COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1673

A Dynamic Analysis of Human Welfare in a Warming Planet

Humberto Llavador, John E. Roemer and Joaquim Silvestre

August 2008

Anthropogenic greenhouse gas (GHG) emissions have caused atmospheric concentrations with no precedents in the last half a million years, inducing serious uncertainties about future climates and their effects on human welfare. Recent climate science supports the view that the climate stabilization will require very low GHG emissions in the future. We ask: Is a path of low emissions compatible with sustainable levels of human welfare? With steady growth in human quality of life? Addressing these questions requires both defining welfare criteria and empirically estimating the possible paths of the economy.

We specify and calibrate a dynamic model with four intertemporal links: education, physical capital, knowledge and the environment. In line with Nordhaus (2008a) and with the Stern Review (2007), we assume that GHG emissions allow increased production, while a higher stock of atmospheric carbon decreases production.

Our index of human welfare, which we call quality of life (QuoL), emphasizes education, knowledge, and the environment, affected by greenhouse gas emissions, in addition to consumption and leisure. Thus, we avoid a Consumptionist Fallacy – that welfare depends only on commodity consumption and perhaps leisure.

We reject discounted utilitarianism as a normative criterion, and consider two alternatives. The first is an intergenerational maximin criterion, which maximizes the quality of life of the first generation subject to maintaining at least that level for all successive generations. The second is human development optimization, that seeks the maximization of the QuoL of the first generation subject to achieving a given, constant rate of growth in all subsequent generations. Hence, our analysis focuses on a human notion of sustainability, as opposed to the conventional "green" sustainability, limited to keeping the quality of the environment constant.

Because our dynamic optimization programs defy explicit analytical solutions, our approach has been computational. As a benchmark, we consider a simple model with physical and human capital, for which we prove a turnpike theorem. We then devise a computational algorithm inspired by the turnpike property to construct feasible, although not necessarily optimal, paths in the more complex and realistic model.
Our analysis indicates that, with GHG emission paths entailing very low emissions in the future, positive rates of growth in QuoL are possible while the first generation experiences a QuoL higher than the historical reference level. We also observe a tradeoff between the quality of life of the first generation and the rate of growth in the quality of life. Yet Generation 1’s sacrifice for the sake of a higher growth rate appears to be small. The paths that we compute involve investments in knowledge at noticeably higher levels than in the past.

Keywords: Quality of life, Climate change, Education, Maximin, Growth

JEL Classifications: D63, O40, O41, Q50, Q54, Q56