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8.4 Addressing Uncertainty

    Because they are estimates, the results of an economic analysis of a regulatory action are never precise; however, many EAs present simple point estimates of expected benefits and costs without characterizing the uncertainties surrounding these values.  Both EPA and OMB guidance require that such uncertainties be acknowledged and addressed in an EA.  Therefore, the purpose of this section is to identify sources of uncertainty in EAs and to discuss methods available to analysts for characterizing and reducing uncertainty in the results of the analysis.
    The term “uncertainty” simply refers to the confidence with which any estimate can be accepted as representing the true result of a process about which the analyst has incomplete knowledge.  It is important to note that in this discussion “uncertainty” is not used as a synonym for risk.  The term “risk” is interpreted to mean the likelihood of a particular event occurring.  For example, some OAQPS regulations are expected to result in a change in the probability that an individual or ecosystem will experience an effect as a result of an exposure to air pollution.  The level of this change in risk is a truth unknown to the analyst and is independent of the techniques used to estimate the risk.  In contrast, uncertainty in the assessment of risk is an artifact of the analysis itself and can often be reduced by further study.
 

8 Methodological
  Issues

 8.0 Intro

 8.1 Specifying the Time
   Period of Analysis

 8.2 Specifying a Baseline
   for Analysis

 8.3 Discounting Benefits
   and Costs

 8.4 Addressing Uncertainty
 
    Uncertainty can arise at any stage in the development of a regulatory analysis.  Within each stage of the analysis, uncertainty can result from any number of factors, including insufficient data, an incomplete understanding of the physical or economic process being modeled, model specification, and the inherent uncertainty in the results of any statistical analysis.  A thorough treatment of all sources of uncertainty in a regulatory analysis is beyond the scope of this document.  Therefore, the remainder of this discussion focuses on the uncertainties associated with the valuation of changes in environmental impacts.
    There are three general sources of uncertainty in the economic analysis of a regulatory action:  input uncertainty, model uncertainty, and estimation uncertainty.  Each of these sources of uncertainty is described below:
  • Input uncertainty—This is a general term used to describe two specific sources of uncertainty inherent in the data on which an economic analysis is based.  These specific sources include the distribution of possible values of the environmental impact being valued and measurement error.  The former source of input uncertainty arises when the impacts being valued are themselves the product of a modeling effort as is often the case when the impact of interest is a change in exposure to a pollutant or a change in the probability of a certain outcome occurring.  The latter source of input uncertainty, measurement error, is common when the data used in an economic analysis are incomplete and analyst judgement or proxy measures are used to fill in data gaps.  The uncertainty surrounding such inputs will naturally be carried through the economic analysis.
  • Model uncertainty—This type of uncertainty is typically a result of the fact that any statistical model represents a simplification of a behavioral or economic process.   This simplification is often necessary because most behavioral and economic processes are highly complex.  In addition, this simplification is necessary if the nature of the behavioral or economic process being modeled is not completely understood.   In modeling such processes, analysts must often rely on a series of assumptions and abstractions, each having a potential impact on the precision of the analytical results.
  • Estimation uncertainty—Economic analyses in which the analyst estimates a parametric model yield results that are variable.  In particular, all statistical modeling techniques result in parameter estimates that are not point estimates, but rather probability distributions of likely values for the parameters.  This distribution in parameter estimates naturally translates into a distribution of the predicted outcome variable.  This estimation uncertainty requires that the analyst take care to assign the appropriate probability ranges around each estimated parameter or prediction.
    Because of the uncertainties described above, the results of an EA must be presented in such a way that the full range of uncertainty is transparent.  There are five basic methods for characterizing uncertainty:
  • scenario analysis—estimating a range of possible outcomes, such as worst-case and best-case scenarios, in addition to the most likely outcome
  • Delphi methods—using input from a group of experts to characterize the potential likelihood of possible outcomes
  • sensitivity analysis—identifying assumptions made about key input variables (e.g., the level of exposure or the discount rate) and conducting the analysis over a range of plausible values for these variables to determine the effect of each assumption on the resulting point estimates
  • meta-analysis—combining data or results from a number of different studies to estimate a more general model or to characterize the range or distribution of key input variables
  • Monte Carlo and other probabilistic methods—simulating a distribution of the results by randomly drawing from the probability distributions of input variables and repeating the analysis numerous times
The draft EPA white paper on uncertainty recommends that, at a minimum, the analyst identify the key assumptions and qualitatively assess the potential impact of each assumption on the results of the analysis ( Hagler-Bailly Consulting, Inc., 1997).
    In addition, sensitivity analysis should be conducted to further characterize the impact of alternative values of key variables whenever possible.  Scenario analysis and Delphi methods are useful when sensitivity analysis fails to adequately characterize the range of possible outcomes, particularly in situations in which there is a small risk of an extreme outcome.  Meta-analysis and probabilistic methods are often superior to the other methods.  Meta-analysis provides a more complete characterization of key input variables, and probabilistic methods provide a probability distribution for the full range of possible cost and benefit values.
    Because Delphi methods, meta-analysis, and probabilistic methods often require substantial time and financial resources, the analyst should determine their likely contribution to the policy implications of the EA results.  For analyses in which benefits unambiguously exceed costs, a sensitivity analysis should be adequate.  However, in cases in which the results vary significantly depending on the underlying assumptions, other methods of characterizing the range and distribution of both input variables and results should be considered.

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12 Both the OMB EA guidance ( OMB, 1996) and the EPA working paper addressing uncertainty in EAs ( Hagler-Bailly Consulting, Inc., 1997) include a discussion of certainty equivalents.  Certainty equivalents are a theoretical construct for the value that a risk-averse individual places on an uncertain outcome.  This type of uncertainty does not represent a lack of knowledge on the part of the analyst but rather a component of an individual’s response to risk.  Therefore, certainty equivalents are more appropriately addressed in a discussion of the expected benefits of a regulatory action rather than in a discussion of analytical uncertainty.
13 Risk and risk assessment are discussed in detail in Section 7 of this guidance document.
14 For an example of the use of meta-analysis in determining the value of a statistical life to use in the analysis of environmental programs, readers are referred to EPA’s analysis of the benefits and costs of the CAA ( EPA, 1996a).  Analysts interested in conducting meta-analyses are referred to  Hedges and Olkin (1985) and  Cook et al. (1992).
15 An example of the use of Monte Carlo simulation in the analysis of a regulation is the CAA retrospective analysis ( EPA, 1996a).  More detailed discussions of probabilistic methods, including Monte Carlo simulations, can be found in most intermediate or advanced statistics and econometrics texts.

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