policies. Note, however, that KK’s method ofpartitioning the set of policies in two steps to find the value of a single policycomponent is not a standard and meaningful economic problem. Note also that ifincomplete multi-stage budgeting occurs, it would exacerbate the predicted effectby depressing WTP to a greater degree for the more inclusive set of policies.

While standard economic-theoretic results predict the valuation phenomena thatKK call embedding, some observers have expressed surprise at the magnitude ofembedding effects reported in some CV studies.2 However, economists have littleguidance, whether from theory or empirical evidence, as to what magnitudes ofembedding effects should be expected.

The embedding effects predicted by economic theory apply logically to marketand nonmarket goods. Valuation, for both types of goods, involves the samepreference concepts and optimization rules. There is, however, an importantdistinction: whereas for market goods we typically evaluate price changes, fornonmarket goods the typical welfare evaluation involves changes in quantity

w xandror quality. The results of Hanemann 2 , who demonstrated that substitutioneffects have a more pronounced influence when quantity-rationed public goods arebeing evaluated, imply that embedding effects might typically be larger for nonmar-

2 KK reported very large embedding effects. However, the survey design and statistical methods usedw xin the KK study have been subject to telling criticism 1, 3, 10, 12 . It is at least possible that better

research methods would reduce the magnitude of the embedding effects found in the KK studies.


ket goods. Nevertheless, we conjecture that an empirical analysis of embeddingeffects for market goods might inform the debate about embedding for nonmarketgoods.

EMBEDDING EFFECTS WITH MARKETED GOODS

For market goods, the effects of embedding are readily examined using marketdemand systems. The present research used a demand system for households in the

w xDominican Republic estimated by Yen and Roe 14 , to examine embedding effectsin welfare evaluation of a series of price changes for private commodities. Thisparticular demand system was selected because it was estimated in a mannerconsistent with economic theory, it encompassed all household expenditures, and

w xthe detailed reports of parameter estimates in Yen 15 enabled us to conduct theembedding and multi-state budgeting simulations reported here.

The Yen and Roe demand system partitions consumer commodities into Rcommodity groups. The utility gained from the r th commodity group, u , isrdescribed by a Gorman polar form utility function,

cu s a y rP y b q Q rP , 1Ž . Ž .r r r r r r r

where a ) 0 is a constant; y is expenditure on the r th commodity group;r rŽ .P s P p is a price index measuring the impact of the price vector, p sr r r r

Ž . Ž .p , . . . , p , for the r th commodity group; b s b z accounts for how householdr1 rK rŽ .demographic characteristics, z s z , . . . , z , . . . , z , affect consumption of the r th1 j J

Ž .commodity group; 0 - c - 1; and Q s Q p , z reflects the interaction of com-r rmodity prices and household characteristics. The term b may be viewed as arminimum subsistence level of expenditure on the r th commodity group since u isrwell-defined only when deflated group expenditure, y rP , exceeds b .r r r

Yen and Roe assign specific functional forms to P , Q , and b . These forms arer r r

Ka r kP s p ,Łr r k

ks1

K J

Q s b z p , andÝ Ýr jk j kks1 js1

J

b s d q d z ,Ýr r 0 r j jjs1

where a , b , d , and d are parameters to be estimated. The index P is ar k jk r 0 r j rCobb]Douglas function of prices so that ÝK a s 1. Q reflects the interac-ks1 r k rtion of prices an demographic characteristics and b depends on demographicrcharacteristics alone.

A household consumes commodities from R commodity groups. Householdutility, u, is described as the sum of the utilities obtained from each of the


commodity groups,

R

u s uÝ rrs1

Rcw xs a y rP y b q Q rP . 2Ž .Ý r r r r r r

rs1

Letting u be an initial level of utility, the expenditure function for the Gormanpolar form is

1rcR

u y Q rPÝ r rR RŽ . rs11r cy1e P , . . . , P , u s P P ra q P b .Ž . Ž .Ý Ł1 R s s s r rRž / rs1Ž .cr cy1ss1 a P raŽ .� 0Ý r r r

rs1

3Ž .

When expenditure on all commodity groups is allowed to vary in response to aprice change, the expenditure on the r th commodity group that maintains house-hold utility constant is

1rcR

u y Q rPÝ r rŽ . rs11r cy1Uy s P P ra q P b . 4Ž . Ž .ž /r s s s r rR

Ž .cr cy1a P raŽ .� 0Ý r r rrs1

When a price of a single good, k, in the r th commodity group changes from p0kr1 Ž 0 0 0 .to p k, the r th price index changes from P p , . . . , p , . . . , p tor r r1 r k rK

Ž 0 1 0 .P p , . . . , p , . . . , p . The compensating variation for this first in sequence pricer r1 r k rKchange is

1 0 0 1 0 0C s y y e P , . . . , P p , . . . , p , . . . , p , . . . , P , u , 5Ž .Ž .k 1 r r1 r k rK R

where the superscript 1 on C1 indicates that it is first in sequence price change andkthe subscript k indicates that it pertains to the k th price.3

When prices of k goods change in the sequence 1, . . . , k, the change in the k thprice is evaluated after the changes in the other k-1 prices. This embeddedvaluation for the k th price change is

k 1 1 0 0 0 0C s e P , . . . , P p , . . . , p , p , p , . . . , p , . . . , P , uŽ .k 1 r r1 r ky1 r k r kq1 rK R

1 1 1 0 0 0y e P , . . . , P p , . . . , p , p , p , . . . , p , . . . , P , u , 6Ž .Ž .1 r r1 r ky1 r k r kq1 rK R

where the superscript k on C k indicates that it is the k th embedded price changek

3 Ž .Written out in full, Eq. 6 depends on both P and Q and, through these indexes on commodityr rŽ .prices, p . Q is left implicit in Eq. 6 to simplify the notation. The key concern is how to account for ar k r

set or sequence of commodity price changes.


and the subscript k indicates that it pertains to the kth price. A valid totalvaluation based on the k embedded valuations is

kjC s C . 7Ž .Ý j

js1

C is path-independent; that is valid total valuation requires that the price changesbe sequenced, but the total value is independent of the particular sequence chosen.

Ž .In contrast, an independent and therefore invalid total valuation is

k1IV s C . 8Ž .Ý j

js1

Ž . Ž .The welfare measures described by Eqs. 5 and 6 were operationalized usingthe parameter estimates reported in Yen for medium income, urban households inthe Dominican Republic.4 The estimated utility structure aggregated individualcommodities into three commodity groups: food, housing, and clothing and othernonfoods. The food group encompassed prices and quantities for ten individualcommodities. These ten commodities included rice, other cereals, legumes, oils,and animal produces. The housing and clothing groups were not broken down intoindividual commodities. This utility structure permitted Yen to estimate all the

Ž .parameters of the expenditure function described in Eq. 3 except for Q for therhousing and clothing groups. The unknown Q terms, however, drop out of therexpenditure function if housing and clothing prices are held constant.5 Hence, theempirical analysis focuses on the welfare effects of food price changes and holdsother prices constant.

To simulate embedding, we calculated first the valid total valuations and theindependent valuations of a series of identical percentage price changes for allfood items and, second, the welfare evaluations of rice price changes as rice was

Ž .moved from first to tenth in a valuation sequence of the food items. Equation 5was used to compute the valid first in sequence valuations for the rice price

Ž .changes, and Eq. 6 the second, third, and tenth in sequence, embedded valuationsŽ .for the rice price changes. Equation 7 was used to compute the valid total

Ž .valuation and Eq. 8 the sum of the independent valuations.Table I lists unembedded and embedded welfare evaluations based on the Yen

and Roe parameter estimates. Each of the evaluations is for a specific percentagechange in the price of food and a particular level of embedding. The first five rowsof the table describe WTP valuations for food price reduction ranging from 20 to95%. The sixth through tenth rows describe WTA valuations for price increases

Ž . Ž .ranging from 20 to 250%. Following Eqs. 6 and 7 , WTA has a negative sign toindicate that compensation is in terms of payments to rather than payments fromthe representative household.

4 Yen reports estimates obtained for six demographic groups. These groups were subsamples basedon income level and place of residence in either a rural or urban area. The simulations used theestimates for the medium income, urban group except as otherwise noted.

5 Ž . Ž . Ž .The level of household utility in Eq. 3 is, in part, an additive function of Q rP by Eqs. 1 and 2 .r rŽ .When Q rP is constant, it cancels with its arithmetic inverse in Eq. 3 . When fixed at a given level, thisr r

ratio of the r th price indexes affects only the level of ordinal utility attained by a household. It does notaffect the expenditure required to maintain utility constant given a change in the prices of commoditygroups.


The third column in Table I presents the valid total valuations of packages ofidentical price changes for all ten food items, while column 4 presents the

Žindependent valuations. Observe that C is always less then IV which means that,.for a price increase, C is larger in absolute value than IV , and that the difference

increases with the magnitude of the price changes. For 95% reductions in all foodprices, IV is almost twice as large as valid C.

Columns 5]8 describe the welfare evaluations for rice price changes at differentlevels of embedding. The fifth column states first in sequence, unembeddedvaluations C1 for different levels of price change. Columns 6]8 list, respectively,r ice

Ž .the second, third, and tenth i.e., last in sequence embedded valuations of theprice changes, C 2 , C 3 , and C10 . Again, the embedding effects predicted byr ice r ice r ice

Žtheory are observed. The welfare effects of the rice price change are reduced i.e.,.for price increases the welfare loss is greater in absolute value as rice is evaluated

later in the sequence. The welfare effect of a 95% reduction in the price of rice isreduced by more than 50% when evaluated after similar price reductions for nineother foods.

Table I demonstrates embedding in a standard demand system for marketcommodities. It highlights the important determinants of embedding: the size of an

TABLE IEffect of Embedding on the Welfare Evaluation of Rice Price changes for Ten Food Items,

aand for Rice

Welfare effect, price Welfare effect, rice price change by degreechange for ten food items, of embedding in a sequence of food price

b c$DR changes, $DR

Price ValidchangeValue total Independent

1 2 3 10Ž .measure % value valuation C C C Cr ice r ic e r ic e r ic e

WTP y20 30.06 31.72 3.80 3.79 3.78 3.60Ž . Ž . Ž . Ž .5.5 y0.3 y0.5 y5.3

y50 81.86 96.41 11.07 10.89 10.84 9.21Ž . Ž . Ž . Ž .17.8 y1.6 y2.1 y16.8

y90 175.55 297.54 31.73 29.55 28.84 16.36Ž . Ž . Ž . Ž .69.5 y6.9 y9.1 y55.9

y95 191.86 375.07 39.55 35.81 34.64 17.46Ž . Ž . Ž . Ž .95.5 y9.5 y12.4 y55.9

WTA q20 y27.58 y26.4 y3.32 y3.33 y3.34 y3.47Ž . Ž . Ž . Ž .y4.3 0.3 0.6 4.5

q50 y65.41 y59.33 y7.71 y7.76 y7.78 y8.45Ž . Ž . Ž . Ž .y9.3 0.6 0.9 9.6

q150 y171.98 y137.57 y19.55 y19.76 y19.83 y23.70Ž . Ž . Ž . Ž .y20.0 1.1 1.4 25.2

q250 y261.1 y191.48 y29.31 y29.63 y29.71 y37.66Ž . Ž . Ž . Ž .y26.7 1, 1 1.4 28.5

a w xDemand system parameter estimates are from the market goods demands reported in 14 . Initialhousehold expenditure is $DR 224.

b The numbers in parentheses are the percentage difference between the valid total value and theindependent valuation, for a package of price changes for ten food items.

c The numbers in parentheses are the percentage difference between the embedded valuation of thatcell and the first in sequence valuation, C1 .r ic e


embedding effect depends on the size of the imposed price or quantity change, andthe number of items that are evaluated prior to or simultaneously with the time ofinterest. The table also illustrates the directional effect of embedding: deepembedding reduces single-item WTP but increases single-item WTA. As theorypredicts, embedding is a routine economic phenomenon that may be observed withmarket, as well as nonmarket, valuation.

MARKETED GOODS AND MULTI-STAGE BUDGETING

Multi-stage budgeting models address the intuition that household discretionarybudgets may amount to only a modest proportion of household wealth. It is theformal development of the idea that all expenditures are variable in the long runbut many kinds of expenditures are fixed in the short run. In formulating WTP,multi-stage budgeting suggests that a respondent works through successive stagesof rebudgeting and valuation. For example,

Stage 1: Rebudgeting to determine WTP for a proposed environmental policytakes place within a short-run discretionary account that include only environmen-tal goods.

Stage 2: Rebudgeting is confined to short-run discretionary expenditures butmay occur across budget categories, e.g., environment, recreation and vacations,food, clothing, etc.

Final Stage: Rebudgeting occurs across all short-term and long-term accounts.

Standard theory assumes that the budget allocation process is complete, i.e.,rebudgeting proceeds through the final stage. However, if rebudgeting is incom-plete, discretionary income is reduced and, theory predicts, the effects of embed-ding are exacerbated.

The Yen and Roe demand system was used to simulate the influences oftwo-stage budgeting on the welfare evaluation of simultaneous price changes for all

Ž .food commodities. In the first incomplete rebudgeting stage, expenditures wererebudgeted only within the food category, while expenditures for clothing, housing,and other goods remained fixed. In the final stage, purchases are reallocated acrossall expenditure categories.

The first stage rebudgeting reallocates expenditures within a commodity group.A group-specific expenditure function states the expenditure on within-groupcommodities necessary to maintain group-specific utility constant at its initial level.

Ž .Since Eq. 1 is an indirect utility function for a specific commodity group, it can beinverted to obtain a commodity group-specific expenditure function for commoditygroup S,

e p , . . . , p , . . . , p , u0 s e p , . . . , p , . . . , p , u0 N y s y0 , all k / sŽ . Ž .s s1 sk sK s s s1 sk sK k k

1rc0u y Q rPs s ss P q P b , 9Ž .s s sž /as

where u0 is the utility that a household derives from the commodity group at thesintitial level of prices for all commodity groups.


Ž . Ž .Equation 9 maintains the sum of group utilities overall household utilityconstant when budget reallocation is incomplete and expenditure on other com-modity groups is held constant. This is the expenditure function appropriate forcalculating welfare changes with stage 1 incomplete rebudgeting. In contrast, Eq.Ž .4 describes group specific expenditure holding overall utility constant and allow-ing all commodity group expenditures to adjust optimally by completing thebudgeting process.

The stage 1 compensating variation for a price change from p0 to p1 , c1 , is thesk sk sk

difference between initial expenditure on commodity group s and the miniumexpenditure required to maintain group-specific utility constant at the initial level,

c1 s y0 y e p0 , . . . , p1 , . . . , p0 , u0 , 10Ž .Ž .sk s s s1 sk sK s

where the superscript 1 indicates the c1 is a first in sequence valuation, thesk

subscript s indicates that it is obtained within the sth commodity group, thesubscript k means that it is for a change in the kth price, and y0 ssŽ 0 0 0 0.e p , . . . , p , . . . , p , u is the initial expenditure on commodity group s.s s1 sk sK s

Ž . Ž .Since the choice set underlying Eq. 10 is a subset of the one underlying Eq. 5 ,it follows from the principles of constrained optimization that the welfare measurec1 cannot be larger than the welfare measure C1. The fixity of expenditures onsk k

groups other than groups s leads to a welfare measure that is equal to or less thanthat resulting from unrestricted budget reallocation. Welfare valuations were

Ž . Ž .computed using Eqs. 6 and 10 and the medium income, urban householdw xparameter estimates obtained from Yen 15 .

In Table II, we impose incomplete multistage budgeting on the welfare changesreported in columns 5]8 of Table I, i.e., rice price changes evaluated first, second,third, and tenth in a sequence of ten food price changes. We report welfare effectsfor medium income households, which spent 64% of their total budgets on food.Thus, first stage rebudgeting permitted reallocation of 64% of the total budget.

Ž .Comparing the welfare effects with first stage rebudgeting only Table II and withŽ .final stage rebudgeting Table I , we observe that incomplete multistage budgeting

exacerbates the effects of embedding. For an extreme example, first stage rebud-geting reduced the welfare effect of a 95% reduction in the price of rice evaluated

Žtenth in a ten-item sequence of price reductions by about one-half $DR9.00, Table.II, versus $DR17.46, Table I . It follows that for commodity groups with smaller

Ž .budget shares e.g., less than 64% , incomplete multistage budgeting would haveproduced even greater effects.

These simulations with an estimated system of market demands confirm theprediction from theory: incomplete rebudgeting tends to reduce WTP and increaseWTA from their fully optimal values, thus exacerbating the embedding effectsdemonstrated above with marketed goods. Furthermore, the effect of incompleterebudgeting is more pronounced the smaller the initial budget allocation to anexpenditure category. For environmental goods, the respondent’s initial directexpenditures are likely to be small and the impact of incomplete budgeting is likelyto be large.


TABLE IIaEffects of Embedding and Incomplete Multistage Budgeting, for Rice

Welfare effect for rice price change by degree of embedding in absequence of food price change $DRPrice changeValue

1 2 3 10Ž .measure % c c c cs r ice s r ic e s r ic e s r ic e

WTP y20 3.78 3.73 3.71 3.30Ž . Ž . Ž .y1.3 y1.9 y12.7

y50 10.89 10.40 10.25 7.15Ž . Ž . Ž .y4.5 y5.9 y34.3

y90 30.25 25.64 24.32 8.84Ž . Ž . Ž .y15.2 y19.6 y70.8

y95 37.26 29.93 27.90 9.00Ž . Ž . Ž .y19.7 y25.1 y75.8

WTA q20 y3.34 y3.38 y3.39 y3.73Ž . Ž . Ž .1.2 1.5 11.7

q50 y7.80 y8.00 y8.07 y9.99Ž . Ž . Ž .2.6 3.5 28.1

q150 y20.10 y21.29 y21.63 y34.90Ž . Ž . Ž .5.9 7.6 73.6

q250 y30.53 y33.01 y33.69 y64.04Ž . Ž . Ž .8.1 10.4 109.8

a w xDemand system parameter estimates are from market good demands reported in 14 . Initialhousehold expenditure is $DR224, and budget share for food is 64%.

b Numbers in parentheses are the percentage difference between the embedded, stage 1 valuation ofa given cell and the embedded, stage 1 first in sequence valuation, c1 .s r ic e

IMPLICATIONS FOR VALUATION

ŽStandard economic theory predicts that the value of a particular prospect a.good or a policy will vary in systematic ways, depending on what additional

prospects are offered prior to or simultaneously with it. We have summarized therelevant theory, and demonstrated the empirical phenomenon with simulationsusing an ordinary, but theoretically consistent, demand system. The results showthat embedding effects are standard economic phenomena induced by substitutionrelationships and constrained endowments, and these effects may be of substantial

w xmagnitude. Hanemann 2 has shown that substitution effects are more pronouncedwith quantity-rationed goods, which implies that embedding effects may be typi-cally larger for policy goods than for market goods.

These results provide a perspective that is essential for resolving the embeddingcontroversy. The claim of Kahneman and Knetsch that embedding effects are amere artifact of CV is clearly insupportable: embedding is real, and evidence of itseffects in CV data sets does not, per se, invalidate the particular studies or themethod in general.

Nevertheless, just as economic theory anticipates embedding effects, the possibil-ity remains that CV may exacerbate these effects. Poor research design andconfusing survey instruments are always a possibility. Problems arise whenever arespondent understands a question in a way that is meaningfully different formwhat the researcher intends. For example, the respondent may modify a CVquestion in light of what she knows about science and policy, before answering.


When told that a proposed policy will reduce one pollutant in one lake, she mayreasonably modify the received information to better accord with her prior beliefsthat treatments often reduce more than one pollutant and policy seldom targetsonly a single lake. If this miscommunication between researcher and respondentoccurred, it would amplify any embedding effects. Improved survey procedures willminimize the impact of these possibilities and rigorous peer review should mini-mize their impact on the literature.

More generally, CV may have a tendency to amplify embedding effects. Hoehnw xand Randall 6 showed that incomplete expenditure maximization would lead a

CV respondent to underestimate her true Hicksian compensating welfare measure.6

In that case, WTP would be understated and WTA overstated for a single policyprospect. Above, we showed that incomplete multi-stage budgeting depresses thevalue of packages of prospects, and of components placed late in a sequence, morethan it depresses independently estimated component values. With incompleteexpenditure minimization and incomplete rebudgeting, CV-elicited WTP would betoo low for packages and first in sequence components, and would fall too fast foritems valued later in the sequence. CV practitioners should be alert to thesepossibilities when interpreting CV data and designing improved methods.

Finally, Kahneman and Knetsch raise the issue of the proper level of embeddingfor policy analysis. This is but a specific case of a general problem in welfareanalysis. Given the conditionality of welfare measures, the challenge for appliedwork is always to identify and impose the side-conditions appropriate for theparticular application. For some settings such as the economic assessment ofnatural resources damage, the side-conditions are clear. The proper welfareconcept for damage assessment is ex ante WTA, but WTP estimates are used forpragmatic reasons. Since WTP for single items is generally lower than WTA, andsince WTP decreases with the level of embedding while WTA increases, it followsthat embedded WTP understates WTA regardless of the level of embedding forWTA. To estimate natural resource damages using WTP, the proper level ofembedding is therefore unembedded.

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Ž .Econom. Re¨ . 81, 636]647 1991 .3. G. W. Harrison, Valuing public goods with the contingent valuation method, J. En¨iron. Econom.

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Ž .544]551 1989 .

6 w xHoehn and Randall 6 identify a value formulation process, in which the respondent seeks todiscover her true valuation, and a value reporting process, where strategic considerations might enter in.They also discuss a model in which the optimal strategic response is truthful reporting of the formulated

w xvalue. Mitchell and Carson 9 report that there is little empirical support for the conjecture that CVMdata sets exhibit strategic response. Accordingly, we concentrate here upon the value formulationprocess.


6. J. P. Hoehn and A. Randall, A satisfactory benefit cost indicator from contingent valuation, J.Ž .Enïron. Econom. Management 14, 226]247 1987 .

7. D. Kahneman and J. L. Knetsch, Valuing public goods: The purchase of moral satisfaction, J.Ž .Enïron. Econom. Management 22, 57]70 1992 .

8. P. Madden, A generalization of Hicksian q substitutes and complements with application to demandŽ .rationing, Econometrica 59, 1497]1508 1991 .

9. R. C. Mitchell and R. T. Carson, ‘‘Using Surveys to Value Public Goods: The Contingent ValuationMethod.’’ Resources for the Future, Inc., Washington, 1989.

10. C. A. E. Nickerson, Valuing public goods: A comment on Harrison’s critique of Kahneman andŽ .Knetsch, J. Enïron. Econom. Management 25, 93]102 1993 .

11. A. Randall, J. P. Hoehn, and G. Tolley, ‘‘The Structure of Contingent Markets: Some Results of aRecent Experiment.’’ Presented to the annual meeting of American Economics Association,Washington, DC., 1981.

12. V. K. Smith, Arbitrary values, good causes, and premature verdicts, J. Enïron. Econom. Manage-Ž .ment 22, 71]89 1991 .

13. E. L. Vockell and J. W. Asher, ‘‘Educational Research,’’ 2nd. ed. Prentice Hall, Englewood Cliffs,NJ, 1995.

14. S. T. Yen and T. L. Roe, Estimation of a two-level demand system with limited dependent variables,Ž .Amer. J. Agric. Econom. 71, 85]98 1989 .

15. S. T. Yen, ‘‘Stagewise Estimation of Complete Demand Systems with Limited Dependent Variables:An Analysis of Dominican Household Consumption.’’ Ph.D. Thesis, University of Minnesota,1987.

embedding in market demand systems

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