Lecture 5 Intergenerational Fairness PDF

Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Lectur...

Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Lecture 5. Intergenerational Fairness Ethics of Risk Risk and justice Framework Expected utilitarianism Ex-ante and ex-post Paolo G. Piacquadio1 utilitarianism Risk and time 1 Institute of Economics, University of St. Gallen St. Gallen, 18th October, 2024  Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Ethics of Risk Risk and justice Framework Expected utilitarianism Discussion of The Ethics of Risk Ex-ante and ex-post utilitarianism Risk and time Comments Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Ethics of Risk I Risk and justice I Framework Expected utilitarianism Ex-ante and ex-post I utilitarianism Risk and time I I I I Comments Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Ethics of Risk I Risk and justice I Framework Expected utilitarianism Ex-ante and ex-post I utilitarianism Risk and time I I I I  Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Ethics of Risk Risk and justice Framework Risk and justice Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Notation Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The I There are I individuals and S states of the world, Ethics of Risk P Risk and justice I each state s has probability ⇡ s 2 [0, 1] and such that s ⇡s = 1 Framework Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Notation Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The I There are I individuals and S states of the world, Ethics of Risk P Risk and justice I each state s has probability ⇡ s 2 [0, 1] and such that s ⇡s = 1 Framework Expected utilitarianism Ex-ante and ex-post utilitarianism I A risky income distribution is: Risk and time 2 3 y11 ··· y1S y = 4....... 7. 6.. 5 yI1 ··· yIS  Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Ethics of Risk Risk and justice Framework Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  How to assess risky income distributions? Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Difficulties: Discussion of The Ethics of Risk I matrix of incomes + vector of probabilities = a lot of information to summarize! Risk and justice Framework Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  How to assess risky income distributions? Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Difficulties: Discussion of The Ethics of Risk I matrix of incomes + vector of probabilities = a lot of information to summarize! Risk and justice Framework Expected utilitarianism Ex-ante and ex-post I individuals might have preferences over income lotteries; utilitarianism Risk and time I should social preferences agree with individuals?  How to assess risky income distributions? Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Difficulties: Discussion of The Ethics of Risk I matrix of incomes + vector of probabilities = a lot of information to summarize! Risk and justice Framework Expected utilitarianism Ex-ante and ex-post I individuals might have preferences over income lotteries; utilitarianism Risk and time I should social preferences agree with individuals? I Time is an essential aspect of risk! I Before (risk is resolved), after (risk is resolved).  How to assess risky income distributions? Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Difficulties: Discussion of The Ethics of Risk I matrix of incomes + vector of probabilities = a lot of information to summarize! Risk and justice Framework Expected utilitarianism Ex-ante and ex-post I individuals might have preferences over income lotteries; utilitarianism Risk and time I should social preferences agree with individuals? I Time is an essential aspect of risk! I Before (risk is resolved), after (risk is resolved). I Information is also fundamental. I Are individuals aware of the risk?  Standard approach Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Assumption 1: I [individual rationality] individuals preferences admit an expected utility Discussion of The Ethics of Risk representation: X Risk and justice Ui (yi ) = ⇡s ui (yis ). Framework Expected utilitarianism s Ex-ante and ex-post utilitarianism Risk and time  Standard approach Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Assumption 1: I [individual rationality] individuals preferences admit an expected utility Discussion of The Ethics of Risk representation: X Risk and justice Ui (yi ) = ⇡s ui (yis ). Framework Expected utilitarianism s Ex-ante and ex-post utilitarianism I Assumption 2: Risk and time I [social rationality] social preferences admit an expected utility representation: X W (y ) = ⇡s w (y s ). s  Standard approach Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Assumption 1: I [individual rationality] individuals preferences admit an expected utility Discussion of The Ethics of Risk representation: X Risk and justice Ui (yi ) = ⇡s ui (yis ). Framework Expected utilitarianism s Ex-ante and ex-post utilitarianism I Assumption 2: Risk and time I [social rationality] social preferences admit an expected utility representation: X W (y ) = ⇡s w (y s ). s I Assumption 3: I Pareto efficiency: if individuals are better off, social welfare is larger  Expected utilitarianism: result Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Theorem: Assumptions 1-3 imply that Discussion of The Ethics of Risk X X X Risk and justice W (y ) = Ui (yi ) = ⇡s ui (yis ) Framework s Expected utilitarianism i i Ex-ante and ex-post utilitarianism Risk and time  Expected utilitarianism: result Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Theorem: Assumptions 1-3 imply that Discussion of The Ethics of Risk X X X Risk and justice W (y ) = Ui (yi ) = ⇡s ui (yis ) Framework s Expected utilitarianism i i Ex-ante and ex-post utilitarianism Risk and time I Social welfare is: I the sum of individuals’ expected utilities, or I the expectation of the social welfare in each state (i.e., the sum of the utilities of individuals in that state).  Expected utilitarianism: result Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Theorem: Assumptions 1-3 imply that Discussion of The Ethics of Risk X X X Risk and justice W (y ) = Ui (yi ) = ⇡s ui (yis ) Framework s Expected utilitarianism i i Ex-ante and ex-post utilitarianism Risk and time I Social welfare is: I the sum of individuals’ expected utilities, or I the expectation of the social welfare in each state (i.e., the sum of the utilities of individuals in that state). I This result is Harsanyi’s (1955) aggregation theorem.  Expected utilitarianism: pros and cons Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Ethics of Risk I Pros: Risk and justice Framework I simple, intuitive, powerful. Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Expected utilitarianism: pros and cons Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Ethics of Risk I Pros: Risk and justice Framework I simple, intuitive, powerful. Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time I Cons: I inequality aversion is given by individuals’ risk aversion; I indifference to the distribution of utilities across states and individuals; I no role for the timing of resolution of risk.  Inequality aversion and risk aversion Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Suppose individuals’ utility is (constant relative risk aversion) Discussion of The Ethics of Risk X X (yis )1 Risk and justice U= ⇡s u (yis ) = ⇡s Framework s s 1 Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time with risk aversion.  Inequality aversion and risk aversion Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Suppose individuals’ utility is (constant relative risk aversion) Discussion of The Ethics of Risk X X (yis )1 Risk and justice U= ⇡s u (yis ) = ⇡s Framework s s 1 Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time with risk aversion. I Expected utilitarianism requires inequality aversion to be exactly !  Inequality aversion and risk aversion Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Suppose individuals’ utility is (constant relative risk aversion) Discussion of The Ethics of Risk X X (yis )1 Risk and justice U= ⇡s u (yis ) = ⇡s Framework s s 1 Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time with risk aversion. I Expected utilitarianism requires inequality aversion to be exactly ! I Why should social inequality aversion equal individual’s willingness to avoid risks?  Inequality aversion and risk aversion Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Ethics of Risk Risk and justice I This is an implication of the theorem. Framework Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Inequality aversion and risk aversion Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Ethics of Risk Risk and justice I This is an implication of the theorem. Framework Expected utilitarianism Ex-ante and ex-post utilitarianism I To avoid it, there are three options: Risk and time I drop individual rationality; or I drop social rationality; or I drop Pareto efficiency.  Expected utilitarianism Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Consider the following lotteries. Discussion of The Ethics of Risk I Expected utilitarianism is insensitive to the distribution of utilities across Risk and justice individuals and equally-likely states. Framework Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Beyond expected utilitarianism Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I In some situations, however, society might be concerned with ex-ante Discussion of The Ethics of Risk egalitarianism and prefer to give equal chances to two individuals Risk and justice (Diamond, 1967). Then, (II) is better than (I). Framework Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Beyond expected utilitarianism Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I In other situations, instead, society might be concerned with ex-post Discussion of The fairness and prefer to give the same outcome to both with 50% probability, Ethics of Risk Risk and justice than randomizing among who gets the prize (Broome, 1984). Then, (III) is Framework better than (II). Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Expected, ex-ante, and ex-post Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Ethics of Risk I Ex-ante and ex-post concerns can be captured, but not jointly! Risk and justice Framework I (One can argue that expected utilitarianism is a middle ground.) Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Expected, ex-ante, and ex-post Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Ethics of Risk I Ex-ante and ex-post concerns can be captured, but not jointly! Risk and justice Framework I (One can argue that expected utilitarianism is a middle ground.) Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time I Ex-ante utilitarianism satisfies Pareto efficiency and violates “social rationality”. I Ex-post utilitarianism satisfies social rationality and violates Pareto efficiency.  Ex-ante vs ex-post utilitarianism Lecture 5. Intergenerational Fairness I Ex-ante utilitarianism: Paolo G. Piacquadio X ea W (y ) = f (ui (yi )) , Discussion of The i Ethics of Risk Risk and justice where f is a concave function expressing aversion for inequality of Framework individuals’ expected utility. Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Ex-ante vs ex-post utilitarianism Lecture 5. Intergenerational Fairness I Ex-ante utilitarianism: Paolo G. Piacquadio X ea W (y ) = f (ui (yi )) , Discussion of The i Ethics of Risk Risk and justice where f is a concave function expressing aversion for inequality of Framework individuals’ expected utility. Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time I Ex-post utilitarianism: X X ep W (y ) = ⇡s g (ui (yis )) , s i where g is a concave function expressing aversion for inequality of individuals utilities in a state.  Ex-ante vs ex-post utilitarianism Lecture 5. Intergenerational Fairness I Ex-ante utilitarianism: Paolo G. Piacquadio X ea W (y ) = f (ui (yi )) , Discussion of The i Ethics of Risk Risk and justice where f is a concave function expressing aversion for inequality of Framework individuals’ expected utility. Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time I Ex-post utilitarianism: X X ep W (y ) = ⇡s g (ui (yis )) , s i where g is a concave function expressing aversion for inequality of individuals utilities in a state. I Expected utilitarianism is the special case when f and g are the identity function.  Introduction Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The I The standard approach is to add the expectation to the standard Ethics of Risk exponentially discounted utilitarian criterion. Risk and justice Framework Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Introduction Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The I The standard approach is to add the expectation to the standard Ethics of Risk exponentially discounted utilitarian criterion. Risk and justice Framework Expected utilitarianism Ex-ante and ex-post utilitarianism I Yet, it is not clear this is an appropriate choice. Risk and time  Introduction Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The I The standard approach is to add the expectation to the standard Ethics of Risk exponentially discounted utilitarian criterion. Risk and justice Framework Expected utilitarianism Ex-ante and ex-post utilitarianism I Yet, it is not clear this is an appropriate choice. Risk and time I Issues: I the timing of resolution of risk is disregarded; I there are no “risk preferences” to be aggregated; I how to consider extinction?  Equality with risk and time? Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Ethics of Risk Risk and justice I A strong underlying assumption is that one should eliminate inequalities. Framework Expected utilitarianism I But what are inequalities in this context? Ex-ante and ex-post utilitarianism Risk and time  Equality with risk and time? Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The Ethics of Risk Risk and justice I A strong underlying assumption is that one should eliminate inequalities. Framework Expected utilitarianism I But what are inequalities in this context? Ex-ante and ex-post utilitarianism Risk and time I Equality without risk is trivial... I...but what is equality with risk when later generations have different risk?  Equality with risk and time? Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Earlier generations are different than later ones! Discussion of The Ethics of Risk Risk and justice Framework Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Equality with risk and time? Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The I If equality is impossible, what is equitable? Ethics of Risk Risk and justice Framework Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Equality with risk and time? Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The I If equality is impossible, what is equitable? Ethics of Risk Risk and justice Framework I When future technology is risky, some precautionary saving might be in Expected utilitarianism Ex-ante and ex-post order. utilitarianism Risk and time I How much is an ethical choice.  Equality with risk and time? Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The I If equality is impossible, what is equitable? Ethics of Risk Risk and justice Framework I When future technology is risky, some precautionary saving might be in Expected utilitarianism Ex-ante and ex-post order. utilitarianism Risk and time I How much is an ethical choice. I An allocation of consumption is equitable if at any point in time, the consumption is socially as desirable as the risky consumption of a later generation.  Equitable consumption: an optimum? Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The I Consider the equitable consumption that allocates all resources. Is it the Ethics of Risk best distribution? Risk and justice Framework Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Equitable consumption: an optimum? Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The I Consider the equitable consumption that allocates all resources. Is it the Ethics of Risk best distribution? Risk and justice Framework Expected utilitarianism Ex-ante and ex-post I Generally no. utilitarianism Risk and time I It is equitable, but one might believe that small deviations could be acceptable if these bring about enough efficiency gains.  Equitable consumption: an optimum? Lecture 5. Intergenerational Fairness Paolo G. Piacquadio Discussion of The I Consider the equitable consumption that allocates all resources. Is it the Ethics of Risk best distribution? Risk and justice Framework Expected utilitarianism Ex-ante and ex-post I Generally no. utilitarianism Risk and time I It is equitable, but one might believe that small deviations could be acceptable if these bring about enough efficiency gains. I How to manage the tradeoff between “deviations from equitable consumption” and “efficiency”?  Ex-ante equity Lecture 5. Intergenerational Fairness I In Piacquadio (2020), I introduce two axioms. Paolo G. Piacquadio Discussion of The Ethics of Risk Risk and justice Framework Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Ex-ante equity Lecture 5. Intergenerational Fairness I In Piacquadio (2020), I introduce two axioms. Paolo G. Piacquadio I Ex-ante equity tells that the equitable (r0 , r1 ) is socially at least as desirable Discussion of The as (x0 , x1 ): Ethics of Risk I there is less inequity between the two generations at (r0 , r1 ) than at (x0 , x1 ). Risk and justice Framework Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Ex-post equity Lecture 5. Intergenerational Fairness Paolo I Ex-post equity tells that the equitable (r0 , r1 ) is socially at least as desirable G. Piacquadio as (x0 , x1 ): Discussion of The I inequity is less likely for generation 1 at (r0 , r1 ) than at (x0 , x1 ). Ethics of Risk Risk and justice Framework Expected utilitarianism Ex-ante and ex-post utilitarianism Risk and time  Main result Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Reference-dependent utilitarianism: " Discussion of The ✓ ◆# Ethics of Risk X xt W r (y ) = E ⇡t rt v , Risk and justice t rt Framework Expected utilitarianism Ex-ante and ex-post where v is a concave function expressing aversion to inequities and r is the utilitarianism Risk and time equitable reference.  Main result Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Reference-dependent utilitarianism: " Discussion of The ✓ ◆# Ethics of Risk X xt W r (y ) = E ⇡t rt v , Risk and justice t rt Framework Expected utilitarianism Ex-ante and ex-post where v is a concave function expressing aversion to inequities and r is the utilitarianism Risk and time equitable reference. I Discounting is endogenous: I higher risk of extinction ) more discounting; I more future risk ) less discounting.  Main result Lecture 5. Intergenerational Fairness Paolo G. Piacquadio I Reference-dependent utilitarianism: " Discussion of The ✓ ◆# Ethics of Risk X xt W r (y ) = E ⇡t rt v , Risk and justice t rt Framework Expected utilitarianism Ex-ante and ex-post where v is a concave function expressing aversion to inequities and r is the utilitarianism Risk and time equitable reference. I Discounting is endogenous: I higher risk of extinction ) more discounting; I more future risk ) less discounting. I Expected utilitarianism is the special case when r is constant.