Climate Change Complementarity: Optimization?

Last week I looked into complementarity, including the Oxford Dictionaries’ definition:

A relationship or situation in which two or more different things improve or emphasize each other’s qualities.

I’d like to follow up on the question posited there: do countries really have to break the complementary relationship between economic prosperity and environmental sustainability? Or can we try to establish an optimized balance?

Climate change’s impacts on almost all global economic activities are now (very slowly) starting to penetrate policymaking on every level. The current political climate in many countries is not exactly encouraging for productive consideration of the matter but it is still under discussion, with the hope that global environmental considerations will play increased roles.

In theory, the US Environmental Impact Statement is the perfect tool for visualizing that added responsibility:

Federal laws and regulations require the government to evaluate the effects of its actions on the environment and to consider alternative courses of action. The National Environmental Policy Act of 1969 (NEPA) specifies when an environmental impact statement (EIS) must be prepared. NEPA regulations require federal agencies, among other things, to include discussion of a proposed action and the range of reasonable alternatives in an EIS. Sufficient information must be included in the EIS for reviewers to evaluate the relative merits of each alternative. Regulations for the Council for Environmental Quality (CEQ) provide the recommended format and content of Environmental Impact Statements.

You can see similar legislation in other countries via Wikipedia.

The EIS is mandated procedure, meaning that it represents the law (as with other laws it can be modified by executive orders or legislation); in  the US, however,  it has been running into some issues.  The executive summary of a paper from Columbia’s Sabin Center for Climate Change Law starts with the following:

In its first year, the Trump Administration undertook a program of extensive climate change deregulation. The Administration delayed and initiated the reversal of rules that reduce greenhouse gas (GHG) emissions from stationary and mobile sources; sought to expedite fossil fuel development, including in previously protected areas; delayed or withdrew energy efficiency standards; undermined consideration of climate change in environmental review; and hindered adaptation to the impacts of climate change. However, the Trump Administration’s efforts have met with constant resistance, with those committed to climate protections bringing legal challenges to many, if not most, of the rollbacks.

We do have other resources for checking up on the damage, though. In industry, for example, Bloomberg terminals now include ESG (Environmental, Social and Governance) information that can be incorporated into many economic decisions [Park Andrew and Ravenel Curtis: Integrating Sustainability into capital markets. Bloomberg LP and ESG’s Quantitative Legitimacy. Journal of Applied Corporate Finance 25, 62 (2013)].

Perhaps the most climate-change-relevant information that can be incorporated in any of these search tools is the social cost of CO₂ (SC-CO2). The US National Academies of Sciences, Engineering, and Medicine published some discussions about possible implementation [The National Academy of Sciences and Engineering Valuing Climate Damages: Updating Estimation of the Social Cost of Carbon Dioxide. (Washington, DC 2017)].

The SC-CO₂ is a measure, in dollars, of the long-term damage done by a ton of carbon dioxide (CO2) emissions in a given year.  This dollar figure also represents the value of damages avoided for a small emission reduction (i.e., the benefit of a CO₂ reduction).

Some are using game theory to push for a version of global sustainability that does not require choosing or prioritizing between countries’ economic development. I have mentioned game theory throughout this blog. Just put the term in the search box and you will find that wherever an apparent conflict shows up, game theory has something to say. For instance, I discussed Peter John Wood’s application of game theory to issues focused on climate change in my March 31, 2015 blog.

Mr. Wood looked at climate change as a two-person game of the Prisoner’s Dilemma [Ann. N.Y. Acad. Sci., 1219, 153-170, (2011)]. The two players have two choices: pollute and abate (equivalent to keep quiet and cooperate). The Nash equilibrium is pollute, pollute (equivalent to cooperate, cooperate).

To those of us who need some reminders about the Nash Equilibrium and the Prisoner’s Dilemma here are some brief refreshers:

Nash Equilibrium is a solution concept of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.^[1] If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitutes a Nash equilibrium.

Prisoner’s Dilemma: Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is:

• If A and B each betray the other, each of them serves two years in prison
• If A betrays B but B remains silent, A will be set free and B will serve three years in prison (and vice versa)
• If A and B both remain silent, both of them will only serve one year in prison (on the lesser charge).

Once expanded to a global conflict between all states, that game can take the following form:

P_i = A_i(e_i) – B_i(∑e_i)

Where the index i refers to the individual countries. P is a utility function, a term economists often use to model worth or value. Here it can signify economic growth that almost all economists view as something of value. e_i represents the pollution that every country generates in the use of energy to power its economic growth and the negative impacts from every country that such pollution can generate. A_i and B_i are the coefficients of the two impacts on every country.

One can try and solve for the Nash Equilibrium by maximizing each utility function subject to constrains that the other utility functions are maximized. The social optimum can be calculated by maximizing ∑ P_i for all players.

To my knowledge a satisfactory solution for our current situation is a work in progress.