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Because the results of economic evaluations are frequently used in planning and policy making, significant uncertainties must be identified and treated explicitly. The most internally consistent (i.e., the uncertainty in specific variables is specifically addressed) and complete methodology to support such decision making under uncertainty is decision analysis, as described, for example, by Howard (Howard 1977; Howard 1990). Although a complete discussion of decision analysis is beyond the scope of this section, a brief description of steps to take when conftonted with uncertainty in an economic analysis is provided. In the second context, predicting economic decisions of others, analysts must sometimes model the response of consumers and other decision makers to uncertainties in a market. For example, energy consumersmakeappliancedecisionsunderuncertainfbture%elprices. Thebasisformanysuchmarket decisions are rudimentary (i.e., the appliance consumer does not perform an analysis accounting for uncertaintyasadvocatedinthissection). Analyses,whentheseconsumerdecisionsareimportant,must insomewayaccountforthislessrigorousresponsetoUncertainty. Simulationofaresponsebyothers to uncertainty may require using approximation methods, such as risk-adjusted discount rates. Uncertainty in Economic Evaluations Figure2-1showsanexampleofthesinglemostimportantformforpresentinguncertaininformation: a probabilitydensityfunction(PDF). Theprobabilitydensityfunctionrepresentsamathematicaldescription of the probability or likelihood of an uncertain variable taking on a given value? Figure 2-1 represents acommonshapeforvariablesthathavepositivevalues,suchaspricesandquantities. Verysmallvalues areunlikely. Thereisamaximumlikelihoodatsomefinitevalueandalong"tail,"whichrepresentssmall probabilitiesofverylargevaluesforthevariable. Theprobabilitydistributionoverelectricitypriceshown in Figure 2-1 will be used in an example later in this section. 25 T 20 15 10 where f(*) is the density function. 0,04 a,o6 a,i Price, $/kWh Figure2-1. Probabilitydensity 'qechnically, the probability of a random variable taking on any exuct value (e.g., exactly 1.0)is zero. However, the probability of the variable lying in a small range around that value (e.g., between 0.99 and 1.01) is given by the area under the density function between those two values, b Probability [a~xdb]= sf(t)dt , a 28PDF Image | A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies
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