Information Exchange and Transnational Environmental Problems


This paper analyzes information exchange in a model of transnational pollution control in which countries use private information in independently determining their domestic environmental policies. We show that countries may not always have an incentive to exchange their private information. However, for a sufficiently high degree of predictability of domestic environmental policy processes, the expected welfare from sharing information is greater than the expected welfare from keeping it private. The minimum degree of policy predictability for which information sharing occurs increases with the level of environmental risk. Intuitively, information exchange can help mitigate the perception of global uncertainty (both political and scientific) that surrounds transnational environmental problems and potentially improve welfare if policymaking processes are sufficiently aligned with evidence-based approaches (predictable).

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Fig. 1
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  1. 1.

    See for instance Holland et al. (2014), Heal (2008), Hulme (2009), Milman and Ray (2011), Parson and Zeckhauser (1993), Gamman (1994), Salehyan and Hendrix (2010), Buhr and Freedman (2001), Haffoudhi (2005), Shock (2004), Drutman (2010), Pielke (2005, 2006), Washington and Cook (2011), Shock (2004), Cairns (1992), Sachs (2008).

  2. 2.

    In USA, lobbying and political contributors are not required to disclose the particular issues for which their contributions are targeted.

  3. 3.

    The predictability of the policymaking process is inextricably linked to transparency and accountability issues. The paper by Juni (2000) discusses factors that may affect transparency in environmental policy making processes.

  4. 4.

    The paper by Espinola-Arredondo and Munoz-Garcia (2011) looks at the management of information in a common pool resource where an incumbent has complete information on the stock while the entrant has incomplete information.

  5. 5.

    In solving the model in Sect. 3, we will focus on the case where \(N=2\) (two countries).

  6. 6.

    We thank an anonymous reviewer for raising this possibility.

  7. 7.

    For instance, each country benefits from burning fossil fuels to run its economy.

  8. 8.

    Accounting for private information in the process of making regulations should be an integral part of the study of the political economy of environmental policy (Millner and Ollivier 2016).

  9. 9.

    Thank you to an anonymous referee for pointing this out.

  10. 10.

    See for instance (Holland et al. 2014; Heal 2008; Hulme 2009; Milman and Ray 2011; Parson and Zeckhauser 1993; Gamman 1994; Salehyan and Hendrix 2010; Buhr and Freedman 2001; Haffoudhi 2005; Shock 2004; Drutman 2010; Pielke 2005, 2006; Washington and Cook 2011; Shock 2004; Cairns 1992; Sachs 2008).

  11. 11.

    Note that this is not equivalent to each country facing the same domestic constraints, \(\mathbf X ^{i}\), on the level of stringency since the values of \(\mathbf X \) are indexed by i.

  12. 12.

    For instance, the parliament in each country can write up a bill to control the domestic amount of pollution. The process of transforming an idea into legislative language is typically an interactive, behind-the-scenes process that can take into account some political factors that are not publicly known.

  13. 13.

    The conditional probability \(P\left( \widetilde{s}^{i}=s^{i}_{L}\Big |\widetilde{\upbeta }={\upbeta }_{H}\right) \) or \(P\left( \widetilde{s}^{i}=s^{i}_{H}\Big |\widetilde{\upbeta }={\upbeta }_{L}\right) \) may be thought of as the likelihood that policymaking processes are not aligned with evidence-based approaches (predictability). For instance, the expression \(P\left( \widetilde{s}^{i}=s^{i}_{L}\Big |\widetilde{\upbeta }={\upbeta }_{H}\right) \) would represent the likelihood that the private information that drives the policymaking process is not aligned with an evidence-based approach (predictability) that supports a stringent stance on transnational environmental problems.

  14. 14.

    Note that this implies that both countries are identical ex ante.

  15. 15.

    In a model where private the signal is first observed before information exchange decision is made, a country can possibly send a noisy signal to another country, therefore allowing an environment in which individual countries can strategically manipulate the information that is being shared.

  16. 16.

    The effect of predictability on the policy outcomes may be thought of as a form of rational expectations.

  17. 17.

    By worst case scenarios, we refer to an asymptotic analysis where the level of uncertainty ( say variance) on the damage parameter grows large, which can also be thought off as the limiting case where the ratio \(\frac{{\upbeta }_{H}}{{\upbeta }_{L}}\) is very large.

  18. 18.

    In the climate agreement reached in Paris in December 2015, it is expected that countries will continue to include more transparent and evidence-based approaches in their domestic policymaking processes (Dimitrov 2016).


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We would like to thank the Editor and two anonymous referees for insightful and constructive suggestions. We appreciate helpful comments from Billy Pizer, Suzanne Dovi, Laura Evans, Steve Van Evera, Peter Maniloff, Brice Nguoghia, Matthew Platt, Quinn Weninger, Abdoul Sam, Charles F. Mason, and Claudia Bradley. We also thank participants at the 2012 Voluntary Pollution Control (VPC) Workshop in Ohio, the 2012 International EcoSummit in Ohio, and the 2012 Southern Economic Association Conference in New Orleans. All remaining errors are our own.

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Correspondence to Johnson Kakeu.


Appendix A: Expression of Probabilities in Eqs. (17) and (18)

Using the Bayes’ rule, The conditional probability of \({\upbeta }_{L}\) given the private signal \(s_{L}^{1}\) is computed as:

$$\begin{aligned} P({\upbeta }_{L}|s_{L}^{1})= & {} \frac{P({\upbeta }_{L},s_{L}^{1})}{P({\upbeta }_{L})},\nonumber \\= & {} \frac{P(s_{L}^{1}|{\upbeta }_{L})P({\upbeta }_{L})}{P(s_{L}^{1}|{\upbeta }_{L})P ({\upbeta }_{L})+P(s_{L}^{1}|{\upbeta }_{H})P({\upbeta }_{H})}, \nonumber \\= & {} \frac{P(s_{L}^{1}|{\upbeta }_{L})P({\upbeta }_{L})}{P(s_{L}^{1}|{\upbeta }_{L})P ({\upbeta }_{L})+\left[ 1-P(s_{H}^{1}|{\upbeta }_{H})\right] P({\upbeta }_{H})}, \nonumber \\= & {} \frac{\frac{1}{2}\upsigma }{\frac{1}{2}\upsigma +\frac{1}{2}(1-\upsigma )},\nonumber \\= & {} \frac{\frac{1}{2}\upsigma }{\frac{1}{2}},\nonumber \\= & {} \upsigma . \end{aligned}$$

The conditional probability of \({\upbeta }_{H}\) given the private signal \(s_{L}^{1}\) is computed by using the complement rule for conditional probabilities:

$$\begin{aligned} P({\upbeta }_{H}|s_{L}^{1})=1-P({\upbeta }_{L}|s_{L}^{1})=1-\upsigma . \end{aligned}$$

Using the multiplication rule (or chain rule) for conditional probabilities, the joint probability \(P({\upbeta }_{L},s_{L}^{2}|s_{L}^{1})\) is computed as follows:

$$\begin{aligned} P({\upbeta }_{L},s_{L}^{2}|s_{L}^{1})= & {} \frac{P({\upbeta }_{L},s_{L}^{2},s_{L}^{1})}{P(s_{L}^{1})}\end{aligned}$$
$$\begin{aligned}= & {} \frac{P(s_{L}^{1},s_{L}^{2},{\upbeta }_{L})}{P(s_{L}^{1})},\nonumber \\= & {} \frac{P(s_{L}^{1},s_{L}^{2}|{\upbeta }_{L})P({\upbeta }_{L})}{P(s_{L}^{1})}\nonumber \\= & {} \frac{P(s_{L}^{1})|{\upbeta }_{L})P({\upbeta }_{L})P(s_{L}^{2}|{\upbeta }_{L})}{P(s_{L}^{1})}\nonumber \\&\qquad (since\,s_{L}^{1}\,and\,s_{L}^{2}\,are\,conditionally\,independent\,given\, {\upbeta }_{L}),\nonumber \\= & {} \frac{P(s_{L}^{1},{\upbeta }_{L})P(s_{L}^{2}|{\upbeta }_{L})}{P(s_{L}^{1})},\nonumber \\= & {} \frac{P({\upbeta }_{L}|s_{L}^{1})P(s_{L}^{1})P(s_{L}^{2}|{\upbeta }_{L})}{P(s_{L}^{1})},\nonumber \\= & {} P({\upbeta }_{L}|s_{L}^{1})P(s_{L}^{2}|{\upbeta }_{L}),\nonumber \\= & {} \upsigma \upsigma ,\nonumber \\= & {} \upsigma ^{2}. \end{aligned}$$

The computation of the following conditional probabilities follows the same reasoning.

$$\begin{aligned} \left\{ \begin{array}{ll} P({\upbeta }_{L},s_{H}^{2}|s_{L}^{L})=\upsigma (1-\upsigma ),\\ P({\upbeta }_{H},s_{L}^{2}|s_{L}^{1})=(1-\upsigma )^{2},\\ P({\upbeta }_{H},s_{H}^{2}|s_{L}^{1})=\upsigma (1-\upsigma ),\\ P({\upbeta }_{L},s_{L}^{2}|s_{H}^{1})=(1-\upsigma )\upsigma ,\\ P({\upbeta }_{L},s_{H}^{2}|s_{H}^{1})=(1-\upsigma )^{2},\\ P({\upbeta }_{H},s_{L}^{2}|s_{H}^{1})=\upsigma (1-\upsigma ),\\ P({\upbeta }_{H},s_{H}^{2}|s_{H}^{1})=\upsigma ^{2}.\\ \end{array} \right. \end{aligned}$$

Note also that \(P({\upbeta }_{L}|s_{H})=1-\upsigma \) and \(P({\upbeta }_{H}|s_{H})=\upsigma \)

Appendix B: Expression of Probabilities in the First Order Eq. (29)

Using the Bayes’ rule, the conditional probability \(P({\upbeta }_{L}|s_{L},s_{L})\) is computed as

$$\begin{aligned} P({\upbeta }_{L}|s_{L},s_{L})= & {} \frac{ P(s_{L},s_{L}|{\upbeta }_{L})P({\upbeta }_{L})}{ P(s_{L},s_{L})}, \end{aligned}$$
$$\begin{aligned}= & {} \frac{ P(s_{L}|{\upbeta }_{L})P(s_{L}|{\upbeta }_{L})P ({\upbeta }_{L})}{ P(s_{L},s_{L}|{\upbeta }_{L})P({\upbeta }_{L})+P(s_{L},s_{L}| {\upbeta }_{H})P({\upbeta }_{H})} , \end{aligned}$$
$$\begin{aligned}= & {} \frac{ P(s_{L}|{\upbeta }_{L})^{2}P({\upbeta }_{L})}{ P(s_{L}|{\upbeta }_{L})^{2} P({\upbeta }_{L})+P(s_{L}|{\upbeta }_{H})^{2}P({\upbeta }_{H})}, \end{aligned}$$
$$\begin{aligned}= & {} \frac{\frac{1}{2}\upsigma ^{2}}{\frac{1}{2}\upsigma ^{2}+\frac{1}{2}(1-\upsigma )^{2}}, \end{aligned}$$
$$\begin{aligned}= & {} \frac{\upsigma ^{2}}{\upsigma ^{2}+(1-\upsigma )^{2}} , \end{aligned}$$

A similar reasoning is used to compute the following probabilities:

$$\begin{aligned} \left\{ \begin{array}{ll} P({\upbeta }_{L}|s_{L},s_{H})=\frac{1}{2},\\ P({\upbeta }_{L}|s_{H},s_{L})=\frac{1}{2},\\ P({\upbeta }_{L}|s_{H},s_{H})=\frac{(1-\upsigma )^{2}}{\upsigma ^{2}+(1-\upsigma )^{2}},\\ P({\upbeta }_{H}|s_{L},s_{H})=\frac{1}{2},\\ P({\upbeta }_{H}|s_{L},s_{L})=\frac{(1-\upsigma )^{2}}{\upsigma ^{2}+(1-\upsigma )^{2}},\\ P({\upbeta }_{H}|s_{H},s_{L})=\frac{1}{2},\\ P({\upbeta }_{H}|s_{H},s_{H})=\frac{\upsigma ^{2}}{\upsigma ^{2}+(1-\upsigma )^{2}}.\\ \end{array} \right. \end{aligned}$$

Appendix C: Expression of Probabilities in the Expected Welfare Eqs. (23) and (32)

$$\begin{aligned} P({\upbeta }_{L},s_{L},s_{L})=P({\upbeta }_{L},s_{L}|s_{L})P(s_{L})=\frac{1}{2}\upsigma ^{2}. \end{aligned}$$

Following the same reasoning, the following probabilities are computed:

$$\begin{aligned} \left\{ \begin{array}{ll} P({\upbeta }_{L},s_{H},s_{L})=\frac{1}{2}\upsigma (1-\upsigma ),\\ P({\upbeta }_{H},s_{L},s_{L})=\frac{1}{2}(1-\upsigma )^{2},\\ P({\upbeta }_{H},s_{H},s_{L})=\frac{1}{2}\upsigma (1-\upsigma ),\\ P({\upbeta }_{L},s_{L},s_{H})=\frac{1}{2}(1-\upsigma )\upsigma ,\\ P({\upbeta }_{L},s_{H},s_{H})=\frac{1}{2}(1-\upsigma )^{2},\\ P({\upbeta }_{H},s_{L},s_{H})=\frac{1}{2}\upsigma (1-\upsigma ),\\ P({\upbeta }_{H},s_{H},s_{H})=\frac{1}{2}\upsigma ^{2}. \end{array} \right. \end{aligned}$$

Appendix D: The Value of Information Sharing

The value of information sharing is given by:

$$\begin{aligned}&E\left[ \widetilde{V}_{sharing}(e_{ij},\widetilde{\upbeta })\right] -E\left[ \widetilde{V}_{no\,sharing}(e_{i})\right] \nonumber \\&\quad =\frac{\upsigma ^{2}}{2}\left[ e_{LL}+e_{HH}-\frac{(1+\upalpha )^2}{2} ({\upbeta }_{L} e_{LL}^{2}+{\upbeta }_{H} e_{HH}^2)\right] \nonumber \\&\qquad + \frac{(1-\upsigma )^{2}}{2}\left[ e_{LL}+e_{HH}-\frac{(1+\upalpha )^2}{2} ({\upbeta }_{L} e_{HH}^{2}+{\upbeta }_{H} e_{LL}^{2})\right] \nonumber \\&\qquad + \upsigma (1-\upsigma )\left[ 2e_{LH}-\frac{(1+\upalpha )^2}{2}({\upbeta }_{L} +{\upbeta }_{H}) e_{LH}^{2})\right] -\log \left( \frac{1}{\upsigma }\right) \nonumber \\&\qquad - \frac{(1-\upalpha ^2)}{4}\left[ \upsigma ({\upbeta }_{L}e^2_{L}+{\upbeta }_{H}e^2_{H}) + (1-\upsigma )( {\upbeta }_{L}e^2_{H} +{\upbeta }_{H}e^2_{L}) \right] -\log \left( \frac{1}{\upsigma }\right) . \end{aligned}$$

where \(e_{LL},\,e_{LH}\) and \(e_{HH}\) are given by Eq. (30) while \(e_{L}\) and \(e_{H}\) are given by Eqs. (20)–(21).

Appendix E: Graph of the Value of Information Sharing, with \(\upalpha =1\)

As shown in Fig. 3 above, the value of information sharing can take either a positive or a negative sign depending on the values taken by the level of riskiness of the environmental damage and the degree of predictability of the environmental policy. This suggests that sharing information or keeping it private are plausible outcomes that may occur in analyzing information exchange in transnational environmental problems.

Fig. 3

The value of information sharing drawn on the \(\left( {\upbeta }_{H}/ \upbeta _{H} \,,\,\upsigma \right) \) plane, with \(\upalpha =1\) and \({\upbeta }_{L}=0.3\)

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Kakeu, J., Johnson, E.P. Information Exchange and Transnational Environmental Problems. Environ Resource Econ 71, 583–604 (2018).

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  • Information exchange
  • Uncertainty
  • Private information
  • Environmental policy
  • Policy predictability
  • Transnational pollution
  • Bayesian game approach

JEL Classification

  • D8
  • Q5
  • F5