A Simple GDP-based Model for Public Investments at Risk

Investment decision rules in risk situations have been extensively analyzed for firms. Most research focus on financial options and the wide range of methods based on dynamic programming currently used by firms to decide on whether and when to implement an irreversible investment under uncertainty. The situation is quite different for public investments, which are decided and largely funded by public authorities. These investments are assessed by public authorities, not through market criteria, but through public Cost-Benefit Analysis (CBA) procedures. Strangely enough, these procedures pay little attention to risk and uncertainty. The present text aims at filling this gap. We address the classic problem of whether and when an investment should be implemented. This stopping time problem is established in a framework where the discount rate is typically linked to GDP, which follows a Brownian motion, and where the benefits and cost of implementation follow linked Brownian motions. We find that the decision rule depends on a threshold value of the First Year Advantage/Cost ratio. This threshold can be expressed in a closed form including the means, standard deviations and correlations of the stochastic variables. Simulations with sensible current values of these parameters show that the systemic risk, coming from the correlation between the benefits of the investment and economic growth, is not that high, and that more attention should be paid to risks relating to the construction cost of the investment; furthermore, simple rules of thumb are designed for estimating the above-mentioned threshold. Some extensions are explored. Others are suggested for further research.