Evaluation of public investments and individual discounting

Arrow and Lind's theorem postulates that 'when the risks associated with a public investment are publicly borne, the total cost of risk-bearing is insignificant and, therefore, the government should ignore uncertainty in evaluating public investments. Similarly the choice of the rate of discount should in this case be independent of considerations of risk.' [Arrow, K. J., Lind, R. C. (1970). Uncertainty and the evaluation of public investment decisions. American Economic Review, LX, June, p.366] The theorem holds regardless security markets are complete, for any public project that is: i) statistically independent of individual income, ii) measured according to an objective probability distribution, iii) evaluated considering individual costs and benefits represented by von Neumann-Morgestern, state-independent utilities; moreover, it holds provided iv) the government spreads the project risks among a 'large' population of people. The independence assumption is necessary to attain that, at the margin, the individual values a public investment as a risk-free claim on future income. Yet, it is a strong one. Arrow and Lind, along with other economists (e.g., Samuelson and Vickrey, 1964), recognize that many public projects alter individuals' income profiles, either providing new (social) insurance opportunities or representing a further source of risk. They, briefly, address the issue in section III of their paper and conclude that in such cases 'it is appropriate to discount for risk as would these individuals' [p. 377]. In this note we discuss and elaborate on Arrow and Lind's consideration that public projects should effectively be evaluated from the perspective of individuals. The main issue at stake is that this approach, although theoretically sound, is informationally very demanding, requiring the measurement of individuals' benefits and costs or, equivalently, the observation of their preferences and income profiles. Our main point is to argue that this requirement can be weakened exploiting the information revealed by security market prices. More precisely, we appeal to well known results in the theory of asset prices in economies with incomplete markets, to discuss how a (public) decision maker could use market data on security prices to infer on traders' discount factors and, ultimately, to construct (approximate) measures of the individuals' willingness to pay for a project. These are the cost-benefit measures suggested by Arrow and Lind, that can be utilized to evaluate any investment project, public and private, independently of the fact they are marketable or give rise to a risk that is uninsurable. At the end of this note we also mention which are the alternative data, different from those on security prices, that can be exploited to attain information on individual discount factors