Okay, so in my previous post on Pigouvian taxes, I said that I would look at a couple of papers to try to determine the methodology behind their social welfare functions. Well, today I did so and I have to say that I don’t think that they really sate my hunger on this issue.
The article from Ross McKitrick entiteld What’s Wrong With Regulating Carbon Dioxide Emissions doesn’t pique my ire at all. I highly recommend it because it is an easy read, is very well-written, and briefly explains the problems with regulation in this case. The only time that he mentions “social costs,” he means nothing more than “aggregated individual costs” and does not attempt to justify a Pigouvian tax. In fact, he criticizes it by noting that there are major costs to individuals brought about by such taxes on carbon dioxide production.
And there is also the Ian Parry and Kenneth Small article entitled Does Britain or the United States Have the Right Gasoline Tax? This is a much more technical paper and I was mostly interested in the methodology rather than the conclusions. In particular, I wanted to know how they determined their social welfare function to justify a Pigouvian tax. Well, there are two tricks here. First of all, they don’t really justify a Pigouvian tax, but rather a “quasi-Pigouvian” tax with a Ramsey tax element to it. Though the interesting thing about their idea of the gasoline tax is that even though the Pigouvian element makes up roughly 75% of the “optimal” tax for the US and UK, pollution itself plays a minor role, and fuel-related pollution is swamped by congestion and accident indicators (though combining fuel-related and distance-related pollution components makes it so that the pollution effect is almost 1/3 of the Pigouvian element, or 1/5 of the total tax).
But that’s not the important part. Rather, the part I consider most important is figuring out how they derive a social welfare function. After all, the only way that a Pigouvian tax makes sense is if the social optimum is different than the individual optimum. And here, we run into a bit of a problem. Their social welfare function is a straight utilitarian function—which itself makes me wonder what a reason (other than methodological simplicity) the authors would have for selecting such a function. And the way they chart said social welfare function is to take a “representative household” approach (so that you can get the entire economy by multiplying the result by the number of individuals in said economy). But this still leaves the big problem of calculating individual utilities and still forces me to ask why this particular function is the most appropriate function to use. From what I’ve read of their methodology, the results would differ greatly if you use a different social welfare function (such as a Nash function or Rawls function or even a weighted utilitarian function), so this is still an important point to consider. And finally, this aggregation method assumes that utilities here are cardinal, or at least can be proxied by cardinal terms (such as using dollar figures, as Parry and Small do), and that’s not something I terribly like, especially when you are attempting to calculate a real value (such as this $1.01 per gallon gasoline tax figure).
So I’m still rather unhappy with the idea of a Pigouvian tax, and am still on the lookout for a paper which deals with social welfare functions rather than assuming that they’ll be fine to use.