I never really embedded Weitzman (1974) into my hard core of econ knowledge. This is a significant flaw in my ongoing education but I can't help it. It doesn't stick with me. It is not Weitzman's problem, the paper is recognized by all as one of the classics. The problem is all mine.
So, I've probably got this all wrong. But, I think, if I make something explicitly wrong, I'll be corrected and then I might remember forever. This post is a self-teaching tool, if you will. Or, you might consider it a new chapter in the ongoing self-destruction of an economist. Yet, I'm pretty sure that most all economists don't know-it-all, they're just too jackass to admit it. Or, is it that they're not jackass enough to admit it. Whatever.
Weitzman wrote about choosing prices (e.g., carbon tax) or quantities (e.g., cap-and-trade) when regulating the environment. With no uncertainty about benefits and costs, prices vs quantities doesn't matter. But if there are uncertain benefits and/or costs it does matter. With climate change future benefits are uncertain combined with uncertain current costs. My guess is that the uncertainty over future benefits swamp the cost uncertainty, but that is just a guess.
It helps to read Pindyck's working paper which is published in the first issue of REEP. Pindyk (2007), channeling Weitzman (1974) says:
Weitzman (1974) ... showed that in the presence of cost uncertainty, whether a price-based instrument or a quantity-based instrument is best depends on the relative slopes of the marginal benefit function and marginal cost function. If the marginal benefit function is steeply sloped but the marginal cost function is relatively flat, a quantity-based instrument (e.g., an emissions quota) is preferable: an error in the amount of emissions can be quite costly, but not so for an error in the cost of the emissions reduction. The opposite would be the case if the marginal cost function is steeply sloped and the marginal benefit function is flat. Of course in a world of certainty, either instrument will be equally effective. [emphasis added] If there is substantial uncertainty and the slopes of the marginal benefit and cost functions differ considerably, the choice of instrument can be crucial.
To expand a bit:
- With steep marginal benefit and flat marginal abatement cost curves:
- A tax that is too high will generate big increase in abatement costs and a small increase in abatement benefits
- A tax that is too low will generate a big decrease in benefits and a small decrease in costs
- A cap that is too high or low will generate the same negative net benefits but the magnitude of losses will be lower
- With flat marginal benefit and steep marginal abatement cost curves:
- A cap that is too high will generate a big increase in abatement costs and a small increase in abatement benefits
- A cap that is too low will generate a big decrease in benefits and a small decrease in costs
- A tax that is too high or low will generate the same negative net benefits but the magnitude of losses will be lower
It seems to me that we're trying to avoid the chance that climate change will cause big future problems and so something that the precautionary principle is a useful guideline. We'd like to make sure that we cut emissions enough so that we don't cross some threshold that causes the world to explode. Past that point, adaptation will occur and the additional damages will be relatively low. This suggests that the marginal benefit function is fairly steep early on. We get big benefits from the first X% of abatement, avoiding the scary carbon threshold, after that the additional benefits are much lower.
Anyway, it all hinges on the slope of the marginal benefits function: flat or steep. My assertion is that it starts off steep and then flattens out (click on picture to the right for a larger image).
It seems that marginal abatement costs are better known, and the curve is flatter, at least for the first X% units of carbon that are likely to be regulated. The uncertainty arises in the near term because firms lie about their costs. In the long term abatement technology should improve driving costs down, but we don't know how far down. Either way, the costs we assume today are likely to fall in the future.
To the left of the efficient level of carbon abatement (i.e., where all of the regulatory action is when no regulation is the status quo), the marginal benefit curve might be steep and the marginal abatement curve might be flat. This might argue for cap-and-trade, rather than a carbon tax. In contrast, note that the CBO argues that marginal benefits are roughly constant for a stock pollutant and a carbon tax is preferred (page 30).
If this is all backwards, as Rosanne Rosannadanna would say: Nevermind.
Er, I'll go ahead and type it: Nevermind.
Corrections are appropriately placed in the comments box.
