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Computing the no-policy equilibrium (business-as-usual) in a representative-agent (RA) model is complicated by the presence of a pollution externality, since simple optimization internalizes the pollution cost. Many researchers use ad-hoc methods, but there is no way to know how reliable these are. A solution is presented in which the RA model is divided into N identical components, each identified with its own sub-agent. Sub-agents play a dynamic game, leading to a Nash equilibrium. For sufficiently large N, this approach keeps most of the pollution cost external, and in the limit it is equivalent to a myopic-firms model, in which the entire cost is external. This approach has the advantage of theoretical consistency, and empirical applications indicate that it is easily implemented. r 2007 Elsevier B.V. All rights reserved. JEL classification: D62; Q5

We assess the extent to which subsidies for home energy efficiency improvements in Canada have been paid to households that would have undertaken the improvements anyway-the so-called free rider rate. We focus on forced-air natural gas furnaces, replaced between April 1, 2007 and March 31, 2011, under both federal and provincial subsidy programs as well as the 2009 federal Home Renovation Tax Credit. Our results indicate that around 50 percent of expenditures under the Canadian subsidy and tax credit programs represented free riding. In the long run, our estimates suggest that over 80 percent of grant recipients would have chosen an identical furnace at the time of replacement. We estimate that the cost effectiveness of the programs in terms of greenhouse gas reduced was between $70 and $110/t CO 2 , depending on the assumptions made. Further, we find that a substantial majority of the grants were received by middle-and high-income households, such that the grant had a regressive effect on the distribution of income. We conclude that such grants are not an optimal way to improve residential energy efficiency.