to produce electricity. Current prices are known, but the future prices evolve stochastically. I show that in equilibrium, the marginal abatement costs of all firms are equalized with the permit price in each period; for each firm, the expected present marginal abatement costs are also equalized across time periods. When future compliance costs are expected to increase, firms will demand positive permits, bidding up the permit price (and therefore marginal abatement cost) until current and expected future prices are equal.

The permit price is subject to output price shocks, which alter firms’ abatement costs by changing the industry-wide counterfactual emission level.<sup>4</sup> I prove analytically that the permit price, as well as firms’ marginal abatement cost, is a convex function of the electricity price. By Jensen’s inequality, this leads to a positive relationship between the marginal abatement cost and the increase in volatility of the stochastic variable. This convexity relationship results from the asymmetric impact of electricity price change on the change in marginal abatement cost. Because marginal abatement cost is convex (as long as the marginal productivity is decreasing), when the electricity price increases (and therefore the abatement level increases), the marginal abatement cost increases faster than it decreases when the electricity price falls. When uncertainty is pronounced, very high and very low electricity prices become more likely, and this asymmetric impact becomes more salient. In the presence of extreme electricity prices, firms would have a much higher incentive to reduce _ex ante_ emission and accumulate permits so as to smooth out the marginal abatement costs over time. This conclusion holds whether the output market is perfectly competitive or not. In addition, the model is extended to allow uncertainties to enter through input costs and industry wide productivity. The conclusion follows the same line.

In the second part of the paper, I empirically test the theoretical prediction using data observed from the U.S. SO2 allowance trading market from 1996 to 2004. Empirical analysis shows that one percent increase in electricity price volatility measured by annualized standard deviation of percentage price change is on average associated with a 0.88% decrease in annual emission rate. Overall, increased price volatility induced by electricity market restructuring over the last decade may explain 8-11% of the total amount of the banked allowances during Phase I of the U.S. SO2 trading program.

To estimate the impact of market uncertainty on social welfare, I simulate the banking pattern, emission stream and the time path of permit price resulting from various degrees of output price uncertainties. Numerical results are quite suggestive and consistent with the empirical evidence. The results indicate that high uncertainty may generate substantially large compliance costs in the early years, deterring new entrants and cause efficiency loss; from the environment perspective, uncertainty encourages overcopmliance in early years; when a pollutant such as a greenhouse gas, creates stock damage, benefits from early abatement could be substantial.<sup>5</sup> The remainder of the paper is organized as follows: Section II provides a literature review. Section III develops a firm model of intertemporal emission trading and derives the relationship

> 4 Counterfactual emission is the level of emission that would prevail when there is no environmental regulation. 5 Currently, the transfer of unused allowances from the period 2005 - 2007 to the first commitment period under the Kyoto Protocol, i.e. 2008-2012, is not allowed under an EU-wide ban on banking (except for Poland and France), which from an  environmental point of view, seems to be a troubling decision.

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