Environmental Economics: Valuing the Environment

Environmental Economics II Dr Anil Markandya hssam@bath.ac.uk – 01225 386954 – Room 3E 4.31b Valuing the Environment • Environmental Valuation • Enable environmental impacts to be included in Cost-BenefitAnalysis (CBA) • To take account of environmental damage in measuring economic performance • To take account of environmental benefits of public programs Categories of environmental benefits • Use Value (UV) • Existence Value (EV) • Option Value (OV)(Option Price = Expected Use Value + OV • Quasi Option Value (QOV) • Bequest Value (BV) • Total Economic Value (TEV) • TEV = UV+EV+OV+QOV+BV Non-market valuation techniques • Stated Preferences – Contingent Valuation – Choice Modelling • Revealed Preferences – Travel Cost Model – Hedonic Pricing The Contingent Valuation Method • • • • - Stated preference technique Questionnaire based Direct method Valuation of a hypothetical scenario It is called “contingent valuation” because the valuation is contingent on the hypothetical scenario put to respondents • Non Use Values + Use Values • Willingness To Pay (WTP) question Stated Preference Techniques: CVM An interview is used to create the hypothetical market within these questions are asked The hypothetical market comprises two key parts: a statement of the proposed change; and an institutional mechanism through which the proposed change is to be provided/avoided and financed The challenge in conducting a CV is to make the market as realistic as possible The process of directly questioning a sample group to ascertain their valuation of a change can be divided into six stages These are (each with a number of steps): definition of survey objectives; design of the questionnaire; surveying the sample population; creating a database and performing an exploratory data analysis; estimating WTP values; and reporting the survey results CVM: Stage - Project Definition - Theoretical Model CV study should begin with a basic theoretical model: two purposes: Identifies the information required from questionnaire Generates predictions allowing results to be checked Number of sources of information that can be used to construct the model, including: predictions of economic theory and existing literature, discussion/meetings with focus groups/affected parties Participants discuss understanding of the context of the good/service in question, the good/service itself, its “value”, who should provide it, how it should be paid for, whether they would contribute, etc The information from the focus groups is particularly valuable in designing the CV survey CVM: Stage - Project Definition - Sample Design For a site-specific resource, the sample may be drawn from: Visitors to the site (‘on-site’ sample) • does not elicit information on the WTP of ‘non-users’; • interviews must be kept short; • procedure is needed to select among visitors to a site Households within a certain radius of the site (‘off-site’ sample) • geographical boundaries need to be defined; • a larger sample required, many households may not visit the site It is also important to carefully select the size of the sample: A larger means more confidence that the sample mean WTP/WTA is a reliable estimate of the ‘true’ mean WTP/WTA (Balance precision and cost) CVM: Stage - Questionnaire Design - Background Questions General background: Questions on general characteristics of the respondents – information for checking the validity of the valuation results Respondents’ tastes and socio-economic characteristics (is the sample representative?) Personal details - should , come at the end of the questionnaire Respondent’s knowledge of the commodity in question, e.g background questions concerning the respondent’s visits to a recreation site should cover such issues as: • attitudes towards environmental issues; • proximity of their home to the site; • frequency of visits; • duration of trip; • reason for visit, etc These questions should be asked at the beginning of the interview as they are relatively straightforward to answer, and will help to build-up the respondent’s confidence CVM: Stage - Questionnaire Design - Preparation Questions To avoid bias, interviewer must make sure the respondent is aware of: budget constraints (you cannot spend more than you have!) their right to refuse to pay for the good If the event of a negative response, the reason must be recorded a ‘zero valuation’ is implied if: the respondent may not be able to pay anything; or the respondent may not be willing to pay anything a ‘protest bid’ is implied if: the respondent may find it too difficult to establish a monetary valuation; the respondent may disapprove of the concept of expressing 10 environmental resources in monetary terms; or may be hostile Other important aspects for questionnaire development (3) • Identify protest respondents after the WTP questions (ask why the respondent voted YY, NN, NY, YN) • Analyze the data for the full sample of respondents, then delete those respondents that show protest behaviours • Income Try to get an answer to the income question In developing countries, sometimes researchers (Cropper, Alberini) ask a list of expenditures If you have no information on income from some respondents, don’t loose those observations Add a dummy equal to for those that did not answer the income question, and otherwise Set equal to the income of those respondents that did not answer the income question In your regression the coefficient of the dummy for those that did not answer the income question tells if they are statistically different from those that reported income In this way you don’t loose the observations! • Clearly define the population of interest • Consider your budget constraint • Make sure that your referendum question avoids free rider behaviours! 20 • • • Payment vehicle Whose welfare are we interested in? => Important for sampling plan TAX => One time Tax is incentive compatible How we choose the tax level? Focus groups, previous research, pretest, optimal bidding design literature, cost of the public program If Data are not as Shown, use NonParameteric Methods 21 CVM: Stage - Questionnaire Design - Payment Vehicle Valuation question needs a realistic institutional context - usually an appropriate payment (or bid) vehicle (instrument) The payment vehicle is the mechanism through which the WTP/WTA values are to be raised/distributed Key considerations when selecting a payment vehicle are: familiarity – does the respondent understand the payment vehicle? credibility – does the payment vehicle represent a realistic situation? empathy – is the respondent favourably or unfavourably disposed towards the recipient of the funds? feasibility – is the recipient of the funds capable of delivering the improvement? universality – would all the respondents be affected by the payment vehicle? 22 WTP and WTA • The goal of contingent valuation is to measure the compensating or equivalent variation for the good in question Both compensating and equivalent variation can be elicited by asking a person to report a willingness to pay amount For instance, the person may be asked to report his WTP to obtain the good, or to avoid the loss of the good Formally, WTP is defined as the amount that must be taken away from the person’s income while keeping his utility constant: 1) V ( y − WTP, p, q1 ; Z) = V ( y, p, q ; Z) where V denotes the indirect utility function, y is income, p is a vector of prices faced by the individual, and q and q1 are the alternative levels of the good or quality indexes (with q 1>q0, indicating that q1 refers to improved environmental quality) Z is a vector of individual characteristics • (Compensating variation is the appropriate measure when the person must purchase the good, such as an improvement in environmental quality Equivalent variation is appropriate if the person faces a potential loss of the good, as he would if a proposed policy results in the deterioration of environmental quality.) 23 • 2) • • • Willingness to accept (WTA) is defined as the amount of money that must be given to an individual experiencing a deterioration in environmental quality to keep his utility constant: V ( y + WTA, p, q ; Z) = V ( y , p, q ; Z) Where q2 indicates a deterioration in quality compared to the status quo, q0 In equations (1) and (2), utility is allowed to depend on a vector of individual characteristics influencing the tradeoff that the individual is prepared to make between income and environmental quality An important consequence of equations (1) and (2) is that WTP or WTA should, therefore, depend on (i) the initial and final level of the good in question; (ii) respondent income; (iii) all prices faced by the respondent, including those of substitute goods or activities; and (iv) other respondent characteristics Internal validity of the WTP responses can be checked by regressing WTP on variables (i)-(iv), and showing that WTP correlates in predictable ways with socio-economic variables 24 Dichotomous-Choice Contingent Valuation • When dichotomous choice questions are used, the researcher does not observe WTP directly: at best, he can infer that the respondent’s WTP amount is greater than the bid value (if the respondent is in favor of the program) or less than the bid amount (if the respondent votes against the plan), and form broad intervals around the respondent’s WTP To estimate the usual welfare statistics, it is necessary to fit binary data models • The simplest such models assume that an individual’s response to the WTP question is motivated by an underlying, and unobserved, WTP amount, which is normally (logistically) distributed Formally, let WTP* be the unobserved WTP: WTPi * =µ µis+ both εi • Where 3) mean and median WTP, ε is a zero-mean normal (logistic) error with mean zero The model is completed by specifying the mapping from the latent variable to the observables: 4) WTPi=1 iff WTPi*>B and WTPi=0 iff WTPi*≤B • where B is the bid that was assigned to respondent i, WTP = means that the response is a “yes,” and WTP = means that the response to the payment question is a “no.” 25 • Because we observe discrete outcomes, we must derive the probabilities of “yes” and “no” responses When attention is restricted to a normal latent WTP, the probability of a “yes” response is, therefore: B µ ε * 5) Pr( yes | Bi ) = Pr(WTPi = | Bi ) = Pr(WTPi > Bi ) = Pr(ε i > Bi − µ ) = Pr  i > i −  σ σ σ • Because ε/σ is a standard normal variate,   Bi µ    Bi µ  − Φ − = Φ   − +    σ σ    σ σ   • where Φ(⋅) is the standard normal cdf If we define α=μ/σ and β=-1/σ, the probability of a yes response can be rewritten as: 6) Pr( yes | Bi ) = Φ (α + β ⋅ Bi ) Equation (6) is the contribution to the likelihood by a “yes” observation (or a one) in a probit model with the intercept and one regressor—the bid As long as β is identified and estimable— which requires that the bid amount be varied to the respondents in the survey, so that it becomes a legitimate regressor in the probit model—mean/median WTP is estimated as: 7) µˆ = −αˆ / βˆ 26 • while the standard deviation of WTP is estimated as: 8) σˆ = −1 / βˆ • The same formulae produce estimates of mean/median WTP and of the scale parameter of WTP from the logit coefficient if WTP is assumed to be a logistic variate • A standard probit routine will automatically produce standard σ and α forβ and , butµnot for errors  σ , you can use the • To obtain the covariance matrix µof and delta method (Cameron, 1991) β • First calculate the covariance matrixαof and produced by the probit routine V: −1 n 9) V = ∑ w( zi )  Bi2   i =1  Bi Bi   ⋅ B  z = α + β w ( z ) = φ ( zi ) {Φ( zi )[1 − Φ( zi )]} , with φ(•) the i , and i where i standard normal probability density function (pdf) Next, compute the matrix G :  − / β  10) G =   2  α / β / β  27 • Finally calculate the matrix product V1=G’VG, with V1 the covariance matrix of µand σ. Nb This can be done in LIMDEP • If WTP is assumed to be a logistic variate, the steps required for the delta method are the same, except that w(z) in expression (9) is equal to {exp(zi) / [1 + exp(zi)]} • in some studies, depending on the frequencies of the “yes” and “no” responses to the payment questions, formula (7) produces a negative mean/median WTP figure • Perhaps a better way to avoid this problem is to work with a WTP distribution that is defined only over the positive semi-axis The Weibull and the lognormal are examples of such distributions • The cdf for a Weibull with parameters θ (θ>0) and σ is θ • Mean WTP is where Γ(•) is the gamma function F ( y ) = − e − ( y /σ ) 1  σ ⋅ Γ + 1 θ  • Median WTP is 1/θ • The log likelihoodσfunction ⋅ [− ln(0.5)]becomes: 11) n • where F is the cdf of the Weibull ∑ [WTPi ⋅ log(1 − F ( Bi ;θ , σ )) + (1 − WTPi ) ⋅ log F ( Bi ;θ , σ )] i =1 28 • median WTP is generally regarded as a robust, and conservative, welfare statistic associated with the good or proposed policy It is usually estimated more precisely than mean WTP, and is interpreted as the value at which 50% of the respondents would vote in support of the program, and hence the cost at which the majority of the population would be in support of it 29 The Double Bounded Dichotomous Choice model • • • • Double bounded models increase efficiency in three ways: YN and NY answers bound WTP NN and YY answers further constrain WTP The number of observation is increased The log likelihood function becomes: n log L = ∑ log[ F (WTP H ; θ ) − F (WTP L ; θ )] i =1 where WTPH and WTPL are the lower and upper bound of the interval around WTP defined above, F(⋅) is the cdf of WTP, and θ denotes the vector of parameters that index the distribution of WTP (Notice that for respondents who give two “yes” responses, the upper bound of WTP may be infinity, or the respondent’s income; for respondents who give two “no” responses, the lower bound is either zero (if the distribution of WTP admits only non-negative values) or negative infinity (if the distribution of WTP is a normal or a logistic.)) 30 Non parametric models for contingent valuation: the Turnbull estimator Consider only the first bid answer For bids indexed j=1,…,M, calculate F j=Nj/(Nj+Yj) where Nj is the number of No responses to tj and Yj is the number of Yes responses to the same bid, Tj= Nj+Yj Beginning with j=1, compare F j and Fj+1 Intuitively, % of No’s should increase with the increase in the bid If Fj+1>Fj then continue If Fj+1≤Fj then pool cells j and j+1 into one cell with boundaries (t j,tj+2], and calculate Fj*=(Nj+Nj+1)/(Tj+Tj+1)=Nj*/Tj* That is, eliminate bid tj+1 and pool responses to bid tj+1 with responses to bid tj Continue until cells are pooled sufficiently to allow for a monotonically increasing CDF Set FM+1*=1, F0*=0 Calculate the PDF as the step difference in the final CDF: fj+1*=Fj+1*-FJ* for each offered price These represent consistent estimates of the probability that WTP falls between price j and price j+1 31 Multiply each offered price (tj) by the probability that WTP falls between it and the next highest price (t j+1) 10 Sum the quantities from step (9) over all prices to get an estimate of the lower bound on WTP: M E LB (WTP) = ∑ t j ( F j*+1 −F j* ) j =0 11 Calculate the variance of the lower bound as: M* V ( E LB (WTP )) = ∑ j =1 F j* (1 − F j* ) T * j (t j − t j −1 ) 32 Unrestricte d Turnbull tj Nj Tj Fj Fj* fj * 20 54 0.370 0.343 0.343 10 15 48 0.313 Pooled back Pooled back 25 46 81 0.568 0.568 0.225 50 55 95 0.579 0.579 0.011 100 106 133 0.797 0.797 0.218 200 82 94 0.872 0.872 0.075 300 72 81 0.889 0.889 0.017 300+ - - 1 0.111 ELB(WTP)=0*0.343+5*0.225+25*0.011+50*0.218+100*0.075+ +200*0.017+300*0.111=$56.50 V(ELB(WTP))=(0.343*0.657/102)*(5-0)2+(0.568*0.432/81)*(25-5)2+ +(0.579*0.421/95)*(50-25)2+(0.797-0.203/133)*(100-50)2+ +(0.872*0.128/94)*(200-100)2+(0.889*0.111/81)*(300-200)2=$29.52 33 Literature for this lecture • • • • • Haab-McConnell “Valuing environmental and natural resources” chapters 1-5 Perman et al Chapter 12 A good book for the CV: Mitchell-Carson “Using surveys to value public goods: the contingent valuation method” Resources for the Future, Washington, DC, 1989 Read the paper Alberini, Rosato, Longo, Zanatta “Information and Willingness to Pay in a Contingent Valuation Study: The Value of S Erasmo in the Lagoon of Venice.” I’ll post the slides and the paper on my website: http://people.bath.ac.uk/al224/ 34 [...]... q1 refers to improved environmental quality) Z is a vector of individual characteristics • (Compensating variation is the appropriate measure when the person must purchase the good, such as an improvement in environmental quality Equivalent variation is appropriate if the person faces a potential loss of the good, as he would if a proposed policy results in the deterioration of environmental quality.)... used, the researcher does not observe WTP directly: at best, he can infer that the respondent’s WTP amount is greater than the bid value (if the respondent is in favor of the program) or less than the bid amount (if the respondent votes against the plan), and form broad intervals around the respondent’s WTP To estimate the usual welfare statistics, it is necessary to fit binary data models • The simplest... those that did not answer the income question, and 0 otherwise Set equal to 0 the income of those respondents that did not answer the income question In your regression the coefficient of the dummy for those that did not answer the income question tells if they are statistically different from those that reported income In this way you don’t loose the observations! • Clearly define the population of interest... through which the WTP/WTA values are to be raised/distributed Key considerations when selecting a payment vehicle are: familiarity – does the respondent understand the payment vehicle? credibility – does the payment vehicle represent a realistic situation? empathy – is the respondent favourably or unfavourably disposed towards the recipient of the funds? feasibility – is the recipient of the funds capable... his WTP to obtain the good, or to avoid the loss of the good Formally, WTP is defined as the amount that must be taken away from the person’s income while keeping his utility constant: 1) V ( y − WTP, p, q1 ; Z) = V ( y, p, q 0 ; Z) where V denotes the indirect utility function, y is income, p is a vector of prices faced by the individual, and q 0 and q1 are the alternative levels of the good or quality... further constrain WTP The number of observation is increased The log likelihood function becomes: n log L = ∑ log[ F (WTP H ; θ ) − F (WTP L ; θ )] i =1 where WTPH and WTPL are the lower and upper bound of the interval around WTP defined above, F(⋅) is the cdf of WTP, and θ denotes the vector of parameters that index the distribution of WTP (Notice that for respondents who give two “yes” responses, the. .. Calculate the PDF as the step difference in the final CDF: fj+1*=Fj+1*-FJ* for each offered price These represent consistent estimates of the probability that WTP falls between price j and price j+1 31 9 Multiply each offered price (tj) by the probability that WTP falls between it and the next highest price (t j+1) 10 Sum the quantities from step (9) over all prices to get an estimate of the lower... Haab-McConnell Valuing environmental and natural resources” chapters 1-5 Perman et al Chapter 12 A good book for the CV: Mitchell-Carson “Using surveys to value public goods: the contingent valuation method” Resources for the Future, Washington, DC, 1989 Read the paper Alberini, Rosato, Longo, Zanatta “Information and Willingness to Pay in a Contingent Valuation Study: The Value of S Erasmo in the Lagoon... Φ(⋅) is the standard normal cdf If we define α=μ/σ and β=-1/σ, the probability of a yes response can be rewritten as: 6) Pr( yes | Bi ) = Φ (α + β ⋅ Bi ) Equation (6) is the contribution to the likelihood by a “yes” observation (or a one) in a probit model with the intercept and one regressor the bid As long as β is identified and estimable— which requires that the bid amount be varied to the respondents... 27 • Finally calculate the matrix product V1=G’VG, with V1 the covariance matrix of µand σ. Nb This can be done in LIMDEP • If WTP is assumed to be a logistic variate, the steps required for the delta method are the same, except that w(z) in expression (9) is equal to {exp(zi) / [1 + exp(zi)]} • in some studies, depending on the frequencies of the “yes” and “no” responses to the payment questions,