Hayward is looking at ambient concentrations of SO2. That is, he is looking at the stock of SO2 in the air, which is a result of past pollution. The stock of SO2 is important; the more there is, the larger the (negative) health effects and the more acid rain. Environmental economists, however, have been looking at the flow of SO2 into the air--that is, the emissions of SO2. This is also important. If we decrease the amount of SO2 we're adding into the air, the stock of SO2 will fall (or fall more quickly). What does the path of emissions look like?
You can get that data from the EPA here. Note that the data is in five-year increments until 1995. It's hard to say much, due to the lack of annual emissions data prior to 1995, but it looks to me like emissions fall more quickly after the 1990 Clean Air Act Emissions, if one were to draw a trend line for the data before and after 1990.
There are a few puzzles, such as the jump in emissions in 1995 (when the first stage of the cap-and-trade market started, and was focused on the 110 largest existing sources) and in 2003, but they're followed by even steeper declines. It turns out that the increases are due to sources that would be regulated under the second stage of the cap-and-trade program in 2000 (which applied to the other large existing sources and all new sources). It makes some economic sense: Squeezing the emissions of big polluters, without constraining the small ones, resulted in a shift of production, and therefore emissions, to those smaller sources. Why did emissions rise, then, and not just stay constant? This is just a conjecture, but I would guess that it is because those slightly smaller producers (of energy or whatever) were initially less efficient; for a given amount of output, they probably produce more SO2. I'm not sure why emissions stabilize from 2002 to 2005, rather than just falling. I could tell some more just-so stories, but they wouldn't be very satisfying.
My point is that environmental economists are, I think, right to view SO2 cap-and-trade as a success story, in terms of emissions. Emissions have fallen at a faster rate as a result of the program. Has this had an effect on ambient SO2? I can't really tell from Hayward's graph. It looks to me like ambient SO2 may have fallen faster after 1990, but to me, the interesting question is "what happened after 1995?"--and his chart only has three years of data there. Here are the EPA's charts of ambient SO2:
No matter which graph one looks at, it doesn't appear to me that there's a clear effect of the SO2 cap-and-trade program on ambient SO2. There's a pronounced drop from 1994 to 1995, but that's it. It looks like SO2 just keeps falling steadily. I don't know much about the physical science involved here, though. Is there a lag between the reduction in emissions and an effect on the stock of SO2? Is there something else going on that I don't understand?
Maybe, when I get some time (which could be some time from now), I'll look at some of the empirical papers on this. If I'm totally off-base, hopefully someone will correct me in the comments.