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Optimal Pollution Taxation and Abatement When Leisure and Environmental Quality are Complements

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Abstract

We study optimal environmental policy in a world featuring multiple stable economic-ecological equilibria. There is a two-way interaction between the macro-economy and the environment. We assume that the society under consideration finds itself in a high pollution equilibrium and show that a benevolent social planner is in principle able to engineer substantial welfare gains by choosing the appropriate mix of Pigouvian (capital) taxation and abatement activities. During the initial phase of the policy, abatement is used to reduce the inflow of dirt to zero whereas the tax is employed to bring down the stock of the polluting capital input in an optimal fashion. In the long run abatement is no longer needed and the capital tax settles down at its externality-correcting Pigouvian level. For a plausible parameterization optimal abatement takes place for up to twenty-five years whilst the long-run pollution tax never exceeds seven percent of gross operating surplus. In order to escape out of the pollution trap the full force of the available environmental instruments is only needed temporarily.

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Notes

  1. The details of the ecological SLD system are spelled out in Heijdra and Heijnen (2013, pp. 50–52). For overviews of the SLD literature, see Muradian (2001), Mäler et al. (2003), Brock and Starrett (2003), and Wagener (2009). Economic applications of SLD include Heijnen and Wagener (2013), Ranjan and Shortle (2007), and Wirl (2004). A related nonlinear approach is used by Prieur (2009).

  2. Brock (1977), John and Pecchenino (1994), Michel and Rotillon (1995), Fullerton and Kim (2008), and Quaas et al. (2013) assume that labour supply is exogenous and preferences are nonseparable in consumption and environmental quality.

  3. If lump-sum taxes are not available then \(\theta \) serves the dual role of corrective tax and revenue raising instrument. See Sandmo (1975) for an overview of environmental Ramsey taxation in a static setting.

  4. Brock (1977) models the gross flow of environmental waste, \(D^{g}(\tau )\), as a joint product and writes the macroeconomic production function (using our notation) as \(F(\Phi \left[ K(\tau ),D^{g}(\tau )\right] ,L(\tau ))\) where \(\Phi \left[ \cdot \right] \) is some aggregator function. This captures the idea that the production of one unit of output requires less capital if a more polluting technique is used (1977, p. 443). Our approach is consistent with his provided the aggregator function is of the Leontief type, i.e. \(\Phi \left[ \cdot \right] \equiv \min \left\{ K(\tau ),D^{g}(\tau )/\kappa \right\} \).

  5. In Sect. 4.2 below we postulate an alternative functional form for \(\Pi \left( P\right) \) consistent with Logistic Dynamics (LOG) and multiple environmental equilibria. We also compare the LOG and SLD cases there.

  6. An alternative mechanism by which pollution could affect labour supply operates via the health nexus. In that approach pollution leads to health problems and loss of labour productivity resulting in lower labour supply. In our model this health-based mechanism has been abstracted from.

  7. In terms of the graphical aparatus developed below, this condition implies that the CKE curve must be steeper than the PE locus at stable equilibrium points—see Fig. 1d.

  8. This \(\mu \)-value implies strong complementarity between leisure and environmental quality. In Subsect. 4.1 below we conduct a robustness analysis of the model by considering alternative values for \(\mu \).

  9. Reichling and Whalen (2010) survey the empirical literature and argue that studies based on micro-data typically find estimates for the Frisch elasticity in the range of 0.1 to more than 1. In contrast, the macro-based estimates usually fall in the range from 2 to 4. Interestingly, in the clean equilibrium of the unmanaged economy we find \(1/\xi _{L}=2.910\).

  10. Heijdra and Heijnen (2014) study optimal environmental policy in a model with exogenous labour supply. Their model is a special case of the model employed here—it is obtained by setting \(\varepsilon _{e}=1\), \(L(t)=1\), and dropping equation (T1.2). With exogenous labour supply the steady-state reduction of the capital stock is quite small.

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Authors and Affiliations

  1. Faculty of Economics and Business, University of Groningen, P. O. Box 800, 9700 AV, Groningen, The Netherlands

    Ben J. Heijdra & Pim Heijnen

  2. CESifo, Munich, Germany

    Ben J. Heijdra

  3. Netspar, Tilburg, The Netherlands

    Ben J. Heijdra

  4. Institute for Macroeconomics and Econometrics, University of Bonn, Adenauerallee 24-42, 53113, Bonn, Germany

    Fabian Kindermann

Authors
  1. Ben J. Heijdra
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  2. Pim Heijnen
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  3. Fabian Kindermann
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Correspondence to Ben J. Heijdra.

Additional information

A very preliminary draft of this paper was presented at the 12th Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics, held at the Vienna University of Technology in May-June 2012. We thank Jan van Ours, Laurie Reijnders as well as various conference and seminar participants for their useful comments.

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Heijdra, B.J., Heijnen, P. & Kindermann, F. Optimal Pollution Taxation and Abatement When Leisure and Environmental Quality are Complements. De Economist 163, 95–122 (2015). https://doi.org/10.1007/s10645-014-9246-4

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