Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T19:56:02.655Z Has data issue: false hasContentIssue false
  • English
  • Français

A Simple GDP-based Model for Public Investments at Risk

Published online by Cambridge University Press:  23 March 2017

Bernard Lapeyre  and
Emile Quinet
Bernard Lapeyre
Affiliation:
Université Paris-Est, CERMICS (École des Ponts), Projet MathRisk, (INRIA), 6-8 Avenue Blaise Pascal, 77455 Champs-sur-Marne, France
Emile Quinet*
Affiliation:
ENPC-PjSE, UMR 8545, 48 Boulevard Jourdan, 75014 Paris, France, e-mail: [email protected]
*
*e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

C61D60D81D92G12H43Brownian motiondecision makingdiscount rateinvestmentriskrisk and uncertainty
Type
Articles
Information
Journal of Benefit-Cost Analysis , Volume 8 , Issue 1 , Spring 2017 , pp. 91 - 114
Copyright
© Society for Benefit-Cost Analysis 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abrantes, Pedro A. L. & Wardman, Mark R. (2011). Meta-Analysis of UK Values of Travel Time: An Update. Transportation Research Part A: Policy and Practice, 45(1), 1–17.Google Scholar
Arrow, Kenneth J., Cropper, Maureen L., Gollier, Christian, Groom, Ben, Heal, Geoffrey M., Newell, Richard G., Nordhaus, William D., Pindyck, Robert S., Pizer, William A., Portney, Paul R., Thomas Sterner, Thomas, Tol, Richard S. J. & Weitzman, Martin L.(2012). How Should Benefits and Costs be Discounted in an Intergenerational Context? The Views of an Expert Panel Ressource for the Future. Technical Report, Discussion Paper.Google Scholar
Bairoch, Paul (1995). Economics and World History: Myths and Paradoxes. Chicago II: University of Chicago Press.Google Scholar
Barro, Robert J. (2006). Rare Disasters and Asset Markets in the Twentieth Century. The Quarterly Journal of Economics, 121(3), 823–866.Google Scholar
Becker, Jean-Jacques, Delache, Xavier, Brunel, Julien, Sigaud, Damien & Sauvant, Alain (2013). Estimation des élasticités des trafics routiers et ferroviaires au pib. In Quinet, Emile (Ed.), Évaluation socio-économique des investissements publics Paris, France: Commissariat général à la stratégie et à la prospective.Google Scholar
Bellinger, William K. (2016). The Economic Analysis of Public Policies. Oxford: Routledge.Google Scholar
Bensoussan, Alain (1984). On the Theory of Option Pricing. Acta Applicandae Mathematicae, 2, 139–158.Google Scholar
Black, Fisher & Scholes, Myron (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81, 635–654.Google Scholar
Bonnafous, Alain & Jensen, Pablo (2005). Ranking Transport Projects by Their Socioeconomic Value or Financial Internal Rate of Return? Transport Policy, 12, 131–136.CrossRefGoogle Scholar
Brussels: Directorate General Regional Policy (2008). Guide to Cost-Benefit Analysis of Investment Projects.Google Scholar
Button, Kenneth (2010). Transport Economics. Cheltenham: Edward Elgar.Google Scholar
De Rus, Ginés (2010). Introduction to Cost Benefit Analysis: Looking for Reasonable Shortcuts. Cheltenham: Edward Elgar.Google Scholar
Department for Transport (2010). Cost Benefit Analysis: TAG Unit 3.5.4. http://www.dft.gov.uk/webtag/documents/expert/unit3.5.4.php.Google Scholar
Dixit, Avinash K. & Pindyck, Robert S. (1994). Investment Under Uncertainty. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Farrow, Scott (2004). Using Risk Assessment, Benefit-Cost Analysis, and Real Options to Implement a Precautionary Principle. Risk Analysis, 24(3), 724–735.Google Scholar
Fisher, Anthony C. (2000). Investment Under Uncertainty and Option Value in Environmental Economics. Ressource and Energy Economics, 22(3), 197–204.CrossRefGoogle Scholar
Florio, Massimo(Ed.) (2007). Cost Benefit Analysis and Incentives in Evaluation. Cheltenham: Edward Elgar.Google Scholar
Framstad, Nils C. & Strand, Jon (2015). Energy Intensive Infrastructure Investments with Retrofits in Continuous Time: Effects of Uncertainty on Energy use and Carbon Emissions. Resource and Energy Economics, 41, 1–18.Google Scholar
Glaister, Stephen & Layard, Richard(Eds.) (1994). Cost Benefit Analysis. Cambridge: Cambridge University Press.Google Scholar
Gollier, Christian (2002). Time Horizon, the Discount Rate, Journal of Economic Theory. Journal of Economic Theory, 107, 463–473.CrossRefGoogle Scholar
Gollier, Christian (2008). Discounting with Fat-Tailed Economic Growth. Journal of Risk, Uncertainty, 37, 171–186.Google Scholar
Gollier, Christian (2011). Pricing the Future: The Economics of Discounting and Sustainable Development. Princeton, NJ: Harvard University Press.Google Scholar
Gollier, Christian(2015). Taux d’actualisation et rémunération du capital. Toulouse School of Economics, Juillet.Google Scholar
Gollier, Christian & Weitzman, Martin (2010). How Should the Distant Future be Discounted When Discount Rates are Uncertain? Economic Letters, 107, 350–353.Google Scholar
Groom, Ben, Koundouri, Phoebe, Panopoulou, Ekaterini & Pantelidis, Theologos (2007). An Econometric Approach to Estimating Long-Run Discount Rates. Journal of Applied Econometrics, 22, 641–656.CrossRefGoogle Scholar
Henry, Claude (1974). Investment Decisions Under Uncertainty: The Irreversibility Effect. American Economic Review, 64, 1006–1012.Google Scholar
Hepburn, Cameron, Koundouri, Phoebe, Panopoulou, Ekaterini & Pantelidis, Theologos (2009). Social Discounting Under Uncertainty: A Cross Country Comparison. Journal of Environmental Economics and Management, 57, 140–150.Google Scholar
Karatzas, Ioannis (1988). On the Pricing of American Options. Applied Mathematics and Optimization, 17(1), 37–60; ISSN: 0095-4616.Google Scholar
Karatzas, Ioannis & Shreve, Steven E. (1988). Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics 113. New York: Springer; ISBN: 0-387-96535-1.Google Scholar
Lamberton, Damien & Lapeyre, Bernard (2008). Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall/CRC Financial Mathematics Series. (2nd edition). Boca Raton, FL: Chapman & Hall/CRC.Google Scholar
Lapeyre, Bernard & Quinet, Emile (2013). Choix des investissements et prise en compte du risqué systémique. In Quinet, Emile (Ed.), Évaluation socio-économique des investissements publics Paris, France: Commissariat général à la stratégie et à la prospective.Google Scholar
Lapeyre, Bernard & Quinet, Emile(2016). A Real Option Approach to Public Investment Decisions in Situation of Risk (Appendix). http://cermics.enpc.fr/bl/pdf/choix-appendix.pdf.Google Scholar
Maurice, Joël, Quinet, Emile & Sauvant, Alain (2007). Optimisation et decentralisation des investissements de transports. Economie et Prévision, 175–176, 31–51.Google Scholar
McKean, Henri P. (1965). A Free Boundary Problem for the Heat Equation Arising from a Problem of Mathematical Economics. Indust. Management Rev., 6, 32–39.Google Scholar
Mehra, Rajnish & Prescott, Edward C. (1985). The Equity Premium: A Puzzle. Journal of Monetary Economics, 15, 145–161.CrossRefGoogle Scholar
Newell, Richard G. & Pizer, William A. (2003). Discounting the Distant Future: How Much Do Uncertain Rates Increase Valuations? Journal of Environmental Economics and Management, 46, 52–71.CrossRefGoogle Scholar
Odgaard, Thomas, Kelly, Charlotte & Laird, James(2005). Current Practice in Project Appraisal in Europe, Developing Harmonised European Approaches for Transport Costing and Project Assessment (HEATCO). Technical Report Deliverable no. 1, Stuttgart University. http://heatco.ier.uni-stuttgart.de/hd1final.pdf.Google Scholar
PIARC (2004). Economic Evaluation of Road Projects in PIARC Member Countries. Permanent International Association of Road Conferences.Google Scholar
Pindyck, Robert S. (1991). Irreversibility, Uncertainty and Investment. Journal of Economic Literature, XXIX, 1110–1148.Google Scholar
Pindyck, Robert S. (2002). Optimal Timing Problem in Environmental Economics. Journal of Economic Dynamics and Control, 26, 1677–1697.Google Scholar
Purvis, Amy, Boggess, William G., Moss, Charles B. & Holt, John (1995). Technology Adoption Decisions Under Irreversibility and Uncertainty: An “ex ante” Approach. American Journal of Agricultural Economics, 77(3), 541–551.Google Scholar
Quinet, Emile(2013). Évaluation socio-économique des investissements publics. Technical Report, Rapport pour le compte du CGSP La documentation française, Paris. Rapport pour le compte du Commissariat général à la stratégie et à la prospective.Google Scholar
Quinet, Emile & Vickerman, Roger (2004). Principles of Transport Economics. Cheltenham: Edward Elgar.Google Scholar
Ramsey, Frank P. (1928). A Mathematical Theory of Saving. Economic Journal, 38, 543–559.Google Scholar
Samuelson, Paul A. (1965). Rational Theory of Warrant Pricing. Industrial Management Review, 6(2), 13–32.Google Scholar
Small, Kenneth A. & Verhoef, Eric T. (2007). The Economics of Urban Transportation. London: Routledge.Google Scholar
Traeger, Christian P. (2014). On Option Values in Environmental and Ressource Economics. Resource and Energy Economics, 37, 242–252.Google Scholar
Van Moerbeke, Pierre (1975). On Optimal Stopping and Free Boundary Problems. Archive for Rational Mechanics and Analysis, 60(2), 101–148.Google Scholar
Weitzman, Martin (1998). Why the Far-Distant Future Should be Discounted at its Lowest Possible Rate. Journal of Environmental Economics and Management, 36(3), 201–208.CrossRefGoogle Scholar
Weitzman, Martin (2001). Gamma Discounting. American Economic Review, 91(1), 260–271.CrossRefGoogle Scholar
Weitzman, Martin(2012). Rare disasters, tail-hedged investments, risk-adjusted discount rates. NBER Working Paper 18496.CrossRefGoogle Scholar