## Abstract

We explore the implications of an increase in clean technology spillovers between developed and developing countries. We build a game of abatements in which players are linked with technology spillovers determined by an initial choice of absorptive capacities by developing countries. We show that, within a non-cooperative framework, the response of clean technology investments in developed countries to an increase in cross-country technology spillovers is ambiguous. If the marginal benefits of these additional abatements are not sufficiently high, developed countries have a strategic incentive to decrease investments. Such a strategic response jeopardizes the initial effects of an increase in technology spillovers on climate change mitigation and decreases the incentives for developing countries to enhance their absorptive capacities.

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## Notes

These initiatives are often combined with more general policies in developing countries (Dechezleprêtre et al. 2008). Changes in absorptive capacities can also be the consequence of changes in environmental regulation (Lanjouw and Mody 1996; Hilton 2001; Gallagher 2006). Other options are openness to trade, foreign direct investment and by strengthening education and skills. See Dutz and Sharma (2012), Popp (2011), World Bank (2010), Dechezleprêtre et al. (2011) and Dechezleprêtre et al. (2013) for discussions.

This objective was reconfirmed in the Paris Agreement of COP 21 in December 2015.

For instance, Popp (2011) discusses evidence on the transfers of climate friendly technologies through projects in the framework of the Clean Development Mechanisms (CDM) of the Kyoto Protocol.

In practice, this encompasses a number of policies in favor of public and private investment in clean technologies, but we follow the standard specification that a country directly invests in a level of technology.

We borrow this specification of imperfect spillovers from Spence (1984).

In the examples we provide, this condition however always holds.

For a Nash bargaining solution to be implementable, the enhancement of absorptive capacities must be contractible. Else, the developing country could perfectly accept a transfer

*T*to increase spillovers and not improve absorptive capacities if it decreases its surplus.The equilibrium abatements in the second stage are given by \(a_1^*=\frac{2x}{1+(1+\gamma )x}\) and \(a_2^*=\gamma \frac{2x}{1+(1+\gamma )x}\). The equilibrium level of absorptive capacities in the first stage is the solution to \(x^* = \arg \max _{x} -\frac{(2-a_1^*-a_2^*)^2}{2} - \frac{(a_{1}^*)^{2}}{2x} - x\).

The equilibrium abatements in the second stage are given by \(a_1^*=\frac{4x}{1+(1+\gamma )2x}\) and \(a_2^*=\gamma \frac{4x}{1+(1+\gamma )2x}\). The equilibrium level of absorptive capacities in the first stage is the solution to \(x^* = \arg \max _{x} -(2-a_1^*-a_2^*)^2- \frac{(a_{1}^*)^{2}}{2x} - x\).

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We thank Antonio Estache, Estelle Cantillon, Jérôme Danguy, Bram De Rock, Christian von Hirschhausen, David Popp, Aurélie Slechten, Anja Schöttner, Cheng Wan and three anonymous referees for helpful comments. G. Garsous gratefully acknowledges the financial support of Fonds National de la Recherche Scientifique (FNRS) and the Belgian American Educational Foundation (BAEF).

## Mathematical Appendix

### Mathematical Appendix

### 1.1 Proof of Lemma 1

In this proof, we analyze the second stage subgame. From Eqs. (6) and (7), we can derive the slopes of the best-responses \(a_{1}(a_{2}, x, \gamma )\) and \(a_{2}(a_{1}, x, \gamma )\):

As a result, the game has a unique and stable equilibrium.

Next, if we assume that *x* is held constant, then we have that:

It follows that \(\pi _{2}\) displays increasing differences in \((a_{2},\gamma )\).

An increase in \(\gamma \) induces a positive shift in player 2’s best response \(a_{2}(a_{1}, x, \gamma )\). As the best responses \(a_{1}(a_{2},x, \gamma )\) and \(a_{2}(a_{1}, x, \gamma )\) both have a slope belonging to \((-1,0)\), the subsequent decrease in \(a^{*}_{1}\) is less than proportional to the increase in \(a^{*}_{2}\). As a result, we have that \((a^{*}_{1}+a^{*}_{2})\) must increase with \(\gamma \). It follows that \({\partial a^{*}_{2}}/{\partial \gamma } \ge 0\) and \({\partial a^{*}_{1}}/{\partial \gamma } \le 0\) and \({\partial (a^{*}_{1}+a^{*}_{2})}/{\partial \gamma } \ge 0\).

### 1.2 Proof of Claim 1

Thanks to the Implicit Function Theorem, we have that

As a result, we have:

### 1.3 Proof of Corollary 1

From Eq. (8), we know that \(a^{*}_{2}= \gamma a^{*}_{1}\). Replacing this value in Eq. (36) in the proof of Lemma 1, it follows directly that

for \(\gamma \in [0,1]\).

### 1.4 Proof of Proposition 2

For an increase in \(\gamma \), the total effect on payoff of country 1 is given by:

as at equilibrium, \(\left( \frac{\partial b}{\partial a} \frac{\partial a^{*}_{2}}{\partial x} - \frac{\partial c}{\partial x} - \alpha \right) =0\) [see condition (11)]. The sign of Eq. (38) is clearly positive as \({\partial b}/{\partial a} \ge 0\) by assumption and \({\partial a^{*}_{2}}/{\partial \gamma } \ge 0\) thanks to Lemma 1.

For an increase in \(\gamma \), the total effect on payoff of country 2 is given by:

thanks to the envelop theorem. We have \({\partial b}/{\partial a} > 0\), \({\partial c}/{\partial x} < 0\) and \({\partial c}/{\partial \gamma } < 0\) by assumption. However, we have that \({\partial x^{*}}/{\partial \gamma }\) and \({d a^{*}_{1}}/{d \gamma }\) are ambiguous by Proposition 1. It follows that the sign of Eq. (39) is ambiguous.

### 1.5 Proof of Proposition 4

A Nash bargaining with bargaining power \(\beta \) to the developing country 2 implies a transfer from country 1 to country 2 equal to the difference between a share \(\beta \) of the additional surplus generated by the technology spillovers and the additional surplus obtained by country 2. As we assume spillovers are the consequence of an agreement, the disagreement point corresponds to the payoffs if \(\gamma =0\). This is, using (38) and (39) and adding the enhancement of absorptive capacities \(\kappa \),

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Foucart, R., Garsous, G. Climate Change Mitigation with Technology Spillovers.
*Environ Resource Econ* **71**, 507–527 (2018). https://doi.org/10.1007/s10640-017-0170-3

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DOI: https://doi.org/10.1007/s10640-017-0170-3