Skip to main content

Advertisement

Log in

Adaptation to Climate Change: Commitment and Timing Issues

  • Published:
Environmental and Resource Economics Aims and scope Submit manuscript

Abstract

We study the impact of timing and commitment on adaptation and mitigation policies in the context of international environmental problems. Adaptation policies present the characteristics of a private good and may require a prior investment, while mitigation policies produce a public good. In a stylized model, we evaluate the impact of strategic commitment and leadership considerations when countries with different attitudes towards environmental cooperation coexist. We obtain equilibrium abatement and adaptation levels and environmental costs under partial cooperation for various timing and leadership scenarios. Crucially, global environmental costs suffered by countries are found to be greater when adaptation measures can be used strategically.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. For a recent survey please refer to Agrawala et al. (2011).

  2. Namely, the decision about the adaptation level is made before, after and simultaneously with the mitigation one, where the last two sequences are shown to be equivalent.

  3. Other papers adopting stylized functional forms in the literature use slightly different assumptions. The model of Buob and Stephan (2011) is consistent with (2), but uses a Cobb–Douglas formulation for the players’ utility. On the other hand, both Farnham and Kennedy (2014) and Marrouch and Ray Chaudhuri (2011) assume that the damage cost is bi-linear, which requires additionnal conditions on parameter values to ensure that the optimization problems are convex and that marginal costs have the expected signs.

  4. The alternative assumption that cooperating countries choose their mitigation levels jointly and their investment in adaptive measures individually is called semi-cooperation in Zehaie (2009).

  5. Notice that, because of this strategic role, the equilibrium results would be different if cooperators agreed to coordinate only their mitigation policies (semi-cooperation).

  6. However, it would be convenient for a group of collaborating countries to make the first move and become leaders.

  7. Numerical investigations show that, under leadership, prior investment is inefficient at the aggregate level, even if it may happen that leaders suffer a lower cost than in the concurrent investment case.

References

  • Agrawala S, Bosello F, Carraro C, De Cian E, Lanzi E (2011) Adapting to climate change: costs, benefits, and modelling approaches. Int Rev Environ Resour Econ 5(3):245–284

    Article  Google Scholar 

  • Barrett S (2008) Dikes vs. windmills: climate treatise and adaptation. Johns Hopkins University, School of Advanced International Studies, Washington

  • Bréchet T, Hritonenko N, Yatsenko Y (2013) Adaptation and mitigation in long-term climate policy. Environ Resour Econ 55(2):217–243

    Article  Google Scholar 

  • Buob S, Siegenthaler S (2011) Does adaptation hinder self-enforcing international environmental agreements?. Department of Economics and Oeschger Centre for Climate Change Research, University of Bern, Bern

    Google Scholar 

  • Buob S, Stephan G (2011) To mitigate or to adapt: how to confront global climate change. Eur J Polit Econ 27(1):1–16

    Article  Google Scholar 

  • De Bruin KC, Weikard HP, Dellink R (2011) The role of proactive adaptation in international climate change mitigation agreements. CERE Working Paper 9

  • Ebert U, Welsch H (2012) Adaptation and mitigation in global pollution problems: economic impacts of productivity, sensitivity, and adaptive capacity. Environ Resour Econ 52(1):49–64

    Article  Google Scholar 

  • Eisenack K, Kähler L (2012) Unilateral emission reductions can lead to Pareto improvements when adaptation to damages is possible. Tech. Rep. Wirtschaftswissenschaftliche Diskussionpapiere V - 344–12, University Oldenburg

  • European Commission Climate Action (2015) Adaptation to climate change. http://ec.europa.eu/clima/policies/adaptation/index_en.htm. Last update on 10/09/2015

  • Farnham M, Kennedy P (2014) Adapting to climate change: equilibrium welfare implications for large and small economies. Environ Resour Econ 61(3):345–363

  • Ingham A, Ma J, Ulph AM (2013) Can adaptation and mitigation be complements. Clim Change 120:39–53

    Article  Google Scholar 

  • IPCC (2014) Climate change 2014: synthesis report. Contribution of Working Groups I, II and III to the fifth assessment report of the Intergovernmental Panel on Climate Change, Core Writing Team, Pachauri RK, Meyer LA (eds). IPCC, Geneva, Switzerland

  • Kane S, Shogren JF (2000) Linking adaptation and mitigation in climate change policy. Clim Change 45(1):75–102

    Article  Google Scholar 

  • Lecocq F, Shalizi Z (2007) Balancing expenditures on mitigation of and adaptation to climate change: an exploration of issues relevant to developing countries. World Bank Policy Research Working Paper 4299

  • Marrouch W, Ray Chaudhuri A (2011) International environmental agreements in the presence of adaptation. FEEM Working Paper (35.2011)

  • President Barack Obama (2013) Climate action plan. https://www.whitehouse.gov/sites/default/files/image/president27sclimateactionplan

  • Tulkens H, Van Steenberghe V (2009) ‘Mitigation, adaptation, suffering’: In Search of the Right Mix in the Face of Climate Change. FEEM Working Paper (79.2009)

  • Yohe G, Strzepek K (2007) Adaptation and mitigation as complementary tools for reducing the risk of climate impacts. Mitig Adapt Strateg Glob Change 12(5):727–739

    Article  Google Scholar 

  • Zehaie F (2009) The timing and strategic role of self-protection. Environ Resour Econ 44(3):337–350

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michèle Breton.

Appendix

Appendix

In the following proofs, we use the auxiliary variables \(k\equiv \theta \omega -1>0\) and XY and W as defined in (12)–(14) to simplify the notation.

Claim 1

\(a_{C}^{\textit{PN}}>a_{I}^{\textit{PN}}\):

$$\begin{aligned} K_{1}\frac{a_{C}^{\textit{PN}}-a_{I}^{\textit{PN}}}{n\omega }=kW\left( Y-\omega \right) \left( X-\omega \right) >0. \end{aligned}$$

\(m_{C}^{\textit{PN}}\gtrless m_{I}^{\textit{PN}}\):

$$\begin{aligned} K_{1}\frac{m_{C}^{\textit{PN}}-m_{I}^{\textit{PN}}}{kn\omega W}=\theta \omega W\left( np-1\right) -XY+np\omega \left( X+Y-\omega \right) .\end{aligned}$$

This difference is negative if

$$\begin{aligned} 0<\theta <\frac{XY-np\omega \left( X+Y-\omega \right) }{\omega W\left( np-1\right) }=np\omega \frac{nq-1-np}{W}, \end{aligned}$$

which requires that \(nq-1>np\) (more defectors than cooperators).

\(c_{C}^{\textit{PN}}>c_{I}^{\textit{PN}}\):

$$\begin{aligned} 2K_{1}^{2}\frac{c_{C}^{\textit{PN}}-c_{I}^{\textit{PN}}}{n^{2}k^{2}W\omega \left( X-\omega \right) }= & {} kW\left( kW^{2}+\omega \left( 2X+\omega ^{2}+Y^{2}+X\left( 2X-\omega \right) +2Y\left( X-\omega \right) \right) \right) \\&+\,\left( \omega +1\right) \left( X+1\right) \left( \left( Y-\omega \right) \left( 3Y+X\omega +1\right) +Y^{2}\left( X-2\omega \right) \right) \\&+\,kW\left( 4\left( X+Y+XY\right) +X\left( 2X+Y^{2}\right) +2\left( Y^{2}+1\right) \right) \\&+\,\omega ^{2}\left( X+1\right) \left( \left( \omega +1\right) \left( Y+1\right) +X^{2}\right) \\&+\,\left( X+1\right) \left( 2\left( X+Y\right) +Y\left( 3X+Y^{2}\right) +X^{2}+1\right) \\&+\,\left( X+1\right) \left( \omega \left( 2\left( X+Y\right) +Y\left( 6X+Y^{2}\right) +2X^{2}+1\right) \right) \\> & {} 0. \end{aligned}$$

\(\square \)

Claim 2

\(m_{C}^{\textit{SN}}>m_{I}^{\textit{SN}}\):

$$\begin{aligned} K_{4}\left( m_{C}^{\textit{SN}}-m_{I}^{\textit{SN}}\right) =nk\left( np-1\right) >0. \end{aligned}$$

Total cost is higher for cooperating countries since the abatement and environmental costs are equal for both types of countries. \(\square \)

Claim 3

\(a_{C}^{PL}<a_{I}^{PL}\):

$$\begin{aligned} K_{5}\frac{a_{C}^{PL}-a_{I}^{PL}}{kn\omega }=-G^{2}U\omega \left( Y+1\right) k-U\omega W\left( G+U\omega \right) \left( Y+1\right) -GXY\left( G+U\omega \right) <0. \end{aligned}$$

Numerical investigations show that mitigation levels and total costs differences can be positive or negative. For mitigation levels, \(m_{C}^{PL}\le m_{I}^{PL}\) when

$$\begin{aligned} np\le \frac{\left( H+W\left( \omega +1\right) \left( \omega \left( Y+1\right) -G\right) \right) \left( \theta \omega H\left( Y+1\right) -XY\left( G+\omega U\right) \right) }{\left( U+\theta G\right) \left( -\omega UW+YG\left( Y+1\right) +\theta \omega \left( H-G^{2}\right) \right) G\omega }. \end{aligned}$$

\(\square \)

Claim 4

\(m_{C}^{\textit{SL}}\gtrless m_{I}^{\textit{SL}}\):

$$\begin{aligned} \omega K_{6}\frac{m_{C}^{\textit{SL}}-m_{I}^{\textit{SL}}}{kn}=k\left( np-nq\omega -1\right) +np-1 \end{aligned}$$

Since adaptation levels are the same for the two types of countries, both \(m_{C}^{\textit{SL}}<m_{I}^{\textit{SL}}\) and \(c_{C}^{\textit{SL}}<c_{I}^{\textit{SL}}\) hold when

$$\begin{aligned} np<1+\frac{k}{k+1}nq\omega . \end{aligned}$$

\(\square \)

Claim 5

  1. (a)

    \(c^{\textit{PI}}>c^{\textit{SI}}>c^{\textit{FB}}\):

    $$\begin{aligned} 2K_{3}^{2}K_{5}^{2}\frac{c^{\textit{PI}}-c^{\textit{SI}}}{k^{2}n^{2}\left( n-1\right) ^{2}}= & {} k\left( \omega +2\right) \left( n\omega +1\right) ^{2}+\left( \omega +1\right) \left( \omega \left( 2n-1\right) +2\right)>0 \\ 2\omega K_{2}K_{5}^{2}\frac{c^{\textit{SI}}-c^{\textit{BF}}}{kn^{2}}= & {} k\left( n-1\right) ^{2}\left( k+1\right) >0. \end{aligned}$$
  1. (b)

    \(a^{\textit{PI}}>a^{\textit{SI}}>a^{\textit{FB}}\):

    $$\begin{aligned} K_{3}K_{5}\left( a^{\textit{PI}}-a^{\textit{SI}}\right)= & {} nk\omega \left( n-1\right) \left( n\omega +1\right) >0 \\ K_{2}K_{5}\frac{a^{\textit{SI}}-a^{\textit{BF}}}{n}= & {} kn\left( n-1\right) . \end{aligned}$$
  2. (c)

    \(m^{\textit{PI}}<m^{\textit{SI}}<m^{\textit{FB}}\):

    $$\begin{aligned} K_{3}K_{5}\frac{m^{\textit{PI}}-m^{\textit{SI}}}{kn}= & {} -\omega \left( n-1\right)<0 \\ K_{2}K_{5}\frac{m^{\textit{SI}}-m^{\textit{BF}}}{kn}= & {} -\left( n-1\right) \frac{k+1}{\omega }<0. \end{aligned}$$

\(\square \)

Claim 6

  1. (a)

    \(c_{C}^{\textit{SN}}>c^{\textit{FB}}\):

    $$\begin{aligned} 2\omega K_{2}K_{4}^{2}\frac{c_{C}^{\textit{SN}}-c^{\textit{FB}}}{k^{2}n^{3}}=knq\omega \left( np-1\right) \left( q+np\left( p+1\right) \right) +q\left( n+np-2\right) \left( k+1\right) >0. \end{aligned}$$

    \(c^{\textit{FB}}>c_{C}^{\textit{PN}},\) \(c^{\textit{FB}}\gtrless c_{I}^{\textit{SN}}\) and \(c^{\textit{FB}}\gtrless c_{I}^{\textit{PN}}\) were checked numerically. For instance, for \(n=100,\) \(np=60,\) \(\omega =0.4\) and \(\theta =4\), the cost of the individualist countries is smaller than in the first best solution for both types of adaptation.

  1. (b)

    \(a^{\textit{FB}}<a_{C}^{\textit{SN}}=a_{I}^{\textit{SN}}\) is immediate since \(K_{4}=\theta +n\left( \left( 1-p\right) +np^{2}\right) k<\theta +kn^{2}=K_{2}.\) We already showed that \(a_{I}^{\textit{PN}}<a_{C}^{\textit{PN}}.\) \(a^{\textit{FB}}<a_{I}^{\textit{PN}}\) was checked numerically.

  2. (c)

    \(m^{\textit{FB}}>m_{I}^{\textit{SN}}\): this is immediate from \(K_{4}<K_{2}\).

    \(m^{\textit{FB}}>m_{I}^{\textit{PN}}\) was checked numerically.

    \(m^{\textit{FB}}\gtrless m_{C}^{\textit{PN}}\): for different set of parameters, we obtained both signs for the difference \(m^{\textit{FB}}-m_{C}^{\textit{PN}}\) and \(m^{\textit{FB}}-m_{C}^{\textit{SN}}\). The mitigation level of cooperating countries is higher than in the first best solution when the mitigation cost coefficient \(\gamma _{M}\) is large compared to the environmental sensitivity \(\gamma _{D}\).

\(\square \)

Claim 7

  1. (a)

    \(c_{C}^{\textit{PN}}>c_{C}^{\textit{SN}}\) and \(c_{I}^{\textit{PN}}>c_{I}^{\textit{SN}}\) were checked numerically.

  1. (b)

    \(a_{C}^{\textit{PN}}>a_{I}^{\textit{PN}}>a_{I}^{\textit{SN}}=a_{C}^{\textit{SN}}\): we already proved that \(a_{C}^{\textit{PN}}>a_{I}^{\textit{PN}}\).

    $$\begin{aligned} K_{1}K_{4}\frac{a_{I}^{\textit{PN}}-a_{I}^{\textit{SN}}}{n}=k\omega W\left( X+Y-\omega \right) \left( Y+kW+XY+1\right) +X^{2}YkW>0. \end{aligned}$$
  2. (c)

    \(m_{C}^{\textit{PN}}<m_{C}^{\textit{SN}}\):

    $$\begin{aligned} K_{1}K_{4}\frac{m_{C}^{\textit{PN}}-m_{C}^{\textit{SN}}}{kn^{2}p}= & {} -YkW\omega \left( \omega \left( nq-1\right) \left( n^{2}p^{2}-1\right) +n^{2}p^{2}\right) \\&-XY\left( \omega +1\right) \left( W-\omega \right) <0 \end{aligned}$$

    \(m_{I}^{\textit{PN}}\gtrless m_{I}^{\textit{SN}}\):

    $$\begin{aligned} K_{1}K_{4}\frac{m_{I}^{\textit{PN}}-m_{I}^{\textit{SN}}}{kn\omega ^{2}}= & {} kW\left( n^{2}p^{2}\omega \left( np-1\right) \left( np+1\right) \left( nq-1\right) \right) \\&-\left( n^{2}p^{2}\omega +1\right) \left( nq\omega +1\right) \left( n^{2}p^{2}+nq-1\right) \\&-\,kW\left( n^{2}p^{2}+nq-1\right) . \end{aligned}$$

    \(m_{I}^{\textit{PN}}>m_{I}^{\textit{SN}}\) if both these conditions are satisfied:

    $$\begin{aligned} \omega>&\frac{n^{2}p^{2}+nq-1}{n^{2}p^{2}\left( np-1\right) \left( np+1\right) \left( nq-1\right) }>0 \\ \left( \theta \omega -1\right)>&\frac{\left( n^{2}p^{2}\omega +1\right) \left( nq\omega +1\right) \left( n^{2}p^{2}+nq-1\right) }{W\left( n^{2}p^{2}\omega \left( np-1\right) \left( np+1\right) \left( nq-1\right) -\left( n^{2}p^{2}+nq-1\right) \right) }>0. \end{aligned}$$

\(\square \)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Breton, M., Sbragia, L. Adaptation to Climate Change: Commitment and Timing Issues. Environ Resource Econ 68, 975–995 (2017). https://doi.org/10.1007/s10640-016-0056-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10640-016-0056-9

Keywords

Navigation