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Emissions tax and second-mover advantage in clean technology R&D

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Abstract

This paper shows that under an emissions tax regime where firms have heterogenous capabilities in clean technology R&D, firms can acquire technology developed by rival firms at a lower cost than developing the technology in-house. In anticipation of such second-mover advantage in R&D, this creates an investment disincentive for technological innovators and resulted in lower social welfare relative to the case where firms’ technological competencies are homogenous and knowledge spillovers are equally shared. To resolve, the government can award a targeted subsidy, instead of a standard uniform subsidy, solely to the innovator to seed research.

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Notes

  1. A typical example is Australia. In 2012 the carbon tax was introduced by the socialist Labor government but was subsequently repealed by the conservative Coalition government when it assume power.

  2. Empirically, political and transaction costs can sometimes delay or prevent policy updating. This occurs whenever preferences between environmentalists and industrial firms differ substantially and political lobbying may hinder policy changes in response to market and environmental conditions. Studies that investigates such issues on environmental policy implementation includes Zhao and Kling (2003) and Coria (2012).

  3. Other related papers in this theoretical literature on absorptive capacity included Suzumura (1992) and Simpson and Vonortas (1994), who provide general comparative static results using generalized cost and demand functions that include absorptive capacity as a special case.

  4. One advantage of the additively separable model is that it is more tractable than the case where R&D effort impacts on the marginal abatement effort of firms so that spillovers are proportional to output, i.e., \(e(q,X_{i})=q(\bar{e}-X_{i})\), where \(\bar{e}\) as emissions per unit of output with the current technology. See Chiou and Hu (2001) and McDonald and Poyago-Theotoky (2015) for examples of the proportional model applied to environmental R&D. Petrakis and Xepapadeas (2003) have shown that the results from the additively separable model are robust to the more general model in which emissions are proportional to output.

  5. Firm 1 is essentially a Stackelberg leader in clean R&D investment while Firm 2 is the Stackelberg follower.

  6. An example of such one-way asymmetric R&D spillovers in clean technology is the case of photovoltaic (PV) industry in China (De la Tour et al. 2011). To conduct reverse engineering, the Chinese firms acquired technological knowledge by purchasing manufacturing equipment (particularly the turnkey production lines) produced by developed countries such as US, German, and Japan. At the same time, these Chinese firms employed highly skilled executives from the Chinese diaspora to further developed the PV systems. On the other hand, the firms in the industrialized countries did not benefit from the process innovations of the Chinese firms. In the theoretical literature, Amir and Wooders (1999, 2000) have analyzed such one-way R&D spillovers from an innovator firm to an imitator firm for cost-reducing process R&D.

  7. Luckraz (2007) uses similar effective spillover benefits to study cost-reducing process R&D.

  8. Gil Moltó et al. (2005) has modeled endogenous R&D spillovers where compatible R&D technologies lead the higher the spillover benefits between firms. This is relevant to model inter-industry spillovers, where the same technology can be applied across many different industries and this requires the firms to have similar R&D profiles. However, our way of modeling is more appropriate for intra-industry spillover, where the same technology is applied within firms for the purpose of pollution abatement.

  9. Amir (2000) argued that models using the additive benefit function, in line with the classic D’Aspremont and Jacquemin (1988) R&D formulation, fails to account for the stylized fact that firms cannot free-ride on its rival without incurring some a priori absorptive cost.

  10. The average cost of R&D for Firm 2 is given by \(AC_{2}(x_{2})=bx_{1}/x_{2}+\gamma x_{2}/2\). The marginal cost of R&D for firm 2 is given by \(MC_{2}(x_{2})=\gamma x_{2}\). Hence, for Firm 2 economies of scale for R&D will exist in the region where \(bx_{1}\ge \gamma x_{2}^{2}/2\).

  11. In the cost-reducing process R&D literature, Cohen and Levinthal (1989) have highlighted that R&D investment has two facets: in addition to improving its own research output, the more a firm invests in R&D the better it is able to make use of the spillovers coming from other firms. In this case, we have explicitly allowed for the cost of investment in absorptive capacity to increase to allow the imitator firm to better assimilate and uses the innovating firm’s technology to reduce pollution.

  12. Our results are robust to the alternative specification of the game where the government sets the emissions tax ex ante (the precommitment tax). It can be shown that the second-mover advantage still exists despite the innovator investing in clean technology R&D before the imitator do so. Proof are available upon request.

  13. The second-order condition is \(\frac{\partial ^{2}\pi _{2}}{\partial x_{2}^{2}}=-\frac{11}{8}\left( 1-b\right) ^{2}-\gamma <0\). This inequality holds for \(0\le b\le 1\) and \(\gamma >0\). The required stability condition is

    $$\begin{aligned} \left| \frac{\partial ^{2}\pi _{2}}{\partial x_{1}\partial x_{2}}/\frac{\partial ^{2}\pi _{2}}{\partial x_{2}^{2}}\right| =\left| \frac{5+(6-11b)b}{11(1-b)^{2}+8\gamma }\right| >1. \end{aligned}$$

    This stability condition is satisfied for \(0<b\le 3/11\) and \(\gamma >0\) and for \(3/11<b\le 1\) and \(\gamma \ge 1/4(-3+14b-11b^{2})\).

  14. The second-order condition is \(\frac{\partial ^{2}\pi _{1}}{\partial x_{1}^{2}}=-\frac{189\left( 1-b\right) ^{4}+2\left( 1-b\right) ^{2}\left[ 313-b\left( 122-121b\right) \right] \gamma +16\left[ 33-b\left( 34-21b\right) \right] \gamma ^{2}+128\gamma ^{3}}{2\left[ 11\left( 1-b\right) ^{2}+8\gamma \right] ^{2}}<0\), which is satisfied for \(\gamma >0\) and \(0\le b\le 1\).

  15. The issue is similar to the self-selection problem and Pareto efficient taxation considered by Stiglitz (1981).

  16. In the symmetric model, the firms’ R&D investment in clean technology, R&D spillovers, and absorptive cost is similar among firms. For similar market size and for all values of R&D spillovers and its associated investment cost efficiency, the social welfare is higher compared to the current asymmetric model formulation. Proof can be provided upon request.

  17. It could be possible to implement a lower subsidy than \(s^{**}\); however, this would be contingent on the size of the emission tax. Our purpose is simply to demonstrate that a suitable subsidy exists; thus \(s^{**}\) is sufficient (but not necessary) to satisfy the self-selection constraint.

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Acknowledgements

The authors thank Joanna Poyago-Theotoky and the seminar participants at the Econometrics Society Australasian Meetings for their helpful comments and suggestions. Funding support from the Global Change Institute and the University of Queensland Early Career Researcher Grant is gratefully acknowledged.

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Authors and Affiliations

  1. International Business School Suzhou, Xi’an Jiaotong-Liverpool University, Suzhou, China

    Soo Keong Yong

  2. Hanqing Advanced Institute of Economics and Finance, Renmin University of China, Haidian, China

    Stuart McDonald

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  1. Soo Keong Yong
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Correspondence to Soo Keong Yong.

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Yong, S.K., McDonald, S. Emissions tax and second-mover advantage in clean technology R&D. Environ Econ Policy Stud 20, 89–108 (2018). https://doi.org/10.1007/s10018-017-0185-6

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