AAEC 6524: Environmental Economic Theory and Policy Analysis. Outline. Introduction to Non-Market Valuation Part C. Klaus Moeltner Spring 2017

Transcription

1 AAEC 6524: Environmental Economic Theory and Policy Analysis Introduction to Non-Market Valuation Part C Klaus Moeltner Spring 2017 March 21, / 28 Outline 2 / 28

2 Quantity is usually understood to mean environmental quality Usually fixed from consumer s perspective (think Public Good ) Deriving welfare measures for change in q = Main focus of non-market valuation Different set of welfare measures Different estimation strategies 3 / 28 Definition via IUF For a change in q from q 0 to q 1 : Compensating Variation (also Compensating Surplus (CS)): V ( p, y, q 0) = V ( p, y CV, q 1) Equivalent Variation (also Equivalent Surplus (ES)) V ( p, y, q 1) = V ( p, y + EV, q 0) 4 / 28

3 Graphical Interpretation Compensating Surplus vs. Equivalent Surplus x CoS M A B BC C IC 1 IC o q x q o q 1 D ES M A B BC IC 1 IC o q o q 1 q 9 5 / 28 Golden Rule for Definition of CS, ES Golden Rule for Definition of CoS, ES (virtually same as before): CoS: What amount of income ($$), given or taken away, would keep me at the old utility level, given the new quantity set. ES: What amount of income ($$), given or taken away, would get me to the new utility level, given the old quantity set. 6 / 28

4 Golden Rule for Interpretation of CS, ES Golden Rule for Interpretation of CoS, ES Welfare Measure Implied Property Rights in: Quantity increase Quantity decrease CoS Status Quo WTP to obtain WAC to accept ES Change ( New Status ) WAC to forgo WTP to avoid 7 / 28 Corollary to Golden Rule 11 Corollary to Golden Rule: If consumer s property rights are not clearly (i.e legally) assigned to either Status, assign them to the Status that corresponds to the lower utility level. Then apply the Golden Rule for Interpretation of ES, CoS as before. 8 / 28

5 Alternative analytical expressions Via expenditure function: CV = E ( p, u 0, q 0) E ( p, u 0, q 1) = y E ( p, u 0, q 1) EV = E ( p, u 1, q 0) E ( p, u 1, q 1) = E ( p, u 1, q 0) y 9 / 28 Inverse demand function We can also define these welfare measured using demand curves. But: q is fixed for the individual. Often provided at zero fee. Thus, q/ p q makes no sense Instead: work with Inverse demand function (IDF) 10 / 28

6 Inverse demand function Compensated IDF show prices a person would pay for different quantities of q. π q (p, u, q) = E(p,u,q) q This is also the marginal WTP for q - function Shows change in income (min. expenditure) that holds utility constant following a marginal change in q Inverse demand function WTP function 11 / 28 Alternative analytical expressions for CV, EV q 1 CV = π q ( p, u 0, q ) dq q 0 q 1 = E ( p, u 0, q ) dq q q 0 = E ( p, u 0, q 0) E ( p, u 0, q 1) q 1 EV = π q ( p, u 1, q ) dq q 0 q 1 = E ( p, u 1, q ) dq q q 0 = E ( p, u 1, q 0) E ( p, u 1, q 1) 12 / 28

7 Virtual prices and income Let π 0, ỹ 0 be the virtual price / virtual income pair that would lead the consumer to freely choose quantity level q 0, if it were sold in the market place. Note: Virtual income is generally greater than actual income (since virtual expenditure on q must be accommodated in the budget) 13 / 28 Ordinary inverse demand function (oidf) θ q (p, y, q) Like regular ordinary demand function, the oidf is uncompensated Maintains income level while allowing utility to change The following figure shows how all these concepts are related 14 / 28

8 Graphical interpretation E(p,u 1,q 0 ) u 0 d EV Figure 14.2 Quantity Change Panel A y CV y 0 E(p,u 0,q 1 ) $ a q 0 37 ( y ) 0 0 b c q 1 ( y ) 1 1 ( y ) 2 2 q ( y ) 3 3 q (p,u 1,q) u 1 3 d E(p,u 1,q 0 ) u 0 d 0 a EV y 0 a b 1 b CV E(p,u 0,q 1 ) c ( y ) c q (p,y,q) q 0 ( y ) 0 0 q 1 ( y ) 2 2 q q 0 q 1 q (p,u 0,q) q $ q (p,u 1,q) 21 April 2010 Panel B 3 d 15 / 28 0 a Welfare measurement 1 b 2 q 0 c q (p,y,q) q (p,u 0,q) Panel B x j (p, y, q), and derive welfare measures. 21 April 2010 q 1 For price-change case, we were able to start with (observed) q Quality change: no observed uncompensated demand curve. We can t use θ (p, y, q) as a starting point - not observed. 16 / 28

9 Welfare measurement For price change, we used the following fundamental relationship: E(p,ū,q) p j = V (.)/ p j V / y = x j (p, y, q) Relate observed behavior to expenditure function Solve differential equation Recover preference parameters Derive welfare measures 17 / 28 Welfare measurement Start with ū V (p, E (p, ū, q), q) Diff. w.r.t. q, re-arrange: E(p,ū,q) q = V (p,y,q)/ q V (p,y,q)/ y = θq (p, y, q) If we could observe θ q (p, y, q), we could recover the quasi-expenditure function for q. But θ q (.) cannot be estimated using observed behavior. This is the fundamental challenge of welfare measurement for NMGs 18 / 28

10 Welfare measurement Conclusion: Quantity-change welfare requires: Additional assumptions on preference function, and / or Additional, preference-related information beyond individual behavior 19 / 28 Interpretation of welfare measures Which one applies depends largely on allocation of property rights If there are no existing rights, in theory either one could be used But they can differ substantially in magnitude (even for same reference utility level) Benefit-Cost-Analysis results could flip, depending on which we use Strong interest in profession as to how much they can differ and why 20 / 28

11 Horowitz and McConnell (2002): Perform a Meta-analysis of welfare measures from 45 studies. Find that WTA WTP 7 There exist several theories to explain this wedge Here: focus on Hanemann (1991) 21 / 28 In theory, divergence should be small for small income effects for both price and quantity changes. Based on Willig (1976) and Randall and Stoll (1980) Hanemann (1991) shows: Wedge depends implicitly on degree of substitution between quasi-fixed good and set of available private goods. 22 / 28

12 Recall virtual price, income π, ỹ that, if real, would lead consumer to choose a given level of Q Define ordinary-demand-for q function q = q (p, π, y + qπ) Shows particular virtual price / income pair that would lead to a choice of q, conditional on all other (observed) prices p If we invert q (.), we obtain the ordinary inverse demand function from before: π = θ q (p, y, q) 23 / 28 We can also derive a hypothetical compensated-demand-for-q function Imagine a hypothetical expenditure minimization problem Given (virtual price) π 0, a minimum expenditure is needed to reach u 0. The solution is q 0 (see figure) Repeat this exercise for price π 1, utility u 1 Get two points on the compensated-demand-for-q function q = h q (p, π, u) 24 / 28

13 We can now stipulate a theoretical Slutsky relationship: h q (p,π,u) π = q(p,π,y+qπ) π + q(p,π,y+qπ) y q None of these terms are observed in practice, but the relationship is theoretically sound Used in Hanemann (1981) in his re-formulation of the Randall / Stoll result for the income elasticity of the ordinary marginal WTP function. 25 / 28 Hanemann (1981) Starting point: Randall and Stoll s (1980) result. They derive the income elasticity of the ordinary marginal WTP function as ξ = θq (p,y,q) y y θ q (.) If income effects are small, ξ is small, and difference between CV, EV, and thus WTP, WTA should be small. Hanemann shows: ξ has two components: pure income effect and pure substitution effect Second effect can dominate the first and lead to large wedge between WTP and WTA. 26 / 28

14 Hanemann (1981) Key result: ξ = η q σ qy where η q = q(p,π,y+qπ) ỹ y+qπ q(.) income elasticity of ordinary demand for q σ qy = Allen-Uzawa elasticity of substitution between q and spending on on market goods (x) 27 / 28 Hanemann (1981) So ξ can be large even if income effects (η) are small if there are no market goods that can substitute for q Often the case for environmental amenities / recreational opportunities Think: New River Gorge rafting trip (q = water level) vs. Mountain Lake Resort Beach visit vs. tanning booth Jogging in cleaner air vs. treadmill 28 / 28