Podcast
Questions and Answers
What does the Social Discount Rate (SDR) represent?
What does the Social Discount Rate (SDR) represent?
- The rate at which benefits and losses are traded off across time (correct)
- The annual growth rate of consumption
- The total utility gained from consumption
- The level of inequality in a society
In the formula for Social Discount Rate (SDR), what does 'g' signify?
In the formula for Social Discount Rate (SDR), what does 'g' signify?
- The growth rate of consumption (correct)
- The rate of inflation affecting consumption
- The discount rate applied to future consumption
- The level of future utility expected
What are the two main components that influence the Social Discount Rate (SDR)?
What are the two main components that influence the Social Discount Rate (SDR)?
- g and U(Ct)
- δ and g (correct)
- δ and η
- η and U(Ct)
Why is there disagreement regarding the parameters used in the Social Discount Rate?
Why is there disagreement regarding the parameters used in the Social Discount Rate?
What does the variable δ represent in the Social Discount Rate formula?
What does the variable δ represent in the Social Discount Rate formula?
Which value of 'η' is the minimum required in the utility function U(Ct) = $\frac{C_t^{1-η}}{1-η}$?
Which value of 'η' is the minimum required in the utility function U(Ct) = $\frac{C_t^{1-η}}{1-η}$?
What does the term 'intergenerational fairness' imply in the context of discounting?
What does the term 'intergenerational fairness' imply in the context of discounting?
Which of the following best describes the standard exponentially discounted utilitarian criterion?
Which of the following best describes the standard exponentially discounted utilitarian criterion?
What does the author suggest about the interests of posterity in relation to a Utilitarian's perspective?
What does the author suggest about the interests of posterity in relation to a Utilitarian's perspective?
According to Ramsey (1928), what is ethically indefensible?
According to Ramsey (1928), what is ethically indefensible?
What was Arrow's key consideration regarding output in his changed view on discounting?
What was Arrow's key consideration regarding output in his changed view on discounting?
What is the general stance of the author towards discounting future enjoyments?
What is the general stance of the author towards discounting future enjoyments?
What aspect of humanity's existence affects a man's happiness, according to the content?
What aspect of humanity's existence affects a man's happiness, according to the content?
Which of the following describes Sidgwick's stance as interpreted by Ramsey?
Which of the following describes Sidgwick's stance as interpreted by Ramsey?
What general topic do the phrases 'Discounting: ethically defensible?' and 'Alternative discounting functions' address?
What general topic do the phrases 'Discounting: ethically defensible?' and 'Alternative discounting functions' address?
What issue does the ongoing debate about discounting primarily revolve around?
What issue does the ongoing debate about discounting primarily revolve around?
What does time inconsistency in social welfare imply?
What does time inconsistency in social welfare imply?
What is a characteristic of a 'smart' planner regarding time inconsistency?
What is a characteristic of a 'smart' planner regarding time inconsistency?
What does a 'modular' theory of intergenerational justice allow for?
What does a 'modular' theory of intergenerational justice allow for?
Which of the following statements is true about discounting in relation to inequality?
Which of the following statements is true about discounting in relation to inequality?
Which approach helps clarify policy implications concerning social welfare?
Which approach helps clarify policy implications concerning social welfare?
What might be a consequence of using a non-exponential discounting function?
What might be a consequence of using a non-exponential discounting function?
What do specific conditions in intergenerational justice allow for?
What do specific conditions in intergenerational justice allow for?
In the context of intergenerational fairness, what is an effect of discounting?
In the context of intergenerational fairness, what is an effect of discounting?
What is the primary purpose of the aggregator function V?
What is the primary purpose of the aggregator function V?
How is the aggregator function V defined mathematically?
How is the aggregator function V defined mathematically?
What characteristic does the aggregator function V possess according to equivalent time definition?
What characteristic does the aggregator function V possess according to equivalent time definition?
Which of the following is NOT an example of a standard social welfare function mentioned?
Which of the following is NOT an example of a standard social welfare function mentioned?
What does the function W represent in the context of the aggregator function?
What does the function W represent in the context of the aggregator function?
In which context is the aggregator function V introduced?
In which context is the aggregator function V introduced?
What is implied about the relationship between time-discounting and equivalent time representation?
What is implied about the relationship between time-discounting and equivalent time representation?
Which term best describes the nature of the aggregator function V?
Which term best describes the nature of the aggregator function V?
What phenomenon is used to model individuals' behavior regarding future rewards?
What phenomenon is used to model individuals' behavior regarding future rewards?
According to Thaler's findings, which amount is preferred immediately over a delayed reward?
According to Thaler's findings, which amount is preferred immediately over a delayed reward?
What is the trend observed in annual discount rates as delays increase, according to Thaler's findings?
What is the trend observed in annual discount rates as delays increase, according to Thaler's findings?
What is the discount rate when an individual is indifferent between $60 after 1 year?
What is the discount rate when an individual is indifferent between $60 after 1 year?
How much does an individual weigh an immediate reward compared to a reward delayed by 3 years?
How much does an individual weigh an immediate reward compared to a reward delayed by 3 years?
What type of discounting shows a declining rate as the time for reward increases?
What type of discounting shows a declining rate as the time for reward increases?
What reward amount is presented after 1 year in Thaler's analysis?
What reward amount is presented after 1 year in Thaler's analysis?
What is the annual discount rate when an individual considers $30 after 3 months?
What is the annual discount rate when an individual considers $30 after 3 months?
What conclusion does Arrow reach regarding the optimal saving rate in the absence of impatience?
What conclusion does Arrow reach regarding the optimal saving rate in the absence of impatience?
What does Koopmans argue about preference ordering over infinite-dimensional consumption streams?
What does Koopmans argue about preference ordering over infinite-dimensional consumption streams?
What ethical concern does Arrow bring into the debate on discounting?
What ethical concern does Arrow bring into the debate on discounting?
Which aspect of investment does Arrow highlight when discussing the first generation's opportunity?
Which aspect of investment does Arrow highlight when discussing the first generation's opportunity?
According to Arrow, what happens when time preference is absent?
According to Arrow, what happens when time preference is absent?
What position did Arrow change regarding discounting due to his analysis?
What position did Arrow change regarding discounting due to his analysis?
What does Arrow imply regarding the relationship between impatience and investment?
What does Arrow imply regarding the relationship between impatience and investment?
What is indicated by the concept of intergenerational fairness in Arrow's discussion?
What is indicated by the concept of intergenerational fairness in Arrow's discussion?
Flashcards
Universal Happiness
Universal Happiness
The concept that the timing of someone's existence shouldn't affect the value of their happiness from a universal standpoint.
Intergenerational Fairness
Intergenerational Fairness
The principle that future generations deserve our concern just as much as individuals living today, considering the potential impact of our actions on them.
Discounting
Discounting
The process of reducing the value of future benefits or costs compared to present ones.
Ethical Indefensibility of Discounting
Ethical Indefensibility of Discounting
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Uncertain Future
Uncertain Future
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Pragmatic Justification for Discounting
Pragmatic Justification for Discounting
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Perishable Output
Perishable Output
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Ethical and Practical Discounting
Ethical and Practical Discounting
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Social Discount Rate (SDR)
Social Discount Rate (SDR)
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Exponentially Discounted Utilitarian Criterion
Exponentially Discounted Utilitarian Criterion
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Growth Rate of Consumption (g)
Growth Rate of Consumption (g)
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Discount Rate (δ)
Discount Rate (δ)
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Inequality Aversion (η)
Inequality Aversion (η)
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Ramsey Rule
Ramsey Rule
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Parameter Selection in Intergenerational Fairness
Parameter Selection in Intergenerational Fairness
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Current Debates in Intergenerational Fairness
Current Debates in Intergenerational Fairness
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Impatience in Economics
Impatience in Economics
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Investment with Perpetual Benefits
Investment with Perpetual Benefits
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Discount Rate
Discount Rate
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Preference Ordering
Preference Ordering
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Sensitive Preference Ordering
Sensitive Preference Ordering
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Continuous Preference Ordering
Continuous Preference Ordering
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Koopmans' Argument for Impatience
Koopmans' Argument for Impatience
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Arrow's Conclusion on Discounting
Arrow's Conclusion on Discounting
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Hyperbolic Discounting
Hyperbolic Discounting
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Indifference Point
Indifference Point
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Thaler's Finding
Thaler's Finding
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Present Value Analysis
Present Value Analysis
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Cost-Benefit Analysis
Cost-Benefit Analysis
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Technological Optimism
Technological Optimism
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Time Consistency
Time Consistency
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Time Inconsistency Problem
Time Inconsistency Problem
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Modular Social Welfare Function
Modular Social Welfare Function
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Disentangling Discounting and Inequality
Disentangling Discounting and Inequality
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Modular Theory of Intergenerational Justice
Modular Theory of Intergenerational Justice
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Key Advantage of Modular Theory
Key Advantage of Modular Theory
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Social Discount Rate
Social Discount Rate
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Aggregator function
Aggregator function
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Time-discounting function
Time-discounting function
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Equivalent time representation
Equivalent time representation
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Additive social welfare function
Additive social welfare function
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Rank-weighted social welfare function
Rank-weighted social welfare function
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Rank-dependent social welfare function
Rank-dependent social welfare function
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Study Notes
Intergenerational Fairness - Lecture 4
- Lecture was on October 16, 2024
- Topics included discounting, inequality, and intergenerational fairness.
- Recap of discounting was given.
- The Social Discount Rate (SDR) is the rate at which benefits and losses are traded off across time.
- The standard exponentially discounted utilitarian criterion is used;
W(Co, C1, ...) = ∑ exp {-t} U(Ct) where U(Ct) = C¹⁻ⁿ / (1-η) for η ≥ 0. - The SDR is given by the Ramsey rule: SDR = δ + ng, where g is the growth rate of consumption.
- δ is about discounting; and ng is about inequality.
- There is disagreement on how to define and use these parameters.
- Several open questions are posed: Why exponential discounting? What are the alternatives? Why the weighted sum of CES utilities? What are the alternatives? How restrictive is thinking in terms of discounting and inequality?
Discounting - Ethical and Defensible?
- Most philosophers oppose discounting, but economists often use it.
- Sidgwick argued that the time a person exists doesn't affect the value of their happiness
- Ramsey agreed with Sidgwick but later included a rate of discount in his analyses.
- Arrow (1999) changed his view, concluding that without impatience, the optimal saving rate could approach 100%.
- Koopmans considered an infinite world and concluded that ethically-based choice requires a preference ordering and needs impatience in infinite consumption streams.
Discounting: A Justification
- The strongest justifications for discounting in general and exponentially-discounted utilitarianism are Koopmans (1960) and Diamond (1965).
- Diamond (1965) showed there is no social welfare function that satisfies efficiency, more consumption is better, and finite anonymity.
Koopmans (1960)
- Koopmans used an axiomatic approach to rank consumption streams.
- Koopmans derived utility functions for each generation and the constant discount factor from a planner's preferences.
- He proposed five postulates to establish the social welfare function.
Koopmans' Postulates
- Continuity: Small variations in consumption streams do not drastically change social welfare.
- Sensitivity: The level of consumption in the first period matters.
- Non-complementarity: Future assessments are independent of the present, and vice versa.
- Stationarity: Ranking of consumption streams is independent of the starting point in time.
- Boundedness: Growing consumption streams cannot be unambiguously better/worse than any constant stream.
Koopmans' Result
-
A social welfare function that satisfies these postulates can be expressed as: W(C) = ∑ β³ U(Ct)
-
β∈ (0,1) and U is a continuous and strictly increasing function.
Discussion
- The equivalence result of Koopmans' postulates is strong, meaning any disagreement with the result requires disagreement with some postulate(s).
- Each postulate should be critically assessed, as some may seem restrictive.
- Stationarity and non-complementarity are particularly controversial postulates.
Alternative Discounting Functions
- Hyperbolic discounting is suggested to model individual behavior.
- Thaler (1981) showed that individuals are indifferent between smaller immediate rewards and larger rewards further in the future.
- This indicates that annual discount rates decrease.
Quasi-Hyperbolic Discounting (Laibson, 1997)
- Quasi-hyperbolic discounting describes discounting with a different rate for immediate vs later periods.
- When β=1 exponentially discounted utilitarianism emerges.
- When β<1, there is first-period discounting, but discounting weakens as time extends.
- Non-exponential discounting functions violate time consistency, which requires that a better option should remain better regardless of the time frame.
Inequality Versus Discounting
- A recent work with Frikk Nesje shows how social welfare functions can disentangle discounting from inequality.
- Under specific conditions, attitudes towards discounting are orthogonal to attitudes towards inequality.
- This "modular" theory offers many new criteria and policy implications.
The Disentanglement
- Transforming consumption streams from calendar time to equivalent time is crucial.
- Duration of each generation is adjusted to create a common moral value for consumption at each point in time.
- This allows use of any standard aggregation function.
Consumption Streams
- Consumption streams are functions from time into the positive reals.
- The set of possible consumption streams is denoted by C.
- A theory of intergenerational justice is described by a social welfare function W: C → R⁺.
Time-Discounting Function
- Time is expressed in calendar time, but can be represented on the unit interval.
- A continuous and strictly increasing function transforms calendar time into a comparable scale.
The Aggregator Function
- Given a social welfare function and a time discounting function , a complete aggregator function can be defined.
- This aggregator function can use different standard social welfare functions depending on the desired criteria.
The Modular Social Welfare Function
- A modular social welfare function is one in which consumption streams can be represented in equivalent time, with a resulting aggregator function (v) dependent on both a time discounting function and another independent welfare function (W).
- All common welfare criteria are modular.
Some Modular Theories
- There is a table of various representations of common modular models in economics for intergenerational justice.
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