A straightforward method of judging the value of information in an uncertain environment has been developed and applied (see Manne and Richels, 1992, for an early and careful description). The idea is simply to compute the expected cost of uncertainty with and without the information and compare the outcomes. For example, it might be that improved information about the range of uncertainty might change the mean and the variance of associated costs. If the researcher were interested only in the resulting change in costs, however, the value of information would simply be the difference between expected cost with and without the new information, and only the mean would matter. If the same researcher wanted to represent the value of information in terms of welfare that displays some degree of risk aversion so that variance also plays a role, however, a comparison of insurance-based estimates of the WTP to avoid uncertainty would be more appropriate.

Uncertainty about costs and/or values that are incurred or enjoyed over time
can be handled in two ways. One method calculates the present value across the
full range of possibilities; means and distributions of present values are the
result. The second method, reported in Arrow *et al*. (1996), converts
outcomes at each point in time into their certainty equivalents and then applies
discounting techniques. This approach raises the possibility of including risk
aversion into the calculation according to the foregoing definition.

The story is quite different when uncertainty surrounds selection of the discount rate itself. It may not be appropriate, in these sorts of cases, to use a certainty-equivalent discount rate (or an average over the range of possible rates). Weitzman (1998) has noted, in particular, that the "lowest possible" discount rate should be used for discounting the far-distant future. The reason, quite simply, is that the expected value of present value over a range of discount rates is not equal to the present value calculated with an average rate. Moreover, the difference between the two is exaggerated in the distant future. Present values computed with low rates, in fact, can dominate those computed with high rates by orders of magnitude when the future is extended; thus, their contribution to the expected value must be recognized explicitly in the selection of a discount rate.

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