An earlier draft of 6th October 2010 by Gaudry and Quinet, entitled Optimisation de l’entretien et de la régénération d’une infrastructure: exploration d’hypothèses, benefitted from comments by Bernard Caillaud and Matthieu de Lapparent and was presented without econometric tests at the Kuhmo Nectar Conference on Transportation Economics in Stockholm on 1st July 2011 under the title “Joint optimization of continuous maintenance and periodic renewal”. The authors thank Marc Antoni, Richard Arnott, David Meunier and Yves Puttalaz for discussions or comments, Cong-Liem Tran for computing assistance and are grateful to Société nationale des chemins de fer français (SNCF) for financial support and for allowing inclusion in this version of estimates based on databases constructed by Michel Ikonomov and Pascaline Boyer. Exploratory estimates obtained from fixed form regression specifications were presented at the Kuhmo Nectar Conference on Transportation Economics in Berlin on 21st June 2012 through David Meunier’s good offices.
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 Brow-nian 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 Ad-vantage/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.
Auteur(s) : Bernard Lapeyre Revue : Journal of Benefit-Cost Analysis
