Séminaire du CIRED : Béatrice Cherrier (CREST)

Séminaire du CIRED : Béatrice Cherrier (CREST)

How the Ramsey formula came to define time discounting in economics (1950-2000)

Béatrice Cherrier (CREST)


The 2023 publication of new guidelines for the choice of discount rates in the cost and benefit evaluation of US federal public policies highlight the curious status of discounting in economics. As during the so-called Stern-Nordhaus controversy in 2006, heated disagreement on numbers coexist with a relative consensus on the framework used to think and debate the discount rate for public projects. The latter is known as the Ramsey formula (sometimes Ramsey rule or Ramsey equation), one that equates the consumption rate of interest with the pure rate of time preference plus consumption growth multiplied by the elasticity of marginal utility with respect to consumption. While the 1928 article cited as the originator of the formula contained the toolbox from which to derive it, its author, Frank Ramsey, did not introduce it. Existing histories of discounting emphasize the financial origins of the technology and its development in the context of the rise of cost-benefit analysis in the 1960s, but they point to business and policy practices that have little to do with the Ramsey formula. In this article, we thus trace the origins, dissemination and dominance of the formula in economics.

We highlight how the rise and stabilization of the Ramsey formula reflected three interwoven concerns: one with the theoretical foundations of discounting (its consistency with individual and collective behavior), one with its ethical underpinnings (in particular how to treat future generations); and one with its tractability role (a way to ensure convergence in intertemporal models). Relying on archival material as well as oral history, we document how the spread of cost-benefit analysis from water resource management to other policies in the postwar led some economists trained in the optimal theory of growth to develop a mathematical framework to model public investment. We then show that the 1970s energy crisis, the rationalization of development policies, as well as efforts to integrate Rawlsian concepts to economics led economists to reflect on how to model “the distant future” and made discounting a standalone academic concern. Finally, we explain how the growing concern with global warming and the rise of climate modeling in the context of IPCC reporting in the 1990s resulted in a paradoxical situation: on the one hand, the fragile consensus of the previous decade broke down and a rift between “prescriptive” and “descriptive” approaches to discounting emerged. On the other, the Ramsey formula became entrenched as a major framework to carry out these disagreements. In the process the formula evolved from being an equilibrium condition to becoming a definition.

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