Abstract
Global warming is now recognized as a significant threat to sustainable development on an international scale. One of the key challenges in mounting a global response to it is the seeming unwillingness of the fastest growing economies such as China and India to sign a treaty that limits their emissions. The aim of this paper is to examine the differential incentives of countries on different trajectories of capital growth. A benchmark dynamic game to study global warming, introduced in Dutta and Radner (2009), is generalized to allow for exogenous capital accumulation. It is shown that the presence of capital execerbates the “tragedy of the common”. Furthermore, even with high discount factors, the threat of reverting to the inefficient “tragedy” equilibrium is not sufficient to deter the emissions growth of the fastest growing economies—in contrast to standard folk theorem like results. However, foreign aid can help. If the slower growth economies—like the United States and Western Europe—are willing to make transfers to China and India then the latter can be incentivized to cut emissions. Such an outcome is Pareto improving for both slower and faster growth economies.
Originally published in Economic Theory, Volume 49, Number 2, February 2012 DOI 10.1007/ s00199-010-0573-7.
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Notes
- 1.
The data is drawn from the World Resource Institute web-site and credits two studies published in 2000—one by Houghton and Hackler and the other by Marland et al. For details see http://earthtrends.wri.org/features/view_feature.php?fid=3&theme=3.
- 2.
The data, corresponding to emissions in 2004, was collected in 2007 by the CDIAC (Carbon Dixide Information Analysis Center) of the US Department of Energy for the United Nations. The data considers only carbon dioxide emissions from the burning of fossil fuels. See http://en.wikipedia.org/wiki/List_of_countries_by_carbon_dioxide_emissions.
- 3.
These numbers are drawn from the US EPA (Environmental Protection Agency) web-site that quotes an article published in the Energy Journal. For details see http://www.epa.gov/climatechange/emissions/globalghg.html.
- 4.
- 5.
All this and more at http://www.nytimes.com/2009/07/16/world/asia/16warming.html.
- 6.
- 7.
One other determinant of economic activity, beyond capital and energy, is labor but that is assumed to remain fixed.
- 8.
Please note that the short-term benefit function is taken to be a Cobb-Douglas function here but is a more general concave function in Dutta and Radner (2009).
- 9.
Though, as noted above, the model is dynamic with intertemporal linkages rather than the static model that a repeated game studies.
- 10.
The effective growth rate is precisely defined in Sect. 4. It coincides with the actual growth rate of capital when there is constant returns to scale.
- 11.
The logic will, of course, be detailed in Sect. 4. But one quick way to see it is to take the extreme case where the other countries’capital does not grow at all. Then the future gain to the fastest growing country, to all other countries following the GGPO emission rather than the GBAU emission, is some finite amount. However, its short-term cost is proportional to is capital stock. As capital stock grows infinitely large, at some period, the short-term cost overwhelms.
- 12.
An example of such a conditional transfer—or foreign assistance—policy is the World Bank’s Climate Investment Fund (CIF).
- 13.
A referee has suggested that the solution offered in this paper—the benefits of foreign aid in ameliorating climate change—is being realized in practice in current climate agreements, and has been implemented through the UNFCCC rules. The referre points out that the solution proposed theoretically in this paper agrees with the actual structure of the Kyoto Protocol carbon market—which is now international law since 2005, and trading in the European Union Emissions Trading System—that allows such foreign aid transfers through the structure of the UNFCCC Clean Development Mechanism, a mechanism that has already transferred over $26 billion to nations such as China and India to create similar incentives for clean development projects.
- 14.
In Dutta and Radner (2009) we consider a more general form of felicity function that includes the Cobb-Douglas form \([a_{i}(t)]^{\beta _{i}}\).
- 15.
We conjecture that this inequality would hold in a variety of models. It certainly does in the concave model of Dutta and Radner (2009). Indeed, one can show in a quite general model that a GPO cannot be a BAU, or even that, starting from a GPO, each country will want to increase its emissions unilaterally by a small amount.
- 16.
That this is the utility consequence to country i from emission \(a_{i}(t)\) is easily seen by noting that that level of emission causes first, an immediate “GDP” payoff \(\left[ a_{i}(t)\right] ^{\beta _{i}}\left[ K_{i}(t) \right] ^{1-\beta _{i}}\) (where we have used the CRS\(\ \)simplification). However, next period there is \(\sigma c_{i}a_{i}(t)\) of GHG damage, the period after that \(\sigma ^{2}c_{i}a_{i}(t)\), two periods after that \(\sigma ^{3}c_{i}a_{i}(t)\), all of which discounted back at rate \(\delta \) yields a present discounted cost of \(\delta w_{i}a_{i}(t)\).
- 17.
As with all Nash equilibrium logic, other countries—whom country 1 is best responding to at time T—will be presumed to be carrying on with the cuts in that period. Hence the T period payoff consequence from the others’ actions is identical for country 1 whether it deviates or not.
- 18.
The closest institutional mechanism to climate change related foreign aid is the aid that is disbursed by the World Bank via its Climate Investment Fund (CIF). In the CIF though, there is no requirement that the transfers should aggregate to zero. Clearly having that as an additional requirement only makes our task of showing the beneficial effects of aid more difficult. Equally clearly, some kind of budget-balance, but possibly over a long horizon, will be required of any such policy. We choose to work with the most stringent budget balance policy.
- 19.
By the equally weighted GGPO emission level what we mean is that we consider the GGPO where each country is given equal weight. In terms of the notation of Sect. 3, the weight \(x_{i}=\frac{1}{I}\), for all i.
- 20.
As always, given Nash equilibrium logic, one can ignore multiple simultaneous deviations.
- 21.
In the CRS case the effective and actual growth rates of capital coincide.
- 22.
The United States House of Representatives passed a bill in June, 2009 that would place tariffs on countries that do not adjust their carbon emissions. See http://www.nytimes.com/2009/06/29/us/politics/29climate.html.
- 23.
Subsequent to Kyoto, at the Hague November 2000 meeting, the most popular proposal (which came from the Dutch Environment Minister Jan Pronk) was that countries would face an escalating series of target reductions in the future if they failed to comply in the current stage. A watered-down version of this proposal was adopted in Bonn in March, 2001.
- 24.
Some of these papers allow asymmetry; however, none of them analyzes the effect of asymmetries. One significant exception is the recent paper of Long and Sorger that explicitly considers asymmetry in appropriation costs within the Tornell and Velasco model.
- 25.
But also see Chichilnisky (2006).
- 26.
To be fair, Nordhaus and Boyer (2000) and Nordhaus and Zhang 1996 do consider strategic models but restrict themselves to open-loop strategies.
- 27.
Recall the convention is that donations are negative while receipts are postive numbers.
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Dutta, P.K., Radner, R. (2016). Capital Growth in a Global Warming Model: Will China and India Sign a Climate Treaty?. In: Chichilnisky, G., Rezai, A. (eds) The Economics of the Global Environment. Studies in Economic Theory, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-319-31943-8_14
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