The price function _Pa_ and its relationship with _Pe_ is intractable without further assumption of the price- or quantity-setting behavior of the dominant firm. However, as the dominant firm has the flexibility to make _ex post_ decisions on _x2_ after the demand for output market is known, the permit price _Pa_ becomes less convex with respect to _Pe_ . When the ability of the dominant firm to affect the permit price increases, the firm would respond less and less to changes in the level of uncertainty. Qualitatively, I show that imperfect competition in an permit market threatens the negative relationship between price uncertainty and _ex ante_ emissions. Further rigorous analysis is needed based upon more detailed assumptions of the market structure of the permit market and the strategic behavior of a dominant firm.

# **IV. Empirical Analysis**

Building on previous discussions on the dynamics of intertemporal emissions trading under uncertainty, this section empirically explores the electricity utilities’ responses regarding emissions reduction to price fluctuations in the U.S. electricity markets.<sup>16</sup> The empirical analysis is based on a panel dataset consisting of 207 Phase I coal-fired generating units from 1996 to 2004. In many ways, the U.S. SO2 allowance trading program can be compared to the emerging global carbon dioxide trading market. With 10 years of observation data and many lessons learned from the SO2 allowance market, to study SO2 trading occurred in the U.S. provides a unique opportunity to estimate the implications of different features of the global carbon dioxide trading program, including the impact of uncertainty on future development of the global carbon market.

The SO2 allowance trading program, also known as the Acid Rain Program, was established under Title IV of the Clean Air Act Amendments of 1990. By creating a national clean air market, it was a grand application of a market-based regulatory approach to achieve emission reduction goals. The basic idea behind permit trading is simple. The regulatory agency first sets a cap that limits the total SO2 emissions by more than 40% from their 1980 level (from 18.9 million tons in 1980 to 8.9 million tons by 2001). It then divides the quantity up to a number of tradable allowances and allocates them to individual firms based on their historical heat input. Each allowance grants the holder the right to emit one ton of SO2. Firms that can reduce emissions relatively cheaply may increase their profits by selling extra allowances; while those that find it expensive to reduce emissions can buy extra allowances from the market. The SO2 allowance trading program institutionalized a couple of innovations in that it not only allows unlimited trading of permits among firms, but also allows permits to be traded over time. Therefore, power producers who can reduce emissions below the number of allowances they hold may sell allowances to other firms, or bank them for future use. The only limitation the U.S. Environmental Protection Agency (EPA) imposes on the trading program is that firms cannot borrow allowances from their future allocation. At the “true-up” date (usually at the end of March of each year), each unit must submit enough allowances to cover its emissions for that year.

> 16 I do not test the effect of coal prices uncertainties. As coal is the most abundant and affordable energy source in the United States, its price in fact remains quite stable during the sample period.

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