Lecture 3 Intergenerational Fairness 2024 Fall PDF

Chapter 2 of Stern Review Discounting Intergenerational Fairness Fall 2024, Lecture 3 Paolo G. Piacquadio1 1FGN-HSG October 11, 2024........................................ Paolo G. Piacquadio Intergenerational Fairne...

Chapter 2 of Stern Review Discounting Intergenerational Fairness Fall 2024, Lecture 3 Paolo G. Piacquadio1 1FGN-HSG October 11, 2024........................................ Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Discounting Chapter 2 of Stern Review........................................ Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Discounting Comments....................................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Discounting Comments....................................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Discounting Comments....................................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting Time and discounting Consider a project that involves costs and benefits at different periods. How to assess this project? One solution is to adopt the Social Discount Rate (SDR): it converts costs and benefits in the future into current units of account, known as ‘present values.’ However, the present value is extremely sensitive to minor alterations to the SDR......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting Time and discounting Consider a project that involves costs and benefits at different periods. How to assess this project? One solution is to adopt the Social Discount Rate (SDR): it converts costs and benefits in the future into current units of account, known as ‘present values.’ However, the present value is extremely sensitive to minor alterations to the SDR......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting Time and discounting Consider a project that involves costs and benefits at different periods. How to assess this project? One solution is to adopt the Social Discount Rate (SDR): it converts costs and benefits in the future into current units of account, known as ‘present values.’ However, the present value is extremely sensitive to minor alterations to the SDR......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The Social Discount Rate (SDR): disagreement Disagreement on the SDR seen in the aftermath of the Stern Review: Stern (2007) took a normative stand and advocated for a SDR of 1.4%; Nordhaus (2008) took a “positive stand” and proposed a SDR of 4.5%. Lengthy debate in academic circles over the appropriate SDR: Less polarized now, with majority of experts forming a “middle ground”; but there is still serious disagreement (Drupp et al., 2018) Policymakers’ disagreement is even larger, but is partially explained by the link between academics and policymakers (Groom & Hepburn, 2017)......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The Social Discount Rate (SDR): disagreement Disagreement on the SDR seen in the aftermath of the Stern Review: Stern (2007) took a normative stand and advocated for a SDR of 1.4%; Nordhaus (2008) took a “positive stand” and proposed a SDR of 4.5%. Lengthy debate in academic circles over the appropriate SDR: Less polarized now, with majority of experts forming a “middle ground”; but there is still serious disagreement (Drupp et al., 2018) Policymakers’ disagreement is even larger, but is partially explained by the link between academics and policymakers (Groom & Hepburn, 2017)......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The Social Discount Rate (SDR): disagreement Disagreement on the SDR seen in the aftermath of the Stern Review: Stern (2007) took a normative stand and advocated for a SDR of 1.4%; Nordhaus (2008) took a “positive stand” and proposed a SDR of 4.5%. Lengthy debate in academic circles over the appropriate SDR: Less polarized now, with majority of experts forming a “middle ground”; but there is still serious disagreement (Drupp et al., 2018) Policymakers’ disagreement is even larger, but is partially explained by the link between academics and policymakers (Groom & Hepburn, 2017)......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The Social Discount Rate (SDR): disagreement To illustrate with few numbers... Stern’s rate favors strong and immediate action on climate change mitigation; For sure benefit of 1000 CHF in 100 years: sacrifice up to 250 today. Nordhaus’ rate is more lenient towards climate change: “unambiguous conclusions about the need for extreme immediate action [do] not survive the substitution of assumptions that are consistent with today’s marketplace real interest rates and savings rates” Fore sure benefit of 1000 CHF in 100 years: sacrifice only 10 today......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The Social Discount Rate (SDR): disagreement To illustrate with few numbers... Stern’s rate favors strong and immediate action on climate change mitigation; For sure benefit of 1000 CHF in 100 years: sacrifice up to 250 today. Nordhaus’ rate is more lenient towards climate change: “unambiguous conclusions about the need for extreme immediate action [do] not survive the substitution of assumptions that are consistent with today’s marketplace real interest rates and savings rates” Fore sure benefit of 1000 CHF in 100 years: sacrifice only 10 today......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The Social Discount Rate (SDR): disagreement To illustrate with few numbers... Stern’s rate favors strong and immediate action on climate change mitigation; For sure benefit of 1000 CHF in 100 years: sacrifice up to 250 today. Nordhaus’ rate is more lenient towards climate change: “unambiguous conclusions about the need for extreme immediate action [do] not survive the substitution of assumptions that are consistent with today’s marketplace real interest rates and savings rates” Fore sure benefit of 1000 CHF in 100 years: sacrifice only 10 today......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The Social Discount Rate (SDR): more disagreement Some argue the SDR should be derived from: the use of the Simple Ramsey Rule; possibly, with extensions to uncertainty, risk, inequality, and limited substitutability of non-market goods. Others argue the SDR should be based on: market price approaches, or alternative societal criteria......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The Social Discount Rate (SDR): more disagreement Some argue the SDR should be derived from: the use of the Simple Ramsey Rule; possibly, with extensions to uncertainty, risk, inequality, and limited substitutability of non-market goods. Others argue the SDR should be based on: market price approaches, or alternative societal criteria......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The Social Discount Rate (SDR): in practice........................................ Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The social time preference approach: STP The Social Time Preference (STP) approach: Consumption-side approach in which the STP reflects the rate at which society is willing to trade-off consumption today for consumption tomorrow Numeraire: Consumption Other approaches exist, such as the production-side approach: it measures the social cost of public investment against the social cost of public funding (SOC) Numeraire: Investment Note: in a perfectly competitive equilibrium, the two coincide........................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The social time preference approach: STP The Social Time Preference (STP) approach: Consumption-side approach in which the STP reflects the rate at which society is willing to trade-off consumption today for consumption tomorrow Numeraire: Consumption Other approaches exist, such as the production-side approach: it measures the social cost of public investment against the social cost of public funding (SOC) Numeraire: Investment Note: in a perfectly competitive equilibrium, the two coincide........................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The social time preference approach: STP The Social Time Preference (STP) approach: Consumption-side approach in which the STP reflects the rate at which society is willing to trade-off consumption today for consumption tomorrow Numeraire: Consumption Other approaches exist, such as the production-side approach: it measures the social cost of public investment against the social cost of public funding (SOC) Numeraire: Investment Note: in a perfectly competitive equilibrium, the two coincide........................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The social welfare calibration of the STP In this case, social welfare is specified as: ∞ ! W (C0 , C1 ,...) = exp {−δt} U (Ct ) t=0 Suppose a potential project will create future benefits Bt at time t, so that consumption raises to Ct + Bt. The current social value of the project, p, can be interpreted as the social planner’s willingness-to-pay......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The social welfare calibration of the STP In this case, social welfare is specified as: ∞ ! W (C0 , C1 ,...) = exp {−δt} U (Ct ) t=0 Suppose a potential project will create future benefits Bt at time t, so that consumption raises to Ct + Bt. The current social value of the project, p, can be interpreted as the social planner’s willingness-to-pay......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The social welfare calibration of the STP In this case, social welfare is specified as: ∞ ! W (C0 , C1 ,...) = exp {−δt} U (Ct ) t=0 Suppose a potential project will create future benefits Bt at time t, so that consumption raises to Ct + Bt. The current social value of the project, p, can be interpreted as the social planner’s willingness-to-pay......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The social welfare calibration of the STP Simplification. Assume the utility function U is isoelastic: " 1−η Ct if η ̸= 1 U (Ct ) = 1−η ln Ct if η = 1 with elasticity η ≥ 0. Simplification. Assume the period-consumption growth rate is constant and equal to g......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The social welfare calibration of the STP Simplification. Assume the utility function U is isoelastic: " 1−η Ct if η ̸= 1 U (Ct ) = 1−η ln Ct if η = 1 with elasticity η ≥ 0. Simplification. Assume the period-consumption growth rate is constant and equal to g......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The social welfare calibration of the STP Then, ! p= Bt exp {−t (δ + ηg)}. t The Simple Ramsey Rule emerges (Ramsey, 1928); the SDR is SDR = δ + η · g. Problem: there is no consensus on how to calibrate these parameters......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The social welfare calibration of the STP Then, ! p= Bt exp {−t (δ + ηg)}. t The Simple Ramsey Rule emerges (Ramsey, 1928); the SDR is SDR = δ + η · g. Problem: there is no consensus on how to calibrate these parameters......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The social welfare calibration of the STP Then, ! p= Bt exp {−t (δ + ηg)}. t The Simple Ramsey Rule emerges (Ramsey, 1928); the SDR is SDR = δ + η · g. Problem: there is no consensus on how to calibrate these parameters......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The pure time discount factor δ What δ would you be comfortable with? Meta−ethical discussions of how to calibrate δ, following the Stern−Nordhaus debate: Positive: Individual patience or altruism (>0%) Normative: Societal weights on future utilities (=0%) Agent-relative ethics: extinction risk (>0%)........................................ Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The pure time discount factor δ What δ would you be comfortable with? Meta−ethical discussions of how to calibrate δ, following the Stern−Nordhaus debate: Positive: Individual patience or altruism (>0%) Normative: Societal weights on future utilities (=0%) Agent-relative ethics: extinction risk (>0%)........................................ Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The wealth effect η · g The wealth effect, η · g, captures the fact that, because of the concavity of the utility function U, the wealthier the future is expected to be (higher g), and the more averse society is to consumption inequality across time (higher η), the less value will be placed on projects that pay off in the future! In applications, the wealth effect dominates the pure time preferences effect!........................................ Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The wealth effect η · g The wealth effect, η · g, captures the fact that, because of the concavity of the utility function U, the wealthier the future is expected to be (higher g), and the more averse society is to consumption inequality across time (higher η), the less value will be placed on projects that pay off in the future! In applications, the wealth effect dominates the pure time preferences effect!........................................ Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The social welfare calibration of the STP: risk? The Extended Ramsey Rule (see Gollier, 2013) enriches the SDR as follows: SDR = δ + η · g −.5η (η + 1) σ 2 , where σ 2 is the variance of the growth rate. In applications, the risk effect is still an order of magnitude smaller than the wealth effect (σ =.3 implies σ 2 =.09!) and has little impact on the SDR. In fact, it is often disregarded in the calibration......................................... Paolo G. Piacquadio Intergenerational Fairness  Chapter 2 of Stern Review Derivation of the SDR Discounting The social welfare calibration of the STP: risk? The Extended Ramsey Rule (see Gollier, 2013) enriches the SDR as follows: SDR = δ + η · g −.5η (η + 1) σ 2 , where σ 2 is the variance of the growth rate. In applications, the risk effect is still an order of magnitude smaller than the wealth effect (σ =.3 implies σ 2 =.09!) and has little impact on the SDR. In fact, it is often disregarded in the calibration......................................... Paolo G. Piacquadio Intergenerational Fairness