Lecture 12

Evaluating Trade-Offs: Benefit–Cost Analysis and Other Decision-Making Metrics

Byeong-Hak Choe

bchoe@geneseo.edu

SUNY Geneseo

September 25, 2024

Benefit–Cost Analysis and Other Decision-Making Metrics

The Treatment of Risk

Understanding Risk in Environmental Policy

• Uncertainty in Outcomes:
  • Policies may have uncertain impacts due to unknown future conditions.
  • Timing and extent of environmental damages are often uncertain.
• Implications:
  • Benefits of risk reduction depend on these uncertain factors.

The Treatment of Risk

Evaluating Risk in Benefit-Cost Analysis

• Policy Choices and Outcomes:
  • Different policies can lead to various possible outcomes.
• Challenge:
  • Difficult to choose the best policy without knowing future outcomes.

The Treatment of Risk

Evaluating Risk in Benefit-Cost Analysis

• Dominant Policy:
  • Maximizes net benefits across all outcomes.
  • Rare in practice, so risk must be considered in decision-making.

The Treatment of Risk

Expected Present Value of Net Benefits (EPVNB)

\[ EPVNB_{j} \,=\, \sum_{i=0}^{I}\, P_{i} \times PVNB_{ij} \]

• EPVNB: the sum of the present value of net benefits for each outcome, weighted by its probability
  • \(EPVNB_j\): expected present value of net benefits for policy \(j\)
  • \(P_i\): probability of the \(i\)-th outcome occurring
  • \(PVNB_{ij}\): present value of net benefits for policy \(j\) if outcome \(i\) prevails
  • \(J\) = number of policies being considered
  • \(I\) = number of outcomes being considered

The Treatment of Risk

Risk-Aversion

• A lottery is a probability distribution over the set of events.

• Lottery Example:

  • Option 1: Receive $50 for sure.
  • Option 2: 50% chance of $100, 50% chance of $0.

• Risk Preferences:

  • Risk-Averse: Prefer the certain $50.
  • Risk-Loving: Prefer the gamble, hoping to get the $100.
  • Risk-Neutral: Indifferent between the two options.

The Treatment of Risk

Society’s Risk Preferences

• Assumption in EPVNB:
  • Assumes society is risk-neutral.
• Evidence:
  • Mixed behaviors indicate both risk-averse and risk-loving tendencies.
• Policy Implication:
  • Arrow & Lind suggest public investments can assume risk-neutrality due to risk sharing.

The Treatment of Risk

Complex Risk Categories

• Systematic Risks:
  • Affect the entire economy (e.g., pandemics like COVID-19).
• Compound Risks:
  • Multiple risks occurring together, increasing overall impact.
  • Example: Wildfires during a pandemic.

The Treatment of Risk

Addressing Risk in Benefit-Cost Analysis

• Dealing with Probabilities:
  • Use ranges of probabilities to calculate multiple EPVNB scenarios.
• Outcome:
  • Provides insights into how probabilities affect policy outcomes.

The Treatment of Risk

Policy Implications

• Risk Aversion in Policy:
  • Environmental policies often reflect high risk aversion.
• Current Focus:
  • Defining acceptable risk levels on a case-by-case basis.

Choosing the Discount Rate

Importance of Discounting in Benefit-Cost Analysis

• Purpose:
  • Compares costs and benefits over time in present value terms.
• Impact:
  • Lower discount rates favor long-term benefits.
  • Higher rates may make future benefits seem less valuable.

Choosing the Discount Rate

Conceptual Framework for Discount Rates

• Components:
  • Riskless Cost of Capital: Return on risk-free investments.
  • Risk Premium: Compensation for taking on risk.
• Influence:
  • Affects the perceived desirability of projects.

Choosing the Discount Rate

Historical Context and Standardization

• Variation:
  • Agencies used different rates (0–20%) historically.
• OMB Standardization:
  • Set a standard rate (initially 10%, later 7%) to ensure consistency.
• Purpose:
  • Reduce bias and improve comparability of projects.

Choosing the Discount Rate

Challenges of Fixed Discount Rates

• Inflexibility:
  • May not reflect current market conditions.
• Example:
  • 2023 water resources rate is 2.5%, lower than standard rates.
• Result:
  • Potential inefficiencies in resource allocation.

Choosing the Discount Rate

Case Studies and Examples

• Passamaquoddy Bay Project:
  • U.S. (2.5% rate) favored the project.
  • Canada (4.125% rate) did not.
  • Highlighted how discount rates influence project evaluation.

Choosing the Discount Rate

Climate Change Policy Debate

• Nicholas Stern (1.4% rate):
  • Advocated for immediate, strong action on climate change.
• William Nordhaus (5.5% rate):
  • Suggested modest immediate actions, with greater future efforts.
• Implication:
  • Discount rate choice affects urgency and scale of climate policies.

Choosing the Discount Rate

Discounting over Long Time Horizons: Should Discount Rates Decline?

• Argument:
  • Declining rates may be more appropriate for long-term, intergenerational projects.
• Approaches:
  • Descriptive: Based on market rates.
  • Normative: Includes ethical considerations for future generations.
• International Practices:
  • Some countries use declining rate schedules.

Choosing the Discount Rate

Discounting over Long Time Horizons: Should Discount Rates Decline?

• Blue-Ribbon Panel Recommendation:
  • Use a “declining certainty-equivalent discount rate.”
• Evidence:
  • Supports declining rates but varies with models and data.
• Suggestion:
  • EPA’s Science Advisory Board to develop appropriate criteria.

Divergence of Social and Private Discount Rates

Efficient Resource Allocation and Discount Rates

• Efficiency Condition:
  • Firms should use the same discount rate as society.
• Consequences of Divergence:
  • Higher Private Rates: Overproduction, resource depletion.
  • Lower Private Rates: Underutilization of resources.

Divergence of Social and Private Discount Rates

Reasons for Divergence Between Social and Private Discount Rates

1. Risk-Free Cost vs. Risk Premium:
   • Riskier industries have higher risk premiums.
2. Differences in Risk Perception:
   • Firms may perceive risks differently (e.g., fear of nationalization).
3. Time Preferences:
   • Developing countries may prioritize immediate benefits (higher rates).
   • Industrialized nations may value future benefits more (lower rates).

Divergence of Social and Private Discount Rates

Implications of Divergence

• Inefficiency:
  • Divergence can lead to resource misallocation.
  • Private decisions may not align with societal best interests.
• Recognition:
  • Identifying divergences is essential.
• Objective:
  • Align market decisions with societal welfare for efficient resource use.