Negative Leakage

We build a simple analytical general equilibrium model to find a closed-form expression for the effect of a small increase in carbon tax on leakage – the increase in emissions elsewhere. The model has two goods produced in two sectors or regions. Many identical consumers buy both goods using income from fixed stocks of labor and capital that are mobile between sectors. The usual result is that an increase in one sector’s carbon tax raises the price of its output, so consumption shifts to the other good, causing positive leakage. Here, we make three contributions. First, we find a new, substantial negative effect on leakage: the taxed sector substitutes away from carbon into capital or labor, so it absorbs resources, shrinks the other sector, and reduces their emissions. This latter “abatement resource effect” could swamp the usual positive effect and reduce emissions in the other sector. Second, we extend that model to identify a total of six leakage terms – two positive and four negative. Third, we use our analytical model to “unpack” existing computer model results [not yet done]. We can aid the interpretation of any model’s numerical result for leakage by showing the relative size of each component, and what parameters are driving the size of each effect. Our emails are: [email protected], [email protected], and [email protected]. We are grateful for comments and suggestions from Mustafa Babiker, Jared Carbone, Fernando Pérez-Cervantes, Brian Copeland, Carolyn Fischer, Larry Goulder, Corbett Grainger, Garth Heutel, Larry Karp, Carol McAusland, Gilbert Metcalf, Sergey Paltsev, Sebastian Rausch, David Weisbach, Martin Weitzman, and Niven Winchester, as well as various seminar and conference participants. A common concern with a unilateral pollution restriction is that one country’s abatement will be offset by “leakage”, defined as the increase in pollution elsewhere. Within a country as well, a carbon policy such as cap-and-trade may apply only to one sector such as electricity, which raises its price and shifts consumption to goods from unregulated sectors. Purely domestic leakage may offset some of the regulated sector’s abatement. In a trade context, even without international capital flows, the regulating country puts itself at a competitive disadvantage. International capital mobility is thought to make leakage worse, if investment flees the taxed region to help produce more polluting output in the other region. In the context of climate policy, carbon leakage is a particular concern due to the global impacts of greenhouse gases. The literature has many estimates for carbon leakage associated with the Kyoto Protocol. For instance, Paltsev (2001) finds a leakage rate of 10%, whereas Babiker (2005) finds rates as high as 130%. In that case, a carbon tax in one country raises worldwide emissions. More typical of other recent estimates, Elliott et al. (2010) find a 20% carbon leakage rate from the Annex-B Kyoto countries. Given this presumption that leakage is positive, academics have searched for particular cases with counter-intuitive results. We cannot review all such literature, but we list a few examples. First, Felder and Rutherford (1993) build a computable general equilibrium (CGE) model with five regions and ten-year intervals, finding that marginal leakage can be negative after several decades if the carbon tax leaves enough unused oil to delay the other region’s introduction of carbon-intensive synthetic fuel. Second, Copeland and Taylor (2005) show how negative leakage can arise through endogenous policy: in response to a cut in one region’s emissions, the other region experiences income gains that induce them to choose more environmental quality by raising their own pollution tax. Third, negative leakage can arise through endogenous technology: the carbon tax may induce R&D into new abatement technology that can be used by the unregulated sector, especially if patents are poorly protected. Fourth, Karp (2010) follows Chua (2003) to find negative leakage in an example with particular cross-price elasticities among three inputs (such as labor, capital, and emissions). 1 See Golombek and Hoel (2004), Di Maria and Smulders (2004), Gerlagh and Kuik (2007), and Di Maria and van der Werf (2008). Each makes particular points, which we cannot review here. 2 In Karp’s example, production is highly labor intensive, but the carbon tax induces much substitution into capital, so it can reduce the return to labor, promote production, and reduce import demand for the dirty good. In a closed economy, Fullerton and Heutel (2007) show that such special cases can generate other perverse results; a carbon tax can even raise emissions in the taxed sector.