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Bovenberg & Goulder OptimalEnvironmental Taxation in the Presence of Other Taxes: General-EquilibriumAnalyses By A. LANS BOVENBERG AND LAWRENCE H. GOULDER* Most economies feature levels of public The present paper contributes to the analyt- spending that require more tax revenues than ical and empirical literature in three ways. would be generated solely from the pollution First, it extends earlier analytical work on op- taxes set accordingto the Pigovianprinciple, that timal environmental taxation in a general- is, set equal to marginalenvironmental damages. equilibrium setting by considering pollution As a consequence,tax systems generallyrely on taxes imposed on intermediate inputs. This is both environmental(corrective) and othertaxes. a useful extension because many actual envi- However, economists typically have analyzed ronmental regulations and taxes affect the environmentaltaxes withouttaking into account costs of intermediate inputs.2 Second, the pa- the presence of other, distortionarytaxes. The per investigates second-best optimal environ- omission is significantbecause the consequences mental taxes numerically. Here we expand on of environmentaltaxes depend fundamentally the analytical work by employing a numerical on the levels of other taxes, including income general-equilibriummodel of the United States. and commodity taxes. The use of a numerical model enables us to This paper examines how optimal environ- employ a realistic specification of taxes and mental tax rates deviate from rates implied by adopt a fairly detailed representationof pro- the Pigovian principle in a second-best setting duction and demand. Our paper thus combines where other, distortionary taxes are present. the strengths of analytical and numerical ap- Previous investigationsof this issue include the proaches: a stylized analytical model uncovers partialequilibrium analyses of Dwight R. Lee the major mechanisms at play, while a numer- and Walter S. Misiolek ( 1986) and Wallace E. ical model explores the empirical significance Oates ( 1991), who derive formulas linking the of these mechanismsin a more realistic setting. optimal rate for a newly imposed environmen- Despite considerable differences in the com- tal tax to the marginal excess burden from ex- plexity of the analytical and numericalmodels, isting taxes. In a general-equilibriumsetting, we find a strong coherence between the two Agnar Sandmo (1975) and Bovenberg and models' results. Frederickvan der Ploeg (1994) have demon- The third contributionof the paper is its nu- strated how the well-known "Ramsey" for- merical investigation of optimal environmen- mula for optimal commodity taxes is altered tal tax policies in the presence of realistic when one of the consumption commodities policy constraints. The constraints involve ei- generates an externality.1 ther the inability to alter all tax rates (so that much of the initial, suboptimal tax system re- * Bovenberg: CPB Netherlands Bureau for Economic Policy Analysis, P.O. Box 80510, 2508 GM The Hague,. ary taxes. A key question is whether "recycling" the rev- The Netherlands, and CentER for Economic Research, enues in this way can make the overall cost of the revenue- Tilburg University; Goulder: Department of Economics. neutralpolicy zero or negative. For general discussions of Landau Economics Building 335, Stanford University, this issue see, for example, David W. Pearce (1991), James Stanford, CA 94305-6072. The authors are grateful to M. Poterba(1993), Oates (1995) and Goulder (1995a). For Jesse David and Steven Weinberg for excellent research analytical treatments see, for example, Bovenberg and assistance, to three anonymous referees for helpful com- Ruud A. de Mooij (1994) and Ian W. H. Parry(1995). For ments, and to the National Science Foundation (Grani numerical investigations see, for example, Robert Shack- SBR-9310362) and IBM Corporation for financial leton et al. (1996) and Goulder (1995b). support. 2 For example, taxes on fossil fuels raise the costs of ' A closely related issue is the extent to which the costs fuel inputs; similarly, specific excises such as taxes on of environmental taxes are lowered when revenues from gasoline raise the costs to producers of the transportation such taxes are devoted to reductions in existing distortion- services they might employ. 985 986 THE AMERICANECONOMIC REVIEW SEPTEMBER1996 mains) or the inability to use revenues from consumption is assumed to be zero.3 The la- environmentaltaxes in optimal ways. We find bor tax rate and the producer (before-tax) that these constraints substantially affect the wage w yield the consumption (after-tax) optimal environmental tax rates. wage, WN (1 - TL)W. The paper is organized as follows. Section I The government budget constraint is G = x develops a stylized general-equilibriummodel TiCXc + T XD + TcCD + TLWL, where rx and to uncover the main determinants of optimal TX stand for the taxes on clean and dirty in- environmental taxes in the presence of distor- termediateinputs, respectively. Environmental tionary taxes. Section II describes the numer- quality, Q, deteriorates with pollution, which ical model, and Section III applies this model is directly related to the quantity used of dirty to evaluate the departures from Pigovian tax intermediateand dirtyconsumption goods; thus, rules implied by second-best considerations. Q = q(xD, CD), with &q/&xD, Oq/9CD < 0. The final section offers conclusions. Private decision makers ignore environmental externalities. I. Theoretical Issues and Analytical Results To derive the optimal tax rates, we solve the government's problem of maximizing house- This section explores analytically how the hold utility subject to the government budget presence of distortionarytaxes affects the op- constraint and the decentralized optimizing timal setting of environmental taxes on both behavior of firms and households. Accord- intermediate inputs and consumption goods. ingly, the government chooses values of its To this end, we extend the model in Bovenberg four tax instruments rL, TC, TX , and TD to and Ruud de Mooij (1994) by incorporating maximize: intermediate inputs. Output derives from a constant-returns-to-scale production function (1) u[V(wN, ric), G, q(xD, CD)] F(L, XC,XD) with inputsnot only of labor(L) but also of "clean" and "dirty" intermediate + (T x Xc + T XD goods (xc and XD, respectively). Output can be devoted to public consumption (G), to + fDCD + fLWL - G) clean or dirty intermediateinputs, or to house- hold consumption of a "clean" or "dirty" where V represents indirect private utility and consumption good (denoted by Cc and CD, re- At denotes the marginal utility associated with spectively). Hence, the commodity market the public goods consumption made possible equilibriumis given by F(L, xc, XD) = G + by one additional unit of public revenue. XC + xD+ CC + CD. We normalize units so Appendix A derives the optimal tax rates. that the constant rates of transformation be- The analysis reveals that the clean intermedi- tween the five produced commodities are ate input should not be taxed (that is, T- = 0). unity. This is an application of the well-known result The representative household maximizes of Peter A. Diamond and James A. Mirrlees utility U(CC, CD, 1, G, Q) = u(N(H(Cc, CD), ( 197 la, b) demonstrating that, if production 1), G, Q). Private utility N(-) is homothetic, exhibits constant returns to scale,4 an optimal while commodity consumption H(*) is sepa- tax system should not distort production. rable from leisure, 1. In addition, private utility is weakly separablefrom the two public goods, environmental quality (Q) and (nonenviron- mental) public consumption (G). These as- sumptions on utility match the specifications 3 A positive tax on consumption is redundantin that the of household behavior in the numerical model equivalent to any tax system with a positive tax on con- (see Section II). sumption can be obtained through suitable combinations The household faces the budget con- of the labor tax and the tax on dirty consumption. This straint CC + ( 1 + T c) CD = (1 - rL) wL, follows from the fact that the labor tax is equivalent to a uniform tax on the two consumption commodities. where i- c and rL denote, respectively, the 4 Under decreasing returns to scale, production effi- tax rates on dirty consumption and labor. ciency continues to be optimal so long as a 100-percent Without loss of generality, the tax on clean tax on pure profits is available. VOL. 86 NO. 4 BOVENBERGAND GOULDER: ENVIRONMENTALTAXATION 987 The optimal tax on the dirty intermediate first-best world without distortionary taxes, a input is (see Appendix A): one-unit reduction in emissions involves a welfare cost corresponding to the loss of tax [aU aq1 revenue due to the erosion of the base of the pollution tax-thus the pollution tax rate rep- I Q aOXD)/1 resents the marginal welfare cost of emissions (2) Tf D J reductions (MWCE). Hence, in a first-best set- d9cc ting, optimality requires that the pollution tax be set equal to the marginal (environmental) benefit from pollution reduction (or marginal The term between the large square brackets damage from pollution), which is given by the on the right-hand side of (2) is the marginal term in the large square brackets in equation environmental damage (MED) from this in- (2) or (3). This is the Pigovian tax rate. put. iq (-i/(OU/dCc)) is defined as the ratio The MCPF term in equations (2) and (3) of the marginal (utility) value of public rev- reveals how the presence of distortionarytaxes enue to the marginal utility of private in- requires a modification of the Pigovian prin- come; it is often referred to as the marginal ciple. In particular,it shows that the Pigovian cost of public funds (MCPF). Analogously, rate is optimal if and only if the MCPF is unity. the optimal tax on the dirty consumption A unitary MCPF means that public funds are good is the marginal environmental damage no more costly than private funds. The higher from the use of this good divided by the the MCPF, the greater the cost of public con- MCPF (see Appendix A):' sumption goods, including the public good of environmental quality.
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