Agenda Monday -Discounting -Hand in pset (what was your calculation of SCC?) Wednesday -Complete discussion of Integrated Assessment Models and RICE-2010 model Friday -Open discussion Next week: - Uncertainty, learning, fat tails

Discounting in economics: The fundamental determinants Economics 331b 2

The choice set 3 Consider a dynamic path for important variables. This should consider a wide range of important variables for different people or generations. Market consumption, non-market consumption, public goods, environmental goods, …

For example, work of John Roemer et al.* 4 A quality of life function with consumption, environment, etc.: (i)Consumption of goods and services (c); (ii)Educated leisure (x); (iii) “Education, which modifies the value of leisure time to the individual; (iv) “Knowledge, in the form of society’s stock of culture and science, which directly increases the value of life (in addition to any indirect effects through productivity), via improvements in health and life expectancy, and because an understanding of how the world works and an appreciation of culture are intrinsic to human well-being (S n ), (v) “An undegraded biosphere, which is valuable to humans for its direct impact on physical and mental health (S m ).” Welfare function takes the form QuoL = *Humberto Llavador, John E. Roemer, Joaquim Silvestre, "A Dynamic Analysis of Human Welfare in a Warming Planet“

This leads to the problem of how to rank paths 5

Start with a consumption (or QuoL) path c 1 (t) time For this, assume that: 1.c is per capita consumption or Roemer’s QuoL 2.Population is constant

Which is the preferable path, c1 or c2? c 1 (t) c 2 (t) time For this, assume that: 1.c is per capita consumption or Roemer’s QuoL 2.Population is constant

Which is the preferable path? c 1 (t) c 2 (t) time For this, assume that: 1.c is per capita consumption or Roemer’s QuoL 2.Population is constant

Which is the preferable path? c 1 (t) c 2 (t) time

Philosophical-ethical foundations of environmental economics Modern economics of welfarism (as in social welfare function): Bergson, Samuelson, Foundations Paretianism: An incomplete ordering of social states based on welfarism used throughout economics Critiques of Utilitarianism, conequentialism, and welfarism: Ordinalists: cannot measure utility Positivism: ethics as esthetics J. Rawls, Theory of Justice: emphasis on equality and justice Amartya Sen, emphasis on capabilities and equity

The optimal growth setup with exogenous technological change 11

The solution In optimal economic growth, we choose the path of K(t) (alternatively, the savings rate) to maximize the utility of future consumption. Here is the semi-technical version (this is in the spirit of the calculus of variations). “Splish splash” optimal growth experiment: Suppose that we invest in period t with a return in period (t+θ). An investment is a withdrawal from consumption of Δ, with the return being an increase in consumption with real rate of return r. The fundamentals are the following (with no population growth): (8) (9)

Splish-splash 13

So the solution for the change in total welfare is:

To add population growth, we change the objective function to the following: If population growth is constant at rate n, we see that the new Ramsey equation is: (12) More… 15

Key distinction, often confused Utility discount rate (pure rate of social time preference), ρ: This refers to the comparison of well-being or utilities over time, space, or generations. Goods discount rate (tradeoff in markets), r: This refers to the return on private or social investments in goods, services, etc.

More… The debate on discounting generally will use the framework of the Ramsey model. Begin with the Ramsey equation from (12) above: This shows the relationship between the equilibrium real interest rate and underlying parameters. Observables: r = real interest rate or real return on capital g = rate of growth of real consumption per capita Non-observables:

Two schools of discounting theory What real interest rate on goods shall we actually use for discounting costs and benefits of long-term investments (climate, radioactive wastes, dams, technology,…)? Descriptive: Argues that we can observe the rate of return and should make sure that our decisions are consistent with opportunity cost on other investments. This leads to a relatively high utility discount rate (Feldstein, Eckstein, Lind, Nordhaus): Prescriptive: Argues that we can know the normative parameters on philosophical grounds and derive the interest rate from that (Cline, Stern):

Why this is so important in climate-change analysis: Damages are so late in the game. Numerical example of effect over 200 years

Why this is so important in climate-change analysis: Damages are so late in the game. Numerical example of effect over 200 years

Problems with each Major criticism of descriptive is that a positive ρ is unethical and violates intergenerational fairness. (Good point) Major criticism of prescriptive is that it leads to distorted investment decisions because actual return on investment is much higher than the prescriptive discount rate. (Good point) Is there any way to reconcile all this?

Two polar cases The standard descriptive model uses market rates of return (circa 5-6 percent per year for goods and services). Assume g = 2 % per year In the Ramsey framework, this can be interpreted as a solution of the following equation: 5.5 = ρ + α 2 We take the solution of ρ = 1.5 and α = 2. The prescriptive approach (Cline, Stern) argues that it is ethically indefensible to have generational discounting. Stern also assumes that α = 1. With their assumed g = 1.4 % per year, this yields: r = (1.4) = 1.5 % per year

Conclusions on discounting Remember the ethical foundations. A key question is whether you take the mixed-market solution (prices) as a constraint on decisions; or whether you want to argue that the preferences as revealed (by market prices) in the market are wrong. In the ethical/prescriptive view, the goods discount rate should be determined by both time discounting and view on income distribution over time. These issues are particularly important for very long-run decisions (global warming, radioactive wastes, …). The arguments also involve questions such as market imperfections, taxes, the equity premium – very technical issues. What does the jury say? HUNG JURY.