Second-Best Pollution Taxes and the Structure of Preferences.

• Author: Cremer, Helmuth

Helmuth Cremer [*]

Firouz Gahvari [+]

Norbert Ladoux [++]

We characterize optimal taxes on polluting and nonpolluting goods in Ramsey and Mirrlees second-best environments. The polluting good tax differs from the Pigouvian tax by Ramsey terms in the first and by Stiglitz/Mirrlees plus another adjustment term in the second. These terms can be positive, negative, or zero. If preferences are weakly separable in public and private goods, with the private good subutility weakly separable in labor and produced goods, nonpolluting goods are taxed uniformly and the concept of a tax differential between polluting and nonpolluting goods is well defined. The differential is then less than the Pigouvian tax in the Ramsey framework, but it can be greater, equal to, or smaller than the Pigouvian tax in the Mirrlees second best. In Mirrlees second best, if preferences are separable in labor supply and other goods, the second-best tax differential is identical to the Pigouvian tax.

1. Introduction

   The Pigouvian prescription for correcting an externality is to levy a tax on it equal to its marginal social damage. This is a first-best remedy, which may have to be modified in the second best. Sandmo (1975) made this point in a pioneering work more than two decades ago. He characterized second-best taxes in an economy where there are other distortionary taxes in the system. More recently, a number of authors have refined and extended Sandmo's results in a number of ways. [1] On the policy front, many European countries are considering carbon taxes, or taxes on energy consumption, to fight global warming. This is aimed at curtailing [CO.sub.2] emissions, from fossil-fuel combustion, deemed as the most important of greenhouse gases. Other counties like Australia, New Zealand, Sweden, Netherlands, and Finland already have carbon taxes in place. Such a tax has also been proposed and discussed in the United States (Poterba [1991, 1993] discusses various aspects of this tax at length). [2]

   An important policy question in this context is to determine how second-best considerations change the level of the optimal tax on a polluting good. This question was first studied by Bovenberg and van der Ploeg (1994) and Bovenberg and de Mooij (1994). The latter paper concluded that "in the presence of preexisting distortionary taxes, the optimal pollution tax typically lies below the Pigouvian tax ... " (p. 1085). As stated, however, this inquiry can take many different meanings. What these authors have in mind resembles Atkinson and Stern's (1974) discussion of the rule for, versus the level of, optimal provision of public goods in the second best. The first-best rule for levying a tax on a polluting good is to set it equal to its marginal social damage. This rule will be modified in the second best. Now suppose we were to set the tax on the basis of this modified rule. Would the resulting tax be lower or higher than that which would have resulted had we followed the first-best conventional rule? [3]

   Posed this way, one sees immediately that one cannot in general provide a clearcut, or even a meaningful, answer to this question. The first-best rule calls for a tax that is solely corrective. The second-best tax rule, on the other hand, embodies both corrective and optimal tax objectives. In a Ramsey tax setting, for example, the tax structure may be described as "Ramsey-plus-Pigou." [4] It thus seems rather odd that one is able to draw a clearcut conclusion regarding the size differential between the second-best and the Pigouvian tax. Indeed, one wonders what exactly one learns by comparing these two conceptually different taxes.

   A second unanswered question arises in the context of the "normalization debate" that followed Bovenberg and de Mooij's contribution. Fullerton (1997) and Schob (1997) challenged the validity of Bovenberg and de Mooij's claim and argued that it is due to their particular normalization in which the tax on the nonpolluting good is set equal to zero. They pointed out that the correct statement of Bovenberg and de Mooij's result should have referred to the tax differential between polluting and nonpolluting goods (and not the tax on the polluting good per se). Fullerton (1997, p. 248) also quotes Bovenberg as writing, "To avoid confusion, we probably should have said that optimal tax differentiation is less than the Pigouvian rule would suggest." Now when there is one polluting good and one nonpolluting good (as the participants in this debate have assumed), the concept of a tax differential between the polluting and nonpolluting good is clear enough. However, one good per category is only a simplification. There must generally be at least many nonpolluting goods. One must then wonder how the tax differential is defined. Can we meaningfully speak of one tax differential when there are many goods per category?

   The first aim of the current paper is to clear up these unanswered questions. To this end, following Bovenberg and van der Ploeg (1994), Bovenberg and de Mooij (1994), Fullerton (1997), and Schob (1997), the article at first examines the optimal tax problem in a traditional Ramsey setting. In contrast with these authors and to shed light on the question of a single tax differential, we allow for m nonpolluting goods. For simplicity, however, we keep the one-polluting-good formulation. We characterize the optimal tax rates on polluting and nonpolluting goods for a general specification of preferences and show that the second-best tax on the polluting good generally reflects both optimal tax considerations as well as Pigouvian concerns. The presence of optimal tax considerations implies that one cannot draw general conclusions regarding the relative size of the second-best polluting tax versus the Pigouvian tax. Nor can one speak of one tax differential.

   We then follow Bovenberg and de Mooij and assume that preferences are weakly separable in public and private goods, with the private good subutility being weakly separable in labor and produced goods. We will argue that this assumption provides the key to answering both of our questions. We prove that these preferences imply that all nonpolluting goods must be taxed at a uniform proportionate rate. This property makes the concept of one tax differential meaningful, thus answering our second question. These preferences also imply that optimal tax considerations do not call for differential tax treatment of polluting and nonpolluting goods. That is, the tax differential reflects solely externality-correcting objectives. The separability assumption thus purges the second-best tax differential from its optimal tax objectives, making its comparison with the Pigouvian tax (set on the basis of the first-best rule) to be meaningful. This answers the first question. We point out that these results are closely linked t o Sandmo's (1974) earlier result concerning uniform commodity taxes in the traditional Ramsey tax framework (and in the absence of externalities). Finally, we formally prove that the tax differential between polluting and nonpolluting goods must be less than the Pigouvian tax regardless of the tax normalization rule (setting the income tax rate or the tax on nonpolluting goods equal to zero).

   The second aim of the current article is to argue that the validity of Bovenberg and de Mooij's claim is very much dependent on the particular second-best environment they posit. Theirs is a one-consumer economy in which lump-sum taxation is ruled out. There are of course many types of second-best distortions. The least arbitrary, we believe, is that of the more modern optimal tax theory a la Mirrlees (1971). This theory allows for individuals to be heterogeneous and justifies the absence of first-best taxes by the existence of informational asymmetries between tax authorities and taxpayers. We thus recast and reexamine the issues raised by Bovenberg and de Mooij in Mirrlees' setting. An important feature of our analysis is that we allow for nonlinear income taxation. The optimal income tax literature typically assumes that incomes are publicly observable. This allows income to be taxed nonlinearly (as well as linearly). Consequently, there are no informational grounds for restricting income taxes to be linea r.

   We consider a model with heterogeneous agents. There are H types of agents who differ in earning abilities and/or tastes. This follows Cremer, Gahvari, and Ladoux (1998). However, our specification of preferences is more general than theirs. We impose no particular restrictions on preferences initially, except for the customary quasi-concavity and differentiability. Additionally, we consider a number of different separability restrictions. Cremer, Gahvari, and Ladoux had assumed, at the outset, that preferences are additive in emissions and goods. [5]

   We give a characterization for the optimal commodity taxes (on polluting and nonpolluting goods) and argue that the second-best tax on the polluting good reflects optimal tax objectives as well as Pigouvian concerns. This dual role prevents one from drawing general conclusions regarding the relative size of the second-best tax and the Pigouvian tax. We define the concept of the optimal environmental levy by the additional terms due to environmental considerations that appear in the optimal tax formula for the polluting good (and are absent in the tax formulas for nonpolluting goods) and show that it is independent of individual types. This is a different concept from the tax differential between polluting and nonpolluting goods (which includes both environmental and optimal tax objectives and may also depend on individual types). We show that the environmental levy thus defined may exceed, fall short of, or be equal to the Pigouvian tax.

   Next we consider the implications of different preference structures for optimal pollution taxes. We prove that, if preferences are separable in labor supply and all other...