مالیات بهینه اثرات جانبی تعامل از طریق بازارها: تجزیه و تحلیل تئوریک تعادل عمومی

This study develops a theoretical general equilibrium model to examine optimal externality tax policy in the presence of externalities linked to one another through markets rather than technical production relationships. Analytical results reveal that the second-best externality tax rate may be greater or less than the first-best rate, depending largely on the elasticity of substitution between the two externality-generating products. These results are explored empirically for the case of greenhouse gas and nitrogen emissions associated with biofuels and petroleum. Research highlights ▶ Given two externalites connected through their sources which are substitutes in the market, the optimal tax rate for one externality could be higher or lower than its first best tax rate, depending on the nature of the distortion in the other externality and the interactions between the final goods. ▶ Under the assumption that gasoline and ethanol are close substitutes, GHG tax increases nitrogen leaching. ▶ The parameter related to market interactions is the most important in determining the effects of one tax on the other externality.

This paper examines optimal externality tax policy in the presence of externalities linked to one another through markets rather than technical production relationships. In lieu of correlations between externalities arising through a single production process, we are interested in interaction that arises from market relationships between multiple processes embedded within the economy. We refer to these as “interacting externalities”. Our analysis elaborates on the theory of the second best (Lipsey and Lancaster, 1956). That theory states that if one of the Paretian conditions cannot be fulfilled, an optimal solution is likely to require departures from other Paretian conditions. As a corollary, if multiple market failures exist in the economy, eliminating one does not necessarily improve welfare. As described in Bennear and Stavins (2007), multiple market failures can be jointly ameliorating (correction of one market failure ameliorates welfare loss from the other), jointly reinforcing (correction of one market failure exacerbates welfare loss from the other), or neutral (correction of one market failure does not affect welfare loss from the other). With multiple market failures, the interrelationships can become complex, requiring explicit numerical examination to penetrate the web. The theory of second best has received extensive study in the analytical environmental policy literature. Many studies examine interactions between an environmental externality and pre-existing distortions from labor or capital taxes (e.g., Bovenberg and Goulder, 1996, Bovenberg and Goulder, 1997, Fullerton and Metcalf, 2001, Oats and Schwab, 1988, Parry, 1995 and Parry, 1997). With varying assumptions about policy instruments and revenue recycling measures, their results differ substantially. For example, a second-best tax on the externality can be either higher or lower than the first-best Pigouvian tax. The optimal environmental tax is a function of multiple terms: (1) a Ramsey term, which represents the revenue-raising function, and (2) the Pigouvian components that relate to each externality (e.g., Bovenberg and Van der Ploeg, 1994 and Sandmo, 1975). Very few studies consider corrective taxes in the presence of multiple simultaneous externalities. Caplan and Silva (2005) introduce the concept of “correlated externalities” to define multiple pollutants jointly produced by a single source that cause differentiated regional and global externalities. Within a multi-stage game theory framework, they find that non-cooperative, command-and-control environmental policies fail to achieve first-best optimality, but a joint permits mechanism can achieve a Pareto optimum. However, different externalities are usually regulated separately, or a single source of multiple externalities is regulated using a single instrument because a joint mechanism could face many political obstacles, especially for a global externality. For example, Peterson (1999) evaluates optimal agricultural land pricing policies considering pollution from agricultural land as well as non-market environmental benefits such as open space. Thus, one source, land, generates both a public good and a public bad. He finds the optimal land subsidy to correct the public goods is not equal the net extra-market regional values of the land amenities. Parry and Small (2005) evaluate the optimal gasoline tax considering externalities from traffic accidents, congestion, and air pollution. In a similar spirit, Khanna et al. (2008) develop a stylized economic model to evaluate the first-best and second-best ethanol policies in the presence of greenhouse gas (GHG) emissions and traffic congestion resulting from transportation uses of fuel. In each of these studies, a simple price-based policy instrument is applied to a single product to correct its multiple externalities. This paper departs from the previous literature by developing a theoretical general equilibrium model incorporating two environmental externalities resulting from different industries that interact through market demands, in an economy with no government revenue requirement. The levels of the two externalities are determined not only by their individual production technologies, but also by the interaction between their sources in the market. In the model, two taxes are available to control the two environmental externalities, and the resulting revenues are transferred to consumers in lump-sum. Ideally, the tax rates for the two externalities are each set at its first-best level. However, if one of the externalities cannot be corrected fully, i.e., one tax is constrained below the marginal environmental damage of the corresponding externality, the optimal tax rate for the other externality is unclear. Our results indicate that the optimal second-best policy depends on the nature of the market relationships between the two goods whose production causes the externalities. By explicitly modeling the production and market interaction of the two sources, this paper evaluates: (1) the effects of a small change in one tax, whether or not the tax rates are optimal, and (2) the optimal tax for one externality given a distortion from the other externality. In an effort to illustrate this problem, our analysis is developed in the context of biofuel and fossil fuel production and the associated environmental externalities of greenhouse gases (GHGs) and nitrogen leaching. The biofuel industry has been developed rapidly in many countries, for its potential in greenhouse gas reductions and reduced dependence on foreign oil. Currently, the leading biofuel is ethanol. In 2009, the world's top ethanol producers were the United States (10.79 billion gallons) and Brazil (6.58 billion gallons), which account for about 89% of the world production (Renewable Fuels Association, 2010). As the most successful ethanol producer in the world, Brazil met 17.6% of its transportation energy requirements with ethanol in 2008, in term of energy balance (Empresa de Pesquisa Energética, 2009). As for the US, ethanol accounts for about 8% of the gasoline market by volume (ERS/USDA, 2010), but growing fast. Both fossil fuel and biofuel production processes emit GHGs, but in different amounts per unit of output. The biofuel production process emits less carbon, but U.S. corn-based ethanol production discharges nitrogen into the water environment.1 Nitrogen in water can cause respiratory problems in infants and exacerbate algae growth and hypoxia in water bodies. For the United States, the most severe problem associated with excessive nutrients is hypoxia in the Gulf of Mexico. A report released by National Oceanic and Atmospheric Administration (Rabalais et al., 1999) concluded that excess nitrogen from the Mississippi River combined with stratification of the Gulf's water is the cause of the hypoxia. Added production of nitrogen-intensive feedstocks, especially corn, to support increasing use of biofuel would add to the problem. Although the nitrogen discharge issue with sugarcane in Brazil is not as bad as with corn, the nitrogen application rate for sugarcane is still 80–100 kg/ha/year (Martinelli and Filoso, 2008), comparing to over 150 kg/ha/year for corn production in USA (ERS/USDA, http://www.ers.usda.gov/Data/FertilizerUse/). With a 60–80% leaching rate, the expansion of sugarcane ethanol production is responsible for eutrophication of dams and reservoirs in Brazil (Martinelli and Filoso, 2008). Given the global expansion of the ethanol market, the nitrogen leaching issue cannot be ignored. So the two environmental externalities, carbon emissions and nitrogen leaching, are associated with two different products, and the two products are substitutes in the market. The interaction between the two pollutants acts through the relative demands for the two products. A first best tax for nitrogen leaching is unlikely because nitrogen leaching is a non-point source pollutant, and its accurate measurement is infeasible. Instead, this externality might be partially corrected by a fertilizer tax, or command-and-control policies applied to fertilizer management. Given a suboptimal policy for nitrogen discharges, the optimal tax for GHG may depend on how it affects nitrogen releases, which is mediated by the relationships between biofuel and fossil fuel. Following the theoretical analysis, we examine these relationships numerically to quantify the second-best GHG tax in the face of inability to apply the first-best tax on nitrogen. The paper is organized as follows. Section 2 describes the basic model. Section 3 describes the method used to solve the system. Section 4 develops the analytical solutions for a small increase of GHG tax and characterizes the optimal GHG tax. Section 5 offers a numerical example to illustrate the nature of the interactions between policies, and it uses sensitivity analysis to determine effects of the most important parameters. Section 6 draws conclusions.

This paper develops a general equilibrium model to address policy issues surrounding a special case of multiple externalities. Unlike previous studies, we incorporate two environmental externalities generated by different sources that also produce substitute goods. Two taxes are available to control the two externalities. Since the two externalites are connected through the fact that their sources are substitutes in the market, the two taxes interact. Emissions of both externalities are jointly determined by the two taxes. The direction of the effects of one tax on the other externality is analytically ambiguous. Using this model, we examine the second-best taxes in the presence of connected externalities. The individually first-best policy scheme sets the tax on each externality equal to its marginal environmental damage. However, the first-best policy may not be feasible, as seems likely for nitrogen leaching. Given a suboptimal tax for one externality, the optimal tax for the other externality depends on the remaining distortions. We find that the second-best tax on carbon could be lower or higher than the first-best tax, depending on the nature of the distortion in the other externality and the interactions between the final goods. Only in the knife-edge case is the second-best tax rate equal to the first-best rate (marginal environmental damage). Because of ambiguity in the analytical results, we insert numerical parameter values to explore plausible empirical relationships between fossil fuels and biofuels, where greenhouse gases and nitrogen pollution are the externalities of concern. Our numerical results confirm that a GHG tax increases nitrogen leaching, under the assumption that gasoline and ethanol are close substitutes. Our analytical solutions suggest that under certain circumstances, the optimal GHG tax could be higher than the marginal damage of GHG emissions. However, if the benchmark nitrogen tax is lower than its marginal environmental damage, and other parameters are set at plausible levels, then the optimal GHG tax is lower, and could be much lower, than the marginal environmental damage of GHG. In our model, the levels of the two externalities are not affected solely by their individual production processes. The market interaction between the final goods also plays an important role in determining the emission levels. Our numerical example illustrates the relative importance of the technical production parameters relative to the market interaction. If τC increases, the technical substitution parameter associated with fossil fuel production, σF, has a significant impact on C but a small impact on N. On the other hand, the technical parameter associated with biofuel production, σB, has a very small impact on both externalities, because σB governs the substitution between L and N in production of B based on their relative price changes, while the change in τC has only a small impact on PL with no impact on τN at all. Thus, with a change in τC, the effect of the technical parameter of production B to the system is minimal. The elasticity of substitution between F and B in production of energy, σE, is the most important parameter in determining the effect on N from an increase in τC. Based on the sensitivity analyses, the parameter related to market interactions is the most important in determining the emission level of the other externality. Since the second-best policies are jointly determined by both emission levels, parameters affecting either or both emission levels matter to the policy design process. The second-best tax rate for one externality is most sensitive to the technical parameter in the production process associated with that externality and to the parameter that determines the substitution in utility between the two final goods.