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First-and second-best allocations under economic and environmental uncertainty

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Abstract

This paper uses a micro-founded DSGE model to compare second-best optimal environmental policy, and the resulting Ramsey allocation, to first-best allocation. The focus is on the source and size of uncertainty, and how this affects optimal choices and the comparison between second- and first-best. While higher economic volatility is bad for social welfare in all cases studied, the welfare effects of higher environmental volatility depend on its size and the effectiveness of public abatement policy. The Ramsey environmental tax is pro-cyclical when there is an economic shock, while it is counter-cyclical when there is an environmental shock.

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Notes

  1. For environmental policy instruments, see the survey by Bovenberg and Goulder (2002). For environmental tax rates in growth models, see the survey by Xepapadeas (2004).

  2. There is a rich literature on the role of uncertainty in environmental policy that goes back to Weitzman (1974). For a review of this literature, see Bovenberg and Goulder (2002).

  3. Higher extrinsic volatility means a mean-preserving higher standard deviation of shocks to these exogenous processes.

  4. The recent BP oil leak in the Gulf of Mexico is an example of such environmental shock.

  5. See also e.g. Economides and Philippopoulos (2008). See Angelopoulos et al. (2010) for other forms of second-best environmental policy.

  6. We abstract from labor-leisure choices to keep the model simpler.

  7. The motion of natural resources in (3) is as in Jouvet et al. (2005); see p. 1599 in their paper for further details. The inclusion of the parameter \(\bar{Q} \ge0\) is helpful when we solve the model numerically.

  8. In an earlier version of this paper, optimal policy was computed by finding the flat over time tax rate that maximized expected discounted lifetime utility. In the present version, we solve for standard Ramsey tax policy as in Chamley (1986). We report that our main qualitative results are not affected. This is similar to the finding in Schmitt-Grohé and Uribe (2005) although in a different model.

  9. As is known, the Ramsey government finds it optimal to confiscate initial capital. To avoid this feature of optimal policy that makes the problem trivial, it is usually assumed that the initial tax rate, τ 0, is given. It is also known that t=0 choices differ from t≥1 ones. In what follows, we focus on t≥1.

  10. We report that first- and second-order approximate solutions produce similar impulse responses. This is as in e.g. Schmitt-Grohé and Uribe (2005). The impulse response functions presented here are based on linear approximations around the associated non-stochastic long-run equilibrium.

  11. An adverse TFP shock has symmetrically opposite effects.

  12. Recall that, by using a second-order approximation to equilibrium equations, we allow for the agents’ optimal policies to respond to volatility.

  13. We thank one of the referees for pointing this out.

  14. Notice that at the level of Decentralized Competitive Equilibrium in Sect. 2.5 above, which was for given tax policy, and if we use τ=0.31 which is close to the EU average for the effective income tax rate, we have ντ−ϕ<0 for both ν=1.5 and ν=0.6.

  15. Similarly, the social planner finds it optimal to increase spending on public abatement as a share of output as ν decreases. In this section, we focus on the second-best. The results for the social planner are generally similar.

References

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Acknowledgements

We thank two anonymous referees and the two guest editors, Thiess Buettner and Christos Kotsogiannis, for many constructive criticisms and suggestions. We thank Nick Hanley, Saqib Jafarey, Ioana Moldovan, Elissaios Papyrakis, Hyun Park and Tassos Xepapadeas for comments and discussions. We also thank seminar participants at the CESifo workshop on the “Fiscal implications of climate change”, held in Venice, July, 2010. Any remaining errors are ours. This research has been co-financed by the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)—Research Funding Program THALIS. Investing in knowledge society through the European Social Fund.

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Authors and Affiliations

  1. University of Glasgow, Adam Smith Building, Glasgow, G12 8RT, UK

    Konstantinos Angelopoulos

  2. Department of International and European Economic Studies, Athens University of Economics and Business, 76 Patission street, Athens, 10434, Greece

    George Economides

  3. Department of Economics, Athens University of Economics and Business, 76 Patission street, Athens, 10434, Greece

    Apostolis Philippopoulos

  4. CESifo, Munich, Germany

    Apostolis Philippopoulos

Authors
  1. Konstantinos Angelopoulos
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  2. George Economides
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  3. Apostolis Philippopoulos
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Correspondence to Apostolis Philippopoulos.

Appendices

Appendix A: DCE given taxes

The first-order conditions of the individual’s problem include the budget constraint in (2) and the Euler equation (7b). Using (4)–(5) into (3), we get (7c). All this gives (7a), (7b) and (7c) in the text.

Appendix B: Social planner’s solution

The planner chooses \(\{ C_{t},G_{t},K_{t + 1},Q_{t + 1}\} _{t = 0}^{\infty}\) to maximize (1a)–(1b) subject to

(B.1a)
(B.1b)

The optimality conditions include the two constraints above and

(B.2a)
(B.2b)
(B.2c)

where ξ t >0 is the multiplier associated with (B.1b), \(\frac{\partial u_{t}}{\partial C_{t}} = C_{t}^{ - \sigma_{1}}\) and \(\frac{\partial u_{t}}{\partial Q_{t}} = \mu Q_{t}^{ - \sigma_{2}}\). Using (B.2c) to substitute out ξ t , we get (10a), (10b), (10c), and (10d) in the text.

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Angelopoulos, K., Economides, G. & Philippopoulos, A. First-and second-best allocations under economic and environmental uncertainty. Int Tax Public Finance 20, 360–380 (2013). https://doi.org/10.1007/s10797-012-9234-z

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