2005年-世界发展银行全球_Techniques_for_Estimating_the_Fiscal_Costs_and_Risks_of_Long-Term_Output-Based_Payments_65页_859kb

Summary of "Techniques for estimating the fiscal costs and risks of long-term output-based payments" (GPOBA Working Paper No. 5, June 2005)

Core Content

This paper explores techniques for estimating the fiscal costs and risks associated with long-term output-based payments (OBA) for infrastructure services. OBA is a strategy used by governments to support the delivery of essential services like water, sanitation, electricity, education, and health care by providing financial incentives to private service providers based on the quantity or quality of output delivered.

The paper emphasizes the importance of understanding the fiscal implications of such commitments, particularly when payments are uncertain and potentially large. It introduces two key risk measures: excess payment probability (EPP) and cash-flow-at-risk (CFaR), and discusses methods for valuing these commitments using modern financial theory.

Main Views

• Output-based payments can encourage private investment in infrastructure, but governments need to understand the associated fiscal costs and risks to make informed decisions.
• The timing of payments and their risk characteristics are crucial in valuing these commitments.
• The paper provides practical tools for estimating fiscal risks, including analytical methods and Monte Carlo simulations, which can be implemented using spreadsheets.
• The mathematical approach is used to model the evolution of economic variables, such as output levels, under uncertainty.
• The concept of risk is defined in terms of downside risk, which is the risk of exceeding a predetermined fiscal threshold.

Key Information

Types of Output-Based Payment Schemes

Risk Measures

• Excess Payment Probability (EPP): The probability that payments will exceed a specified upper bound. It is calculated using either analytical methods or Monte Carlo simulations.
• Cash-Flow-at-Risk (CFaR): A measure of the potential loss in cash flow due to uncertain outcomes. It is also estimated using similar methods as EPP.

Mathematical Modeling

• The paper uses Ito processes to model the evolution of output variables over time, assuming that they follow a geometric Brownian motion.

• This model is useful because it ensures that output variables remain positive, which is important for real-world applications.

• The model can be expressed as:

  $$
  \frac{dW}{W} = \mu dt + \sigma dZ
  $$

  where $W$ is the output variable, $\mu$ is the growth rate, $\sigma$ is the volatility, and $dZ$ is a normally distributed random variable.

• The expected value and standard deviation of $\ln Y_t$ can be derived from the model, allowing for the calculation of EPP using the formula:

  $$
  EPP_t = 1 - \Pr\left(Z_t \leq \frac{\ln Y_{up} - E[\ln Y_t]}{\sigma_{\ln Y_t}}\right)
  $$

Practical Applications

• The paper provides worked examples and spreadsheet-based techniques to implement the models.
• It discusses the difference between capped and uncapped schemes, noting that capped schemes limit government risk but complicate the analysis.
• The certainty equivalent method is emphasized as a practical and superior approach for valuing commitments under uncertainty.

Example Illustrations

• Example 1 shows the calculation of EPP for an uncapped utility connection subsidy over five years, assuming a geometric Brownian motion.
• Example 2 uses Monte Carlo simulation to estimate EPP for total expenditure over the life of the scheme.
• Example 3 applies Monte Carlo simulation to estimate CFaR for an uncapped utility connection subsidy.
• Example 4 illustrates the valuation of an uncapped utility connection subsidy using an analytical approach.
• Example 5 shows the valuation of an annually capped subsidy.
• Example 6 and Example 7 provide further examples of valuation under different OBA schemes.

Conclusion

The paper provides a comprehensive framework for governments to assess the fiscal costs and risks of long-term output-based payments. It highlights the importance of risk modeling, statistical analysis, and financial valuation techniques in making informed decisions. The approach is mathematically rigorous but practically applicable, with spreadsheet-based tools to facilitate implementation.