International Environmental Agreements: Politics, Law and Economics

International Environmental Agreements: Politics, Law and Economics

RESEARCH ARTICLE

Bargaining and climate change

Supplementary online appendix: Damage function methodology

The simplified methodology used here for calculating damages from greenhouse gas emissions (treated as CO2-equivalents in warming potentials) is based on the model in Fankhauser and Kverndokk (1996). Although highly stylized and simplified, several steps are nonetheless required to represent the mechanisms that translate emissions into damages in this model.

A damage function is assumed in this form:

Dit( It ) = ki ( 1 + hi ) t * ( It / Λ ) (1)

Annual damage is assumed to grow proportionally with income, where the rate of economic growth in country iis denoted by hi ;kidenotes the damage for country I caused by a hypothetical temperature increase of Λ˚C in period 0.[1]It is the temperature rise between period 0 and the current period.

Sinceki is a point estimate of damage at Λ˚C, the latter temperature level is essentially the baseline for assessing potential damages from climate change. For many studies, including that of Fankhauser and Kverndokk, this baseline is 2.5˚C above pre-industrial levels, corresponding to a doubling of CO2 concentrations in the atmosphere. For the purposes of the present study, two of the estimated k-values from Fankhauser and Kverndokk are employed: kUS = 104.94, and kChina = 36.34. These two values correspond to the low- and high-damage scenarios for each country, respectively, and have been chosen in order to reflect better the higher-than-expected degree of economic convergence that has occurred between the two countries since 1993.

Next, we assume a rate of economic growth (in present value terms, after discounting, if any), hi, that is 1% for the US and 3% for China, which is consistent with the consensus projections in the literature.[2] Finally, for calculating It, which we derive from Tt, or the cumulative industrial-era rise in temperature, we use a range of estimates in accordance with the system of equations used in Fankhauser and Kverndokk(1996, 89ff.) to represent a stylized climate system.

First, the stock constraint relates previous-period emissions, Et-1, to the concentration of CO2 in the atmosphere:

Qt = λ Eit-1+( 1 – σ ) Qt-1 (2)

Qt is the atmospheric greenhouse gas concentration at time t (in CO2-equivalents). The parameter λ translates emissions units (GtC) into the concentration units (ppm), and is estimated here to be 0.47. σrepresents the constant rate at which is assumed to dissipate, through absorption into the oceans and other natural processes; the assumed value here is 0.005, corresponding with an atmospheric lifetime of 200 years for CO2 .

Next, the temperature constraint represents how temperatures adjust over time in response to a change in atmospheric CO2 concentrations:

Tt =α∙ωln ( Qt / QP ) + ( 1 - α ) Tt-1 (3)

QP is the pre-industrial atmospheric concentration of CO2. α is the delay parameter which determines the speed of adjustment, 0 ≤α ≤ 1; here it is assumed that α= 0.10, corresponding to a lag of 50 years. ω is a climate sensitivity parameter, assumed here to have a value of 3.61.[3]

Finally, to obtain values for temperature increases attributable only to post-2015 emissions, or It, the rise in temperature until period 0 must be backed out:

It =α∙ω ( ln ( Qt / QP ) - ln ( Q0 / QP ) ) + ( 1 - α ) Tt-1 (4)

Q0 for the purposes of this analysis is assumed to be 385 parts per million (ppm), while QP is assumed to be 280 ppm. Lastly, the values for Eit and hence Qt are taken from the projected estimates of the International Energy Agency's World Energy Outlook, 2009 and 2010.

[1]See Fankhauser and Kverndokk (1996: 93). The analysis here differs most importantly from that of Fankhauser and Kverndokk in that we are interested in the marginal damage resulting from the temperature increase caused by each year's emissions after 2015 (the assumed baseline year for a conjectural international agreement), rather than the total damage caused by the cumulative rise in temperatures (and greenhouse gas concentrations) above pre-industrial levels – in other words, the variable of interest here is It, instead of Tt. The other minor modification that has been made to the damage function here is its simplification to exclude convexity, which does not meaningfully affect the results.

[2]See Manne and Richels (1991); Fankhauser and Kverndokk (1996: 94); Blanford, Richels, and Rutherford (2009, Supplementary Data, "pessimistic scenario": 2).

[3]The relationship between atmospheric concentrations and the equilibrium change in global mean temperature (i.e. the change which will occur after full adjustment) is usually approximated by a simpler logarithmic function, Tt * = ωln( Qt / QP ); equation (3) therefore represents a partial equilibrium during a process of gradual adjustment characterized by thermal inertia.